tag:blogger.com,1999:blog-29800041242835939612024-03-23T10:15:09.748+00:00Christof Schwiening's random thoughts and writingsPhysiological feedback makes life interestingUnknownnoreply@blogger.comBlogger36125tag:blogger.com,1999:blog-2980004124283593961.post-9918478356459462202022-07-15T17:13:00.000+01:002022-07-15T17:13:33.087+01:00Are you feeling hot yet?<h2 style="height: 0px; text-align: left;">Record high temperatures forecast for the UK - worrying trends, but it should not be a physiological problem.</h2><h1 style="height: 0px;"><br style="font-size: medium; font-weight: 400;" /></h1><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgwDLdC65494od4T-jexH3-LrYcTFP1kR-fGz5yW3hqQMPlFhEO4J8of3_jIuHGwimbH_HTevoErNp9TKw3VFzoqlmtsLAa5L51Sn2Q66fag41cIUmMbiUZ-MxEBj31lx1Q50VG5qAAlKBrBPqNwqsxj38-uzUDuw0t8yEBYLM_bVRi5j0Er8ziQnse" style="margin-left: auto; margin-right: auto;"><img alt="" data-original-height="659" data-original-width="1288" height="330" src="https://blogger.googleusercontent.com/img/a/AVvXsEgwDLdC65494od4T-jexH3-LrYcTFP1kR-fGz5yW3hqQMPlFhEO4J8of3_jIuHGwimbH_HTevoErNp9TKw3VFzoqlmtsLAa5L51Sn2Q66fag41cIUmMbiUZ-MxEBj31lx1Q50VG5qAAlKBrBPqNwqsxj38-uzUDuw0t8yEBYLM_bVRi5j0Er8ziQnse=w640-h330" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">BBC weather predicts highs of 40 degrees C early next week</td></tr></tbody></table><br />There seems little doubt that the frequency of 'record high temperatures' in the UK is increasing - our last record was set in July, 2019 and it now looks like that might be broken by more than 1 degree C next week. To have such a large jump in record temperatures within such a short space of time is unusual and worrying too. For sure this is caused by a weather pattern dragging hot air up from southern Europe just at the point at which they are experiencing record temperatures, so it is hard to claim that it is a result of 'average' temperature rises, but the warmer the World gets the more likely these events are going to be.</div><div><br /></div><div>From a physiological point of view these temperatures are not yet problematic - or at least they would not be if we were properly prepared and therein lies the problem. Just as a small flurry of snow in Winter stops transportation these mini-heat waves also cause problems in the UK whereas in other countries such temperatures would barely raise an eyebrow. The problem is illustrated by the BBC weather forecast with temperatures ramping up from and back down to the low 20s with a peak of 40 for just a couple of days. It is entirely possible to physiologically adapt (acclimate) to the heat, but it takes longer than a couple of days to do so. By Monday when we expect the high temperatures, those who don't exercise, live in cool indoor environments and therefore have little ability to sweat will face a potential thermoregulatory problem. The problem is that radiant heat loss requires a cool environment - or at least one cooler than core body temperature. By the time the temperature is up at 40 degrees C radiant heat loss is useless - the only way of losing the heat we produce (even at rest) is by evaporation. Of course breathing carries away some heat, but not enough: we need to sweat. But, just like you can't suddenly grow strong arm muscles, you can't suddenly grow big sweat glands either. Sweating takes practice. If you don't regularly sweat then your maximal sweating rate will be low. Advice to drink plenty of water will not help as much as you might think - drinking won't promote sweating. Drink if you are thirsty is much better advice.</div><div><br /></div><div>So, if you do daily exercise, enough to get hot and sweat, you are probably (like me) sitting quite comfortably and looking forward to the warm weather. You will have a cooler resting core body temperature and a capacity to sweat more than enough to deal with the warm weather. But, most people either don't or can't do that amount of exercise and will struggle to raise much of a sweat. Even people who consider themselves to be 'healthy-fit' may fall into this category. About 6 years ago my wife came into the lab to be a subject for a 'sweating' experiment. She sat on an exercise bike and pedalled whilst we measured her core body temperature rise to 39 degrees C. She went red, very red - but, not a drop of sweat. It wasn't that she was dreadfully unfit or overweight - it was just that she never worked hard enough to induce any sweating. Being able to sweat takes training, and by training I mean getting hot enough to need to sweat. There are essentially two ways of doing this - either generate the heat internally by doing exercise, or use external heat (e.g. hot baths or saunas). My wife decided to take-up running and did the wonderful NHS couch-to-5km and now runs (albeit rather irregularly).</div><div><br /></div><div>There are many strategies to stay cool and most of them are blindingly obvious: reduce activity levels (internal heat generation), stay in a cool environment and use water (applied directly to the skin) to mimic sweating. A wet cloth and a draught is more than enough to stay cool when humidity levels are relatively low. Hot weather and high humidity is a different beast. I recall, as a youngster, sitting very comfortably in a sauna (probably about 100 degrees C - my father built one in our garage) and putting quite a lot of water on the stones. The effect was immediate pain as the humidity rose rapidly causing a dramatic rise in skin temperature. I fled the sauna. Humid hot environments are a real physiological problem to which we don't have a solution.</div><div><br /></div><div>You might wonder why we don't all have large sweat glands, one that don't need training to keep them big. If having large sweat glands that can produce copious amounts of sweat make Summer heat so easy to deal with, why hasn't evolution caused them to just exist in our skin all of the time? The best guess for why we have trainable sweat glands is that in the Winter sweating is a very dangerous activity - wet skin after running could easily induce hypothermia in Winter. I had not realized just how dangerous this was until I got injured about 2 miles from home one Winter whilst out running. I was dressed in several running jackets, and nicely hot, but they were soaked in sweat and I was forced to walk. I wasn't too concerned since 2 miles seemed entirely 'walkable' but, I had not factored in just how quickly body temperature can fall when you are soaking wet and heat production drops. I now run with a mobile phone and, more importantly, a foil (space) blanket.</div>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2980004124283593961.post-85704805295048408432019-07-29T14:20:00.003+01:002019-07-29T14:36:29.902+01:00Measuring (accurately) run coursesRunners often compare distance measurements from GPS devices only to be surprised by the extent of the variation. Some devices do perform better than others (and many enthusiasts have published good comparisons: <a href="https://fellrnr.com/wiki/GPS_Accuracy" target="_blank">fellrnr</a>, <a href="https://www.dcrainmaker.com/2011/06/2011-sport-device-gps-accuracy-in-depth.html" target="_blank">dcrainmaker</a>, <a href="https://the5krunner.com/2019/05/23/garmin-forerunner-945-gps-accuracy/" target="_blank">the5krunner</a>) but the errors are often hard to predict and depend upon the atmospheric conditions, the number of turns in the route, visibility of the sky, the positioning of the GPS satellites and the data sampling rate. The importance of accurate distance measurements is easy to appreciate when looking at race data. A twenty minute 5km runner takes 0.24s to cover a metre, so a course that is 50m short (1% error in the distance measurement over 5K) should take 12s less to complete and that is a significant amount of time when comparing 5km race efforts. The problem is that GPS devices generally have errors greater than 1% (<a href="https://fellrnr.com/wiki/GPS_Accuracy" target="_blank">fellrnr</a>) often the errors can be <a href="https://www.goodrunguide.co.uk/MeasuringRoutes.asp" target="_blank">closer to 5%</a>.<br />
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For road-running races one ideally needs a measurement technique that has less than 0.1% error. Even at 0.1% error the performances can differ by enough of a margin to begin to cause problems, but even using the best techniques it is hard to achieve a higher level of accuracy than that. This level of error is equivalent to 1 m per km, so 5 meters in a 5 km race. Whilst this error is significant in performance terms, it is the level of accuracy where other factors, like the choice of racing line, become more significant even for the seasoned competitor. By way of an example: imagine running a 5000m on an <a href="https://www.iaaf.org/responsive/download/downloaddirect?filename=5a5b59ac-eb58-45e4-a9a3-003c1e61d619.pdf&urlslug=IAAF%20Track%20and%20Field%20Facilities%20Manual%202008%20Edition%20-%20Chapters%201-3" target="_blank">athletics track</a>. If you run the 12.5 laps in lane 1, the regulation 30cm from the inside edge, you will cover 5,000m precisely. Now imagine you could run closer to the inside edge, say 12cm away from it - then, you will save yourself 14 meters. If you run 12cm within the outer line of lane 1 you would have to run a further 76m than the person hugging the inside lane. This example of poor racing line is a 1.5% error in distance. So, most runners should be happy once a course has a distance measurement of 0.1% accuracy since their choice of racing line will be the biggest source of error.<br />
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To get within 0.1% accuracy is not difficult. Steel measuring tape is available in 30m lengths and has a thermal expansion coefficient that is so low that we don't need to worry about it (0.001% per degree C). But, laying out this long tape 167 times to make a 5km measurement would be terrible. This is where wheel-based techniques win since each revolution of the wheel is the equivalent of laying down a new length of tape. As long as we can measure how far the wheel travels per revolution and count the number of revolutions then an accurate measurement would seem to be easy to make. Of course surveyor's wheels are readily available and for a modest investment (~£100) a model with calibration certificate can be found. However, they still have the drawback of requiring a person to push it along the whole course and they typically cannot easily deal with rough terrain. It is for these reasons that many prefer to use the wheels on a bicycle - a bicycle that can be ridden at a sensible speed. Indeed, the IAAF only allow race measurements made with 'Jones' counters that follow their <a href="https://aims-worldrunning.org/measurement/MeasurementOfRoadRaceCourses.pdf" target="_blank">extensive manual</a>. The <a href="http://coursemeasurement.org.uk/lessons/index.htm" target="_blank">Association of UK Course Measurers</a> replicates most of these procedures including a free (but lengthy) certification process. The Jones counter is nothing terribly special - it is a physical counter turned by a sprocket mounted on the front wheel which provides about 24 counts per wheel revolution (it isn't actually 24, they make great play of the use of prime numbers within their counters to minimize wear). Since Jones counters are relatively expensive, I have implemented a cheaper version (£6, a <a href="https://www.ebay.co.uk/itm/Digital-Punch-Electronic-Counter-Magnetic-Inductive-Proximity-Switch-Magnet-K3/173686444258?ssPageName=STRK%3AMEBIDX%3AIT&_trksid=p2057872.m2749.l2649" target="_blank">Hall effect pulse counter</a>) which has slightly lower accuracy (1 revolution) but still sufficient to get within 0.1%.<br />
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Whilst the IAAF and <a href="http://www.jonescounter.com/jr-mounting/" target="_blank">Jones</a> themselves use the front wheel for measurements, it seems to me that the rear wheel should be more repeatable. The front wheel will almost always take a longer course than the rear wheel when cycling due to <a href="https://www.rain.org/~mkummel/stumpers/09mar01a.html" target="_blank">wobble</a>. I think the idea behind using the front wheel is that the rider can see the line the wheel is taking and also read the counter - but, in doing so it accumulates the additional distance from small steering corrections, these corrections represent errors, and are much smaller on the rear wheel.<br />
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The process of calibrating the wheel</h3>
After mounting my counter I made the magnet, which was attached to the spokes, highly visible with red insulation tape. This is because the counter only reports whole, completed revolutions, and I was going to have to look back at my back wheel and judge the fractions of a revolution completed beyond each full revolution. I also ensured that my counting probe was mounted just off the vertical axis of the wheel so that I could begin each ride with the red-tape on the magnet at the 12 o'clock position making judging the fractions of a revolution much easier.<br />
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After I inflated my rear tyre to 80 PSI (the recommended maximum for the tyre) I then found a 10m steel tape measure and a flat smooth indoor surface with a clear line and measured the distance travelled during 4 complete revolutions of the wheel whilst pushing the bike. Simple arithmetic then yielded a calibration of 2144 mm per revolution. Since I was interested in the effect of tyre pressure on the pushing calibration I lower the pressure to 40 PSI and found the circumference hardly changed (2143mm). Clearly with no rider weight there was very little compression of the tyre.<br />
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I then set-off to create a calibrated distance that I could also cycle to allow me to determine the change in effective wheel diameter which occurs between pushing the bike and when it is being ridden. I found a solid white line, between a cycle-path and pavement, close to my home that was little-travelled, clear of debris, with well defined start and end points and over 300m long. I did a series of repeated measurements whilst pushing my bike and determined it was 339.3m long. I then did a series of rides along the line at a range of different tyre pressures each time noting down the number of revolutions completed. I calculated the effective tyre circumference when I (68 kg including clothing) was riding the bike with a tyre pressure of 80 PSI. From that data I produced the graph shown in Figure 1.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDJzuMJvIF4N-4a-mgXFPCkC_oLh3Yvi7l8vYVaUpjaUfnkFaWTEx_QJLoKHHMnFdWQ6HnZm15j1uMyum0Rln-KC25OiEuV1GjRdCqgpHKleouLPXZ7lgGo6JlBAhtgZdnl7q_d_ePMvE/s1600/Capture.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="420" data-original-width="629" height="426" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDJzuMJvIF4N-4a-mgXFPCkC_oLh3Yvi7l8vYVaUpjaUfnkFaWTEx_QJLoKHHMnFdWQ6HnZm15j1uMyum0Rln-KC25OiEuV1GjRdCqgpHKleouLPXZ7lgGo6JlBAhtgZdnl7q_d_ePMvE/s640/Capture.PNG" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1. The percentage error in the distance estimate resulting from applying the 80 PSI calibration to measurements made whilst cycling a bike with the 'counting' tyre at a range of different pressures. The steepness of the line (2nd order polynomial fit) indicates the least sensitivity to tyre pressure is at high pressures.</td></tr>
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It shows the percentage error in the distance measurement which would result from using the 80 PSI calibration when the tyre was actually at a different pressure. It is clear that tyre pressure is important since a fall in tyre pressure to 60 PSI produces a 0.25% error (or 12.5m on a 5km route). For this reason it is important to have a calibrated distance close to the site of the course measurement such that the calibration can be done with the tyres inflated to exactly the same extent as they were when the course measurement took place (and with the same rider weight).<br />
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The choice of tyre pressure is an interesting one. Whilst Figure 1 does show that high pressures are likely to result in more consistent measurements, there is a problem with rough courses. High pressures mean the tyre is more likely to slip over the ground and also the bike will tend to 'measure' small undulations due to stones/rocks. A lower tyre pressure may allow small stones to pass under the tyre with increased deformation allowing the 'real' distance to be more accurately assessed. This problem is analogous the the problem of measuring a coast-line which has fractal-like properties - the more accurate the measurement the longer the distance becomes. In this case, we are aiming to approximate the course of a 70kg mass on springs with a stride length of over a meter and for such a system one would not want to take small surface undulations into account.<br />
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In my limited experience, so far, it is reasonably clear that by far the biggest error comes from the choice of racing-line. Whilst it is simple to <a href="http://www.usatf.org/Products-/-Services/Course-Certifications/USATF-Certified-Courses/Procedures-Manual/The-Shortest-Possible-Route.aspx" target="_blank">specify the shortest line</a>, measuring it is not always easy especially when there are other road users on the course.<br />
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<br />Unknownnoreply@blogger.com3tag:blogger.com,1999:blog-2980004124283593961.post-75616311949069424742019-05-07T16:18:00.002+01:002019-06-17T16:37:00.537+01:00Understanding race predictors - Riegel versus TandaPredicting the speed (or intensity) that can be maintained for different durations is a difficult subject that has concerned runners for many years. It has long been recognized that as the race duration increases the average speed that can be maintained decreases. This is not surprising since the higher the intensity the more physiological systems are out of steady-state and the faster they will fail.<br />
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What is interesting is that the 'average' person can be modelled reasonably well with a very simple equation. There are multiple forms of the equation but the most popular in running is the one <a href="https://en.wikipedia.org/wiki/Peter_Riegel" target="_blank">Peter Riegel</a> introduced back in the late 1970s/early 1980s. The equation is a simple scaling of one performance to another using an exponent, Whilst the value of that exponent has been discussed and argued about at length, most agree that the equation provides one of the better 'ball-park' values[<a href="http://www.markwk.com/2017/12/running-race-predictors.html" target="_blank">1</a>,<a href="https://wismuth.com/running/calculator.html" target="_blank">2</a>]. I don't intend to add to that discussion, but I do want to start from the premise that the formula does 'sort-of-work' and that it also represents a way of estimating what a 'maximum' effort might look like at a range of distances.<br />
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I have plotted Riegel's formula in the graph below (Figure 1) as the dotted lines for five different marathon preformances.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLXEDbeEWN2tjRXLggIa8weGppg9v5-ao6sYoJoYGoGY1aKmReCTWjaUvl258PmkTItEdWAt-IX8tNiOKuX3mkSMfbTMrOkv1zz1xyPb3a705l-ms0rIcMumNB_GRjvutxKieBiUzxEr8/s1600/Capture.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="435" data-original-width="618" height="449" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLXEDbeEWN2tjRXLggIa8weGppg9v5-ao6sYoJoYGoGY1aKmReCTWjaUvl258PmkTItEdWAt-IX8tNiOKuX3mkSMfbTMrOkv1zz1xyPb3a705l-ms0rIcMumNB_GRjvutxKieBiUzxEr8/s640/Capture.PNG" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1. Average run speed plotted against distance for five different levels of performance and for two race predictors (Riegel dotted lines, Tanda solid lines). The line colours indicate marathon performance times (blue 3:30, green 3:15, yellow 3:00, red 2:45, black 2:30). The very thick purple line indicates the intercepts between the Riegel race performance and the Tanda prediction lines.</td></tr>
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First, this graph is complicated for a number of reasons. But, the graph is worth a bit of effort since it encapsulates much of why people hit performance limits. Let me start by taking the example of the yellow dotted lines which is the Riegel line for a 3 hour marathon runner. The dotted yellow line shows the speed the 3 hour marathon runner might hope to maintain for a range of race distances. In a 5km race the runner should manage around 16 km h<sup>-1</sup> and in a 15km race about 15 km h<sup>-1</sup>. The dotted line is simply plotting how a maximum 'race' effort scales with distance. What is noticeable about the dotted lines (which are for faster and slower runners - see figure legend for details) is that the maximum speed that can be maintained drops dramatically at short distances and then changes relatively little at longer distances.<br />
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Also plotted on this graph are the race predictions (solid lines) from the Tanda equation. Now here I have taken the liberty of playing with the 'meaning' of the axis labels. Whilst the x-axis is still distance and the y-axis is speed, they are the distance covered in training on an average day and the speed at which it was done. Again the colours match the Riegel prediction times. So, let's go back to the yellow lines. The solid yellow line shows you the average distance and speed you need to run each day to become a 3 hour marathon runner. You could run 10 km each day at 14 km h<sup>-1</sup> or 5 km each day at 16 km h<sup>-1</sup> or a mixture of the two. As long as you stay on that line (on average) for eight weeks, you should get the 3 hour marathon (actually it is a bit more complicated than that, but to a first approximation it will do). Now, the interesting observation is how the dotted line and the solid line relate to each other. If you train above the dotted line then you are doing an effort, each day, that is HARDER than a race effort. You must be doing the effort as interval training, by definition since you could not have kept up a faster run than your Riegel prediction. If you train below the line then you are below a race effort - each day.<br />
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Now, look at the thick purple line. That shows the trajectory for training by doing a race effort every day! If you want to become a 3 hour marathon runner you will need to race a 5km every day. If you want to be a 2:45 marathon runner (red line) you need to race 9km every day. Notice that for a 3:15 marathon runner and slower any race effort every day is more training than necessary to get that time.<br />
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So, the faster you are the closer you need to be to sustaining a race effort every day and the longer that race effort has to be. The benefit of running more miles is that you are training much slower than race speed. The damage is far less and the training is 'possible'. <b><i>So, you definitely want to train below and to the right of the purple line.</i></b><br />
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Now the take-home message from this is that both the Riegel formula and the Tanda predictor are both race predictors using similar data - they are just different equations. For Riegel you put in any race and time but for Tanda you put in an 8 week average. As I have said before (but, it has not got traction) the Tanda 8 week period is just another race. It is the training race - a race with no defined distance or time but a race nevertheless.<br />
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The difference between Riegel and Tanda is that Riegel is the output of a short race effort whereas Tanda is the output of a long race effort - they work from opposite ends of the spectrum. The great thing about the Tanda equation is that you don't need to RACE before the marathon - you just use the training data you have (that is the training race). The second great thing about the Tanda equation is that it predicts from the very stimulus that makes you a marathon runner in the first place, namely the training. It is the <a href="https://www.phrases.org.uk/meanings/the-bees-knees.html" target="_blank">bees-knees</a>.<br />
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OK, there are other things you need to be aware of - and some of you will out-perform it by some margin - but the formula captures what it takes to train for a marathon. It is just running (and heat adaptation and growing large adrenals etc....but those are either previous posts or posts to come).Unknownnoreply@blogger.com2tag:blogger.com,1999:blog-2980004124283593961.post-45163327521027225952019-04-30T12:08:00.001+01:002019-04-30T12:08:13.304+01:00Can marathon performance be predicted? - Tanda and beyondI, and others, have made great play of Giovanni Tanda's marathon prediction equation. We have promoted it's use, both as a predictive tool and as a way of shaping training. Yet, it continues to fail for many people - they head-off at what seems an appropriate pace and fail. Whilst some claim it is the execution of the marathon plan that is at fault, and others simply junk the Tanda equation, I think the problem may lie elsewhere.
First, I think that the Tanda equation is one of the best equations to predict marathon performance. It is simple to calculate and of all of the equations that I have come across seems to get closest to predicting performance, especially once it is customised to the individual. But, it still fails and can fail spectacularly. Some of those failures are easy to predict because they involve obvious changes in physiology that the equation cannot know about. Colds and infections a few days before a race can wreck the possibility of a decent performance. But, even in the absence of these obvious problems the equation can still fail. And, we should expect it to do so. The statistics tell us it will.
The equation was derived from optimal performances - from a dataset of races where a near flat pace was maintained. The Tanda equation (with some individualization) represents the best that can be hoped for. For the best to happen many things need to align - not just the weather, course, pacing, grouping of runners but also a myriad of internal physiological and psychological parameters need to be in the right place. Executing a plan based on 'the best' happening is risky. And, given the cliff edge drop in performance that occurs with even a modestly over-enthusiastic pace, the most likely outcome will be failure.
Before Tanda constructed his dataset, a number of performances would have been filtered out. These were performances where the training went well but one of a number of problems occurred to result in a non-flat pace. The result being that the equation is not a fit of what is 'most likely' to be achieved, but what happens when things go well. What many runners want to know is the probability that the prediction will work - and how to finesse that function so that there is a high probability of getting something positive out of the event. Many runners adopt an all-in or should it be an all-out approach. They have a primary goal and adopt an uncompromising strategy to reach it. Modelling this on a pay-out basis would be $1,000,000 for achieving the A goal and $0 for missing it. It is a binary approach which will occasionally work. This is often seen as an heroic approach with the massive detonation or collapse as a sign of willingness to push for the highest level of achievement. I do not doubt this is the case - and respect those capable of committing to this - but, don't blame the science when it goes wrong. You could, however, blame the lack of science.
Risk distribution within a race is something we all instinctively engage with. Several times now I have listened to runners justify the collection of gels on their belts at the start of a marathon. Many believe them necessary, but the interesting ones are those people who suspect that the gels probably aren't - but, why take the risk of not having them? When running drafting is common - the closer the better. Now, there is a risk-based decision. How close do you get? When do you over-take? How close to the course edge can you run? The risk profile is important in knowing if the decision being taken is sensible. Your stomach rumbles and the sensations are present - but, do you stop at the portaloo or press on? At the London Marathon the risk is very different to that at a rural event - our nervous systems convolve probability and risk to arrive at an optimal strategy with no graph-plotting involved. Many risks we take, or should they be 'cautions' are instinctive with almost no proper conscious analysis.
The problem here arises when the risk is non-linear, highly non-linear. The analogous game that comes to mind is what I think was known as 'Shoffe-Groat'. It can easily be played with a few coins and a table. The idea is to launch your coin towards the other end of the table, getting as close to the edge as possible. The winner is the person who gets closest to the edge without falling off. He or she takes all of the money either on the floor or on the table. Now, in the case of marathon running few people are playing against other players - people are competing with their PBs. By definition those PBs were the best performances - the ones where most things went right. Of course, if you don't have many performances, you may not be close to the limit. But, for anyone who has given the event a good few tests they are going to be close to the table-edge.
Of course additional training can make the 'distance' between a previous PB and the failure that is represented by dropping-off the table a bit bigger. But, the space that you are trying to nestle into is tight. The odds are stacked against you. Now, the Tanda prediction - which worked for you before - is getting ever more difficult to achieve. The probability of success is dropping the more you train and the faster you go even though the prediction of what might be possible is correct - it is now simply that the number of times that the equation will 'work' is much smaller.
Here is lies an interesting observation. The Tanda equation does not tell us the probability of success. It tells us that people who trained in a certain way have achieved certain times. But, we don't know how many times they have trained that way and failed. It is almost certain that the Tanda equation has a much higher 'success' rate at lower performance times than faster ones. And, this is what is misleading about it. Just because the equation worked before, don't rely on being able to use it to extrapolate your new training space to a faster PB. To be safe you will need to push your training further - that is your PB race pace needs to be executed at a level of fitness which is greater than what you are trying to do. Of course, you may get lucky and get the performance predicted by training. But, a more likely scenario is that you will get your PB and an underperformance relative to the equation - at least until you repeat it a few times.
There is an in-race way of doing exactly this. It is the planned negative-split. Start the race somewhat slower than your fitness might warrant. At the appropriate time - and this needs discussion as to when this is - you ramp-up the pace carefully. If this is 'your day' you will sustain the ramp and get a very mildly disappointing time - not the best you could have done, but if you have put in the 'over-training' it will be the PB you wanted. If this isn't your day the ramp won't happen the best you will get is a flattish pace - it is the finishing time you deserved from your fitness and your 'luckiness'.
As Alberto Salazar is claimed to have said; “If anyone goes out at a suicidal pace, I’ll probably sit back”.
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2980004124283593961.post-5360806553775397832019-04-22T20:11:00.000+01:002019-04-22T20:13:00.850+01:00Marathon performance and junk mile calculator (Tanda race predictor)<html>
<head>
<meta name="description" content="Race predictor">
<meta charset="utf-8">
<title>Race predictor Version 0.2</title>
<meta name="viewport" content="width=device-width, initial-scale=1">
<STYLE TYPE="text/css">
<!--
TD{font-family: Arial; font-size: 10pt;}
H1{font-family: Arial; font-size: 12pt;}
P{font-family: Arial; font-size: 10pt;}
--->
</STYLE>
</head>
<body>
<div id='OpeningText'></div>
<form>
<!-- Wrapper table start -->
<table border="0" style="width:100%;" >
<tr>
<td>
<!-- Performance table start -->
<table border="1">
<tr>
<th align="right">Age:</th>
<td>
<input type="text" id="Age" style="width:40px;" onchange="changeFunc();">
<input type="radio" id="M" name="Sex" value="M" onchange="changeFunc();">Male
<input type="radio" id="F" name="Sex" value="F" onchange="changeFunc();" checked>Female
</td>
</tr>
<tr>
<th align="right">Previous race distance:</th>
<td><select id="PerformedDistance" onchange="changeFunc();"> </select></td>
</tr>
<tr><th>Time achieved (h:m:s):</th><td id="TimeAchieved"></td></tr>
<tr><th align="right">Pace (mm:ss):</th><td id="Pace"></td></tr>
<tr><th align="right">Age-grade:</th><td id="AgeGrade"></td></tr>
</table>
<!-- Performance Table end -->
</td>
</tr><tr><td>
<!-- Options table start -->
<br><table border=1>
<tr>
<th>Pace:</th>
<td>
<input type="radio" id="metric" name="Units" value="metric" onchange="changeFunc();">per km
<input type="radio" id="imperial" name="Units" value="imperial" onchange="changeFunc();" checked>per mile
</td>
</tr>
<tr>
<th>Distances:</th>
<td>
<input type="radio" id="StandardDistances" name="ListLength" value="StandardDistances" onchange="changeFunc();" checked>Standard
<input type="radio" id="CustomDistances" name="ListLength" value="CustomDistances" onchange="changeFunc();" >Custom
</td>
</tr>
</table><br>
<!-- Options table end -->
</td>
</tr>
<tr>
<td colspan=2>
<!-- Tanda input table start -->
<table border=1 style="width:100%; max-width:600px;" >
<tr>
<th>Average weekly distance:</th>
<td id="WeeklyDistance" align="center" style="width:45%"></td>
<tr><td align="center" id="DistanceSliderText" colspan=2> </td></tr>
</tr>
<tr>
<th>Average weekly pace:</th>
<td id="WeeklyPace" align="center"></td>
<tr><td align="center" id="PaceSliderText" colspan=2></td></tr>
</tr>
<tr>
<!--<th align="center" id="WeeklyTime" colspan=2>Average weekly time:</th> -->
<!-- <td id="WeeklyTime" align="center"></td> -->
<!-- <tr><td colspan=2> </td></tr> -->
<th id="TandaPrediction" align="center" colspan=2></th>
</tr>
</table>
<!-- Tanda input table end -->
</td>
</tr>
<tr><td colspan=2><table id="RemovedDistanceTable"><tr><td><div id="Distances"></div></td></tr></table></td></tr>
<tr><td colspan="2"><div id="tablePrint"> </div></td></tr>
</table>
<!-- Wrapper table end -->
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M3km,3km,3,440,0.6526,0.6899,0.725,0.7579,0.7886,0.8171,0.8434,0.8675,0.8894,0.9091,0.9266,0.9419,0.955,0.967,0.979,0.9893,0.9962,0.9996,1,1,1,1,1,0.9999,0.9991,0.9975,0.9952,0.9922,0.9885,0.984,0.9788,0.9729,0.9662,0.9592,0.9521,0.9451,0.938,0.931,0.924,0.9169,0.9099,0.9028,0.8958,0.8888,0.8817,0.8747,0.8676,0.8606,0.8536,0.8465,0.8395,0.8324,0.8254,0.8184,0.8113,0.8043,0.7972,0.7902,0.7832,0.7761,0.7691,0.762,0.755,0.7479,0.7402,0.7319,0.723,0.7134,0.7031,0.6923,0.6808,0.6687,0.6559,0.6425,0.6285,0.6138,0.5985,0.5825,0.566,0.5488,0.5309,0.5124,0.4933,0.4735,0.4531,0.4321,0.4104,0.3881,0.3652,0.3416,0.3174,0.2926,0.2671,0.2409,0.2142,0.1868
M2Mile,2Mile,3.218,474.6,0.6526,0.6899,0.725,0.7579,0.7886,0.8171,0.8434,0.8675,0.8894,0.9091,0.9266,0.9419,0.955,0.967,0.979,0.9893,0.9961,0.9996,1,1,1,1,1,0.9999,0.9991,0.9975,0.9952,0.9922,0.9885,0.984,0.9788,0.9729,0.9662,0.9592,0.9521,0.9451,0.938,0.931,0.924,0.9169,0.9099,0.9028,0.8958,0.8888,0.8817,0.8747,0.8676,0.8606,0.8536,0.8465,0.8395,0.8324,0.8254,0.8184,0.8113,0.8043,0.7972,0.7902,0.7832,0.7761,0.7691,0.762,0.755,0.7479,0.7402,0.7319,0.723,0.7134,0.7031,0.6923,0.6808,0.6687,0.6559,0.6425,0.6285,0.6138,0.5985,0.5825,0.566,0.5488,0.5309,0.5124,0.4933,0.4735,0.4531,0.4321,0.4104,0.3881,0.3652,0.3416,0.3174,0.2926,0.2671,0.2409,0.2142,0.1868
M4km,4km,4,598,0.6526,0.6899,0.725,0.7579,0.7886,0.8171,0.8434,0.8675,0.8894,0.9091,0.9266,0.9419,0.955,0.967,0.979,0.9893,0.9961,0.9996,1,1,1,1,1,0.9999,0.9991,0.9975,0.9952,0.9922,0.9885,0.984,0.9788,0.9729,0.9662,0.9592,0.9521,0.9451,0.938,0.931,0.924,0.9169,0.9099,0.9028,0.8958,0.8888,0.8817,0.8747,0.8676,0.8606,0.8536,0.8465,0.8395,0.8324,0.8254,0.8184,0.8113,0.8043,0.7972,0.7902,0.7832,0.7761,0.7691,0.762,0.755,0.7479,0.7402,0.7319,0.723,0.7134,0.7031,0.6923,0.6808,0.6687,0.6559,0.6425,0.6285,0.6138,0.5985,0.5825,0.566,0.5488,0.5309,0.5124,0.4933,0.4735,0.4531,0.4321,0.4104,0.3881,0.3652,0.3416,0.3174,0.2926,0.2671,0.2409,0.2142,0.1868
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M6kmRoad,6kmRoad,6,942,0.6056,0.6596,0.7096,0.7556,0.7976,0.8356,0.8696,0.8996,0.9256,0.9476,0.9656,0.9796,0.9916,0.9993,1,1,1,1,1,1,1,1,1,1,0.9995,0.9983,0.9965,0.994,0.9908,0.987,0.9824,0.9773,0.9714,0.9649,0.958,0.9511,0.9442,0.9373,0.9304,0.9235,0.9166,0.9096,0.9027,0.8958,0.8889,0.882,0.8751,0.8682,0.8613,0.8544,0.8475,0.8406,0.8337,0.8268,0.8199,0.813,0.8061,0.7992,0.7923,0.7854,0.7785,0.7715,0.7646,0.7577,0.7501,0.7419,0.7331,0.7237,0.7136,0.7028,0.6915,0.6795,0.6668,0.6535,0.6396,0.625,0.6098,0.594,0.5775,0.5604,0.5427,0.5243,0.5052,0.4856,0.4653,0.4443,0.4228,0.4005,0.3777,0.3542,0.3301,0.3053,0.2799,0.2538,0.2272,0.1998
M6km,6km,6,919,0.6526,0.6899,0.725,0.7579,0.7886,0.8171,0.8434,0.8675,0.8894,0.9091,0.9266,0.9419,0.955,0.967,0.979,0.9893,0.9961,0.9996,1,1,1,1,1,0.9999,0.9991,0.9975,0.9952,0.9922,0.9885,0.984,0.9788,0.9729,0.9662,0.9592,0.9521,0.9451,0.938,0.931,0.924,0.9169,0.9099,0.9028,0.8958,0.8888,0.8817,0.8747,0.8676,0.8606,0.8536,0.8465,0.8395,0.8324,0.8254,0.8184,0.8113,0.8043,0.7972,0.7902,0.7832,0.7761,0.7691,0.762,0.755,0.7479,0.7402,0.7319,0.723,0.7134,0.7031,0.6923,0.6808,0.6687,0.6559,0.6425,0.6285,0.6138,0.5985,0.5825,0.566,0.5488,0.5309,0.5124,0.4933,0.4735,0.4531,0.4321,0.4104,0.3881,0.3652,0.3416,0.3174,0.2926,0.2671,0.2409,0.2142,0.1868
M4MileRoad,4MileRoad,6.437376,1014,0.6056,0.6596,0.7096,0.7556,0.7976,0.8356,0.8696,0.8996,0.9256,0.9476,0.9656,0.9796,0.9916,0.9993,1,1,1,1,1,1,1,1,1,1,0.9997,0.9987,0.9971,0.9948,0.9918,0.9881,0.9837,0.9787,0.973,0.9666,0.9597,0.9527,0.9457,0.9387,0.9318,0.9248,0.9178,0.9108,0.9038,0.8968,0.8899,0.8829,0.8759,0.8689,0.8619,0.8549,0.8479,0.841,0.834,0.827,0.82,0.813,0.806,0.7991,0.7921,0.7851,0.7781,0.7711,0.7641,0.7571,0.7495,0.7412,0.7323,0.7228,0.7126,0.7018,0.6903,0.6782,0.6655,0.6521,0.6381,0.6235,0.6082,0.5923,0.5758,0.5586,0.5407,0.5223,0.5032,0.4834,0.463,0.442,0.4204,0.3981,0.3751,0.3516,0.3273,0.3025,0.277,0.2509,0.2241,0.1967
M4Mile,4Mile,6.436,990,0.6526,0.6899,0.725,0.7579,0.7886,0.8171,0.8434,0.8675,0.8894,0.9091,0.9266,0.9419,0.955,0.967,0.979,0.9893,0.9961,0.9996,1,1,1,1,1,0.9999,0.9991,0.9975,0.9952,0.9922,0.9885,0.984,0.9788,0.9729,0.9662,0.9592,0.9521,0.9451,0.938,0.931,0.924,0.9169,0.9099,0.9028,0.8958,0.8888,0.8817,0.8747,0.8676,0.8606,0.8536,0.8465,0.8395,0.8324,0.8254,0.8184,0.8113,0.8043,0.7972,0.7902,0.7832,0.7761,0.7691,0.762,0.755,0.7479,0.7402,0.7319,0.723,0.7134,0.7031,0.6923,0.6808,0.6687,0.6559,0.6425,0.6285,0.6138,0.5985,0.5825,0.566,0.5488,0.5309,0.5124,0.4933,0.4735,0.4531,0.4321,0.4104,0.3881,0.3652,0.3416,0.3174,0.2926,0.2671,0.2409,0.2142,0.1868
M8kmRoad,8kmRoad,8,1272,0.6056,0.6596,0.7096,0.7556,0.7976,0.8356,0.8696,0.8996,0.9256,0.9476,0.9656,0.9796,0.9916,0.9993,1,1,1,1,1,1,1,1,1,1,1,0.9996,0.9986,0.9968,0.9944,0.9913,0.9874,0.9829,0.9777,0.9719,0.9653,0.9581,0.9509,0.9436,0.9364,0.9292,0.922,0.9147,0.9075,0.9003,0.893,0.8858,0.8786,0.8714,0.8641,0.8569,0.8497,0.8424,0.8352,0.828,0.8208,0.8135,0.8063,0.7991,0.7918,0.7846,0.7774,0.7702,0.7629,0.7557,0.7482,0.7401,0.7314,0.722,0.7119,0.7012,0.6899,0.6779,0.6653,0.652,0.638,0.6235,0.6082,0.5923,0.5758,0.5586,0.5408,0.5223,0.5032,0.4835,0.463,0.442,0.4203,0.3979,0.3749,0.3512,0.3269,0.302,0.2764,0.2501,0.2232,0.1957
M8km,8km,8,1247,0.6526,0.6899,0.725,0.7579,0.7886,0.8171,0.8434,0.8675,0.8894,0.9091,0.9266,0.9419,0.955,0.967,0.979,0.9893,0.9961,0.9996,1,1,1,1,1,0.9999,0.9991,0.9975,0.9952,0.9922,0.9885,0.984,0.9788,0.9729,0.9662,0.9592,0.9521,0.9451,0.938,0.931,0.924,0.9169,0.9099,0.9028,0.8958,0.8888,0.8817,0.8747,0.8676,0.8606,0.8536,0.8465,0.8395,0.8324,0.8254,0.8184,0.8113,0.8043,0.7972,0.7902,0.7832,0.7761,0.7691,0.762,0.755,0.7479,0.7402,0.7319,0.723,0.7134,0.7031,0.6923,0.6808,0.6687,0.6559,0.6425,0.6285,0.6138,0.5985,0.5825,0.566,0.5488,0.5309,0.5124,0.4933,0.4735,0.4531,0.4321,0.4104,0.3881,0.3652,0.3416,0.3174,0.2926,0.2671,0.2409,0.2142,0.1868
M5MileRoad,5MileRoad,8.04672,1279,0.6056,0.6596,0.7096,0.7556,0.7976,0.8356,0.8696,0.8996,0.9256,0.9476,0.9656,0.9796,0.9916,0.9993,1,1,1,1,1,1,1,1,1,1,1,0.9996,0.9986,0.9969,0.9944,0.9913,0.9875,0.983,0.9778,0.972,0.9654,0.9582,0.951,0.9438,0.9365,0.9293,0.9221,0.9148,0.9076,0.9004,0.8931,0.8859,0.8787,0.8714,0.8642,0.8569,0.8497,0.8425,0.8352,0.828,0.8208,0.8135,0.8063,0.7991,0.7918,0.7846,0.7774,0.7701,0.7629,0.7557,0.7482,0.7401,0.7314,0.722,0.7119,0.7012,0.6899,0.6779,0.6653,0.652,0.638,0.6235,0.6082,0.5924,0.5758,0.5587,0.5409,0.5224,0.5033,0.4835,0.4631,0.442,0.4203,0.398,0.375,0.3513,0.327,0.3021,0.2765,0.2502,0.2234,0.1958
M5Mile,5Mile,8.045,1255,0.6526,0.6899,0.725,0.7579,0.7886,0.8171,0.8434,0.8675,0.8894,0.9091,0.9266,0.9419,0.955,0.967,0.979,0.9893,0.9961,0.9996,1,1,1,1,1,0.9999,0.9991,0.9975,0.9952,0.9922,0.9885,0.984,0.9788,0.9729,0.9662,0.9592,0.9521,0.9451,0.938,0.931,0.924,0.9169,0.9099,0.9028,0.8958,0.8888,0.8817,0.8747,0.8676,0.8606,0.8536,0.8465,0.8395,0.8324,0.8254,0.8184,0.8113,0.8043,0.7972,0.7902,0.7832,0.7761,0.7691,0.762,0.755,0.7479,0.7402,0.7319,0.723,0.7134,0.7031,0.6923,0.6808,0.6687,0.6559,0.6425,0.6285,0.6138,0.5985,0.5825,0.566,0.5488,0.5309,0.5124,0.4933,0.4735,0.4531,0.4321,0.4104,0.3881,0.3652,0.3416,0.3174,0.2926,0.2671,0.2409,0.2142,0.1868
M10kmRoad,10kmRoad,10,1603,0.6056,0.6596,0.7096,0.7556,0.7976,0.8356,0.8696,0.8996,0.9256,0.9476,0.9656,0.9796,0.9916,0.9993,1,1,1,1,1,1,1,1,1,1,1,1,0.9996,0.9984,0.9966,0.9941,0.9908,0.9869,0.9822,0.9769,0.9708,0.964,0.9566,0.9491,0.9417,0.9342,0.9267,0.9192,0.9117,0.9043,0.8968,0.8893,0.8818,0.8743,0.8669,0.8594,0.8519,0.8444,0.8369,0.8295,0.822,0.8145,0.807,0.7995,0.7921,0.7846,0.7771,0.7696,0.7621,0.7547,0.7471,0.7391,0.7305,0.7211,0.7112,0.7005,0.6892,0.6772,0.6646,0.6513,0.6374,0.6228,0.6075,0.5916,0.575,0.5577,0.5398,0.5213,0.502,0.4821,0.4616,0.4404,0.4185,0.396,0.3728,0.3489,0.3244,0.2993,0.2734,0.247,0.2198,0.192
M10km,10km,10,1580,0.6526,0.6899,0.725,0.7579,0.7886,0.8171,0.8434,0.8675,0.8894,0.9091,0.9266,0.9419,0.955,0.967,0.979,0.9893,0.9961,0.9996,1,1,1,1,1,0.9999,0.9991,0.9975,0.9952,0.9922,0.9885,0.984,0.9788,0.9729,0.9662,0.9592,0.9521,0.9451,0.938,0.931,0.924,0.9169,0.9099,0.9028,0.8958,0.8888,0.8817,0.8747,0.8676,0.8606,0.8536,0.8465,0.8395,0.8324,0.8254,0.8184,0.8113,0.8043,0.7972,0.7902,0.7832,0.7761,0.7691,0.762,0.755,0.7479,0.7402,0.7319,0.723,0.7134,0.7031,0.6923,0.6808,0.6687,0.6559,0.6425,0.6285,0.6138,0.5985,0.5825,0.566,0.5488,0.5309,0.5124,0.4933,0.4735,0.4531,0.4321,0.4104,0.3881,0.3652,0.3416,0.3174,0.2926,0.2671,0.2409,0.2142,0.1868
M12km,12km,12,1942,0.6056,0.6596,0.7096,0.7556,0.7976,0.8356,0.8696,0.8996,0.9256,0.9476,0.9656,0.9796,0.9916,0.9993,1,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.9989,0.9973,0.995,0.992,0.9882,0.9838,0.9786,0.9727,0.9662,0.9589,0.9513,0.9438,0.9362,0.9287,0.9211,0.9136,0.906,0.8984,0.8909,0.8833,0.8758,0.8682,0.8607,0.8531,0.8456,0.838,0.8305,0.8229,0.8154,0.8078,0.8003,0.7927,0.7852,0.7776,0.77,0.7625,0.7549,0.7474,0.7395,0.731,0.7218,0.7119,0.7013,0.6901,0.6782,0.6656,0.6524,0.6385,0.6239,0.6087,0.5928,0.5762,0.5589,0.541,0.5224,0.5031,0.4832,0.4626,0.4413,0.4194,0.3968,0.3735,0.3495,0.3249,0.2996,0.2736,0.247,0.2197,0.1917
M15km,15km,15,2455,0.6056,0.6596,0.7096,0.7556,0.7976,0.8356,0.8696,0.8996,0.9256,0.9476,0.9656,0.9796,0.9916,0.9993,1,1,1,1,1,1,1,1,1,1,1,1,1,0.9994,0.998,0.996,0.9932,0.9898,0.9856,0.9807,0.975,0.9687,0.9616,0.954,0.9464,0.9387,0.9311,0.9235,0.9158,0.9082,0.9005,0.8929,0.8852,0.8776,0.87,0.8623,0.8547,0.847,0.8394,0.8317,0.8241,0.8165,0.8088,0.8012,0.7935,0.7859,0.7782,0.7706,0.763,0.7553,0.7477,0.7399,0.7315,0.7224,0.7127,0.7022,0.6911,0.6793,0.6668,0.6537,0.6398,0.6253,0.6101,0.5942,0.5776,0.5603,0.5424,0.5238,0.5045,0.4845,0.4638,0.4425,0.4204,0.3977,0.3743,0.3502,0.3255,0.3,0.2739,0.2471,0.2196,0.1914
M10Mile,10Mile,16.09344,2640,0.6056,0.6596,0.7096,0.7556,0.7976,0.8356,0.8696,0.8996,0.9256,0.9476,0.9656,0.9796,0.9916,0.9993,1,1,1,1,1,1,1,1,1,1,1,1,1,0.9995,0.9982,0.9963,0.9936,0.9902,0.9861,0.9813,0.9758,0.9695,0.9625,0.9549,0.9472,0.9396,0.9319,0.9242,0.9166,0.9089,0.9012,0.8935,0.8859,0.8782,0.8705,0.8629,0.8552,0.8475,0.8399,0.8322,0.8245,0.8168,0.8092,0.8015,0.7938,0.7862,0.7785,0.7708,0.7631,0.7555,0.7478,0.7401,0.7317,0.7227,0.713,0.7026,0.6915,0.6797,0.6673,0.6542,0.6403,0.6258,0.6106,0.5947,0.5782,0.5609,0.543,0.5244,0.505,0.485,0.4644,0.443,0.4209,0.3982,0.3748,0.3506,0.3258,0.3004,0.2742,0.2473,0.2198,0.1916
M20km,20km,20,3315,0.6056,0.6596,0.7096,0.7556,0.7976,0.8356,0.8696,0.8996,0.9256,0.9476,0.9656,0.9796,0.9916,0.9993,1,1,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.9988,0.9972,0.9948,0.9916,0.9878,0.9832,0.9779,0.9719,0.9651,0.9577,0.9499,0.9422,0.9344,0.9266,0.9189,0.9111,0.9034,0.8956,0.8878,0.8801,0.8723,0.8646,0.8568,0.849,0.8413,0.8335,0.8258,0.818,0.8103,0.8025,0.7947,0.787,0.7792,0.7715,0.7637,0.7559,0.7482,0.7404,0.7322,0.7234,0.7138,0.7035,0.6926,0.6809,0.6686,0.6555,0.6418,0.6273,0.6122,0.5963,0.5798,0.5625,0.5446,0.5259,0.5066,0.4866,0.4658,0.4444,0.4223,0.3994,0.3759,0.3517,0.3267,0.3011,0.2748,0.2478,0.2201,0.1917
MHalf.Mar,Half.Mar,21.0975,3503,0.6056,0.6596,0.7096,0.7556,0.7976,0.8356,0.8696,0.8996,0.9256,0.9476,0.9656,0.9796,0.9916,0.9993,1,1,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.9989,0.9973,0.995,0.992,0.9882,0.9837,0.9784,0.9725,0.9658,0.9584,0.9506,0.9428,0.935,0.9273,0.9195,0.9117,0.9039,0.8961,0.8884,0.8806,0.8728,0.865,0.8572,0.8495,0.8417,0.8339,0.8261,0.8183,0.8106,0.8028,0.795,0.7872,0.7794,0.7717,0.7639,0.7561,0.7483,0.7405,0.7324,0.7236,0.714,0.7038,0.6929,0.6813,0.6689,0.6559,0.6422,0.6277,0.6126,0.5968,0.5802,0.563,0.5451,0.5265,0.5071,0.4871,0.4664,0.4449,0.4228,0.4,0.3764,0.3522,0.3273,0.3017,0.2753,0.2483,0.2206,0.1921
M25km,25km,25,4205,0.6056,0.6596,0.7096,0.7556,0.7976,0.8356,0.8696,0.8996,0.9256,0.9476,0.9656,0.9796,0.9916,0.9993,1,1,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.9989,0.9973,0.995,0.992,0.9882,0.9837,0.9784,0.9725,0.9658,0.9584,0.9506,0.9428,0.935,0.9273,0.9195,0.9117,0.9039,0.8961,0.8884,0.8806,0.8728,0.865,0.8572,0.8495,0.8417,0.8339,0.8261,0.8183,0.8106,0.8028,0.795,0.7872,0.7794,0.7717,0.7639,0.7561,0.7483,0.7405,0.7324,0.7236,0.714,0.7038,0.6929,0.6813,0.6689,0.6559,0.6422,0.6277,0.6126,0.5968,0.5802,0.563,0.5451,0.5265,0.5071,0.4871,0.4664,0.4449,0.4228,0.4,0.3764,0.3522,0.3273,0.3017,0.2753,0.2483,0.2206,0.1921
M30km,30km,30,5110,0.6056,0.6596,0.7096,0.7556,0.7976,0.8356,0.8696,0.8996,0.9256,0.9476,0.9656,0.9796,0.9916,0.9993,1,1,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.9989,0.9973,0.995,0.992,0.9882,0.9837,0.9784,0.9725,0.9658,0.9584,0.9506,0.9428,0.935,0.9273,0.9195,0.9117,0.9039,0.8961,0.8884,0.8806,0.8728,0.865,0.8572,0.8495,0.8417,0.8339,0.8261,0.8183,0.8106,0.8028,0.795,0.7872,0.7794,0.7717,0.7639,0.7561,0.7483,0.7405,0.7324,0.7236,0.714,0.7038,0.6929,0.6813,0.6689,0.6559,0.6422,0.6277,0.6126,0.5968,0.5802,0.563,0.5451,0.5265,0.5071,0.4871,0.4664,0.4449,0.4228,0.4,0.3764,0.3522,0.3273,0.3017,0.2753,0.2483,0.2206,0.1921
MMarathon,Marathon,42.195,7377,0.6056,0.6596,0.7096,0.7556,0.7976,0.8356,0.8696,0.8996,0.9256,0.9476,0.9656,0.9796,0.9916,0.9993,1,1,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.9989,0.9973,0.995,0.992,0.9882,0.9837,0.9784,0.9725,0.9658,0.9584,0.9506,0.9428,0.935,0.9273,0.9195,0.9117,0.9039,0.8961,0.8884,0.8806,0.8728,0.865,0.8572,0.8495,0.8417,0.8339,0.8261,0.8183,0.8106,0.8028,0.795,0.7872,0.7794,0.7717,0.7639,0.7561,0.7483,0.7405,0.7324,0.7236,0.714,0.7038,0.6929,0.6813,0.6689,0.6559,0.6422,0.6277,0.6126,0.5968,0.5802,0.563,0.5451,0.5265,0.5071,0.4871,0.4664,0.4449,0.4228,0.4,0.3764,0.3522,0.3273,0.3017,0.2753,0.2483,0.2206,0.1921
M50km,50km,50,8970,0.6056,0.6596,0.7096,0.7556,0.7976,0.8356,0.8696,0.8996,0.9256,0.9476,0.9656,0.9796,0.9916,0.9993,1,1,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.9989,0.9973,0.995,0.992,0.9882,0.9837,0.9784,0.9725,0.9658,0.9584,0.9506,0.9428,0.935,0.9273,0.9195,0.9117,0.9039,0.8961,0.8884,0.8806,0.8728,0.865,0.8572,0.8495,0.8417,0.8339,0.8261,0.8183,0.8106,0.8028,0.795,0.7872,0.7794,0.7717,0.7639,0.7561,0.7483,0.7405,0.7324,0.7236,0.714,0.7038,0.6929,0.6813,0.6689,0.6559,0.6422,0.6277,0.6126,0.5968,0.5802,0.563,0.5451,0.5265,0.5071,0.4871,0.4664,0.4449,0.4228,0.4,0.3764,0.3522,0.3273,0.3017,0.2753,0.2483,0.2206,0.1921
M50Mile,50Mile,80.46736,16080,0.6056,0.6596,0.7096,0.7556,0.7976,0.8356,0.8696,0.8996,0.9256,0.9476,0.9656,0.9796,0.9916,0.9993,1,1,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.9989,0.9973,0.995,0.992,0.9882,0.9837,0.9784,0.9725,0.9658,0.9584,0.9506,0.9428,0.935,0.9273,0.9195,0.9117,0.9039,0.8961,0.8884,0.8806,0.8728,0.865,0.8572,0.8495,0.8417,0.8339,0.8261,0.8183,0.8106,0.8028,0.795,0.7872,0.7794,0.7717,0.7639,0.7561,0.7483,0.7405,0.7324,0.7236,0.714,0.7038,0.6929,0.6813,0.6689,0.6559,0.6422,0.6277,0.6126,0.5968,0.5802,0.563,0.5451,0.5265,0.5071,0.4871,0.4664,0.4449,0.4228,0.4,0.3764,0.3522,0.3273,0.3017,0.2753,0.2483,0.2206,0.1921
M100km,100km,100,21360,0.6056,0.6596,0.7096,0.7556,0.7976,0.8356,0.8696,0.8996,0.9256,0.9476,0.9656,0.9796,0.9916,0.9993,1,1,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.9989,0.9973,0.995,0.992,0.9882,0.9837,0.9784,0.9725,0.9658,0.9584,0.9506,0.9428,0.935,0.9273,0.9195,0.9117,0.9039,0.8961,0.8884,0.8806,0.8728,0.865,0.8572,0.8495,0.8417,0.8339,0.8261,0.8183,0.8106,0.8028,0.795,0.7872,0.7794,0.7717,0.7639,0.7561,0.7483,0.7405,0.7324,0.7236,0.714,0.7038,0.6929,0.6813,0.6689,0.6559,0.6422,0.6277,0.6126,0.5968,0.5802,0.563,0.5451,0.5265,0.5071,0.4871,0.4664,0.4449,0.4228,0.4,0.3764,0.3522,0.3273,0.3017,0.2753,0.2483,0.2206,0.1921
M150km,150km,150,36300,0.6056,0.6596,0.7096,0.7556,0.7976,0.8356,0.8696,0.8996,0.9256,0.9476,0.9656,0.9796,0.9916,0.9993,1,1,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.9989,0.9973,0.995,0.992,0.9882,0.9837,0.9784,0.9725,0.9658,0.9584,0.9506,0.9428,0.935,0.9273,0.9195,0.9117,0.9039,0.8961,0.8884,0.8806,0.8728,0.865,0.8572,0.8495,0.8417,0.8339,0.8261,0.8183,0.8106,0.8028,0.795,0.7872,0.7794,0.7717,0.7639,0.7561,0.7483,0.7405,0.7324,0.7236,0.714,0.7038,0.6929,0.6813,0.6689,0.6559,0.6422,0.6277,0.6126,0.5968,0.5802,0.563,0.5451,0.5265,0.5071,0.4871,0.4664,0.4449,0.4228,0.4,0.3764,0.3522,0.3273,0.3017,0.2753,0.2483,0.2206,0.1921
M100Mile,100Mile,160.9344,39850,0.6056,0.6596,0.7096,0.7556,0.7976,0.8356,0.8696,0.8996,0.9256,0.9476,0.9656,0.9796,0.9916,0.9993,1,1,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.9989,0.9973,0.995,0.992,0.9882,0.9837,0.9784,0.9725,0.9658,0.9584,0.9506,0.9428,0.935,0.9273,0.9195,0.9117,0.9039,0.8961,0.8884,0.8806,0.8728,0.865,0.8572,0.8495,0.8417,0.8339,0.8261,0.8183,0.8106,0.8028,0.795,0.7872,0.7794,0.7717,0.7639,0.7561,0.7483,0.7405,0.7324,0.7236,0.714,0.7038,0.6929,0.6813,0.6689,0.6559,0.6422,0.6277,0.6126,0.5968,0.5802,0.563,0.5451,0.5265,0.5071,0.4871,0.4664,0.4449,0.4228,0.4,0.3764,0.3522,0.3273,0.3017,0.2753,0.2483,0.2206,0.1921
M200km,200km,200,52800,0.6056,0.6596,0.7096,0.7556,0.7976,0.8356,0.8696,0.8996,0.9256,0.9476,0.9656,0.9796,0.9916,0.9993,1,1,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.9989,0.9973,0.995,0.992,0.9882,0.9837,0.9784,0.9725,0.9658,0.9584,0.9506,0.9428,0.935,0.9273,0.9195,0.9117,0.9039,0.8961,0.8884,0.8806,0.8728,0.865,0.8572,0.8495,0.8417,0.8339,0.8261,0.8183,0.8106,0.8028,0.795,0.7872,0.7794,0.7717,0.7639,0.7561,0.7483,0.7405,0.7324,0.7236,0.714,0.7038,0.6929,0.6813,0.6689,0.6559,0.6422,0.6277,0.6126,0.5968,0.5802,0.563,0.5451,0.5265,0.5071,0.4871,0.4664,0.4449,0.4228,0.4,0.3764,0.3522,0.3273,0.3017,0.2753,0.2483,0.2206,0.1921
F800m,800m,0.8,113.28,0.5989,0.6645,0.7177,0.7622,0.8001,0.8327,0.8609,0.8853,0.9064,0.9247,0.9406,0.9541,0.9656,0.9755,0.9836,0.9903,0.9957,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0.9997,0.9906,0.9814,0.9722,0.9638,0.9554,0.9471,0.9387,0.9303,0.9226,0.9149,0.9072,0.8995,0.8918,0.8806,0.8693,0.8581,0.8468,0.8356,0.8239,0.8121,0.8004,0.7886,0.7769,0.7621,0.7473,0.7324,0.7176,0.7028,0.6893,0.6759,0.6624,0.649,0.6355,0.6205,0.6054,0.5904,0.5753,0.5603,0.547,0.5336,0.5203,0.5069,0.4936,0.4808,0.468,0.4552,0.4424,0.4296,0.4172,0.4048,0.3925,0.3801,0.3677,0.3549,0.3421,0.3293,0.3165,0.3037,0.2913,0.2789,0.2665,0.2541,0.2417
F1000m,1000m,1,146.5,0.6157,0.6699,0.7185,0.7623,0.8016,0.8367,0.8676,0.8947,0.918,0.9379,0.9545,0.9681,0.9792,0.9879,0.9946,0.9997,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0.9996,0.9912,0.9827,0.9738,0.9647,0.9559,0.9469,0.938,0.9289,0.9198,0.9113,0.9028,0.8942,0.8856,0.8771,0.8661,0.8549,0.8439,0.8327,0.8217,0.8103,0.7988,0.7874,0.7759,0.7645,0.7509,0.7373,0.7236,0.7099,0.6963,0.6836,0.671,0.6583,0.6457,0.633,0.6192,0.6054,0.5916,0.5778,0.564,0.5515,0.5389,0.5263,0.5137,0.5011,0.4888,0.4761,0.463,0.4496,0.4359,0.4221,0.4079,0.3935,0.3787,0.3635,0.3478,0.3316,0.3151,0.2983,0.2811,0.2639,0.2464,0.2284,0.2102,0.1916
F1500m,1500m,1.5,232.47,0.725,0.7579,0.7886,0.8171,0.8434,0.8675,0.8894,0.9091,0.9266,0.9419,0.955,0.967,0.979,0.9893,0.9961,0.9996,1,1,1,1,1,1,1,1,0.9998,0.9989,0.9971,0.9946,0.9913,0.9871,0.9822,0.9765,0.9701,0.9628,0.9547,0.9459,0.9362,0.9258,0.9151,0.9044,0.8937,0.8831,0.8724,0.8617,0.851,0.8403,0.8297,0.819,0.8083,0.7976,0.7869,0.7763,0.7656,0.7549,0.7442,0.7335,0.7229,0.7122,0.7015,0.6908,0.6801,0.6695,0.6588,0.6481,0.6374,0.6267,0.6161,0.6054,0.5947,0.584,0.5733,0.5627,0.552,0.5413,0.5306,0.5199,0.5087,0.4962,0.4825,0.4676,0.4515,0.4343,0.4158,0.3961,0.3752,0.3531,0.3299,0.3054,0.2797,0.2528,0.2247,0.1955,0.165,0.1333,0.1004,0.0663
F1Mile,1Mile,1.609,251.6,0.725,0.7579,0.7886,0.8171,0.8434,0.8675,0.8894,0.9091,0.9266,0.9419,0.955,0.967,0.979,0.9893,0.9961,0.9996,1,1,1,1,1,1,1,1,0.9998,0.9989,0.9972,0.9948,0.9915,0.9875,0.9827,0.9771,0.9707,0.9636,0.9557,0.9469,0.9375,0.9272,0.9165,0.9058,0.8951,0.8844,0.8737,0.863,0.8523,0.8416,0.8309,0.8202,0.8095,0.7988,0.7881,0.7774,0.7667,0.756,0.7453,0.7346,0.7239,0.7132,0.7025,0.6918,0.6811,0.6704,0.6597,0.649,0.6383,0.6276,0.6169,0.6062,0.5955,0.5848,0.5741,0.5634,0.5527,0.542,0.5313,0.5206,0.5091,0.4965,0.4827,0.4678,0.4516,0.4343,0.4158,0.3961,0.3752,0.3532,0.3299,0.3055,0.2799,0.2532,0.2252,0.1961,0.1658,0.1343,0.1016,0.0677
F2km,2km,2,321.5,0.725,0.7579,0.7886,0.8171,0.8434,0.8675,0.8894,0.9091,0.9266,0.9419,0.955,0.967,0.979,0.9893,0.9961,0.9996,1,1,1,1,1,1,1,1,0.9999,0.9991,0.9976,0.9953,0.9923,0.9885,0.984,0.9787,0.9727,0.9659,0.9584,0.9501,0.9411,0.9313,0.9208,0.91,0.8992,0.8885,0.8777,0.867,0.8562,0.8454,0.8347,0.8239,0.8132,0.8024,0.7916,0.7809,0.7701,0.7594,0.7486,0.7378,0.7271,0.7163,0.7056,0.6948,0.684,0.6733,0.6625,0.6518,0.641,0.6302,0.6195,0.6087,0.598,0.5872,0.5764,0.5657,0.5549,0.5442,0.5334,0.5225,0.5106,0.4976,0.4834,0.4682,0.4517,0.4341,0.4154,0.3956,0.3746,0.3524,0.3292,0.3047,0.2792,0.2525,0.2246,0.1957,0.1655,0.1343,0.1019,0.0684
F3km,3km,3,501.42,0.725,0.7579,0.7886,0.8171,0.8434,0.8675,0.8894,0.9091,0.9266,0.9419,0.955,0.967,0.979,0.9893,0.9961,0.9996,1,1,1,1,1,1,1,1,1,0.9994,0.9981,0.9962,0.9935,0.9902,0.9861,0.9813,0.9759,0.9697,0.9628,0.9553,0.947,0.938,0.9283,0.918,0.9071,0.8962,0.8854,0.8745,0.8636,0.8527,0.8419,0.831,0.8201,0.8092,0.7984,0.7875,0.7766,0.7657,0.7549,0.744,0.7331,0.7222,0.7114,0.7005,0.6896,0.6787,0.6678,0.657,0.6461,0.6352,0.6243,0.6135,0.6026,0.5917,0.5808,0.57,0.5591,0.5482,0.5373,0.5257,0.5131,0.4993,0.4845,0.4686,0.4517,0.4336,0.4145,0.3942,0.3729,0.3506,0.3271,0.3026,0.277,0.2503,0.2225,0.1936,0.1637,0.1327,0.1006,0.0674
F2Mile,2Mile,3.218,541.5,0.725,0.7579,0.7886,0.8171,0.8434,0.8675,0.8894,0.9091,0.9266,0.9419,0.955,0.967,0.979,0.9893,0.9961,0.9996,1,1,1,1,1,1,1,1,1,0.9994,0.9982,0.9963,0.9937,0.9904,0.9864,0.9817,0.9764,0.9703,0.9635,0.9561,0.9479,0.9391,0.9295,0.9193,0.9085,0.8976,0.8867,0.8758,0.8649,0.854,0.8431,0.8322,0.8213,0.8104,0.7995,0.7886,0.7777,0.7668,0.7559,0.745,0.7341,0.7232,0.7123,0.7014,0.6906,0.6797,0.6688,0.6579,0.647,0.6361,0.6252,0.6143,0.6034,0.5925,0.5816,0.5707,0.5598,0.5489,0.538,0.5263,0.5135,0.4997,0.4848,0.4688,0.4518,0.4337,0.4146,0.3944,0.3731,0.3508,0.3275,0.303,0.2775,0.251,0.2234,0.1947,0.165,0.1342,0.1023,0.0694
F4km,4km,4,683,0.725,0.7579,0.7886,0.8171,0.8434,0.8675,0.8894,0.9091,0.9266,0.9419,0.955,0.967,0.979,0.9893,0.9961,0.9996,1,1,1,1,1,1,1,1,1,0.9996,0.9985,0.9967,0.9943,0.9912,0.9874,0.983,0.9779,0.9721,0.9656,0.9585,0.9507,0.9422,0.9331,0.9233,0.9128,0.9019,0.8909,0.88,0.869,0.8581,0.8471,0.8361,0.8252,0.8142,0.8033,0.7923,0.7814,0.7704,0.7594,0.7485,0.7375,0.7266,0.7156,0.7047,0.6937,0.6827,0.6718,0.6608,0.6499,0.6389,0.628,0.617,0.606,0.5951,0.5841,0.5732,0.5622,0.5513,0.5401,0.528,0.5149,0.5007,0.4855,0.4693,0.4521,0.4339,0.4147,0.3944,0.3731,0.3508,0.3275,0.3031,0.2777,0.2514,0.2239,0.1955,0.1661,0.1356,0.1041,0.0716
F3Mile,3Mile,4.827,833,0.725,0.7579,0.7886,0.8171,0.8434,0.8675,0.8894,0.9091,0.9266,0.9419,0.955,0.967,0.979,0.9893,0.9961,0.9996,1,1,1,1,1,1,1,1,1,0.9997,0.9987,0.997,0.9947,0.9918,0.9882,0.9839,0.979,0.9735,0.9673,0.9604,0.9529,0.9448,0.936,0.9265,0.9164,0.9056,0.8946,0.8836,0.8726,0.8616,0.8506,0.8396,0.8286,0.8176,0.8066,0.7955,0.7845,0.7735,0.7625,0.7515,0.7405,0.7295,0.7185,0.7075,0.6965,0.6854,0.6744,0.6634,0.6524,0.6414,0.6304,0.6194,0.6084,0.5974,0.5864,0.5753,0.5643,0.5533,0.5419,0.5294,0.516,0.5015,0.4861,0.4696,0.4522,0.4337,0.4143,0.3938,0.3724,0.3499,0.3265,0.302,0.2766,0.2501,0.2227,0.1942,0.1648,0.1343,0.1029,0.0704
F5kmRoad,5kmRoad,5,886,0.701,0.7343,0.7658,0.7954,0.8232,0.8493,0.8734,0.8958,0.9164,0.9351,0.952,0.968,0.984,0.996,1,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.999,0.9977,0.9959,0.9935,0.9906,0.9871,0.9831,0.9785,0.9734,0.9678,0.9616,0.9549,0.9476,0.9398,0.9314,0.9225,0.9131,0.9034,0.8937,0.884,0.8743,0.8645,0.8548,0.8451,0.8354,0.8257,0.816,0.8063,0.7966,0.7869,0.7772,0.7674,0.7577,0.748,0.7383,0.7286,0.7189,0.7092,0.6995,0.6898,0.6801,0.6703,0.6606,0.6509,0.6412,0.6315,0.6218,0.612,0.6013,0.5897,0.5772,0.5637,0.5493,0.534,0.5177,0.5004,0.4823,0.4632,0.4431,0.4221,0.4002,0.3773,0.3535,0.3288,0.3031,0.2764,0.2489,0.2204,0.1909
F5km,5km,5,864.68,0.725,0.7579,0.7886,0.8171,0.8434,0.8675,0.8894,0.9091,0.9266,0.9419,0.955,0.967,0.979,0.9893,0.9961,0.9996,1,1,1,1,1,1,1,1,1,0.9997,0.9987,0.9971,0.9948,0.9919,0.9883,0.9841,0.9793,0.9737,0.9676,0.9608,0.9533,0.9452,0.9365,0.9271,0.917,0.9063,0.8953,0.8843,0.8733,0.8623,0.8512,0.8402,0.8292,0.8182,0.8072,0.7961,0.7851,0.7741,0.7631,0.7521,0.741,0.73,0.719,0.708,0.697,0.6859,0.6749,0.6639,0.6529,0.6419,0.6308,0.6198,0.6088,0.5978,0.5868,0.5757,0.5647,0.5537,0.5422,0.5297,0.5161,0.5016,0.4861,0.4696,0.4521,0.4335,0.414,0.3935,0.372,0.3495,0.3259,0.3014,0.2759,0.2494,0.2219,0.1933,0.1638,0.1333,0.1018,0.0692
F6kmRoad,6kmRoad,6,1071,0.693,0.7263,0.7578,0.7874,0.8152,0.8413,0.8654,0.8878,0.9084,0.9271,0.944,0.96,0.976,0.9893,0.9973,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.999,0.9977,0.9958,0.9933,0.9904,0.9868,0.9827,0.9781,0.9728,0.9671,0.9608,0.9539,0.9465,0.9385,0.93,0.9209,0.9112,0.9013,0.8914,0.8815,0.8716,0.8616,0.8517,0.8418,0.8319,0.822,0.8121,0.8021,0.7922,0.7823,0.7724,0.7625,0.7526,0.7426,0.7327,0.7228,0.7129,0.703,0.693,0.6831,0.6732,0.6633,0.6534,0.6435,0.6335,0.6236,0.6137,0.6036,0.5926,0.5807,0.5678,0.554,0.5393,0.5236,0.507,0.4894,0.4709,0.4515,0.4311,0.4098,0.3875,0.3643,0.3402,0.3151,0.2891,0.2621,0.2342,0.2054,0.1756
F6km,6km,6,1051,0.725,0.7579,0.7886,0.8171,0.8434,0.8675,0.8894,0.9091,0.9266,0.9419,0.955,0.967,0.979,0.9893,0.9961,0.9996,1,1,1,1,1,1,1,1,1,0.9997,0.9988,0.9972,0.995,0.9922,0.9888,0.9848,0.9801,0.9749,0.969,0.9624,0.9553,0.9475,0.9391,0.9301,0.9205,0.9103,0.8994,0.8883,0.8771,0.866,0.8548,0.8437,0.8325,0.8214,0.8102,0.7991,0.7879,0.7768,0.7657,0.7545,0.7434,0.7322,0.7211,0.7099,0.6988,0.6876,0.6765,0.6653,0.6542,0.643,0.6319,0.6208,0.6096,0.5985,0.5873,0.5762,0.565,0.5539,0.5426,0.5305,0.5174,0.5033,0.4882,0.472,0.4549,0.4368,0.4177,0.3976,0.3765,0.3543,0.3312,0.3071,0.282,0.2559,0.2288,0.2007,0.1715,0.1414,0.1103,0.0782
F4MileRoad,4MileRoad,6.437376,1152,0.693,0.7263,0.7578,0.7874,0.8152,0.8413,0.8654,0.8878,0.9084,0.9271,0.944,0.96,0.976,0.9893,0.9973,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.999,0.9977,0.9958,0.9933,0.9903,0.9867,0.9826,0.9779,0.9726,0.9668,0.9605,0.9535,0.946,0.938,0.9294,0.9202,0.9105,0.9005,0.8905,0.8805,0.8705,0.8605,0.8505,0.8405,0.8305,0.8205,0.8105,0.8005,0.7905,0.7805,0.7705,0.7605,0.7506,0.7406,0.7306,0.7206,0.7106,0.7006,0.6906,0.6806,0.6706,0.6606,0.6506,0.6406,0.6306,0.6206,0.6106,0.6004,0.5893,0.5772,0.5642,0.5503,0.5354,0.5196,0.5029,0.4852,0.4665,0.447,0.4265,0.405,0.3826,0.3593,0.335,0.3098,0.2837,0.2566,0.2285,0.1996,0.1697
F4Mile,4Mile,6.436,1132,0.725,0.7579,0.7886,0.8171,0.8434,0.8675,0.8894,0.9091,0.9266,0.9419,0.955,0.967,0.979,0.9893,0.9961,0.9996,1,1,1,1,1,1,1,1,1,0.9997,0.9988,0.9972,0.9951,0.9924,0.989,0.985,0.9804,0.9752,0.9694,0.963,0.956,0.9483,0.9401,0.9312,0.9217,0.9117,0.901,0.8898,0.8786,0.8674,0.8562,0.845,0.8338,0.8226,0.8114,0.8002,0.789,0.7778,0.7666,0.7554,0.7443,0.7331,0.7219,0.7107,0.6995,0.6883,0.6771,0.6659,0.6547,0.6435,0.6323,0.6211,0.6099,0.5987,0.5875,0.5763,0.5651,0.5539,0.5427,0.5309,0.518,0.5041,0.4893,0.4734,0.4565,0.4387,0.4198,0.3999,0.3791,0.3572,0.3343,0.3105,0.2856,0.2598,0.2329,0.205,0.1762,0.1463,0.1154,0.0836
F8kmRoad,8kmRoad,8,1442,0.693,0.7263,0.7578,0.7874,0.8152,0.8413,0.8654,0.8878,0.9084,0.9271,0.944,0.96,0.976,0.9893,0.9973,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.999,0.9976,0.9956,0.9931,0.99,0.9864,0.9821,0.9773,0.972,0.966,0.9595,0.9524,0.9447,0.9365,0.9276,0.9183,0.9083,0.8981,0.8878,0.8776,0.8673,0.8571,0.8468,0.8366,0.8263,0.8161,0.8058,0.7956,0.7854,0.7751,0.7649,0.7546,0.7444,0.7341,0.7239,0.7136,0.7034,0.6931,0.6829,0.6727,0.6624,0.6522,0.6419,0.6317,0.6214,0.6112,0.6009,0.5904,0.5788,0.5664,0.553,0.5387,0.5234,0.5072,0.4901,0.472,0.453,0.433,0.4121,0.3903,0.3675,0.3438,0.3191,0.2935,0.2669,0.2395,0.211,0.1817,0.1514
F8km,8km,8,1425,0.725,0.7579,0.7886,0.8171,0.8434,0.8675,0.8894,0.9091,0.9266,0.9419,0.955,0.967,0.979,0.9893,0.9961,0.9996,1,1,1,1,1,1,1,1,1,0.9997,0.9988,0.9974,0.9953,0.9927,0.9895,0.9857,0.9813,0.9764,0.9708,0.9647,0.958,0.9507,0.9428,0.9343,0.9253,0.9157,0.9055,0.8947,0.8834,0.872,0.8607,0.8493,0.838,0.8266,0.8153,0.804,0.7926,0.7813,0.7699,0.7586,0.7472,0.7359,0.7245,0.7132,0.7019,0.6905,0.6792,0.6678,0.6565,0.6451,0.6338,0.6224,0.6111,0.5997,0.5884,0.5771,0.5657,0.5544,0.543,0.5315,0.519,0.5055,0.491,0.4755,0.459,0.4416,0.4231,0.4036,0.3831,0.3616,0.3391,0.3157,0.2912,0.2657,0.2392,0.2117,0.1832,0.1537,0.1233,0.0918
F5MileRoad,5MileRoad,8.04672,1452,0.693,0.7263,0.7578,0.7874,0.8152,0.8413,0.8654,0.8878,0.9084,0.9271,0.944,0.96,0.976,0.9893,0.9973,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.999,0.9976,0.9956,0.9931,0.99,0.9864,0.9821,0.9773,0.9719,0.966,0.9594,0.9523,0.9447,0.9364,0.9276,0.9182,0.9082,0.898,0.8877,0.8775,0.8672,0.857,0.8467,0.8365,0.8262,0.816,0.8057,0.7955,0.7852,0.775,0.7647,0.7545,0.7442,0.734,0.7237,0.7134,0.7032,0.6929,0.6827,0.6724,0.6622,0.6519,0.6417,0.6314,0.6212,0.6109,0.6007,0.5901,0.5786,0.5661,0.5527,0.5384,0.5231,0.5069,0.4897,0.4716,0.4526,0.4326,0.4117,0.3899,0.3671,0.3433,0.3187,0.293,0.2665,0.239,0.2106,0.1812,0.1509
F5Mile,5Mile,8.045,1435,0.725,0.7579,0.7886,0.8171,0.8434,0.8675,0.8894,0.9091,0.9266,0.9419,0.955,0.967,0.979,0.9893,0.9961,0.9996,1,1,1,1,1,1,1,1,1,0.9997,0.9988,0.9974,0.9953,0.9927,0.9895,0.9857,0.9813,0.9764,0.9709,0.9647,0.958,0.9507,0.9429,0.9344,0.9254,0.9158,0.9056,0.8948,0.8835,0.8722,0.8608,0.8495,0.8381,0.8268,0.8154,0.8041,0.7927,0.7814,0.77,0.7587,0.7473,0.736,0.7246,0.7133,0.7019,0.6906,0.6792,0.6679,0.6565,0.6452,0.6338,0.6225,0.6111,0.5998,0.5884,0.5771,0.5657,0.5544,0.543,0.5315,0.519,0.5055,0.491,0.4756,0.4591,0.4416,0.4231,0.4037,0.3832,0.3617,0.3392,0.3157,0.2913,0.2658,0.2393,0.2118,0.1833,0.1539,0.1234,0.0919
F10kmRoad,10kmRoad,10,1820,0.693,0.7263,0.7578,0.7874,0.8152,0.8413,0.8654,0.8878,0.9084,0.9271,0.944,0.96,0.976,0.9893,0.9973,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.9989,0.9975,0.9955,0.993,0.9898,0.986,0.9817,0.9768,0.9713,0.9652,0.9585,0.9512,0.9433,0.9349,0.9259,0.9162,0.906,0.8955,0.885,0.8745,0.864,0.8535,0.843,0.8325,0.822,0.8115,0.801,0.7905,0.78,0.7695,0.759,0.7485,0.738,0.7275,0.717,0.7065,0.696,0.6855,0.675,0.6645,0.654,0.6435,0.633,0.6225,0.612,0.6015,0.591,0.5801,0.5681,0.5553,0.5415,0.5268,0.5111,0.4945,0.4769,0.4585,0.439,0.4187,0.3973,0.3751,0.3519,0.3278,0.3027,0.2767,0.2497,0.2219,0.193,0.1633,0.1325
F10km,10km,10,1801.09,0.725,0.7579,0.7886,0.8171,0.8434,0.8675,0.8894,0.9091,0.9266,0.9419,0.955,0.967,0.979,0.9893,0.9961,0.9996,1,1,1,1,1,1,1,1,1,0.9997,0.9989,0.9975,0.9955,0.993,0.99,0.9863,0.9821,0.9774,0.9721,0.9662,0.9598,0.9528,0.9453,0.9372,0.9285,0.9193,0.9096,0.8992,0.8883,0.877,0.8655,0.854,0.8425,0.831,0.8195,0.808,0.7965,0.785,0.7735,0.762,0.7505,0.739,0.7275,0.716,0.7045,0.693,0.6815,0.67,0.6585,0.647,0.6355,0.624,0.6125,0.601,0.5895,0.578,0.5665,0.555,0.5435,0.532,0.52,0.507,0.493,0.478,0.462,0.445,0.427,0.408,0.388,0.367,0.345,0.322,0.298,0.273,0.247,0.22,0.192,0.163,0.133,0.102
F12km,12km,12,2194,0.693,0.7263,0.7578,0.7874,0.8152,0.8413,0.8654,0.8878,0.9084,0.9271,0.944,0.96,0.976,0.9893,0.9973,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.9989,0.9975,0.9955,0.993,0.9898,0.986,0.9817,0.9768,0.9713,0.9652,0.9585,0.9512,0.9433,0.9349,0.9259,0.9162,0.906,0.8955,0.885,0.8745,0.864,0.8535,0.843,0.8325,0.822,0.8115,0.801,0.7905,0.78,0.7695,0.759,0.7485,0.738,0.7275,0.717,0.7065,0.696,0.6855,0.675,0.6645,0.654,0.6435,0.633,0.6225,0.612,0.6015,0.5908,0.5792,0.5667,0.5533,0.539,0.5238,0.5077,0.4907,0.4729,0.4541,0.4344,0.4139,0.3924,0.37,0.3468,0.3226,0.2976,0.2716,0.2448,0.2171,0.1884,0.1589,0.1285
F15km,15km,15,2755,0.5945,0.6382,0.6793,0.7178,0.7537,0.787,0.8177,0.8458,0.8713,0.8942,0.9145,0.9335,0.9525,0.9696,0.9829,0.9924,0.9981,1,1,1,1,1,1,1,1,0.9997,0.9989,0.9975,0.9956,0.9931,0.9901,0.9865,0.9823,0.9776,0.9724,0.9666,0.9602,0.9533,0.9458,0.9378,0.9293,0.9201,0.9105,0.9003,0.8898,0.8793,0.8688,0.8583,0.8478,0.8373,0.8268,0.8163,0.8058,0.7953,0.7848,0.7743,0.7638,0.7533,0.7428,0.7323,0.7218,0.7113,0.7008,0.6903,0.6798,0.6693,0.6588,0.6483,0.6378,0.6273,0.6168,0.6063,0.5956,0.5841,0.5718,0.5587,0.5447,0.5299,0.5142,0.4977,0.4804,0.4622,0.4432,0.4233,0.4026,0.381,0.3586,0.3354,0.3113,0.2864,0.2606,0.234,0.2065,0.1782,0.1491,0.1191
F10Mile,10Mile,16.09344,2961,0.6525,0.6924,0.7301,0.7656,0.7989,0.83,0.8589,0.8856,0.9101,0.9324,0.9525,0.9715,0.9905,1,1,1,1,1,1,1,1,1,1,1,1,0.9997,0.9989,0.9975,0.9956,0.9931,0.9901,0.9865,0.9823,0.9776,0.9724,0.9666,0.9602,0.9533,0.9458,0.9378,0.9293,0.9201,0.9105,0.9003,0.8898,0.8793,0.8688,0.8583,0.8478,0.8373,0.8268,0.8163,0.8058,0.7953,0.7848,0.7743,0.7638,0.7533,0.7428,0.7323,0.7218,0.7113,0.7008,0.6903,0.6798,0.6693,0.6588,0.6483,0.6378,0.6273,0.6168,0.6063,0.5954,0.5837,0.5713,0.5579,0.5438,0.5288,0.513,0.4964,0.479,0.4607,0.4416,0.4217,0.401,0.3794,0.357,0.3338,0.3097,0.2849,0.2592,0.2326,0.2053,0.1771,0.1481,0.1183
F20km,20km,20,3700,0.6525,0.6924,0.7301,0.7656,0.7989,0.83,0.8589,0.8856,0.9101,0.9324,0.9525,0.9715,0.9905,1,1,1,1,1,1,1,1,1,1,1,1,0.9997,0.9989,0.9975,0.9956,0.9931,0.9901,0.9865,0.9823,0.9776,0.9724,0.9666,0.9602,0.9533,0.9458,0.9378,0.9293,0.9201,0.9105,0.9003,0.8898,0.8793,0.8688,0.8583,0.8478,0.8373,0.8268,0.8163,0.8058,0.7953,0.7848,0.7743,0.7638,0.7533,0.7428,0.7323,0.7218,0.7113,0.7008,0.6903,0.6798,0.6693,0.6588,0.6483,0.6378,0.6273,0.6168,0.606,0.5945,0.5823,0.5692,0.5554,0.5408,0.5255,0.5093,0.4924,0.4747,0.4563,0.4371,0.4171,0.3963,0.3748,0.3525,0.3294,0.3055,0.2809,0.2555,0.2293,0.2023,0.1746,0.1461,0.1169
FHalf.Mar,Half.Mar,21.0975,3912,0.5945,0.6382,0.6793,0.7178,0.7537,0.787,0.8177,0.8458,0.8713,0.8942,0.9145,0.9335,0.9525,0.9696,0.9829,0.9924,0.9981,1,1,1,1,1,1,1,1,0.9997,0.9989,0.9975,0.9956,0.9931,0.9901,0.9865,0.9823,0.9776,0.9724,0.9666,0.9602,0.9533,0.9458,0.9378,0.9293,0.9201,0.9105,0.9003,0.8898,0.8793,0.8688,0.8583,0.8478,0.8373,0.8268,0.8163,0.8058,0.7953,0.7848,0.7743,0.7638,0.7533,0.7428,0.7323,0.7218,0.7113,0.7008,0.6903,0.6798,0.6693,0.6588,0.6483,0.6378,0.6273,0.6168,0.6059,0.5942,0.5818,0.5687,0.5548,0.5401,0.5246,0.5084,0.4915,0.4738,0.4553,0.436,0.416,0.3953,0.3738,0.3515,0.3284,0.3046,0.2801,0.2548,0.2287,0.2018,0.1742,0.1459,0.1168
F25km,25km,25,4665,0.6525,0.6924,0.7301,0.7656,0.7989,0.83,0.8589,0.8856,0.9101,0.9324,0.9525,0.9715,0.9905,1,1,1,1,1,1,1,1,1,1,1,1,0.9997,0.9989,0.9975,0.9955,0.993,0.9899,0.9863,0.9821,0.9774,0.972,0.9662,0.9597,0.9528,0.9452,0.9371,0.9284,0.9192,0.9094,0.8991,0.8885,0.8778,0.8672,0.8566,0.846,0.8354,0.8247,0.8141,0.8035,0.7929,0.7822,0.7716,0.761,0.7504,0.7398,0.7291,0.7185,0.7079,0.6973,0.6866,0.676,0.6654,0.6548,0.6441,0.6335,0.6229,0.6123,0.6011,0.5891,0.5764,0.5629,0.5486,0.5335,0.5177,0.5011,0.4838,0.4657,0.4468,0.4271,0.4067,0.3855,0.3635,0.3407,0.3172,0.293,0.2679,0.2421,0.2155,0.1881,0.16,0.1311,0.1014
F30km,30km,30,5660,0.6525,0.6924,0.7301,0.7656,0.7989,0.83,0.8589,0.8856,0.9101,0.9324,0.9525,0.9715,0.9905,1,1,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.9989,0.9975,0.9954,0.9928,0.9895,0.9857,0.9813,0.9762,0.9706,0.9643,0.9575,0.95,0.942,0.9333,0.9241,0.9142,0.9038,0.893,0.8822,0.8715,0.8607,0.85,0.8392,0.8285,0.8177,0.807,0.7962,0.7855,0.7747,0.764,0.7532,0.7424,0.7317,0.7209,0.7102,0.6994,0.6887,0.6779,0.6672,0.6564,0.6457,0.6349,0.6241,0.6133,0.6018,0.5894,0.5763,0.5625,0.5478,0.5323,0.5161,0.4991,0.4813,0.4628,0.4434,0.4233,0.4024,0.3807,0.3583,0.335,0.311,0.2862,0.2606,0.2342,0.2071,0.1792,0.1504,0.121,0.0907
FMarathon,Marathon,42.195,8125,0.693,0.7263,0.7578,0.7874,0.8152,0.8413,0.8654,0.8878,0.9084,0.9271,0.944,0.96,0.976,0.9893,0.9973,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.9989,0.9974,0.9953,0.9926,0.9893,0.9854,0.9808,0.9757,0.9699,0.9635,0.9565,0.9489,0.9406,0.9318,0.9223,0.9122,0.9016,0.8906,0.8796,0.8686,0.8576,0.8466,0.8356,0.8246,0.8136,0.8026,0.7916,0.7806,0.7696,0.7586,0.7476,0.7366,0.7256,0.7146,0.7036,0.6926,0.6816,0.6706,0.6596,0.6486,0.6376,0.6266,0.6156,0.6042,0.592,0.579,0.5652,0.5506,0.5352,0.519,0.502,0.4842,0.4656,0.4462,0.426,0.405,0.3832,0.3606,0.3372,0.313,0.288,0.2622,0.2356,0.2082,0.18,0.151,0.1212,0.0906,0.0592
F50km,50km,50,9820,0.693,0.7263,0.7578,0.7874,0.8152,0.8413,0.8654,0.8878,0.9084,0.9271,0.944,0.96,0.976,0.9893,0.9973,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.9989,0.9974,0.9953,0.9926,0.9893,0.9854,0.9808,0.9757,0.9699,0.9635,0.9565,0.9489,0.9406,0.9318,0.9223,0.9122,0.9016,0.8906,0.8796,0.8686,0.8576,0.8466,0.8356,0.8246,0.8136,0.8026,0.7916,0.7806,0.7696,0.7586,0.7476,0.7366,0.7256,0.7146,0.7036,0.6926,0.6816,0.6706,0.6596,0.6486,0.6376,0.6266,0.6156,0.6042,0.592,0.579,0.5652,0.5506,0.5352,0.519,0.502,0.4842,0.4656,0.4462,0.426,0.405,0.3832,0.3606,0.3372,0.313,0.288,0.2622,0.2356,0.2082,0.18,0.151,0.1212,0.0906,0.0592
F50Mile,50Mile,80.4672,17760,0.693,0.7263,0.7578,0.7874,0.8152,0.8413,0.8654,0.8878,0.9084,0.9271,0.944,0.96,0.976,0.9893,0.9973,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.9989,0.9974,0.9953,0.9926,0.9893,0.9854,0.9808,0.9757,0.9699,0.9635,0.9565,0.9489,0.9406,0.9318,0.9223,0.9122,0.9016,0.8906,0.8796,0.8686,0.8576,0.8466,0.8356,0.8246,0.8136,0.8026,0.7916,0.7806,0.7696,0.7586,0.7476,0.7366,0.7256,0.7146,0.7036,0.6926,0.6816,0.6706,0.6596,0.6486,0.6376,0.6266,0.6156,0.6042,0.592,0.579,0.5652,0.5506,0.5352,0.519,0.502,0.4842,0.4656,0.4462,0.426,0.405,0.3832,0.3606,0.3372,0.313,0.288,0.2622,0.2356,0.2082,0.18,0.151,0.1212,0.0906,0.0592
F100km,100km,100,23591,0.693,0.7263,0.7578,0.7874,0.8152,0.8413,0.8654,0.8878,0.9084,0.9271,0.944,0.96,0.976,0.9893,0.9973,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.9989,0.9974,0.9953,0.9926,0.9893,0.9854,0.9808,0.9757,0.9699,0.9635,0.9565,0.9489,0.9406,0.9318,0.9223,0.9122,0.9016,0.8906,0.8796,0.8686,0.8576,0.8466,0.8356,0.8246,0.8136,0.8026,0.7916,0.7806,0.7696,0.7586,0.7476,0.7366,0.7256,0.7146,0.7036,0.6926,0.6816,0.6706,0.6596,0.6486,0.6376,0.6266,0.6156,0.6042,0.592,0.579,0.5652,0.5506,0.5352,0.519,0.502,0.4842,0.4656,0.4462,0.426,0.405,0.3832,0.3606,0.3372,0.313,0.288,0.2622,0.2356,0.2082,0.18,0.151,0.1212,0.0906,0.0592
F150km,150km,150,39700,0.693,0.7263,0.7578,0.7874,0.8152,0.8413,0.8654,0.8878,0.9084,0.9271,0.944,0.96,0.976,0.9893,0.9973,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.9989,0.9974,0.9953,0.9926,0.9893,0.9854,0.9808,0.9757,0.9699,0.9635,0.9565,0.9489,0.9406,0.9318,0.9223,0.9122,0.9016,0.8906,0.8796,0.8686,0.8576,0.8466,0.8356,0.8246,0.8136,0.8026,0.7916,0.7806,0.7696,0.7586,0.7476,0.7366,0.7256,0.7146,0.7036,0.6926,0.6816,0.6706,0.6596,0.6486,0.6376,0.6266,0.6156,0.6042,0.592,0.579,0.5652,0.5506,0.5352,0.519,0.502,0.4842,0.4656,0.4462,0.426,0.405,0.3832,0.3606,0.3372,0.313,0.288,0.2622,0.2356,0.2082,0.18,0.151,0.1212,0.0906,0.0592
F100Mile,100Mile,160.9344,43500,0.693,0.7263,0.7578,0.7874,0.8152,0.8413,0.8654,0.8878,0.9084,0.9271,0.944,0.96,0.976,0.9893,0.9973,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.9989,0.9974,0.9953,0.9926,0.9893,0.9854,0.9808,0.9757,0.9699,0.9635,0.9565,0.9489,0.9406,0.9318,0.9223,0.9122,0.9016,0.8906,0.8796,0.8686,0.8576,0.8466,0.8356,0.8246,0.8136,0.8026,0.7916,0.7806,0.7696,0.7586,0.7476,0.7366,0.7256,0.7146,0.7036,0.6926,0.6816,0.6706,0.6596,0.6486,0.6376,0.6266,0.6156,0.6042,0.592,0.579,0.5652,0.5506,0.5352,0.519,0.502,0.4842,0.4656,0.4462,0.426,0.405,0.3832,0.3606,0.3372,0.313,0.288,0.2622,0.2356,0.2082,0.18,0.151,0.1212,0.0906,0.0592
F200km,200km,200,57600,0.693,0.7263,0.7578,0.7874,0.8152,0.8413,0.8654,0.8878,0.9084,0.9271,0.944,0.96,0.976,0.9893,0.9973,1,1,1,1,1,1,1,1,1,1,1,0.9998,0.9989,0.9974,0.9953,0.9926,0.9893,0.9854,0.9808,0.9757,0.9699,0.9635,0.9565,0.9489,0.9406,0.9318,0.9223,0.9122,0.9016,0.8906,0.8796,0.8686,0.8576,0.8466,0.8356,0.8246,0.8136,0.8026,0.7916,0.7806,0.7696,0.7586,0.7476,0.7366,0.7256,0.7146,0.7036,0.6926,0.6816,0.6706,0.6596,0.6486,0.6376,0.6266,0.6156,0.6042,0.592,0.579,0.5652,0.5506,0.5352,0.519,0.502,0.4842,0.4656,0.4462,0.426,0.405,0.3832,0.3606,0.3372,0.313,0.288,0.2622,0.2356,0.2082,0.18,0.151,0.1212,0.0906,0.0592
</textarea>
</form>
<script type="text/javascript">
var CommonDistances=true, GradeTable, AgeGrade, grading=[], TandaRaceTime, TandaAgeGrade, PreviousDistanceUnit="", CurrentDistanceUnit;
var DistancesToShow=["1500m", "5kmRoad", "10kmRoad", "Half.Mar","Marathon"];
var TandaPace, TandaDistance, Age, GradeTableLine;
var title="<h1>Race predictor: age, training & physiology</h1>";
var OpeningText="<p>There are three separate ways of predicting racing performance at a distance which you have not recently raced. The most common method is to extrapolate the same 'age-graded' performance from a recent race of different distance. The second technique is to estimate the fitness that your training may have produced. The third is to extrapolate aerobic fitness from your heart rate (either resting, or at a given pace).</p>"
+"<p>The 'reliability' of these techniques will depend upon the nature of the race (weather, terrain, elevation), your training (have you trained appropriately for the event), your pacing strategy (conservative or optimistic) and the actual limit you hit during the race (are you aerobically limited, or does pain prevent you from running at your aerobic maximum).</p>"
+"<p>Using all three calculators can help you to select an optimal pacing strategy to maximize your performance.";
HideOpeningText();
document.getElementById("TimeAchieved").innerHTML=InsertTimeAchieved();
SetTandaSliders();
grading=ImportGradingData();
for (i=0; i<grading.length;i++)
{
addItem('PerformedDistance', grading[i][1]);
}
var Minutes = document.getElementById("Minutes");
var Seconds = document.getElementById("Seconds");
for(var i = 0; i < 60; i++)
{
var MinItem = document.createElement("option");
var SecItem = document.createElement("option");
MinItem.textContent = i;
MinItem.value = i;
SecItem.textContent = i;
SecItem.value = i;
Seconds.appendChild(SecItem);
Minutes.appendChild(MinItem);
}
Age=getCookie("Age"); Sex=getCookie("Sex"); Units=getCookie("Units");
Hours=getCookie("Hours"); Minutes=getCookie("Minutes"); Seconds=getCookie("Seconds");
ListLength=getCookie("ListLength");
document.getElementById("imperial").checked=true;
document.getElementById("StandardDistances").checked=true;
PerformedDistance=getCookie("PerformedDistance");
//alert(getCookie("Minutes"));
//if(getCookie("Hours")!=="")
//{
echo (PerformedDistance);
if(PerformedDistance=""){PerformedDistance=0;}
if(Hours==""){Hours=0;}
if(Minutes==""){Minutes=0;}
if(Seconds==""){Seconds=0;}
document.getElementById("Hours").value=Hours;
document.getElementById("Minutes").value=Minutes;
document.getElementById("Seconds").value=Seconds;
//}
//else
//{
// document.getElementById("Hours").selectedIndex=0;
// document.getElementById("Minutes").selectedIndex=0;
// document.getElementById("Seconds").selectedIndex=0;
//}
if(Age>0){document.getElementById("Age").value=Age;}
if(Sex!==""){document.getElementById(Sex).checked=true;}
if(PerformedDistance>0)
{
document.getElementById("PerformedDistance").selectedIndex=PerformedDistance;
changeFunc();
}
document.getElementById("Distances").innerHTML=DistanceTable(Sex);
changeFunc();
function ImportGradingData()
{
var i=0;
GradingData=document.getElementById("GradingData").value
g=CSVToArray(GradingData, "\r\n");
for(i=0; i<g.length; i++)
{
var z=g[i][0];
var b=z.split(',');
grading[i]=b;
}
return(grading);
}
function getTime()
{
var hours, minutes, seconds;
Hours=document.getElementById("Hours").value;
Minutes=document.getElementById("Minutes").value;
Seconds=document.getElementById("Seconds").value;
setCookie("Hours", Hours, 1);
setCookie("Minutes", Minutes,1);
setCookie("Seconds", Seconds,1);
return(Hours*60*60 + Minutes*60 + Seconds*1);
}
function changeFunc()
{
var Time;
//alert("changeFunc started");
Age=document.getElementById("Age").value;
Sex=document.querySelector('input[name = "Sex"]:checked').value;
Units=document.querySelector('input[name = "Units"]:checked').value;
ListLength=document.querySelector('input[name = "ListLength"]:checked').value;
PD=document.getElementById("PerformedDistance");
PerformedDistance=PD.options[PD.selectedIndex].text;
Time=getTime();
if(ListLength=="StandardDistances")
{document.getElementById("RemovedDistanceTable").style.display="none";}
else
{document.getElementById("RemovedDistanceTable").style.display="";}
setCookie("Age", Age, 1); setCookie("Sex", Sex, 1);
setCookie("PerformedDistance",PD.selectedIndex,1);
setCookie("Units", Units, 1); setCookie("ListLength", ListLength,1);
if(Time!==0)
{
AgeGrade=AgeGrading(Age, Sex, PerformedDistance, Time);
//alert(PerformedDistance);
if(Units=="metric")
{
PerformedPace=secondsToHms(Time/grading[GradeTable][2])+" per km";
}
else
{
PerformedPace=secondsToHms(1.61*Time/grading[GradeTable][2])+" per mile";
//alert (grading[GradeTableLine]);
}
document.getElementById("Pace").innerHTML=PerformedPace;
if(Age!=="")
{
//alert("Going to get AgeGrade from changeFunc");
document.getElementById("AgeGrade").innerHTML=AgeGrade.toPrecision(4)+"%";
myTable=AgeGradePredictions(Age, Sex, PerformedDistance, Time);
document.getElementById('tablePrint').innerHTML = myTable;
document.getElementById("Distances").innerHTML=DistanceTable(Sex);
}
}
SetTandaSliders();
}
//populate Tanda Sliders
function SetTandaSliders()
{
//var person = {firstName:"John", lastName:"Doe", age:46};
var kmslider = {distancemin:25, distancemax:200, pacemin:3, pacemax:8};
var mileslider = {distancemin:15, distancemax:125, pacemin:5, pacemax:13};
var currentslider;
if(document.getElementById("metric").checked){CurrentDistanceUnit="metric";}else{CurrentDistanceUnit="imperial";}
if(CurrentDistanceUnit!==PreviousDistanceUnit)
{
if(PreviousDistanceUnit=="")
{TandaDistance='62'; TandaPace='8';}
else
{
TandaDistance=document.getElementById("distanceslide").value;
TandaPace=document.getElementById("paceslide").value;
}
if(CurrentDistanceUnit=='metric'){currentslider=kmslider;scaler=1.61;}else{currentslider=mileslider;scaler=1/1.61;}
document.getElementById("DistanceSliderText").innerHTML='<input id="distanceslide" type="range" min='+currentslider.distancemin+' max='+currentslider.distancemax+' step="1" style="width: 100%;" value="' + TandaDistance*scaler + '" oninput="updateSlider(this.value)" />';
document.getElementById("PaceSliderText").innerHTML='<input id="paceslide" type="range" min='+currentslider.pacemin+' max='+currentslider.pacemax+' step="0.0167" style="width: 100%;" value="' + TandaPace/scaler +'" oninput="updateSlider(this.value)" />';
}
PreviousDistanceUnit=CurrentDistanceUnit;
//alert("Update Slider from SetTandaSliders");
updateSlider();
}
function InsertTimeAchieved()
{
var TimeAchievedText='', a;
TimeAchievedText='<select title="Hours" id="Hours" onchange="changeFunc();">';
for(a=0;a<7;a++){TimeAchievedText+='<option value="'+a+'">'+a+'</option>';}
TimeAchievedText+='</select>:<select title="Minutes" id="Minutes" onchange="changeFunc();"></select>:';
TimeAchievedText+='<select title="Seconds" id="Seconds" onchange="changeFunc();"></select>';
//alert (TimeAchievedText);
return (TimeAchievedText);
}
//calculates and returns the age grading from the provided data.
function AgeGrading(Age, Sex, PerformedDistance, Time)
{
var AgeGrade;
PerformedEvent=Sex+PerformedDistance;
for (i=0; i<grading.length;i++)
{
if(grading[i][0]==PerformedEvent)
{
GradeTable=i;
OC=grading[i][3];
fraction=grading[i][Age-1];
AgeGrade=OC/(Time*fraction)*100;
break;
}
}
return (AgeGrade);
}
//calculates and returns the race predictions from the provided data
function AgeGradePredictions(Age, Sex, PerformedDistance, Time)
{
var i=0;
var pacetable="";
var TandaPredictedTime;
for (i = 0; i < grading.length; i++)
{
if(grading[i][0].substring(0,1)==Sex)
{
PredictedTime=grading[i][3]/(AgeGrade/100*grading[i][Age-1]);
if(TandaAgeGrade!==""){TandaPredictedTime=grading[i][3]/(TandaAgeGrade/100*grading[i][Age-1]);}
if(ListLength=="CustomDistances"){state=getCookie("Hide"+grading[i][1]);}else{state=isStantardDistance(grading[i][1]);}
RacePace=PredictedTime/grading[i][2];
if(Units=="metric"){RacePace=" ("+secondsToHms(RacePace)+ " per km)";}else{RacePace=" ("+secondsToHms(RacePace*1.61)+ " per mile)";}
pacetable+="<tr style='display: "+state+";' id='Hide"+grading[i][1]+"'>";
var extratext=" colspan=2";
if(ListLength=="CustomDistances")
{
pacetable+="<td align='center' title='Click to remove distance'><input id='Distance' type='button' value='Hide' onclick='HideDistance(\"Hide"+grading[i][1]+"\");'/></td>";
extratext="";
}
pacetable+="<td style='text-align:center' "+extratext+">" + grading[i][1] + "</td>";
pacetable+="<td style='text-align:center'>"+secondsToHms(grading[i][3])+"</td>";
pacetable+="<td style='text-align:center'>"+secondsToHms(PredictedTime*AgeGrade/100)+"</td>";
pacetable+="<td style='text-align:center; width:160px;'>" +secondsToHms(PredictedTime) + RacePace +"</td>";
pacetable+="<td style='text-align:center; width:160px;'>" +secondsToHms(TandaPredictedTime)+"</td></tr>";
}
}
pacetable+="</table>";
TandaHeading="Prediction based on ";
if(CurrentDistanceUnit=="metric")
{TandaHeading+=TandaDistance+" km at "+secondsToHms(TandaPace);}
else
{TandaHeading+=TandaDistance+" miles at "+ secondsToHms(TandaPace);}
paceTableHeader="<H3>Predictions assuming equal age-grading across all distances</H3><table border=1><tr><th colspan=2>Event</th><th style='width:80px'>Grade table World Record</th><th style='width:80px'>Record for aged "+Age+"</th><th style='width:80px'>"+AgeGrade.toPrecision(4)+"% age-graded prediction</th><th>"+TandaHeading+"</th></tr>";
pacetable=paceTableHeader+pacetable;
return (pacetable);
}
function DistanceTable(Sex)
{
var i=0, NumberInTable=0; var count=0;
var distanceTable=""; var addStyle="";
for(i=0; i<grading.length;i++)
{
if(count==10){count=0;distanceTable+="</tr><tr>";}
if(grading[i][0].substring(0,1)==Sex)
{
state=getCookie(grading[i][1]);
//alert(state);
if(grading[i][1]=="Marathon"){addStyle=" color:red; "; }else{addStyle="";}
if(state!=="none"){state="none";} else {state="";}
distanceTable+="<td align='center'><input id='ShowDistance:"+grading[i][1]+"' style=' display: "+state+";"+addStyle+" width:80px;' type='button' value='"+grading[i][1]+"' onclick='ShowDistance(\""+grading[i][1]+"\");'/></td>";
count++;
}
}
distanceTable="<table border=0><tr><th colspan=10>Click to select these additional distances</th></tr><tr>"+distanceTable+"</tr></table>";
if(NumberInTable==0){distanceTable="";}
return(distanceTable);
}
//function to add an item to an HTML dropdown box - it checks to see if the name already exists in the list.
function addItem(ItemID, value)
{
var i=0;
var x = document.getElementById(ItemID);
var option = document.createElement("option");
//check if the value already exists
found=false;
for (i = 0; i < document.getElementById(ItemID).length; i++)
{
if (document.getElementById(ItemID).options[i].value == value)
{
found=true;
}
}
if(found==false)
{
option.text = value;
option.value=value;
x.add(option);
}
}
function JunkPace(Distance, Pace)
{
if(CurrentDistanceUnit=="imperial"){Distance=Distance*1.6; Pace=Pace/1.6;}
// =((1+Distance)/(1390/(98.5 *(EXP(-Distance*7/189) -EXP(-(Distance+1)*7/189))+1390/Speed))-Distance/Speed)/24
Speed=3600/Pace;
Distance=Distance/7;
JunkPaces=((1+Distance)/(1390/(98.5 *(Math.exp(-Distance*7/189)-Math.exp(-(Distance+1)*7/189))+1390/Speed))-Distance/Speed)*60*60;
if(CurrentDistanceUnit=="imperial"){JunkPaces=JunkPaces*1.6;}
JunkPaces="Junk pace is slower than: " + secondsToHms(JunkPaces);
return(JunkPaces);
}
function updateSlider(amount)
{
var TandaRaceTime, Time, Today, NowTime, DistanceUnit;
if(CurrentDistanceUnit=="imperial"){DistanceUnit="mile";}else{DistanceUnit="km";}
Today=new Date();
NowTime=Today.getTime();
console.log("update slider"+NowTime);
Time=getTime();
TandaDistance=document.getElementById("distanceslide").value
TandaPace=document.getElementById("paceslide").value*60
document.getElementById("WeeklyDistance").innerHTML=TandaDistance+" "+DistanceUnit;
document.getElementById("WeeklyPace").innerHTML=secondsToHms(TandaPace)+" per "+DistanceUnit;
//document.getElementById("WeeklyTime").innerHTML=secondsToHms(TandaDistance*TandaPace);
TandaRaceTime=TandaPrediction(TandaDistance, TandaPace);
TandaPredictionText= JunkPace(TandaDistance, TandaPace) + " per " + DistanceUnit + "<br />";
TandaPredictionText=TandaPredictionText+"Weekly training time: " + secondsToHms(TandaDistance*TandaPace) + "<br />";
TandaPredictionText=TandaPredictionText + "Predicted marathon time: " + secondsToHms(TandaRaceTime)
if(Age!=="" && typeof Sex !== 'undefined')
{
TandaAgeGrade=AgeGrading(Age, Sex, "Marathon", TandaRaceTime);
TandaPredictionText=TandaPredictionText + " ("+TandaAgeGrade.toPrecision(4)+"%)";
if(Time!==0)
{
//alert("Going to get AgeGrade from updateSlider "+Time);
myTable=AgeGradePredictions(Age, Sex, PerformedDistance, Time);
document.getElementById('tablePrint').innerHTML = myTable;
}
}
document.getElementById("TandaPrediction").innerHTML=TandaPredictionText;
}
function TandaPrediction(Distance, Pace)
{
var RacePace;
if(CurrentDistanceUnit=="imperial"){Distance=Distance*1.61; Pace=Pace/1.61;}
RacePace=17.1+140.0*Math.exp(-0.0053*Distance)+0.55*Pace;
return(42.2*RacePace);
}
function HideDistance(Event)
{
document.getElementById(Event).style.display='none';
cookietext=Event+"=none";
setCookie(Event, "none",1);
//document.cookie=cookietext;
document.getElementById("Distances").innerHTML=DistanceTable(Sex);
//changeFunc();
//alert(DistanceTable(Sex));
}
function ShowDistance(Event)
{
document.getElementById("Hide"+Event).style.display='';
//cookietext="Hide"+Event+"=";
setCookie(Event, "",1);
document.cookie=cookietext;
document.getElementById("Distances").innerHTML=DistanceTable(Sex);
}
function HideOpeningText()
{
var text;
text=title+"<p>"+OpeningText.substring(0,40)+"...<a onclick='InsertOpeningText()' href='javascript:void(0);'>[more]</a></p>";
document.getElementById("OpeningText").innerHTML=text;
}
function InsertOpeningText()
{
var text;
text=title+OpeningText+"<a onclick='HideOpeningText()' href='javascript:void(0);'>[Less]</a>";
document.getElementById("OpeningText").innerHTML=text;
}
function isStantardDistance(EventName)
{
var i, state="none";
for(i=0; i<DistancesToShow.length;i++)
{
if(DistancesToShow[i]==EventName){state="";}
}
return(state);
}
function secondsToHms(d)
{
d = Number(d);
var h = Math.floor(d / 3600);
var m = Math.floor(d % 3600 / 60);
var s = Math.floor(d % 3600 % 60);
return ((h > 0 ? h + ":" + (m < 10 ? "0" : "") : "") + m + ":" + (s < 10 ? "0" : "") + s);
}
function setCookie(name,value,days)
{
var cookieCode="";
if (days)
{
var date = new Date();
date.setTime(date.getTime()+(days*24*60*60*1000));
var expires = "; expires="+date.toGMTString();
}
else var expires = "";
cookieCode = name+"="+value+expires+";";
document.cookie = name+"="+value+expires+";";
}
function getCookie(cname)
{
var name = cname + "=";
var ca = document.cookie.split(';');
for(var i=0; i<ca.length; i++)
{
var c = ca[i];
while (c.charAt(0)==' ') c = c.substring(1);
if (c.indexOf(name) == 0) return c.substring(name.length,c.length);
}
return "";
}
function CSVToArray( strData, strDelimiter ){
// Check to see if the delimiter is defined. If not,
// then default to comma.
strDelimiter = (strDelimiter || ",");
// Create a regular expression to parse the CSV values.
var objPattern = new RegExp(
(
// Delimiters.
"(\\" + strDelimiter + "|\\r?\\n|\\r|^)" +
// Quoted fields.
"(?:\"([^\"]*(?:\"\"[^\"]*)*)\"|" +
// Standard fields.
"([^\"\\" + strDelimiter + "\\r\\n]*))"
),
"gi"
);
// Create an array to hold our data. Give the array
// a default empty first row.
var arrData = [[]];
// Create an array to hold our individual pattern
// matching groups.
var arrMatches = null;
// Keep looping over the regular expression matches
// until we can no longer find a match.
while (arrMatches = objPattern.exec( strData )){
// Get the delimiter that was found.
var strMatchedDelimiter = arrMatches[ 1 ];
// Check to see if the given delimiter has a length
// (is not the start of string) and if it matches
// field delimiter. If id does not, then we know
// that this delimiter is a row delimiter.
if (
strMatchedDelimiter.length &&
strMatchedDelimiter !== strDelimiter
){
// Since we have reached a new row of data,
// add an empty row to our data array.
arrData.push( [] );
}
var strMatchedValue;
// Now that we have our delimiter out of the way,
// let's check to see which kind of value we
// captured (quoted or unquoted).
if (arrMatches[ 2 ])
{
// We found a quoted value. When we capture
// this value, unescape any double quotes.
strMatchedValue = arrMatches[ 2 ].replace(
new RegExp( "\"\"", "g" ),
"\""
);
}
else
{
// We found a non-quoted value.
strMatchedValue = arrMatches[ 3 ];
}
// Now that we have our value string, let's add
// it to the data array.
arrData[ arrData.length - 1 ].push( strMatchedValue );
}
// Return the parsed data.
return( arrData );
}
//-->
</script> </body></html>Unknownnoreply@blogger.com2tag:blogger.com,1999:blog-2980004124283593961.post-1421760622562559612019-01-28T11:37:00.002+00:002019-01-28T12:22:05.322+00:00Treadmill and road running - equivalent pace estimationsThe effort expended running on a <b>treadmill</b> differs from that on <b>road</b> for a number of reasons, the main one being the lack of wind resistance. It is often stated that a gradient, which is easily set on most treadmills, of between 0.5-1.5% makes treadmill paces equivalent to running on a flat road. Of course, a single value of gradient cannot work for all paces since fast runners will experience a greater wind resistance on the road. Fast runners must therefore require a greater gradient on a treadmill to create an equivalent effort to that experienced when moving through air quickly on road. Equally, we might expect a zero gradient to be required for slow runners as they experience very little wind resistance.<br />
<br />
Creating equivalent pace tables, for comparison between running on the road and treadmill, is not only useful for setting the right gradient to mimic a road-based effort - such tables might allow runners to trade treadmill-speed with gradient. This has some important implications, not least making high intensity efforts on a treadmill safer. If one could use gradient increments, in a semi-quantitative way, to replace speed increments then near maximal efforts become possible without recourse to harnesses and large amounts of padding.<br />
<br />
If you Google for such tables what pops-up are mostly straightforward pace and speed conversion tools. There does, however, appear to be one table that might provide some better data and that is from <a href="https://www.hillrunner.com/calculators/treadmill-pace-conversions/">HillRunner</a>. That table is in miles per hour and ranges from gradients of 0%-10% and speeds from 5-12mph. In the FAQ Ryan Hill mentions that the data came from some students who were making oxygen measurements both on a track and treadmill, however, no references exist. This is not 'published' work in any formal sense. But, in all likelihood, it is a decent starting point.<br />
<br />
In the FAQ Ryan Hill states that the data does not 'nicely' fit a formula and that he cannot see how a 'meaningful' calculator can be produced. I found this a slightly odd statement. My experience is that physiology is often well-modelled by simple maths, and running on a treadmill should be relatively simple to model. Looking at the table of data I wondered if using pace data was what made the maths appear to be 'complicated'. So, I attempted to produce a model. My first step was to convert the pace values to something likely to be easily modelled. We know that oxygen consumption values tend to scale linearly with speed, so that is where I started. I choose meters per second (m/s), although any distance and time unit would have done.<br />
<br />
I then plotted the relationship between treadmill speed and the equivalent speed on road, given by the table, for each gradient. What was apparent was that for any one gradient there was a very good linear fit between treadmill speed and road speed (r2>0.99). That surprised me - I was expecting some kind of curve due to wind resistance. But, the straight-line nature of the relationship made the model easy to construct since it was now a simple matter of deriving an equation for the parameters that determine each straight-line fit for a given gradient. Plotting the straight-line fit coefficients (gradient and offset: y=mx+c) against the treadmill gradient revealed that they could be modelled well by second order polynomials. In fact plotting my modelled coefficients versus those calculated from the linear fit showed a linear correlation of r2>0.99999 - so, the model was able to predict the real values very well indeed. In most cases the model calculation of equivalent pace was within 0.5s per km of the table value - and at worst 1.5s away for a few values. The difference between this model and the table was 0.02 seconds per km with an SD of 0.33 seconds per km. That is a pretty good fit.<br />
<br />
Here is the formula (metric) where treadmill speed is in kph and grade in percent (i.e. 1% is 0.01) which returns equivalent road pace in mm:ss per km as fractions of 24 hours (which is Excel's built in time unit).<br />
<br />
Equivalent Road Pace =0.01157/(Speed*(Grade^2*0.72+Grade*0.0528+0.266)-Grade^2*29.27+Grade*13.656+0.006)<br />
<br />
For those who want a 'turn-key' solution or to see the fitting, here is a link to the spreadsheet:<br />
https://universityofcambridgecloud-my.sharepoint.com/:x:/g/personal/cjs30_cam_ac_uk/EXJxIKQ55ylCh4KdY6lNvwgBpTE0H2Tcj-DWM8YVi98B4Q?e=ZX9U6e<br />
(This link will become inactive after 28th May, 2019 - after which you will need to email: cjs30@cam.ac.uk for a new link)<br />
<br />
If you just want to convert a treadmill speed (kph) and gradient to the equivalent road speed then this is the formula you might want to use:<br />
<br />
Road speed (kph) =Treadmill Speed*(Grade^2*2.59+Grade*0.19+0.958)-Grade^2*105+Grade*49.2+0.0216<br />
<br />
If you would like a bespoke table (either metric or imperial) over a set of gradients, let me know and I will endeavour to produce one (if it makes sense to do so - i.e. it isn't a vast extrapolation).Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-2980004124283593961.post-70767333863351388882018-11-23T12:28:00.002+00:002018-11-23T12:28:55.928+00:00<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<meta http-equiv="content-type" content="text/html; charset=utf-8">
<script src="https://cdn.plot.ly/plotly-latest.min.js"></script>
<title>Heal Force Extraction</title>
</head>
<body><H1>Heal Force data extraction utility</H1>
<P>This script will extract heart rate data from the Heal Force Prince 180D .DAT (or .ESK) files.</p>
<p>You will need to install and run the ECG Viewer Manager program to import the data from the device into your computer.</p>
<p>Choosing a file then use the 'Select' buttons followed by Ctrl+C to copy the data to the clipboard for export.</p>
<p>[Notes: ECG State: 1=below 0, 2=above 0, 129=QRS. A 300 Hz sampling rate is assumed. There is a 512 byte block of data that is ignored which probably contains useful information...]</p>
<p><input id="file-input" type="file" name="name" accept=".dat" style="" /></p><hr>
<div id="div1"></div>
<table>
<tr valign='top'>
<td><p id="output"></p></td>
<td><p id="beatstable"></p></td>
</tr>
</table>
<SCRIPT>
//set a trigger to showresult once a file is selected
document.getElementById('file-input').addEventListener('change', ExtractFile, false);
function ExtractFile()
{
input = document.getElementById('file-input');
file = input.files[0];
fr = new FileReader();
//set trigger for function when the file loads
fr.onload = showResult;
//now go and get it
fr.readAsBinaryString(file);
}
function showResult()
{
var ECGArray = [], BeatArray =[];
var ECGTime =[], BeatTime=[];
Beats=''; byteVal=''; lastbeat='';numbeats=0; rate=0;
samplefrequency=300;
result = fr.result;
for (n = 512; n < result.length-2; n+=2)
{
aByte = result.charCodeAt(n);
bByte = result.charCodeAt(n+1);
if(aByte==255 && bByte==255){break;}
time=Number((n-512)/samplefrequency).toFixed(3);
if(aByte>127){aByte=aByte-256;}
if(bByte>128)
{
numbeats+=1;
Beats=Beats+"<tr><td>"+numbeats+"</td><td>"+time+"</td><td>";
if(lastbeat>''){rate=Number(60/(time-lastbeat)).toFixed(2); Beats=Beats+rate;}else{firstbeat=time;}
BeatArray.push(rate);BeatTime.push(time);
Beats=Beats+"</td></tr>";
lastbeat=time;
}
byteVal=byteVal+"<tr><td>"+time+"</td><td>"+aByte+"</td><td>"+bByte+"</td></tr>";
ECGArray.push(aByte); ECGTime.push(time);
}
averagerate=Number((numbeats-1)/((lastbeat-firstbeat)/60)).toFixed(2);
Beats=selectbutton('beats')+"<table id='beats' border=1><tr><th colspan=3>Average "+averagerate+"</th></tr><tr><th>#</th><th>Time</th><th>BPM</th></tr><tr>"+Beats+"</table>";
document.getElementById('beatstable').innerHTML=Beats;
byteVal=selectbutton('ECG') + "<table id='ECG' border=1><tr><th>Time</th><th>ECG</th><th>State</th></tr>"+byteVal+"</table>";
document.getElementById('output').innerHTML=byteVal;
var layout = {title: 'ECG and Heart Rate',
xaxis: {title: 'Time (s)'},
yaxis: {title: 'HR (bpm)/ECG level (arb)'}};
trace1 = {type: 'scatter', x: ECGTime, y: ECGArray, mode: 'lines', line:{color:'rgb(255,0,0)', width: 1}, name:'Raw ECG'};
trace2 = {type: 'scatter', x: BeatTime, y: BeatArray, mode: 'markers', marker:{color:'rgb(0,255,0)', size: 5}, name:'Heart rate'};
var data = [trace1, trace2];
Plotly.newPlot('div1', data, layout);
}
function selectbutton(name){return "<tr><td><button onclick=\"select('"+name+"');\">Select</button></td></tr>";}
function select(name)
{
el=document.getElementById(name);
var body = document.body, range, sel;
if (document.createRange && window.getSelection)
{
range = document.createRange();
sel = window.getSelection();
sel.removeAllRanges();
try {range.selectNodeContents(el);sel.addRange(range);} catch (e) {range.selectNode(el);sel.addRange(range);}
}
else if(body.createTextRange)
{
range = body.createTextRange();
range.moveToElementText(el);
range.select();
}
}
</SCRIPT>
</body></html>
Unknownnoreply@blogger.com3tag:blogger.com,1999:blog-2980004124283593961.post-1733499736389388492018-10-19T11:45:00.000+01:002019-02-02T16:13:38.848+00:00Preparing for a fast marathon is all about winning the training race<h2>
<span style="font-family: "verdana" , sans-serif;">
Winning the Training-race</span></h2>
<div>
<span style="font-family: "verdana" , sans-serif;">Yet again I am trying to get into decent shape so that I can run a fast marathon. But, at the age of 52, running a sub-2:45 marathon is looking increasingly unlikely. I was not a runner as a kid and only started running a bit less than 10 years ago. I have completed 41 marathons but have yet to break 2:45. I know that to do it I will first need to win the <i>training-race</i>. By training-race I don't mean win a race in training, or even beat someone else or a previous time of mine on a training run. The training-race is the long period leading up to a marathon where the performance (hence the term race) is the main determinant of the marathon race time.</span></div>
<div>
<span style="font-family: "verdana" , sans-serif;"><br /></span></div>
<div>
<h3>
<span style="font-family: "verdana" , sans-serif;">Redefining the meaning of race</span></h3>
</div>
<div>
<span style="font-family: "verdana" , sans-serif;">A race is usually an event with a single fixed parameter. Most commonly races are of a fixed distance (e.g. 5K, 10K, half marathon etc). A variant of the fixed distance race is a race of poorly defined distance but all runners complete the same course. Cross-country races are a good example of that. Other races are of a fixed time where the aim is to cover as much distance as possible such as a 12 hour or 24 hour race. The training race is a race of undefined distance and undefined time that starts about 6-8 weeks before the 'real' marathon race. Whilst the training race seems a hard one to win, because neither the distance nor time are defined, your performance in that race is critical - it will determine how fast you can run the marathon you are training for. Most people don't realize that training is a race because the rules of the race aren't obvious - few coaches ever explain what the rules are. There are some parallels here with other races or competitions where the rules are unclear. The caucus-race (Alice in Wonderland) is such a race where everyone runs around in circles for an undetermined length of time before everyone is declared the winner. The rules here are simple, as long as you are 'in the race' and running around you will be one of the winners. In other competitions the rules are more complicated and less obvious, but nonetheless exist. <a href="https://en.wikipedia.org/wiki/Mornington_Crescent_(game)" target="_blank">Mornington Crescent</a> is such an example. Here the players submit to the pretence that rules exist - which, formally, they don't. Any player can win, at any time by saying; "Mornington Crescent". But, to achieve a real win the player must delay saying Mornington Crescent until it can be done so with great comic effect. The suspense generated by prevarications has to be carefully calibrated, in response to audience and player reactions, for the comic effect to work. The rules here are complex but the great comedians have an innate understanding of them.</span></div>
<div>
<span style="font-family: "verdana" , sans-serif;"><br /></span></div>
<div>
<h3>
<span style="font-family: "verdana" , sans-serif;">Performance in one race predicts performance in another</span></h3>
</div>
<div>
<span style="font-family: "verdana" , sans-serif;">We know that many types of human 'performance' can be predicted or estimated from other similar performances. This is a wide ranging observation. Someone who has an organized desk at work is also likely to have an organized filing cabinet, someone who wears expensive suits is likely to wear expensive shoes. Of course, there are going to be contradictions - but, the saying; "If You Want Something Done, Ask a Busy Person To Do It" has a good deal of truth to it. Someone who does a lot is likely to get a lot done. In many endurance sports we use this form of extrapolation to estimate race performances over different distances. In rowing the obvious example is Paul's Law whilst in running it is the Riegel formula. They are both equations that allow performance at one race distance to predict performance over a different distance. This form of performance-equivalence has become embedded within running in the form of age-graded performance tables. These tables work slightly differently from the Riegel formula in that they are based on the World Record performances at different distances of men and women of different ages. By way of example, as a 52 year old male who has recently completed a 5km road race in 20 mins, I would be ranked as a 73.3% age-grade. Assuming that the age-grade is some form of measure of my aerobic fitness then it would predict that I could run a 3:13:42 marathon - since that would also give a 73.3% age-grade for a 52 year old male. The Riegel formula is a little bit more aggressive, predicting a 3:11:49 marathon from a 20 min 5km. There are plenty of other examples of such predictive formulae that take one race effort and estimate performance over another distance. But, these races are single efforts - they take place at one point in time and are over relatively quickly. Would a formula that takes race performance over a longer period not be more accurate? This is where the training race becomes useful. It is not just a race we all do before a marathon (whether we intend to or not), it is also the training stress that determines our performance.</span></div>
<div>
<span style="font-family: "verdana" , sans-serif;"><br /></span></div>
<div>
<h3>
<span style="font-family: "verdana" , sans-serif;">Defining the training race</span></h3>
</div>
<div>
<span style="font-family: "verdana" , sans-serif;">Many scientists have tried to define what we might refer to as the training race - that is the combined set of parameters that can be used to predict marathon performance. Many of these predictors are just correlates of performance not causative. For instance, amongst the elite field having dark skin seems to correlate relatively well with performance. Some mistake correlation with causation and then attempt to justify the correlation with spurious assertions. The dark skin issue is just such an example where dark skin becomes the assertion that some athletes are genetically-gifted. Science seems to differ. There are very few genes that have been associated with endurance performance. Of course genes are important - but, the probably only determine a very small fraction of performance, and the number of important genes is likely to be very large indeed.</span></div>
<div>
<span style="font-family: "verdana" , sans-serif;">There are some factors that are both correlative and causative. Weight is a decent example of that. We know that most fast marathon runners are fairly light - and of course being light does not mean you will be able to run a fast marathon. But, if you are training for a marathon losing excess fat - again within reason - will probably result in better performances. It is very simple energetics - the less you weight the faster you travel for a given power output. So, weight probably belongs in the 'formula' that makes-up the definition of the training race. Marathon training will involve some optimization of weight, but it is not the primary determinant.</span></div>
<div>
<span style="font-family: "verdana" , sans-serif;">Of the attempts to correlate training performance with race performance the best that I have come across was a relatively short paper by Giovanni Tanda in 2011. In that paper, which I discuss elsewhere, he proposes that a combination of the number of miles run in the 8 weeks before the marathon and the time it took to run those miles is a good correlate of marathon performance. So, here we have a definition of the training race. It is not a fixed distance, or a fixed time but the output of a formula which includes both distance and time. This is not as complicated as Mornington Crescent, it is a simple collapse of two variables (distance and speed) into a single metric which is the marathon prediction. The winner of this training race is the person that can push this formula to the best marathon performance prediction. By that I mean, when training we need to understand that formula and stop thinking about either just speed or just distance and think about the way in which the two are mathematically combined to produce the marathon prediction.</span><br />
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<span style="font-family: "verdana" , sans-serif;">The Training-Race - an eight week event of undefined distance and duration</span></h3>
<span style="font-family: "verdana" , sans-serif;">So, all of this might sound a bit like waffle, but it isn't. There is a race to be won in training. It is real and we are all taking part. It is a race that determines the performance in the marathon. The winner of the training race is also, most likely, going to be the winner of the marathon. The training race is won by running as far as possible and as fast as possible for 8 weeks before the marathon. You can calculate who has won by putting the average distance and speed into the Tanda formula. The Tanda formula contains within it the mathematical relationship that governs how speed and distance trade. The person with the fastest predicted marathon time is the winner. They have pushed to two parameters (speed and distance) as far as possible. Of course, how you do that is the key question - how do you trade speed in training with distance. Is it better to run another 1 km fast or 5 km slower? These things can be calculated.</span></div>
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<span style="font-family: "verdana" , sans-serif;">[Hastily written - due to be edited 19th Oct, 2018]</span></div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2980004124283593961.post-53142801100808776942018-04-20T11:36:00.002+01:002018-04-20T11:36:48.613+01:00Open Letter to Haruki Murakami<br />
<br />
Dear Haruki,<br />
Yesterday a colleague, who has an office opposite mine in the Department of Physiology, Development and Neuroscience here at Cambridge University (UK), stopped me just as I was about to get changed for my habitual lunchtime run to give me a copy of your book <i>What I talk about when I talk about running</i>. I confess I was slightly rude to him as I was in a rush to meet my running partner - but, when I saw that he had picked your book deliberately and inscribed it with some kind words - I fained a level of politeness, after all, Thorsten Boroviak is one of the politest people I know. I told him that I would read your book last night - and that is exactly what I did.<br />
<br />
I had not come across any of your works, and I make it a general rule to never read books about running, so it was a new experience for me in more ways than one. I started reading it with some trepidation and a nagging concern that I would have to read what I hear about all too often - runners talking about running. Of course, my family would find that statement deeply ironic because our dinner time conversation is usually dominated by some form of running talk.<br />
<br />
As I began to read, in many senses, my worst fears began to be confirmed. Here was a person, clearly passionate about running, who had labelled themselves as a runner of a particular type (3:30 marathon runner) on a gradual yearly decline to failure. You categorised your running, by mileage, into two groups and detailed occasionally your transition from building-up in training to tapering again as a pyramid. But, whilst I was impressed that you did not claim to know much about training and pace plays little role in the book, I was depressed as I read about the training in the months preceding each marathon.<br />
<br />
The concept of training runs through the book with a continual comparison to the act of writing - something which comes far from easily to me. As a species we evolved to do a few things well by necessity of survival. We are good lovers, convincing liars (or possible intelligent sociopaths), excellent story tellers and superb runners. Without continual and effective reproduction, we would have disappeared long ago and part of that ability to acquire as many mating opportunities as possible relies on being able to hide our base instincts and portray our most attractive side. We are, as you say, not terribly nice people. The story telling is not just a way of cloaking our true nature but has played an important part in pre-history. Without handed-down tales of dangers, catastrophes, cautionary tales, great successes and hopes, human knowledge would have vanished with each generation. A novelist performs, in hard copy and lonely isolation, the function previously performed by the tribal elders in a more sociable form around the camp fire. The running bit was, of course, the critical requirement for each person - not just the next generation. It was the way we got our food - our reward. A successful hunt is much like a modern race, perhaps a marathon. But, it is one where successfully getting food is the equivalent of not just finishing, but finishing well. Perhaps a personal best, but more often than not simply getting to the end feeling that the execution was as good as it could have been. What I read in your book was a string - but, perhaps it was just one or two - failures. One time was expect, but something slower resulted.<br />
<br />
I am of course a youngster - some 17 years younger than you. But, I run with a youngster who is 17 years younger than me (Kevin O'Holleran, a optical physicist here in the department). Quite why we run isn't clear - I guess it is little different from what you describe and certainly a lot more obsessive. We just run, and normally three times a day totally over 100 miles per week. I started running in my mid-forties just at the time you seemed to identify as the tipping point where age eats into performance. I too labelled myself as a 3:30 marathon runner, but by my late forties after about five mediocre years had managed to pull myself down to a 2:45 marathon - it was hard work and something I would have never thought possible until I applied my intellect to the process of training for a marathon. I guess this is where you and I differ. I looked at runners around me and found it hard to accept that they were better than me despite their better running style, youth and speed. In true Cambridge academic style I considered myself intellectually, and therefore also physically superior to them - I really am not a nice person!<br />
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I still run with a painful shuffle, pilling in as much training as possible such that suffering has become inevitable. Of course I will get slower as I age, but may be not yet. In three days time I will be running my 7th consecutive London Marathon - one each year since I started running - it will be the 38th marathon - if I finish. There will be no personal best this time since I only started training four weeks ago. But, like the last four, I hope to collect the race T-shirt so that I can place it - still within its sealed bag - at the back of my wardrobe.<br />
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Greetings,<br />
Christof Schwiening, Cambridge, UK<br />
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<br />Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2980004124283593961.post-89815755314069385362016-10-02T07:45:00.000+01:002016-01-30T23:39:47.330+00:00Table of contents<h3>
<br />January 2016 posts related to marathon training</h3>
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<ul>
<li><a href="http://christofschwiening.blogspot.co.uk/2016/01/meeting-load.html">Meeting the load</a></li>
<li><a href="http://christofschwiening.blogspot.co.uk/2016/01/what-is-training-load.html" target="_blank">What is a training load?</a></li>
<li><a href="http://christofschwiening.blogspot.co.uk/2016/01/predicting-marathon-performance-from.html" target="_blank">Predicting marathon performance from training data</a></li>
<li><a href="http://christofschwiening.blogspot.co.uk/2016/01/tanda-2011-viewpoint.html" target="_blank">Tanda (2011) - A viewpoint</a></li>
<li><a href="http://christofschwiening.blogspot.co.uk/2016/01/filling-training-parameter-space.html" target="_blank">Filling the training parameter space</a></li>
<li><a href="http://christofschwiening.blogspot.co.uk/2016/01/what-makes-you-faster-runner-pace-or.html" target="_blank">What makes you a faster runner - pace or distance?</a></li>
<li><a href="http://christofschwiening.blogspot.co.uk/2016/01/can-we-calculate-what-might-constitute.html" target="_blank">Mathematical definition of a junk mile</a></li>
<li>Training with the dragons</li>
</ul>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2980004124283593961.post-56919255900855538532016-01-30T23:38:00.003+00:002021-02-16T17:31:04.850+00:00Can we calculate what might constitute a junk mile in marathon training?<table>
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<tr><td>Runners often worry that they are wasting their time and effort doing slower additional miles - distance that is referred to as <i>junk miles</i>. But, how do we know when we are heading towards junk miles and the <i>quantity</i> no longer makes up for a lack of <i>quality</i>? What follows is a simple logical extension of a <a href="http://christofschwiening.blogspot.co.uk/2016/01/tanda-2011-viewpoint.html" target="_blank">marathon performance prediction equation</a> and how it can be used to calculate when it is not worth running an additional mile - just how slow does it need to be before it is junk?</td><td><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1VMYvV6xlYEhBlff3BY8A6f_2Mz2ZakbV16uaOWa6FXd-mZ0ih7oMesglyH9GmWzgktQYzjJZu5LNU5TDe5w4APd7Tu-6Ttpb8WOzmeZBv5j13N5XcuvXx8jxcgw_-GPZLcvwNgWpgEM/s1600/johnny-automatic-trash-can.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="100" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1VMYvV6xlYEhBlff3BY8A6f_2Mz2ZakbV16uaOWa6FXd-mZ0ih7oMesglyH9GmWzgktQYzjJZu5LNU5TDe5w4APd7Tu-6Ttpb8WOzmeZBv5j13N5XcuvXx8jxcgw_-GPZLcvwNgWpgEM/s200/johnny-automatic-trash-can.png" width="70" /></a></div>
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<a name='more'></a>The Tanda (2011) (<a href="https://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwil9r2439PKAhVIyRQKHa8RDpEQFggtMAA&url=http%3A%2F%2Frua.ua.es%2Fdspace%2Fbitstream%2F10045%2F18930%2F1%2Fjhse_Vol_VI_N_III_511-520.pdf&usg=AFQjCNHXcH2s-NbzO21oM2sqPstXbnf6Uw&sig2=xMt8sfCF7bNL8GB_vXsOIw" target="_blank">link to the paper</a>, <a href="http://christofschwiening.blogspot.co.uk/2016/01/tanda-2011-viewpoint.html" target="_blank">my viewpoint</a>) marathon performance prediction equation is based on average training distance and pace over an eight week period. Since any additional distance run in training alters those averages, it is relatively easy to calculate when any additional mile fails to produce a better prediction of marathon performance. Actually, the calculation took me a while, but I blame that on my glass of wine and the late hour this Saturday evening - I do these things on a Saturday night so that you don't have to!<br />
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The idea here is to attempt to define what pace might represent the cut-off for a <i>junk mile</i>. As you might expect the pace is dependent on both the average distance and pace that you are currently training at over an eight week period. But, to make it easier to work with I have plotted the function based on average daily distance. The shape of the junk mile function (in metric!) is shown in Figure 1. This figure requires a little bit of explanation. It is simply a rearrangement of the Tanda equation where I have solved the pace/distance which moves a runner along the same performance line. I will give some specific examples on how to use it.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigM2dPPw18pU2JlirmQ8GT2dSQxnLB3WZaxjyWjIhW9Oagax9UX9mXipySL5EkfRhxY9BbEclImYTJFhIs6-P_ssFg3Cyenr79vjHmORAudft8YXI8t9pt0C4AR106YlI91J5F-6UkhMM/s1600/Capture.PNG" style="margin-left: auto; margin-right: auto;"><img border="0" height="430" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigM2dPPw18pU2JlirmQ8GT2dSQxnLB3WZaxjyWjIhW9Oagax9UX9mXipySL5EkfRhxY9BbEclImYTJFhIs6-P_ssFg3Cyenr79vjHmORAudft8YXI8t9pt0C4AR106YlI91J5F-6UkhMM/s640/Capture.PNG" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1. The junk mile pace offset curve. The red line shows the additional mm:ss per km at which additional distance does not produce a predicted improvement in marathon performance. To work out your current junk mile pace threshold you need to calculate your current average daily distance and pace. If, for instance, you are currently doing an average of 5km per day then running additional kms slower than your current average pace plus 47s would constitute a junk mile. If you are averaging 25 km per day then you can afford to run 1min 37s slower per km than your average pace before you hit junk mile territory. </td></tr>
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One interesting feature of the maths is that the junk mile pace is an offset from your average pace. So, whether you are averaging 4 mins per km or 6 mins per km the offset that defines a junk mile is the same. However, the offset pace changes dramatically with distance. At short distances only a moderate slowing takes you into junk mile territory. But, if you are running long then you can afford to run quite a bit slower and it will still produce a better prediction of marathon performance. There are two easy numbers to remember. If you are averaging 5km per day then 45s slower than your average pace and you begin to enter junk miles. But, if you are running above 17 km per day on average then you can afford to run 1 min 30s slower than your average pace before the extra distance becomes worthless according to the Tanda equation. There is a calculator <a href="http://christofschwiening.blogspot.com/2019/04/test.html" target="_blank">here</a> that shows the junk pace threshold for a given weekly distance and pace.<br />
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Anyway, that is what Tanda says is a junk mile. Of course, if you are injured and doing damage to yourself then even a faster km can be counter-productive. This calculation only works if you are fatigued but healthy......Unknownnoreply@blogger.com4tag:blogger.com,1999:blog-2980004124283593961.post-71822887029136809182016-01-29T17:41:00.000+00:002016-01-31T10:29:54.631+00:00What makes you a faster runner - pace or distance?<table>
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<tr><td>Before I show what actually happens if one trains in the lands where 'dragons may lie' (long distance slow running), I thought it might be a good idea to consider what we know or think we know about those lands. Common phrases suggest that running high mileage at slow pace is not a useful strategy for a performance runner - <i>Running slowly makes for a slow runner - Junk miles - Quality not quantity - Race pace training - Tempo running is a key session - He's a plodder - No pain, no gain!</i><br />
<br />
However, we also know that elite runners engage in high mileage - or at least relatively high mileage - compared to most club runners. So, what does that training space look like when plotted on a graph?
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDZ9ejrnB_IFDkKvOwZsLNr2oPKlVugsqqQwgR64gQsaWrrRz-GRTZqmINsfkNkWQhIKI27W30GSna3B1uNVG63BxgC4ExD4A0YK5xd3BMO3NDPwMxxExsD2aeqMgMgvYNCmIbvum4fiw/s1600/dragon-clipart-9.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDZ9ejrnB_IFDkKvOwZsLNr2oPKlVugsqqQwgR64gQsaWrrRz-GRTZqmINsfkNkWQhIKI27W30GSna3B1uNVG63BxgC4ExD4A0YK5xd3BMO3NDPwMxxExsD2aeqMgMgvYNCmIbvum4fiw/s200/dragon-clipart-9.png" width="200" /></a></div>
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<a name='more'></a>In the figure below (just one - I am short of time this evening!) I have plotted three versions of training space (the 8 week average of training pace against daily distance run). All of the panels have the Tanda (2011) dataset plotted as filled circles together with a thick black line to the right of which there is no data - runners normally don't train with those types of averages. In panel A I have plotted shortened Tanda marathon prediction lines (i.e. without extrapolating the formula into areas where there is no data). This is a pure form of use of the Tanda prediction equation. We have no evidence that the formula correctly predicts data that extends beyond the dataset shown by the black circles. So, the space to the right of the thick black line is uncharted territory - and in keeping with tradition (we are in Cambridge!) we mark our map "<a href="https://en.wikipedia.org/wiki/Here_be_dragons" target="_blank">Here be dragons</a>". But, of course, most people believe that there is greener grass the other side of the line, just not quite green enough to be worth taking the time and effort to explore.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHl9dUMuy382aQJhMNWPQ31_VB77IbNZuLGNpbL_MX9WRCv12Bpm0roEUMdgN0WxprSUMJuLeBqZ_PJXSmVpNNbIWeM8GrtQ7jGw1Hcnzc6OWZpfuaGvvnaof9mRADiUGzelFzAl3XQcI/s1600/Capture.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="492" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHl9dUMuy382aQJhMNWPQ31_VB77IbNZuLGNpbL_MX9WRCv12Bpm0roEUMdgN0WxprSUMJuLeBqZ_PJXSmVpNNbIWeM8GrtQ7jGw1Hcnzc6OWZpfuaGvvnaof9mRADiUGzelFzAl3XQcI/s640/Capture.PNG" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1. Training parameter space (8 week average pace versus distance) with three views of the unexplored area to the right of the thick black line. A, Tanda (2011) contour lines plotted approximately over the space for which data exists. Within this region the equation predicts marathon performance time reasonably accurately from average training data. B, The Tanda contour lines have been extrapolated beyond the dataset to longer distances in the general form that many people believe may represent the performance from training - running longer makes you faster, but not much faster. C, The Tanda (2011) equation extrapolated well beyond the original dataset - it is a mathematical prediction of a very different training load on marathon performance. The extrapolation contradicts notions of specificity and suggests that training load is a 'scalable' function.</td></tr>
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In Panel B I have attempted to capture that in the form of modified Tanda contour lines. These coloured lines (in Panel B) are not a mathematical equation - although they could be - but represent the commonly held notion that running further does make you a faster runner, but not by much. So, the pink arrow in Panel B shows that a 3:00 marathon runner could train at 4:25 mins per km at about 11 km per day - or at 4:55 mins per km at 24 km per day. But, the extra mileage (twice as much) gets him/her no gain in performance just a potentially slower training pace. The obvious cost-benefit analysis - if one believes that the unexplored territory has performance benefits of that shape - is that adding on additional miles is of limited value: they are <i>Junk miles</i>. The underlying assumption is that pace is critical and that high mileage is just necessary for the fastest runners. However, the Tanda (2011) equation, when extrapolated into the dragon infested land suggests something rather different. In Panel C I have extended the Tanda prediction curves by simple extrapolation. The coloured lines suggest that a marathon runner of a given speed can train much slower if he/she runs further. Indeed, as the pink arrow indicates, a runner who covers a greater distance can afford to run slower and still show a performance improvement. Junk miles do still exist: if you run too slowly the all that happens is that you move along the same performance curve. I have calculated what pace would cause that to happen <a href="http://christofschwiening.blogspot.co.uk/2016/01/can-we-calculate-what-might-constitute.html" target="_blank">here</a>.<br />
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The shape of these performance prediction lines suggest that the uncharted territory might actually be a rich source of potential improvement and personal bests - not dissimilar to Dick Whittington's streets paved with gold (helpfully protected by the 'Dragons'!).<br />
<br />
But, to believe such an extrapolation one also needs to believe that the physiological systems which limit a marathon and are being trained are being done so by 'scalable' stresses rather than by highly specific types of training. The tempo run is no more important or effective than an easy longer run as far as producing marathon fitness - one just feels an awful lot harder than the other. <b><i>This is somewhat heretical.</i></b> Can it really be the case that a 5 km interval session produces no more benefit than a 20 km easy run? If so, it removes the focus from the leg muscles as the main system that is being trained since long slow running is a completely different stimulus to the muscles from fast running.<br />
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My feeling is that most people don't believe there are dragons to the right of the line - but, nor do they believe there is gold either - they see fatigue, injury, loss of form and speed: a pointless waste of time. Now, that is surely worth a test - time to train with the dragons!<br />
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Next: <a href="http://christofschwiening.blogspot.co.uk/2016/01/can-we-calculate-what-might-constitute.html" target="_blank">Junk miles</a><br />
<br />Unknownnoreply@blogger.com6tag:blogger.com,1999:blog-2980004124283593961.post-70248330244453098612016-01-28T17:20:00.001+00:002016-02-01T18:08:57.353+00:00Filling the training parameter space<table>
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<tr><td>The marathon prediction equation produced by Tanda (2011) did not look at the performance of any sub-elite runners, his fastest was 2:47. In this post I have added in some data from a few faster runners - the results are surprising.</td><td><div class="separator" style="clear: both; text-align: center;">
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<a name='more'></a><br />
In the last post I talked a bit about Tanda (2011) and how his group of 22 runners trained in terms of average distance and pace over an 8 week period. I ended-up showing this graph (Figure 1) which demonstrates that most marathon runners tend to train in rather similar ways - at least in terms of the average speed and distance - there are no runners to the right of the thick black line.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh13jzk8viJoqDaXH2sOlgeO2xkSV66FnjmZQMgEkwAam_ysGbrnXrrVbmcpvEowkHDnDDlC1VqvXmwialme2yIJwx3Uvt3uSa-8DrcxQyoC5IwaurkpD4-KvJ4ZsJqW7Vw0cXuIOjWfyA/s1600/Capture.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="374" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh13jzk8viJoqDaXH2sOlgeO2xkSV66FnjmZQMgEkwAam_ysGbrnXrrVbmcpvEowkHDnDDlC1VqvXmwialme2yIJwx3Uvt3uSa-8DrcxQyoC5IwaurkpD4-KvJ4ZsJqW7Vw0cXuIOjWfyA/s640/Capture.PNG" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1 Tanda (2011) dataset shown plotted in training parameter space. There were no runners to the right of the thick black line. Why is this? Is running 20 km per day at 5 mins per km not a viable training strategy for a marathon? Is it necessary to have a training diary average to the left of the thick black line to be successful at a marathon?</td></tr>
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<br />
I thought it might be useful to see whether this is generally the case - or whether there is something odd about Tanda's dataset. I thought the first person I could look at is me! I have a lot of marathon performances from BEFORE I knew about the Tanda prediction equation from when I was training in a normal fashion with Cambridge and Coleridge Athletics Club. It might also be a good test of the general applicability of the Tanda equation. Whilst Tanda's paper was subject to peer review, that is it was read and vetted by experts in the field, it is possible that it only applies to Italian marathon runners training in an Italian fashion on an Italian diet etc. etc.......</div>
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In Figure 2 I have plotted my distribution of training averages for 10 marathons over a two year period from 2011 together with Tanda's dataset.</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUzZ-L_7RjpoAjYd-2qSCgzSF1Vr-dvaZtIUNGacqFt6pzP9Y50cmV0oGLPVB3Q7wAbsN-wyQR1ux_ylJ7rm6Y_5wN_QdUdFa3esJfblaG9UYuW_gjiGHRb5gbhTyBALmIcvFDM6FxrpE/s1600/Capture.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="380" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUzZ-L_7RjpoAjYd-2qSCgzSF1Vr-dvaZtIUNGacqFt6pzP9Y50cmV0oGLPVB3Q7wAbsN-wyQR1ux_ylJ7rm6Y_5wN_QdUdFa3esJfblaG9UYuW_gjiGHRb5gbhTyBALmIcvFDM6FxrpE/s640/Capture.PNG" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 2. The Tanda dataset (black circles) and mine for 10 marathons from 2011 to 2013. My training looks very similar to the Tanda runners in terms of distance and pace.</td></tr>
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It is clear that during this period I was training in a very similar space - but, did my training produce the performance the Tanda prediction equation suggests it should have. In Figure 3 I have plotted my Tanda prediction from the pace and distance against my actual performance time.</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmjz5OVr1ii_KIXq0k5BkXwjKSl50CREwjY0mEaX-ME8G5dgJoY7l5WQz8rXWkY3nJ8mZ1t-pMKgjf_HT_6zcR1rMnFDyVzX7OHpYEpY5hoT-Ss6nEctBTcmfWIbCF9zXrWQluK8T4kY4/s1600/Capture.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="432" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmjz5OVr1ii_KIXq0k5BkXwjKSl50CREwjY0mEaX-ME8G5dgJoY7l5WQz8rXWkY3nJ8mZ1t-pMKgjf_HT_6zcR1rMnFDyVzX7OHpYEpY5hoT-Ss6nEctBTcmfWIbCF9zXrWQluK8T4kY4/s640/Capture.PNG" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 3. My Tanda prediction time for 10 marathons plotted against my actual performance time all from before I knew about the equation. The correlation coefficient is surprisingly high.</td></tr>
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It appears that the Tanda prediction equation rather closely matches my actual performances. Indeed, it is rather surprising since not all of the marathons went 'to plan'. If I remove the marathons with 'odd' (toilet-related) events (which we do not need to discuss here) then the fit is considerably better (r<sup>2</sup>=0.91).<br />
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I have found some runners who lie to the right of the thick black line in Figure 1 - and they are fast runners. In Figure 4. I show data for 4 fast marathon runners - Nathan Kilcourse, Frank Berersford &<br />
Jonathan Walton all at the Yorkshire Marathon (2015) and Aly Dixon at Berlin. Interestingly they suggest that runners tend to train with their average distance and pace around a curve (indicated in Figure 4).<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEd4Qw7bIbw3sTalY5q9FIahHGmzcMnc_4BX7WFBG9ykGX4tjZiA_H8z6BVRiCsEGQ0hraXN5my-6n4qj5EL-iXSPvCryI7ZJ1U1eIOyKKLsSgPMn2V0KvScOXvZAujVljZjsIhpbwUr0/s1600/Capture.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="384" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEd4Qw7bIbw3sTalY5q9FIahHGmzcMnc_4BX7WFBG9ykGX4tjZiA_H8z6BVRiCsEGQ0hraXN5my-6n4qj5EL-iXSPvCryI7ZJ1U1eIOyKKLsSgPMn2V0KvScOXvZAujVljZjsIhpbwUr0/s640/Capture.PNG" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 4. Tanda data (black circles) and four faster runners (yellow diamonds) plotted in training space. The red line shows the general (vague) region around which runners tend to cluster. To the right of the thick black line, now repositioned for the fast runners, there is still no-one. There must be something terrible there - perhaps dragons?</td></tr>
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Now it is worth wondering whether Tanda's formula predicts these faster runners' times. In Figure 5. I have plotted their predictions against their performances.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPZzDjVF8BvzrOvCT53iN3HgXej_Uv1eUaz8RTodsyPu0zF9tnU7Pnl-JC4W-gUDQGGCsF_uSBdD4dzBNFQSw3DizIZtdLgGj_0xvkz8E4aZ3nQACPcVbtIPrCruhod085OuF1iJrsfaE/s1600/Capture.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="520" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPZzDjVF8BvzrOvCT53iN3HgXej_Uv1eUaz8RTodsyPu0zF9tnU7Pnl-JC4W-gUDQGGCsF_uSBdD4dzBNFQSw3DizIZtdLgGj_0xvkz8E4aZ3nQACPcVbtIPrCruhod085OuF1iJrsfaE/s640/Capture.PNG" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 5. Tanda predictions (y-axis) against actual marathon performances for the Tanda dataset (black circles) and the faster runners (yellow diamonds). The black line is the Tanda prediction projected to the faster times (it is the equality line). The green line is the best fit to the faster runners.</td></tr>
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Given that the Tanda equation was generated from runners slower than 2:46 the equation does a remarkably good job of predicting the performance of these four runners. The fit to their data suggests that the Tanda equation might need some refinement - however, the basic idea of combining speed and distance in this form works for fast runners too.<br />
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So, my conclusion is that there are areas of training space that could be occupied by runners - but is not generally used. The prediction equation seems to be able to extrapolate to faster runners that operate within the normal training curve (red line in Figure 4). This led me to wonder whether it might also work in the area of training space which might be occupied by dragons. The benefit of training in that region becomes clear when the Tanda prediction contours are plotted (Figure 6).<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjK44cIlJqnYqJx33XLu9AVRvmbr-WgUwoX9TDCDDOS3xZkxHXTALObWpI7xrH9W5D3JHyhYA891wNu7LkHwfsPu3nk4YoimbBnrL5RLlcT1ha_qBBFiWaw8ZMXlPMLu_Gtqcb1C39wP6o/s1600/Capture.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="384" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjK44cIlJqnYqJx33XLu9AVRvmbr-WgUwoX9TDCDDOS3xZkxHXTALObWpI7xrH9W5D3JHyhYA891wNu7LkHwfsPu3nk4YoimbBnrL5RLlcT1ha_qBBFiWaw8ZMXlPMLu_Gtqcb1C39wP6o/s640/Capture.PNG" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 6. Training space with the pink (magenta) line revealing an opportunity. Could a 3 hour marathon runner training in the normal way (i.e. average of 10 km per day at 4:25 per km) turn themselves into a 2:45 marathon runner by slowing down and just running more?</td></tr>
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The contours show that in the space to the right hand side of the thick black line lies a performance within the grasp of an averagely capable runner. If I could increase my mileage and slow down (follow the pink arrow) could I get to a 2:45 marathon performance. The Tanda extrapolation reveals that possibility - but, I would be training slower - and to make that distance each day I would not be able to do any fast running at all. Indeed, most of my running would have to be at the same speed as a 3:15 marathon runner training with a normal program but I would be running over twice the distance each day.<br />
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Next: <a href="http://christofschwiening.blogspot.co.uk/2016/01/what-makes-you-faster-runner-pace-or.html" target="_blank">What makes you faster, pace or distance?</a>.<br />
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2980004124283593961.post-77969155094674579262016-01-28T11:12:00.004+00:002016-01-31T09:38:16.184+00:00Tanda (2011) - A viewpoint<span id="goog_1635483476"></span><span id="goog_1635483477"></span>Giovanni <a href="https://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwil9r2439PKAhVIyRQKHa8RDpEQFggtMAA&url=http%3A%2F%2Frua.ua.es%2Fdspace%2Fbitstream%2F10045%2F18930%2F1%2Fjhse_Vol_VI_N_III_511-520.pdf&usg=AFQjCNHXcH2s-NbzO21oM2sqPstXbnf6Uw&sig2=xMt8sfCF7bNL8GB_vXsOIw" target="_blank">Tanda (2011)</a> looked at the marathon performance of 22 runners who had run a total of 46 marathons (over a 5 year period) at near flat-pace race effort (halfway splits <±4 min) - i.e. near optimal aerobically limited efforts. He looked for correlations between marathon performance time and the following elements of the training diary (warm-ups and recoveries were included):<br />
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<li>number of previous marathons</li>
<li>number of training days per week</li>
<li>the mean distance run for each workout</li>
<li>the longest run each week</li>
<li>the mean workout distance per week</li>
<li>the mean training pace</li>
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The training data he considered included 11 week, 10 week and 8 week average data leading up to one week before the race. Using the 8 week data he found the best correlations between performance time (marathon finishing time) came from mean training pace and mean distance per week (see Figure 1).<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdWjpX2sEEAmtZEGB3sdEt7vWDFG8tQehMds2wPIgPL95TkkwFNVDz3H6c9cDCbXzQga-4jv0BW8_bnwdnjx95QyJCrvpMzs-QzUlgCI94vEltSiYsZGCm7AIiO41z5McW_393PA88g3Y/s1600/Capture.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="316" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdWjpX2sEEAmtZEGB3sdEt7vWDFG8tQehMds2wPIgPL95TkkwFNVDz3H6c9cDCbXzQga-4jv0BW8_bnwdnjx95QyJCrvpMzs-QzUlgCI94vEltSiYsZGCm7AIiO41z5McW_393PA88g3Y/s400/Capture.PNG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1. Data taken from Tanda (2011) showing the relationship between performance time for the 46 flat paced marathons and weekly distance in the preceding 8 weeks. </td></tr>
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The distance run per week correlated, albeit with a lot of noise, with a decaying exponential but the majority of the data is clustered around a mean of 60 km per week. He had two performances (possibly just one runner) with times near 2:47 with average distance of close to 110 km per week.<br />
The relationship between training pace and marathon performance was also rather scattered, but can be fitted with a straight line (see Figure 2).<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEix3rUUktTyOHfk_vAw-CqH19rgqFf1esrBi6tzxhoU6vZNPsSpoBT5WTKcBzOk5Oms_VUOO6aL6ULshphAKEh0-ypxLfDsYqfXCfIAo2XrE_HgHWcU_R-likjFXnhJLxo6SSqwYi-LKVc/s1600/Capture.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="317" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEix3rUUktTyOHfk_vAw-CqH19rgqFf1esrBi6tzxhoU6vZNPsSpoBT5WTKcBzOk5Oms_VUOO6aL6ULshphAKEh0-ypxLfDsYqfXCfIAo2XrE_HgHWcU_R-likjFXnhJLxo6SSqwYi-LKVc/s400/Capture.PNG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 2. Data take from Tanda (2011) showing the relationship between performance time for the 46 flat paced marathons and average training pace in the preceding 8 weeks.</td></tr>
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Although marathon performance time could be predicted from either just the average weekly distance or just the average training pace, the prediction is not terribly good - there is rather a large amount of scatter. However, the two variables combined together produce a better prediction since the faster marathon runners not only tended to run further each week, they also ran faster. In fact it is possible to show how Tanda's dataset is distributed in what one might be refer to as 'training space' (a plot of training pace against distance). I have plotted this in Figure 3.<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-OmBxudaxZnk02j56psrPOKVzW18t6nT0vVz8WuF9GZsXyNgSIx8C4_Doo7UJS5Kqhsn52nNAddjEiWr6YUH84wM148wk9QyfYaToKSbwgr8QzRIDw2mtYmPvxyZCHWFn-Z9_-OOa1OY/s1600/Capture.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="363" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-OmBxudaxZnk02j56psrPOKVzW18t6nT0vVz8WuF9GZsXyNgSIx8C4_Doo7UJS5Kqhsn52nNAddjEiWr6YUH84wM148wk9QyfYaToKSbwgr8QzRIDw2mtYmPvxyZCHWFn-Z9_-OOa1OY/s400/Capture.PNG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 3. Data from Tanda (2011) showing the training space that the runners occupied over the 8 week period leading up to the marathon.</td></tr>
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This scatter in training space can be used to produce a predicted marathon performance by combining both pace and distance into one equation with the relevant relationships. For his dataset Tanda suggested the following equation (rearranged for race time and average speed):<br />
<span style="background-color: white; color: blue; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px;">Race time (min) = 12 + 98.5 * e</span><sup style="background-color: white; color: blue; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">(-km per week/189)</sup><span style="background-color: white; color: blue; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px;">+1390/average speed in km per hour</span><br />
Figure 4 shows the predicted marathon time plotted against the actual marathon performance.<br />
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<tr><td style="text-align: center;"><div style="text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqKuC3UJG2A2yXYh3iGqOpiMY8DXuM9xPhyphenhyphenjKWE8ovsc9gT16DbDRSE-k17jLWyLJOhR5Q4ZUszx_5tF2aVlHfzggjBphilRJGxmPaJEhvKkDT2gs-2G28QEZhHGePOrlmZLKK1PyUJEg/s1600/Capture.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto; text-align: center;"><img border="0" height="365" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqKuC3UJG2A2yXYh3iGqOpiMY8DXuM9xPhyphenhyphenjKWE8ovsc9gT16DbDRSE-k17jLWyLJOhR5Q4ZUszx_5tF2aVlHfzggjBphilRJGxmPaJEhvKkDT2gs-2G28QEZhHGePOrlmZLKK1PyUJEg/s400/Capture.PNG" width="400" /></a></div>
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<tr><td class="tr-caption" style="text-align: center;">Figure 4. Data taken from Tanda (2011) showing the predicted marathon time plotted against the actual marathon performance time.</td></tr>
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Looking at the equation, one can see that race time is made-up of three components. First, everyone gets 12 mins, this is what one can refer to as an offset. Next there is an exponential function of distance. The 'steepness' of the exponential is set by the number 189 and is what electrophysiologists call the '<a href="https://en.wikipedia.org/wiki/Length_constant" target="_blank">length constant</a>' (<span style="font-size: 13.3333px;">λ)</span>. When km is small (i.e. no training has been done) the term tends to 98.5 - or you get 1 hour 38 mins if you don't do any distance at all. If you run an infinite distance (which is rather hard to actually achieve!) the term tends towards zero. If you run the same distance as <span style="font-size: 13.3333px;">λ </span>(i.e. 189 km) you get ~37% of the 1:38 (hh:mm) or about 36 mins added on to your performance pace. The nature of exponential functions is that there are diminishing returns for greater distances. Looking at Tanda's dataset it is hard to have much confidence in the exact values - there are simply no runners with distances between about 85-105 km per week (Figure 3). The final value is for speed and is simply 1390 divided by the average speed in kph.<br />
As I showed in the last post the equation is remarkably well behaved at the extremes. It predicts sensible values for someone who does no running and for an elite runner. But, to demonstrate I have plotted the data for a range of other runners (see next post).<br />
Finally, it is possible to plot the marathon prediction times, as contour lines, on the training parameter space plot (Figure 5).<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfsV_A3Mdzmi8BFjuUk7qAvljwEmY6ynQE3pPWe5mHDK0xphntr8BxO8ARPgx0YOyAuid0wXIU1I3NnyDJeL-HyomUTqOc5v4GEFjuLMeJgR-ju-5cjQr-_iFo1CyqHF7ac1tKJioJIg4/s1600/Capture.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="376" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfsV_A3Mdzmi8BFjuUk7qAvljwEmY6ynQE3pPWe5mHDK0xphntr8BxO8ARPgx0YOyAuid0wXIU1I3NnyDJeL-HyomUTqOc5v4GEFjuLMeJgR-ju-5cjQr-_iFo1CyqHF7ac1tKJioJIg4/s640/Capture.PNG" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 5. Tanda's dataset plotted in training parameter space (average 8 week training pace against average daily distance). Each data point has been coloured by marathon performance time (blue for the slowest then 'hotter' colours for the faster performances - red being the fastest). The thick colours lines are the contour lines from the prediction equation. The blue line shows the range of distance and paces that would predict a 3:30 marathon, green are the distance and paces for a 3:15 marathon etc. The thin coloured lines are the age-graded 90% effort lines for the four prediction lines. So, the thin blue lines shows a 90% daily age-graded effort for a 3:30 marathon runner. Note that most 3:00 runners (near the 3:00 thick line) are training at above 90% age-graded effort whereas the 2:45 runner(s) and the 3:30 are training (mostly) below 90% effort. Note that most of the parameter space (to the right of the thick line) contains no runners.</td></tr>
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The thick lines are the Tanda prediction contour lines for four different marathon finishing times. The thin lines show 90% age-graded effort for daily training for each of the marathon prediction times. Thus, the 2:45 runners are training below 90% effort - whilst the 3:00 runners are putting in over 90% effort each day. The 3:30 runners are also mostly training below 90% age-graded effort. The Tanda equation can be extrapolated out of the fitted parameter space. That is shown to the right of the thick straight line. No one in Tanda's dataset runs these types of averages. The big question is; "Why?". Is it that the equation fails in this space (i.e. is it impossible to complete a marathon in 2:45 by training at an average of 5 mins per km and 26 km per day for 8 weeks) or is it that no-one does that form of training? This question has some critical consequences. Tanda's dataset shows that marathon runners attempt to get faster by increasing their speed up to a 90% daily age-grade. At this point training is very hard. The 3:00 marathon runners are almost certainly unable to progress further using speed as a training tool.</div>
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Next: <a href="http://christofschwiening.blogspot.co.uk/2016/01/filling-training-parameter-space.html" target="_blank">Filling the training parameter space</a></div>
Unknownnoreply@blogger.com2tag:blogger.com,1999:blog-2980004124283593961.post-53014194606469451112016-01-20T11:39:00.000+00:002016-01-31T00:12:06.762+00:00Predicting marathon performance from training data<table><tbody>
<tr><td>Those who train for a marathon following a pre-prepared plan, of which there are many available, should have a reasonable expectation of achieving their goal: a 3:15 marathon plan should get you a 3:15 marathon time if you execute both the plan and the race appropriately. Unfortunately runners train in the 'real-world' where sessions get skipped and targets missed. The effect of failing to precisely execute 'The Plan' is hard to predict. Can missing one day/week really have a measurable effect? The lack of predictability presents a serious problem to many runners and can lead to injury as they attempt to make-up for missed sessions or bonk badly in the race by failing to scale back their speed to match their lack of diligence in training.</td><td><div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPuiSxoWOoMojCXmhJqakx_YnNbSa5vONymsv4NBqLAlFBP63sJcEb8Sy2G4zPW19Worw-M-1agKL0BQo9UJuYuYoExiYLIrAGKvsUIJx2dsQ6W00AZzVtrXa0penJEjlt88t7bGwZvvs/s1600/crystal-ball.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPuiSxoWOoMojCXmhJqakx_YnNbSa5vONymsv4NBqLAlFBP63sJcEb8Sy2G4zPW19Worw-M-1agKL0BQo9UJuYuYoExiYLIrAGKvsUIJx2dsQ6W00AZzVtrXa0penJEjlt88t7bGwZvvs/s200/crystal-ball.jpg" width="200" /></a></div>
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There are ways of predicting marathon performance from race data - <a href="http://www.runningforfitness.org/calc/racepaces/rp" target="_blank">multiple rules of thumb and scalers exist</a>. They all work to a greater or lesser degree depending upon the race distance used and the training performed. It is most often the case that novice marathon runners, slower runners and those who yo-yo between fitness levels have the greatest problem with these race predictors especially when scaling from 5K to marathon distance. It is simply the case that for most people the mechanisms that limit performance at 5K are not quite the same as those that limit performance at marathon distance.<br />
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<h3>
Using 'data' to predict marathon pace</h3>
The literature is scattered with attempts to predict marathon performance from training and other data - each paper having its own focus. There has yet to be a very large cohort study that uses advance machine learning algorithms to study the complexity that represents athletics training - the interaction between different types of training done in succession, macro cycles, sub-km efforts and additional loads (thermal, altitude, ground surface, clothing weight, nutritional status etc). The complexity requires that the first attempts are based on simple 'average metrics'. This is a sensible first approach since once one can identify the major drivers of fitness one can begin to look for individuals who appear to be able to do better than their prediction. In studying these individuals one can then begin to identify the other elements that drive athletic performance.<br />
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To give you a flavour of what is out there in terms of predictions based on average metrics here is a list of a few of them.<br />
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<a href="http://journals.lww.com/acsm-msse/abstract/1981/03000/marathon_performance_in_relation_to_maximal.7.aspx" target="_blank">Hagan et al. (1981) </a>looked at male runners and found that marathon finishing time was predicted using the equation:<br />
<span style="background-color: white;"><span style="color: blue;">Race time (min) = 525.9 + 7.09* distance per workout in km - 0.45* workout speed in meters per min - 0.17*(distance run in 9 weeks in km) - 2.01*(VO<sub>2</sub>max in ml of O<sub>2</sub> per kg body weight per min) - 1.24*age in years</span></span><br />
<span style="background-color: white;"><span style="color: blue;"><br /></span></span>
Whilst the equation may well work (and it doesn't for me - see later for a hint as to why) it contains a few problems that make it less useful than others. First it contains the parameter VO<sub>2</sub>max - the maximal rate of oxygen uptake. Most runners will not know what their VO<sub>2</sub>max is at a given time. Second the implication is that you get faster with age. Whilst older marathon runners may well, on average, run a faster marathon than younger ones, it is likely that beyond the age of about 30 performance declines. Ageing may well be associated with better training and race execution, but these are not necessarily directly associated with age - i.e. a dedicated, careful and informed young runner would not fit the equation.<br />
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<a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1478599/" target="_blank">Hagan et al. (1987)</a> looked at female runners (around 4 hour finishing times) and found the following equation predicts the finishing time:<br />
<span style="color: blue;">Race time (min)=449.88-7.61*distance run per day-10.5*speed in km per hour</span><br />
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<a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3426727/" target="_blank">Schmid et al. (2012)</a> looked at recreational female runners finishing in just over 4 hours and stated that the marathon performance could be estimated (although not terribly well) from the equation:<br />
<span style="color: blue;">Race time (min)= 184.4 + 5* calf circumference in cm - 11.9*training speed in km per hour.</span><br />
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<a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3781899/" target="_blank">Barandun et al. (2012)</a> looked at male runners and suggested that marathon finishing time could be 'estimated to some extent' by the formula:<br />
<span style="color: blue;">Race time (min)= 326.3+2.394 * Body fat percentage - 12.06* training speed in km per hour.</span><br />
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Tanda (2011) looked at mostly male runners and found that gross descriptive data for an 8 week block of training, ending one week before the marathon could predict marathon performance relatively well compared to the equations above. The equation (although published in a slightly different arrangement) is:<br />
<span style="color: blue;">Race time (min) = 12 + 98.5 * e<sup>(-km per week/189)</sup>+1390/average speed in km per hour</span><br />
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The value of such equations is their applicability to other datasets including those that extrapolate beyond the original dataset - and the extent to which they represent 'over-fitting' to the subject group on which they were based. The two easiest to compare in this regard are Hagan et al. 1987 and Tanda 2011. To test this we can calculate the performance time for a mild extrapolation. If we take an average daily distance of 30 km at an average pace of 5 mins per km (12 kph). Hagan 1987 predicts a 1 hour 35 min marathon time - which is obviously ridiculous since it is about 30 mins faster than the World Record. Tanda 2011 predicts 2 hours 35 mins which is at least possible. If we look at higher pace running: 4 mins per km (15 kph) for 30 km per day (something that an elite runner might do) Hagan predicts a 1 hour 5 min finish and Tanda a 2 hour 12 min time. At the other end of the performance scale is someone who has not trained for a marathon and perhaps covers 5 km per day by walking at 12 mins per km (5 kph). In this case both equations predict a marathon finish in around 6 hours.<br />
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Equations fitted to physiological data need to be treated with care. Some are very good at describing the dataset to which they are fitted - but lack meaningful variables and fail dramatically on extrapolation - others may appear less good but contain variables with some fundamental relevance to the physiology such that they fail gracefully outside their fitted range. The Tanda (2011) equation could, potentially, be a bit better in this regard - however, it passes the 'extrapolation' test in that it does not produce impossible values at the extreme ends of pace and distance. Indeed, the failure at the edges seems very graceful indeed lending some confidence that it might be of more general use.<br />
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In the next post I will consider the Tanda (2011) formula in more detail.<br />
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Next: <a href="http://christofschwiening.blogspot.co.uk/2016/01/tanda-2011-viewpoint.html" target="_blank">Tanda (2011)</a>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2980004124283593961.post-46782872804089172132016-01-19T12:53:00.003+00:002016-01-31T09:30:53.166+00:00What is a training load?<table><tbody>
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Training: pushing adaptations in limiting systems</h3>
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Most runners training for a marathon follow some form of standard plan containing a mix of running speeds and durations with a gradual build towards race day. The plans are constructed to induce adaptations within different systems that might limit marathon performance. These plans also contain elements that enable further training to occur - i.e. the concept of <i>training to train</i>. Whilst most runners are aware of the standard adaptations that are required: muscle mass, glycogen content, mitochondrial density and enzyme expression, capillary density, 'fibre-type', circulatory capacity (stroke volume etc), tendon and bone strength, mental capability, 'endurance' there is often little understanding as to just how specific or non-specific the types of training are in terms of the adaptations they produce. The result is that there is sometimes an impression that particular types of training can produce disproportionately large benefits. There are three of those types that have developed cult followings within the community: tempo running, hills/hard intervals and the long run. It is worth - very quickly - looking at some of the evidence supporting a benefit of one type compared to another.
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtqEQ5AkV3GtxYsAPQMv685gO9OJe4DL0witPHcU86pmc-hXI7gnsqURcMpG_l8BvBq6MQ4HqzdbVvU6dilxPOKkcUO4EwFKU-VQI75BPgiUCcfdJHJfmkJtMPLsauKoPkkI0JJTowLB4/s1600/eTM6pzqTn.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="193" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtqEQ5AkV3GtxYsAPQMv685gO9OJe4DL0witPHcU86pmc-hXI7gnsqURcMpG_l8BvBq6MQ4HqzdbVvU6dilxPOKkcUO4EwFKU-VQI75BPgiUCcfdJHJfmkJtMPLsauKoPkkI0JJTowLB4/s200/eTM6pzqTn.jpeg" width="200" /></a></div>
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<h4>
<a name='more'></a><br />High Intensity Interval Training (HIT)</h4>
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Having just returned from Mara Yamauchi's marathon talk, where she mentioned all-out 10s hill efforts, I was reminded of a paper I had read some years ago by <a href="http://onlinelibrary.wiley.com/doi/10.1113/jphysiol.2009.181743/pdf" target="_blank">Little et al. (2010)</a> which will do for this example. Their test was of a milder form of HIT training. In the paper they examined the effect of about ten one minute high, but not maximal, efforts with just over a minutes recovery between them every other day. They found similar adaptations using their 'practical model of low-volume high intensity training' as are found with all-out HIT. Most studies on HIT generally state that the adaptations in skeletal muscle that occur resemble what is obtained by long or endurance running. Thus, there is evidence - at least from muscle - that a continuum of training loads exists that can produce similar adaptations. All-out HIT, mild-HIT and long runs have 'much' the same effect on skeletal muscle (if the exercise program can be tolerated) but consuming different amounts of time. HIT is without doubt time efficient. However, there are some major differences between the two extremes. First HIT is associated with remarkably little total energy consumption - and almost all of it will be in the form of carbohydrates stored in the muscle. Long runs consume a lot of energy and a large proportion comes from fat. Together with the energy difference comes a large difference in thermal load and the consequential effects on the training of the skin and osmoregulatory systems. So, whilst skeletal muscle can be trained over a wide range of intensities, other systems require more specific loads to force adaptations.</div>
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<h4>
Characteristics of a training load</h4>
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FITT is an oft used acronym for describing a training load: <b>frequency</b>, <b>intensity</b>, <b>time</b> and <b>type</b>. Mara used the abbreviated acronym FIT in her talk. These characteristics have different units (e.g. frequency might be, per day; intensity could be characterised as grade-adjusted pace, time is simply time, and type might be represented by muscle groups). What is hard to achieve is an understanding of how one of these domains interacts with another with regards to the likely effects on performance. Frequency and time might be conflated if one simply assumes that it is the total amount of activity that counts. So session frequency multiplied by the session time might represent a measure of training benefit. However, intensity is more difficult to combine with time. The efficacy of HIT suggests a non-linear or power relationship with very high intensities being worth considerably more than the simple multiplication of speed and distance would suggest. Indeed, athletes generally feel that this is the case - the hard work associated with fast running instinctively feels more worthwhile than a longer slow run.</div>
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<h4>
The consensus view on the benefits of specific training types</h4>
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There are two Midgley papers, that I came across some time ago, that suggest there is little evidence for believing that there are specific intensity or distance domains that can produce disproportionately large performance benefits. The <a href="http://www.ncbi.nlm.nih.gov/pubmed/16464121" target="_blank">2006 review</a> considered maximal oxygen uptake. The abstract is relatively informative and tends to the conclusion that there are no sufficiently well controlled studies to differentiate between exercising at 70-80% or 95-100% of maximal aerobic effort. Importantly the review acknowledges that whilst exercising at maximal aerobic effort is effective, lower intensity training can be equally effective - at least in moderately trained individuals - because it can be done for longer. For the well trained runner higher intensity work may be necessary - but the evidence supporting that is limited. The <a href="http://www.ncbi.nlm.nih.gov/pubmed/17887811" target="_blank">2007 review</a> considers race performance and the advice that can be given to coaches and runners. It contains - in the abstract - the following statement; "<i>Scientists should be cautious when giving training recommendations to runners and coaches based on the limited available scientific knowledge.</i>" I agree with this - our knowledge is indeed limited and there is a tendency within the literature for Sport Scientists to attempt to apply a particular set of training loads to cohorts. The idea is simple and obvious; Is intensity A better than intensity B? But, the experiment is fraught with all of the problems associated with human nature, the placebo effect, sub-conscious corrective actions and intensity matching. For instance imagine that intensity A is better tolerated than intensity B but less effective at producing performance benefits. If the tolerance is ignored one might conclude the intensity B is better. But, if the subjects had been allowed to do more of intensity A - since it was easier - then it is possible that it may have been equally or even more effective. The devil really does lie in the detail. </div>
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It seems rather better to study athletes who are attempting to become fast and to extract training characteristics that are associated with enhanced performance. One of the problems with doing this is making sense of the diverse dataset. Each athlete will tend to perform a different mix of FITT sessions. However, if one can begin to draw some form of general relationship between the FITT sessions and performance it might well be possible to identify the most important training elements. Whilst the benefit of doing this is that one can develop a 'recipe' for success, it does not necessarily reveal all of the different ways that an athlete might be able to train to become successful. Furthermore, it is likely that there will be a degree of 'noise' within such an analysis since the number of individuals required per parameter included within the model rises rapidly if one is to avoid what is known as <a href="https://en.wikipedia.org/wiki/Overfitting" target="_blank">over-fitting</a>.</div>
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Fortunately, there have been many studies that have attempted to predict both VO<sub>2</sub>max and race performance from both anthropometric (i.e. body characteristics) and training-based indices. I will consider one of those next.</div>
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Next: <a href="http://christofschwiening.blogspot.co.uk/2016/01/predicting-marathon-performance-from.html" target="_blank">Predicting marathon performance from training data</a> </div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2980004124283593961.post-1125644832363723222016-01-18T16:52:00.000+00:002016-01-28T17:40:55.336+00:00Meeting the load<h4>
<i>Physiological control systems - hypertrophy and atrophy</i></h4>
Running a 'fast' marathon requires a body prepared for the stresses that arise during the race. The order and extent of the stresses depends upon the relative effort expended by the runner. Training is usually considered to be the best way of adapting the physiological systems such that they do not fail dramatically during the race. The degree to which different elements of training prepare the body is often considered to be highly individualistic - <i>Everyone is different</i> - is a common refrain. The underlying idea being that what makes one person fast will not necessarily work for another. <br />
<a name='more'></a>Or, to put it another way, if one applies the same set of stresses to a group of humans there will be a diversity of training responses that prevents generalized trends from being seen. The idea presumably being that some people are destined to be slow runners and others fast by virtue of their 'train-ability'. The complexity of training often makes it hard to investigate whether this is actually the case. However, the question has some important consequences for athletes trying to become fast. If we believe that we are entirely unique then we can only progress by experimenting with our own training since what will work for one runner will not necessarily work for another. But, if we share some general training characteristics with others then we can apply the same successful ideas that they have used to make themselves faster to also make ourselves faster. Instinctively we know that this must be true. Training improves performance and more training improves performance more. Our entire system of education and science is based upon the knowledge that systems arise through interactions and those interactions are subject to certain rules.<br />
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Physiological systems tend to adapt to stresses that are applied to them. Usually the response does not involve producing a greater adaptation than the stress requires. If you look at the size of someone's leg muscles, they are usually in proportion to their body weight (as long as they are not doing some special form of exercise training). Biology is quite clever - rarely does it allow excess or inadequate amounts of muscle to exist. We are in a balance of hypertrophy (growth) and atrophy (shrinkage) such that we have 'just the right amount of stuff'. It allows us to cope with the normal loads without consuming an excess of energy. This ability of our body to match the response to the load is central to physiology.<br />
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The same principles apply to run training. If we increase the load the body produces a greater adaptation - if we remove the load the adaptations reduce. This is what is referred to as a control system. Whilst the adaptations are insufficient hypertrophy continues, once the adaptations are sufficient to meet the load then there is no longer a stimulus to drive further adaptations. The effect of this control is that the same training load applied to different individuals should result in similar levels of adaptation - an adaptation capable of coping with the load. In this case the differences between individuals may appear as either an inability to adapt to the load or the speed with which the adaptations occur.<br />
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Specifically with regard to running a fast marathon, there are two obvious extremes for producing the necessary load. One could either attempt to run at the same target speed of the marathon one is aiming for, but over progressively longer distances to force the adaptations, or one could run the same distance as the marathon and then gradually increase the speed. The question is; "With which technique can one achieve that best results?". To consider this fully we must also remain open to the possibility that the systems that limit our marathon performance might be adapted by other stresses than running alone. This is critical since we have a limited capacity for run training. To force the maximum amount of adaptation one needs to apply the greatest load possible. However, as the load increases one tends towards the point at which the rate of damage caused by the load first matches the rate of the repair and hypertrophy process before eventually exceeding it. At this point we effectively lose the ability to increase the training load. The very structures we are attempting to adapt are incapable of producing a greater load. It is thus minimizing the rate of damage accumulation with respect to the training benefit that limits the size of the adaptation that can be produced.<br />
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This points at the need for a virtuous cycle within training whereby the hypertrophy induced by a load allows for a progressive rise in the load (training to train). The hypertrophy in this case is a combination of many systems not just skeletal muscle. However, where speed is an essential driver of the increase in load then skeletal muscle hypertrophy together with the ability of the legs to cope with the stress is critical. Where distance is the key driver for the load increases other factors than simple muscle strength are likely to dominate.<br />
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Next: <a href="http://christofschwiening.blogspot.co.uk/2016/01/what-is-training-load.html" target="_blank">What is a training load?</a><br />
<br />Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2980004124283593961.post-76024992194609689642015-11-09T01:51:00.000+00:002016-01-28T17:41:13.803+00:00A test (n=1) of weight loss during running<h4>
There are reasons why different runners <b><i>might</i></b> best adopt 'slightly' different pacing strategies (profiles), even in flat corner-free road marathons, to get their optimal times - if it is critical to maintain a constant metabolic rate in skeletal muscle. One of the reasons has to do with physics, the other physiology. I thought I would try and calculate what that optimal pacing profile (for that 'mythical' flat wind-free cool road marathon) might look like for me. Just how much of a change in pace should I be aiming for if I were to make the very best use of my skeletal muscle carbohydrate stores? [The real world importance of this may be limited since it is possible that I am not limited by my carbohydrate reserves at the pace I can sustain and other runners may fail to make the best of their reserves because they start too quickly in the first place.]</h4>
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<a name='more'></a><br /></div>
It is well known that increases in muscle power-output disproportionately consume carbohydrate reserves. The reason is that the relationship between carbohydrate usage relative to fat usage is highly non-linear with pace. Since carbohydrate stores in skeletal muscle are limited, and once they are 'exhausted' fat metabolism remains as the only option and it has a relatively low rate of energy production. Thus, it is also widely accepted that near flat power-output (or metabolic rate) - of an appropriate power that 'exhausts' the carbohydrate stores by the end of the marathon - also results in the best performance.<br />
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Thus, we arrive at the question; "What should the pace profile look like to achieve that flat power-output?". There are two main factors that I think we need to consider - "How does weight change during the marathon?" and "How does efficiency change during the marathon?" If weight decreases during the marathon then a steady power output should result in a proportional increase in speed (and vice versa). If efficiency decreases (which is likely) then speed will need to decrease for a constant power output to be maintained.<br />
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I thought I would do a little n=1 experiment to test this on myself. It is a reasonably good example of how a very simple set of measurements can help us address questions of pacing. The equipment I have used is easily and cheaply available and accessible to anyone wanting to investigate how they respond. Your response <b><i>may</i></b> be different - but, probably not that much different from a weight-scaled version of me.<br />
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This evening I did a sequence of 12 laps (2.86 km; see <a href="https://www.strava.com/activities/429132020" target="_blank">Strava</a>) whilst weighing myself between each lap). I used a Salter Ultimate Accuracy domestic scales (they read to 50g) - which I had previously calibrated. I weighed myself 8 times in succession at each lap using an 'anti-defeat' protocol (these scales do not register a new weight unless it is more that ~200g different from the last one, so I alternated holding a 1.74 kg weight). I was wearing leggings, heavy trainers and a long sleeve base layer (no hat, gloves or jacket). The clothes were chosen to limit radiant heat loss but allow sweat evapouration. All weights were made wearing these clothes. The weather was mild (~13C) but the wind was reasonably strong. I set out at 4:57 mins per km pace and attempted to minimize pace and heart rate deviations - however, the wind and lack of lighting made this difficult. After each lap I returned inside and at the entrance weighed myself (it took ~2 min to make the 8 measurements). I did not use a towel or drip sweat - all weight loss, other than where indicated - was evaporative.<br />
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The graph of my weight (mean+/-SD) against distance is plotted in Figure 1. At point A I emptied my bladder and bowel and at point B I consumed (rapidly) roughly a pint of water - exact weights in figure legend. The step changes in weight were planned. As expected there was a gradual loss of weight, although careful observation reveals that at the start, after point A and after point B the first weight loss appears smaller.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcAAyvQ9Kdu935EpKXUgFvObvdQThSogN9T_ialRwx5jLSqtqUeGAqZf65GP1LwJWb0a-me-qoyDtuScX-jKlOzn4t1tZYJ8FCH0mp4pURe2FmCn8shpX3ZfCC6qv9XzFG0bplQxeXmYU/s1600/Capture.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcAAyvQ9Kdu935EpKXUgFvObvdQThSogN9T_ialRwx5jLSqtqUeGAqZf65GP1LwJWb0a-me-qoyDtuScX-jKlOzn4t1tZYJ8FCH0mp4pURe2FmCn8shpX3ZfCC6qv9XzFG0bplQxeXmYU/s1600/Capture.PNG" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1. Weight measured at 2.86 km intervals. Each data point consists of eight measurements (mean+/-SD). At point A I went to the toilet where I lost 263g (urine and faeces), I weighed myself before and after. At point B I consumed 581g tap water again weighing myself before and after.</td></tr>
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To look at the weight changes in more detail I have plotted the absolute weight loss over the course of each lap in Figure 2. The open symbols show the first lap and the laps after the pause for the toilet (A) and after drinking (no pause but the consumption of room temperature water, B). With each lap I lost on average 177g of water (or 62g per km). This represents a weight loss of 0.1% of my body weight per km travelled and if scaled over a whole marathon would be 2.6 kg for me (~60kg). This is a bit less than the 3.15 kg I lost at Frankfurt (although there was a time lag between the race and the measurements in that case). This weight loss (4.2% of body weight over the course of a marathon is in agreement with the faster runners in published studies). The 0.1% decrease in body weight would require an equivalent increase in speed to keep muscle power output constant - i.e. 0.3 s per km increase in pace with each km. For a marathon at this pace it would mean starting at 4:57 per km and finishing at 4:45 per km creating a ~2 min negative split.<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyZo95M5kkCVP25TWV08TOGFa3vaxCsVXy2LBrKS87MSftaFoA92j5w8_0iWI-WAqEXwND5pvV9zraqqI3zazlhXag4L2BQt2YIK7sUEXeMuFLxHe0Sr-IAh7SqFb9Un5lJcWqgWqD2Vk/s1600/Capture.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyZo95M5kkCVP25TWV08TOGFa3vaxCsVXy2LBrKS87MSftaFoA92j5w8_0iWI-WAqEXwND5pvV9zraqqI3zazlhXag4L2BQt2YIK7sUEXeMuFLxHe0Sr-IAh7SqFb9Un5lJcWqgWqD2Vk/s1600/Capture.PNG" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 2. Weight change over the course of each lap plotted against distance.</td></tr>
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However, it is possible that running becomes progressively less efficient and that the effect is to require greater muscle power to produce the same speed. The weight loss data should allow us to investigate this. Evaporatiing water carries away 0.54 kcal per g. In Figure 3 I have used this number to calculate the total evaporative metabolic energy loss - the best representation of muscle power that we can calculate with these data. To make this calculation I have assumed an incremental efficiency of 21% through out. The legend contains details of the calculation.</div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEileFmWL8F9tHnB9rGhx410-sd18G0H8Ckv8dq40GaK7twTcOLENZFKlS2k32z5tMVqEG1PTC2dbIMkZ7FllVA1bCBitEk-nAfc-Stz6zhT92Y3thYi-R2ryNRcLto25Ublij3zTJIFD5Y/s1600/Capture.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEileFmWL8F9tHnB9rGhx410-sd18G0H8Ckv8dq40GaK7twTcOLENZFKlS2k32z5tMVqEG1PTC2dbIMkZ7FllVA1bCBitEk-nAfc-Stz6zhT92Y3thYi-R2ryNRcLto25Ublij3zTJIFD5Y/s1600/Capture.PNG" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 3. Data from Figure 2 replotted as the metabolic rate supported by evaporation in kcal per kg of body weight per km covered. To calculate this I took the weight of water lost and divided it by the body weight and by the distance travelled whilst multiplying it by the latent heat of vaporization (540 cal per g) and dividing it by 0.79 since 21% of the energy is lost as useful mechanical work (79% is lost as the waste heat by the water loss).</td></tr>
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The metabolic rate supported by evaporation is approximately 0.8 kcal per kg of body weight per km. This is lower than the standard value of 1 kcal per kg per km which is widely cited within the literature (and used by some GPS watches to calculate calorific cost) since some heat is lost through radiation. Assuming the radiant heat loss remains constant throughout the run, any increase in this value represents a loss of efficiency. Indeed, there might be a slight upward trend in my data suggesting a loss in efficiency. Fitting the data with a straight line yields a slope of 0.25% per km. If this same loss of efficiency were to occur in the marathon this would more than offset the negative split suggested by the weight loss. However, I did not taper for this run and I am at the end of a 180km week only two weeks after a marathon - so I am unlikely to be as robust as I would going into a race. The other confounding factor here is that I consumed a pint of water which I would not in a marathon - this negated some of the weight loss.</div>
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Unfortunately the dataset is not good enough to detect the changes in efficiency on the step change loss or gain in weight (toilet and drink) - more data points or a large weight change might be necessary - and perhaps better pacing to reduce the noise. It is by no means perfect. But, I am pleased with the amount of information that can be extracted from such a simple test.</div>
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So, to conclude. Weight loss seems to occur at a rate of about 0.1% per km suggesting an optimal pace might be a negative split, but this might be offset by a potential decrease in efficiency of 0.25%, something which suggests an optimal pace might be a 2 min positive split. But, the precise value will depend upon the temperature (i.e. sweating rate) and the rate of decrease in efficiency. The 'take home' message is probably that near flat pace - for someone who does NOT drink during the marathon might be best. If you drink and gain weight during the marathon and your efficiency declines faster then a positive split profile (i.e. slowing from the very start) might be optimal for the fastest possible marathon. However, for less well trained runners there are likely to be more important factors at play. I will investigate this further in my next post.</div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2980004124283593961.post-16127744698266301032015-11-07T00:52:00.002+00:002016-01-28T17:41:34.275+00:00The problem with using race predictors for choosing marathon race pace.<h3>
Is there a problem with using race predictors for marathon pace setting?</h3>
Often marathon runners use race predictors to help set their marathon pace - but, there is a <b>real problem</b> with that approach. I thought it might be interesting to give a few real world examples from people at opposite ends of the performance spectrum to illustrate the problem (and one in the middle). This is not a full scientific analysis - and you could accuse me of cherry picking my data. But, this is real data from runners who I know were making serious attempts to produce their best performance. These are runners I respect and have given their all in pursuit of a good marathon time. Of course there are plenty of examples of where race pace predictors work reasonably well - and I will try and do a statistical analysis of just how well they work for different types of runners at a later date. But, for now I want to show that care needs to be taken when extrapolating from shorter distance race performance to longer distances. What limits performance at 10km is not necessarily what limits performance in a marathon. This is not just a minor problem.<br />
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My first example comes from Michael Salt. Let me first tell you about him. He really is an awesome runner - he is way above my ability. Here is a link to his Powerof10 profile http://www.thepowerof10.info/athletes/profile.aspx?athleteid=45117 At 44 years old he is a very experienced runner. Last year he did a 16:31 5K (84.5% age-grading) and in 2011 he did a 1:11:37 half marathon (86.8% age-grading). He is a seriously tough runner and knows how to push through the pain barrier. In April this year he ran the Virgin Money London Marathon (VMLM) for the second time, it was his third marathon. Just over a month before he had raced two half marathons, the one listed on thepowerof10 was in 1:15:48 (83.35%) which predicts a 2:37:26 marathon (flat pace 3:43 per km). He finished the VMLM in 3:16:09 - nearly <i><b>40 minutes </b><b>slower</b></i> than the predictor. Clearly the most obvious explanation for this dramatic failure of the predictor is that he got his pacing wrong. But, his splits don't support this. He went out on the first 5km at 3:41 per km - only two seconds too fast for a flat pace strategy. This looks like pretty good pacing. He then slowed to 3:43 per km for the next 5km - perfect pacing apparently. However, his pace continued to slide from 10km to halfway he did 3:50 mins per km which then slowed further to 4:23 per km by 30km before ending the last 10km at 6:40 per km. The plan of racing at exactly the scaled age-graded performance ended miserably for an experienced, tough runner on his third marathon. Clearly what limits Mike's performance at a half marathon is not the same as what limits him at the marathon. The predictors did not work for him.<br />
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My second example is Calvin Sambrook (age 52). He is my brother-in-law. He does not have a powerof10 profile (he is not a member of an athletics club, nor is he particularly fast) but, here are links to his <a href="https://www.strava.com/athletes/1722521?oq=sambrook" target="_blank">Strava</a> and <a href="http://www.parkrun.org.uk/cambridge/results/athletehistory/?athleteNumber=375505" target="_blank">parkrun</a> profiles. In September this year he ran a PB 19:57 parkrun (age-grading 75.1%) which predicts a 3:09 marathon. He ran the Frankfurt Marathon just over a month later, I don't know for sure, but it must have been about his 10th marathon - may be more. He finished in 3:34:54 which is about <i><b>25 mins slower</b></i> than the prediction. Again, the most obvious explanation is that he went out too fast. But, his first three 5km splits were all within 2 seconds of 4:40 per km (which is flat pace for a 3:17 marathon time - he wanted Good For Age for VMLM) - a very conservative pace for someone who the race predictors said should have been in 3:09 shape. Calvin held close to that pace up until 30 km before slowing. He did not give-up, my nephew was with him right up until he was taken away on a stretcher at the finish. He was desperate for a good performance and he did everything he could during the race to achieve it. But, the race predictors let him down too.<br />
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For the final example I will use myself. I think I must have done over 25 marathons - most, but not all, are listed on my <a href="http://www.thepowerof10.info/athletes/profile.aspx?athleteid=116274" target="_blank">powerof10</a> profile. For those who don't know, I am not an athlete with much history. I took up running in 2009 and did my first marathon in 2011 with a PB of 3:29:33 (link <a href="https://www.strava.com/activities/124682723" target="_blank">here</a>). Six months earllier I had set my parkrun PB of 19:37 (71.7% age-grading) which predicted a marathon time of 3:04:31 - 25 mins faster than I achieved. But, I had set-off at roughly 4:50 per km pace (the splits are only available on the Strava file) which should have seen me finish in about 3:24. I did a slight positive split, but my failure to achieve my age-grading was not that I went too fast at any point. But, what I want to illustrate is how age-grading predictions can fail in the opposite direction - it is entirely possible (but I admit unlikely) that you could run a faster marathon than the predictors would suggest. This year I decided to try and run a 2:45 marathon and in Frankfurt I got pretty close with 2:45:10 (age-grading 83.6%). It was a 6 min faster than my London PB from this year, which was also 6 min faster than my PB from November the year before. My previous highest age-grading was from May this year - a half-marathon where I ran a 1:21:59 (age-grading 80.3%) which predicted that I should have been able to do a 2:50:41 marathon. I did <i><b>5 mins better</b></i> than that. Of course there are reasons for this, some of which I know. But, the point here is that simply using an age-grading or race performance predictor may well produce an unreliable answer. If it predicts a slower time, like for me, it is no big deal - I would have just thrown away a slightly better performance than I could have achieved as a slow start in a marathon allows for a faster finishing pace. But, if the prediction is too fast the results are terrible - there is almost no limit to how slowly you may have to 'run' in the final stages to get to the finish. It is critical to understand why and when the predictors fail and to develop strategies (like a training log) that will enable you to produce a better guess of what a sustainable pace might be. If you want to read more about the predictors, <a href="https://www.wpi.edu/Pubs/E-project/Available/E-project-060107-132716/unrestricted/AlexWhite_MQP.pdf" target="_blank">Alexander White</a> wrote a publically available degree project on it, which although rather old, gives an overview of some of the models. <a href="http://www.hillrunner.com/jim2/id70.html" target="_blank">Hillrunner</a> has a lot to say on the topic, <a href="http://fellrnr.com/wiki/Running_Calculator" target="_blank">Fellrnr</a> attempts to take account of other factors (but, I think he makes some mistakes on pacing strategy). There is much discussion on the Net as to what sort of pacing strategy is best - negative or positive split, flat, U or inverted U. My view is that for most runners it is an unnecessary debate - near flat (within a few seconds per km on flat terrain) is best. The important question is; "What is the fastest time I could possibly achieve?".<br />
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So, I need to sign-off - and I am aware that none of this has helped you to work out what pace to choose, but if you want a clue as to how I do it then look at some of my past posts.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2980004124283593961.post-34769225747136904572015-10-17T17:13:00.000+01:002016-01-28T17:42:37.697+00:00One week to the Frankfurt Marathon<div>
<i><b><span style="font-family: "verdana" , sans-serif;">It is time again to consider where I have managed to drag my fitness to and consider what level of performance might be possible at the Frankfurt Marathon. With one week to go I think all of the 'training' is now done and I should have enough data to produce a reasonable guess.</span></b></i></div>
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<span style="font-family: "verdana" , sans-serif;">My marathon performance has been gradually improving over the last 4 years, I started 'competing' in marathons in 2011 about two years after I started running (mostly 5Ks). Here are my PBs for each of the years:</span></div>
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<span style="font-family: "verdana" , sans-serif;">2011 <a href="https://www.strava.com/activities/124682723" target="_blank">Prague Marathon</a> 3:29:33 (HR 146)</span></div>
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<span style="font-family: "verdana" , sans-serif;">2012 <a href="https://www.strava.com/activities/124635963" target="_blank">Prague Marathon</a> 3:07:52 (HR 146)</span></div>
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<span style="font-family: "verdana" , sans-serif;">2013 <a href="https://www.strava.com/activities/87503386" target="_blank">Berlin Marathon</a> 3:05:39 (I did a track marathon faster, but it doesn't count...) (HR 155)</span></div>
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<span style="font-family: "verdana" , sans-serif;">2014 <a href="https://www.strava.com/activities/219565589" target="_blank">Autumn Shakespeare Marathon</a> 2:57:00 (HR 152)</span></div>
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<span style="font-family: "verdana" , sans-serif;">2015 <a href="https://www.strava.com/activities/293103662" target="_blank">Virgin Money London Marathon</a> 2:51:34 (HR 150)</span></div>
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<span style="font-family: "verdana" , sans-serif;">Whilst there is a gradual improvement in times, as one might expect with continued training, there were a few strategy changes that I think have had an effect. In 2012 at Prague I tried using lightweight trainers for the first time (Asic Hyperspeeds) and I think they leveraged a 5-7 min advantage. In 2013 I spent most of my training doing <a href="https://www.strava.com/activities/87503639" target="_blank">stair reps</a> which I think did improve my leg strength allowing me to pace my nephew Josh through his first marathon and get a PB despite my relative lack of cardiovascular fitness (average heart rate 155 - the highest I have yet achieved over a marathon). In 2014 I ran the Raceway to get my first sub-3 using a zero in-race fuelling strategy. By then I had realized that taking gels, fruit jellies and water was not necessary and it was easier to just run. I was also shifting my training towards training layered-up, wearing heavy shoes and a light rucksack. I then began to seriously engage with glycogen depleting on a daily basis (by not eating at lunch) on top of a high mileage diet of running. Those adaptations brought me down to 2:51:34 (on what was a day of perfect conditions). My weight has also gradually declined to an average of about 59 kg (the precise value depends upon the state of my glycogen loading - I can easily swing by 3 kg over the course of a week) and for those of you concerned about my health...my BMI is ~20.5.</span></div>
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<span style="font-family: "verdana" , sans-serif;">Distance over the last 8 weeks 1,380 km (~173 km / 108 miles per week) at 4:55 per km</span></div>
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<span style="font-family: "verdana" , sans-serif;">Two rest days - either side of a <a href="https://www.strava.com/activities/395869356" target="_blank">20 km race effort</a>.</span></div>
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<span style="font-family: "verdana" , sans-serif;">Peak week: ~227 km (142 miles, 5th-11th October) at 4:51 per km</span></div>
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<span style="font-family: "verdana" , sans-serif;">My Tanda (2011) marathon prediction (a published correlative formula) based upon the distance covered in the last 8 weeks and the time taken is ~2:46 but is heavily biased by an increase in my training over the last 4 weeks. Whether that is good or bad I don't know. Figure 1 shows how the Tanda prediction varies depending upon how far back you look in my training diary. All of those calculations are based on looking back at the training I have done up until today. So -3 weeks is the Tanda prediction using the past 3 weeks worth of data and it suggests a marathon performance of ~2:36. Obviously this is incorrect since it is unlikely one can expect that 3 weeks of a particular training intensity would bring the same results as the full 8 weeks of training that the formula is based upon.</span></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNYhMe3crUJbRAOIBmN-QTJgJre_k0Oqcr3Thn48IDIFLP6CSQ90dlP2G9m4K-fy2_oB61ot8-oExkJ3bSLaZPYfR9qXXkxczLg5_XXclCuz_oF3JGJqjSz9GH8qKSgfTpUxR5AghQAjM/s1600/Capture.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: "verdana" , sans-serif;"><img border="0" height="347" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNYhMe3crUJbRAOIBmN-QTJgJre_k0Oqcr3Thn48IDIFLP6CSQ90dlP2G9m4K-fy2_oB61ot8-oExkJ3bSLaZPYfR9qXXkxczLg5_XXclCuz_oF3JGJqjSz9GH8qKSgfTpUxR5AghQAjM/s640/Capture.PNG" width="640" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: "verdana" , sans-serif;">Figure 1 Tanda predictions of marathon performance using different time periods. The published formula uses the full 8 weeks and predicts a time close to 2:45, however, it is biased by an intense training block over the last 5 weeks.</span></td></tr>
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<span style="font-family: "verdana" , sans-serif;">So, the question is whether the recent tough short block (5 to 1 week ago) of lots of running but relatively slow, is going to pay-off. There are good reasons for thinking it could go either way. But, this represents a test of Tanda in two dimensions - the formula never claimed to be causative and I am operating some way beyond the dataset on which it was based (extrapolation). I have tested the extrapolative validity of the Tanda equation on a few runners, some of them considerably faster than me, and under the right conditions it seems to do a reasonable job. But, these were runners doing a standard marathon training plan. My plan was not a standard one. I have done no fast running over the past 8 weeks - I have only done one run faster than marathon pace and that was a parkrun today (19 min 5 km) and only two runs that came close to marathon pace (the 20 km effort, see above, and a <a href="https://www.strava.com/activities/389340495" target="_blank">5 km pacing</a> for a friend on the 10th September) - neither was easy. I have done no tempo runs and no speed sessions. I also have done no long runs. I don't 'train' for a marathon I just run to work and back and typically do a 10 km run instead of lunch. My longest single run was the 20 km effort (see above), otherwise my longest continuous run was 12 km (although I do a fragmented run on a Saturday to the parkrun and back that amounts to 25-30 km with no drinking or fuelling. My strategy has been to select pace and distance to optimize the amount of 'intensity' that I could put into my running over the 8 week block. Fast running causes me too many injuries and limits the amount I can do - running too slowly chews through too much time. So, I have run to and from work and added as much training stress as I could (rucksack, heavy trainers, coat and glycogen depletion) to maximize the benefit of my 'optimal-Tanda' plan although only distance and pace is used by the Tanda equation. This is where considering heart rate becomes important.</span></div>
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<span style="font-family: "verdana" , sans-serif;">Figure 2 shows heart rate data from the last 8 weeks. It does not include my 3rd run of the day since it is usually pretty horrific since I am glycogen-depleted probably even beyond the level I would expect during a marathon. On the y-axis is my average heart rate on each run plotted against speed (on the x-axis) in units of meters per min, which may seem odd. First, I use speed rather than pace since heart rate is typically linear with speed over a reasonable range which allows some simple predictions to be made. I also use units of minutes since heart rate is measured in beats per min. The straight line is a simple linear regression fit to the heart rate versus speed data. This fit predicts a heart rate of 28 beats per minute for me when I am running at 0 meters per min and a rise in heart rate of ~0.47 beats for each meter per min increase in speed. I have plotted on the graph (in magenta) two symbols which happen to overlay one another. The first is a square, the x value of which is the Tanda predicted speed (using the 8 week dataset) with a y-value that is my 'expected' marathon heart rate (148). The second point is a triangle which is plotted at 2 hour 45 min marathon speed and again at my expected marathon heart rate. </span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDD5KlT1rHVqOImS2aE5IhmhM35wxGZOZqiLj3w3P9S2kx4tSD1b4CaYSfhJV0H0oQGt8G5PZklowliTK2PiMvwSLpZcnGUXCFRf4az_cVTZaTcVj1OUHyhizbBrgK7VZ5p5wSa0c4qcc/s1600/Capture.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: "verdana" , sans-serif;"><img border="0" height="368" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDD5KlT1rHVqOImS2aE5IhmhM35wxGZOZqiLj3w3P9S2kx4tSD1b4CaYSfhJV0H0oQGt8G5PZklowliTK2PiMvwSLpZcnGUXCFRf4az_cVTZaTcVj1OUHyhizbBrgK7VZ5p5wSa0c4qcc/s640/Capture.PNG" width="640" /></span></a></td></tr>
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<tr><td class="tr-caption" style="font-size: 12.8px;"><span style="font-family: "verdana" , sans-serif;">Figure 2. Heart rate data for runs over the past 8 weeks plotted against the average speed of the run. The magenta lines show 2 hour 45 min marathon finishing time speed and the heart rate I think I could currently hold for a marathon.</span></td></tr>
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<span style="font-family: "verdana" , sans-serif;">Three faster runs are visible on Figure 2. The top two are my 5 km pacing on the 10th September and the 20 km effort on the 20th September. Neither of these runs fall on the line. There are several possible reasons for this the most obvious of which is that I have got fitter since then. The other fast point - which sits directly on the line is my parkrun today. This causes me some concern since the line is the average of 8 weeks and my performance today suggests that all I can do is the average of those data points - I was hoping that things would be better than that and I might be able to pull off a performance closer to my recent runs. To illustrate I have replotted the graph using just the last two weeks worth of heart rate data (see Figure 3).</span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7ZDHapHIK_z9lS3TwOiTqwQtCPLNommzfFowJ_2dMkm0lqy7jZLGDyMiAGFoiKToMqqfZM_lGRyIaUExDqr0sy93oEiRyVKjTmYU38D9DKDJhiniSqbuA9Yg7oPIIniV0c3EsiF1gBlQ/s1600/Capture.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: "verdana" , sans-serif;"><img border="0" height="364" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7ZDHapHIK_z9lS3TwOiTqwQtCPLNommzfFowJ_2dMkm0lqy7jZLGDyMiAGFoiKToMqqfZM_lGRyIaUExDqr0sy93oEiRyVKjTmYU38D9DKDJhiniSqbuA9Yg7oPIIniV0c3EsiF1gBlQ/s640/Capture.PNG" width="640" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: 12.8px;"><span style="font-family: "verdana" , sans-serif;">Figure 3. Heart rate data for the last 2 weeks plotted against the average speed of the run. The triangle is plotted at 2 hour 45 min marathon speed and a heart rate of 148. The square is the 2 week Tanda prediction (2 hour 37 mins).</span></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;">Obviously the 2 week Tanda prediction is not realistic since the heart rate scaling would suggest I would need to hold an average of 152 beats per min. But, now the average of my last 2 weeks heart rate data suggests the 2 hour 45 should be achievable under a heart rate of 148. It also suggests that my parkrun today was sub-optimal (by more than is shown here since that data point is biasing the line upwards). I am concerned that the sub-optimal nature of my 5 km performance is that my heart rate does not scale in a linear fashion at high speed and that as a result such extrapolations are dangerous....without more data it is hard to know whether tracking close behind Fergie on a winding route wearing a coat at the end of a tough week and following a 10 km warm-up was the problem - or whether I am bio-mechanically limited in some way....</span></div>
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<span style="font-family: "verdana" , sans-serif;">On the question of whether the full 8-week period for the Tanda prediction is optimal for a 'non steady-state' training regime (i.e. one where there is a rapid ramp-up of fitness) I do have a bit of relevant data. The 7-week Tanda prediction was reasonably accurate for my performance at VMLM and for what might have happened at Amsterdam had my legs, intestines and the weather been more 'helpful'. The current 7-week Tanda for Frankfurt is sitting nicely at 2:43:37. </span></div>
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<span style="font-family: "verdana" , sans-serif;">So, I have got a stack of three marathons - Frankfurt, The Raceway and Pisa - before the end of the year, if necessary, to try and see whether 2:45 is possible. I will gain 'battle-testing' from each failure and learn more about what this data means. I know that 2:45 is going to be tough to achieve and probably rate my current chances of success at around 10% on my first outing. If the weather is perfect, I get a good draught from a group of steady runners who are tracking the line, my guts play ball, I don't lose the feeling in my legs and feet for 10 km and I get my carb-loading and my plasma-volume in the right place who knows perhaps it might just work. But, there is no limit to just how far things can go wrong in a marathon.......Now, I hope my Achilles settles down this week, my heels stop hurting, the pain in my hamstrings disappears and my groin strain doesn't flare-up. I am now off to find some even lighter socks, underpants and shorts and shave-off any hair that isn't performance enhancing! I am not obsessed, just motivated - Kevin will be trying to beat me and I can't let a youngster win without a fight.</span></div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2980004124283593961.post-63780784533425852002015-10-09T16:55:00.002+01:002016-01-28T17:42:11.907+00:00Sweat: sweet is better than salty for marathon runnersThinking back to some lectures I attended, probably about 20 years ago now, I came across another good reason why marathon runners might want to 'over' heat acclimate (i.e. train in more clothing than is comfortable so that they can produce large amounts of sweat).<br />
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Heat acclimation has been long been known to improve sweating rates, produce bigger sweat glands as well as increase plasma volume. The end result of heat acclimation includes an improvement in aerobic performance whether measured by VO<sub>2</sub>max or direct race performance. So far I have generally been concerned with the importance of the expanded plasma volume and its importance during a marathon. A large plasma volume will tend to keep heart rates relatively low. During a marathon it is also well known that there is fluid loss (sweating and breathing) causing a decline in plasma volume resulting in a rise in heart rate. This rise in heart rate may eventually limit the aerobic capacity of a runner causing them to slow - the full explanation for this is rather complicated since it involves understanding the importance of venous return to the heart. But, the key point to understand here is that training can dramatically alter the rate at which plasma volume declines even if it does NOT alter (or reduce) the sweating rate. That is, a heat acclimated runner and one that is not heat acclimated may appear to sweat sufficiently and at the same rate - losing the same amount of weight over the course of the marathon - but one will show a much larger decline in plasma volume than the other. The non-heat acclimated runner is much more likely to exhibit a typical bonk or Wall-like slow down because of the loss of plasma volume. So, what is going on here and why does heat acclimation that may result in <i>slightly more</i> sweat loss, during a marathon, result in the protection of plasma volume?</div>
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Kirby & Convertino (1986) looked at sodium loss (amongst other things) during exercise following a 10-day period of heat acclimitization. They found that heat acclimation reduced sodium loss by ~50% (as well as increasing the amount of sweat produced). The question can thus be refined: How does maintaining sodium levels also help maintain plasma volume? To understand this - and how the sodium gives us access to 'free' internal water - we need to look at where water is in the human body (see Figure 1).<br />
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<tr><td style="text-align: center;"><a href="https://upload.wikimedia.org/wikipedia/en/2/25/Cellular_Fluid_Content.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="308" src="https://upload.wikimedia.org/wikipedia/en/2/25/Cellular_Fluid_Content.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1. Water distribution in the human. Only about 7% of the water is in the blood (plasma). Two thirds of the water in a typical human is inside cells, the rest (about one quarter of the total) is fluid around those cells.</td></tr>
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The plasma (or blood) contains a relatively small amount (7% or about 5.5 L) of the total water inside an average person. Most of the water in the human body is <b>inside cells</b>. During a marathon, if you don't drink (and some people do run marathons without drinking) you might lose about 5 L of water - clearly it cannot all come from the blood otherwise there would be nothing left to circulate around the body. So, where does the water come from? The interstitial space is one possible source. Individuals who suffer from a blood haemorrhage (bleeding) certainly do auto transfuse water from the extracellular fluid compartment to the plasma but that is driven by a drop in blood pressure - this is not what happens, or what you want to happen when running a marathon. To get water out of the cells and into the plasma an osmotic gradient is required, and this is where sodium is critical. If sodium levels are maintained in the plasma whilst its volume decreases (because of a dilute sweat production) then the osmolarity of the plasma rises. This rise in osmolarity drives water from the intracellular space into the blood plasma. Under such conditions 5 L of water flow is not a major problem - it is a loss that can easily be tolerated by most of the cells within the body. Or, to put it another way - if you have got large sweat glands capable of producing a dilute sweat you can effectively distribute the water loss between all of the compartments of your body so the 'hit' to the blood plasma is minimized. If you have poorly trained sweat glands then most of the water loss will be from the plasma and interstitial space with an associated loss of blood pressure and increase in heart rate.<br />
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So, training wearing clothes that cause you to sweat a lot induces a hypertrophy (growth or training) of the sweat glands. This growth means that the sweat glands can produce more sweat if necessary - but more importantly they retain sodium. By retaining the sodium the effect of sweating is to make the blood plasma more concentrated which drives water out of the large fluid compartment that you are carrying around. The result is you become gradually LIGHTER which makes you more efficient, your blood plasma volume is better maintained so you are less likely to bonk/hit the wall and you may not need to drink at all during a marathon.<br />
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This is just one benefit of training HOT. If you are out running feeling thermally comfortable then you are probably missing one important physiological adaptation to homeostasis.<br />
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References:</div>
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<a href="http://www.ncbi.nlm.nih.gov/pubmed/3759782" target="_blank">Kirby CR, Convertino VA (1986) Plasma aldosterone and sweat sodium concentrations after exercise and heat acclimation. J Appl Physiol 61, 967-970.</a></div>
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Unknownnoreply@blogger.com5tag:blogger.com,1999:blog-2980004124283593961.post-61014711851542918512015-04-24T09:45:00.000+01:002016-01-28T17:43:07.937+00:00Virgin Money London Marathon 2015 - Pre-race thoughtsSo, this year my race preparation has consisted of more miles than in previous years (Figure 1). In the 8 week run-up to the week before London I covered an average of 130.5 km per week at an average pace of 4:50.3 mins per km.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-pjkOeJdZd1kzEiR1eUoGKvBNSqH2PDf0mvh6pWNYyEuXYNaffZne0gyJ4oeibvb39x3_XTBX_nSyy4gRjc8LWA47r3dwVWuGGHNnhYpVDymQTRbBkmoHEvywCtj-afzzmLBnQiUXpV8/s1600/New-1.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="124" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-pjkOeJdZd1kzEiR1eUoGKvBNSqH2PDf0mvh6pWNYyEuXYNaffZne0gyJ4oeibvb39x3_XTBX_nSyy4gRjc8LWA47r3dwVWuGGHNnhYpVDymQTRbBkmoHEvywCtj-afzzmLBnQiUXpV8/s1600/New-1.jpg" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1. Strava plot of my weekly distance (km) with the peak week (181 km) marked as the darker column.</td></tr>
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Most of the runs during that period consisted of commutes to and from work (12.5km each way) with a light rucksack and heavy trainers. At the start of the year I was wearing some Saucony Echelons which I later discovered were the source of heel pain (my heel spur was hitting the rather hard plastic support and bruising it). I threw them away about 4 weeks ago and the heel pain has subsided dramatically.<br />
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I think the distance training has had an effect. I accidentally put in a 5km PB last weekend after two years stuck around 18:40. It was a soft target since I don't think I have attempted a fast 5km for sometime. But, the PB may not reflect my full aerobic adaptations since I was not in race kit and rather fatigued. I suspect I may be able to go a little bit faster - we will see.<br />
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My weight is finally back down to 60 kg (7 am weight - neither glycogen depeleted nor loaded). I would have liked to be a bit lighter, but this year I have paid less attention to it. I have resumed an Alpen breakfast, no lunch and normal tea regime. Tea in the evening usually involves more calories than most would happily eat....The 'skipping' lunch remains a deliberate strategy to force my second run of the day to bias away from carbohydrate metabolism and to ensure that during my evening feed my muscles are 'eager' to clear the glucose from my blood stream. It also creates a bit more time in the day for work: running has been eating into my working day.<br />
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The heavy shoes and running with a rucksack were designed to promote a general 'overload' response and produce a bit more muscle. But, I was being - perhaps - a bit too conservative because I wanted to ensure hitting a reasonable distance each week - I will use a heavier load in my next training period. Equally, I wore a coat - and earlier in the year - my pink hat and gloves to provide a thermoregulatory stress. There are three reasons for this. First, the warmer arms ensure that my sweat glands remained trained. They are essential for losing heat during a race (when the heat load rises tremendously). Second, the additional blood flow to the skin during training (in an attempt to lose heat) produces an additional cardiovascular load that won't be present during the race. The effect is that the cardiovascular training component of the run increases without having to run faster. This is critical for the older runner where high running speeds cause significant damage and limit training. Third the effect of this additional cardiovascular load during training is to promote plasma volume expansion. This is what results in the 'blood doping'-like effect of prolonged endurance training together with remodelling the heart around a larger stroke volume.<br />
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During the training block I did have a rather steep increase in distance - which luckily didn't break me. It was an attempt to see what sort of training a 2:45 marathon runner might look like. I did two weeks of it and decided that it might be something I could attempt in the future. I then rapidly regained my senses and dived into the London taper.<br />
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My taper is, as a result of the high distance, rather short. Currently my thigh muscles are twitching away and I am wondering if I have got it right. But, as usual I need to decide what to do at London.<br />
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Since I am a scientist I need to weigh-up the evidence. The training-based marathon performance correlation equation (Tanda) - based solely on how far and how fast I have run in the 8 weeks before the race - predicts around a 2:54 marathon. But, I have pushed that correlative equation into 'full causation-mode' and well outside from the dataset that Tanda used to produce the coefficients. This form of extrapolation makes it unreasonable to expect the equation to be more than a general indication of my likely performance - although it has been rather good in the past. My training diet has been a monoculture of relatively slow short distances with little race-specific training. However, much of it was done with coat, heavy trainers and a rucksack. So there are reasons to believe that I might either be in worse or even better shape than the formula suggests. My heart beats per km (a measure based on heart rate at a given speed which I have used to predict previous marathon performance) agrees with Tanda at around 2:54 - but, I have optimized my training to bring my heart rate down. The result of biasing my training in that way is that I may have broken that predictive formula too by failing to attend to other training adaptations. Finally my age-graded 5 km performance projected to a marathon is also around 2:54 - but, such predictions require that you follow some average aerobically-limited declining function with distance. Such predictions have over-estimated performance for me in the past and I have not - on the whole - been able to produce the long distance performance that my 5 km suggests.<br />
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Now, whilst almost all objective measures say that around 2:54 should be possible, my brain does not. This is, of course, a problem, and one of my own making. My training has not been 'steady-state' but consisted of a fairly steep and consistent increase in load with a progressive improvement in fitness that I have not really been able to test by racing. I suspect that what makes my brain adapt to improvements, in the absence of racing, may well be a slower time course than the physical adaptations. It is perhaps the key value of races - they provide hard fast efforts that are powerful confidence builders (i.e. mental confirmation of physical attributes that can only be known through testing them).<br />
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So, the aim here is a longer term one. I think high mileages may well produce results - given the appropriate training duration. Clearly, my short exploration into that area is not yet long enough to expect the proportionate results. Once London is over the real training begins - a longer haul towards 2:45. Quite how far I get before I either break or fail is part of the fun - but, I remain convinced that for most normal healthy people the limit of performance remains the extent to which they are willing to force training adaptations and the strategy they use to do so.<br />
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For London I am starting in Green Pen 2 - which is where the 3:15 runners are. I will get a sensible slow start there and plan a first mile around 7 mins per mile. Then I plan to gradually ease to 145 beats per minute which I should hit at close to 6:45 mins per mile. Then it will be a matter of keeping heart rate below 154 to halfway - how close I get depends on the conditions. I hope by then to have an average pace of a second or so faster than 6:45 per mile. The trick will be to manage the heart rate rise smoothly to about 162 at the end. I will look and see if I can find 'The Wall' at 20-23 miles. If I can't find it I will try and approach my aerobic limit for the last 3 miles - thanks to the inhaler my breathing feels like it can be tested. Ideally I don't want to push the last 800 m - but, I guess that is racing. If my heart rate rises faster than I expect I will deliberately slow down.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2980004124283593961.post-82885198225488093572014-11-26T18:18:00.001+00:002016-01-28T17:43:45.133+00:00Thinking new stuff: 3D printingComputers are great in so many ways - not least their ability to consume time, vast amounts of it. But, in the process of filling that space between birth and death they provide a good degree of fun. <br />
<a name='more'></a>During the first flush of my youth one kilobyte of RAM was plenty to occupy me for hours at night - occasionally I forgot to go to sleep and my parents found me early in the morning 'back' on my computer. I committed Op codes to both my memory and the altogether more volatile RAM with easy and programmed directly in ASCII symbols (no interpreters were available back then). Then games came along - like C, UCSD Pascal, and CPM before eventually giving way to other challenges. There was definitely a divide between doing stuff and using a computer. The computer output was, at best, inky paper of some description - mere words or symbols. But, by the early 1990s things were beginning to change and computer interfaces were making control of the external world possible. Data collection interfaces were able to control amplifiers, valves and solenoids. There was definitely much fun in that. The real fun has, however, taken 20 years to reach the man on the street. We are now in the decade of the 3D printer. The device that allows you to dream an object into existence. Where before 'crafting' skill was required to produce objects of either utility or beauty, now only a clear head and a moderation of computing skill are required. Of course, for most of us, the objects that can be produced are limited to those suitable for heat moldable plastics. Nevertheless the possibilities are nearly endless.<br />
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For the scientist 3D printer knowledge will become a 'must-have' skill. Have you used Slic3r? Do you know what Gcodes are? At what temperature does ABS flow? How is your heated bed? Is your Bowden tube clear?</div>
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I started, as many parents do, with an excuse. It was my son's 17th birthday. Ah, hah - what you need is a 3D printer! A tad on the expensive side, but what fun. That is when the time-consumption began. After construction, commissioning and trouble-shooting the best part of a month had gone. But, then the objects began to appear. Need some tri-bars for a bike? No problem - <a href="http://www.thingiverse.com/thing:395291" target="_blank">here</a> are some that I designed and made: a hundredth of the price and a tenth of the weight of the commercial version - and unique to boot. How about a <a href="http://www.thingiverse.com/thing:455850" target="_blank">microscope</a>, we can do that too with a unique twist. My son is, of course, now a dab-hand at turning out his own objects - including a rather nice set of dimbled and ragged fans for a physics project.</div>
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I now find myself looking at objects and wondering - could I do better? Well, the feet for our step stool aren't great in ABS - rubber would have been better. However, the plastic house numbers certainly would do the job if only someone would put them up. But, time is short and there is more design work to be done. This time it is a big project: I need to print myself a tidy office. Now, ABS or PLA?</div>
Unknownnoreply@blogger.com2tag:blogger.com,1999:blog-2980004124283593961.post-44626591689675502142014-10-09T12:09:00.002+01:002016-01-28T17:44:37.753+00:00Radio 4: The Philosopher's Arms - Sex EqualityI much prefer arguments that are based on facts rather than 'urban myths' or extrapolations 50 years into the future. I was listening to the Philosopher's Arms on Radio 4 and heard (12min 55s in to the episode on <a href="http://www.bbc.co.uk/programmes/b04jjz47" target="_blank">Sex Equality</a>) the often repeated claim that Women<i> can</i> run faster than Men over long distances. I think it was <a href="http://www.beatrixcampbell.co.uk/" target="_blank">Beatrix Campbell</a> talking and, in this case, the <a href="http://www.dailymail.co.uk/news/article-2420999/Women-day-faster-long-distance-running-men-predict-experts.html" target="_blank">Daily Mail</a> seems to be more accurate! <br />
<a name='more'></a>The particular claim was that if Paula Radcliffe were to run another 20 km over marathon distance she would beat the Men because Women respond better at the 'fatigue, burn, horror point'. Now, I have several problems with this (and we will leave this 'fatigue, burn horror point' for another post), but before providing a bit of evidence let us consider a proceeding statement she made since it tells us a little about her.<br />
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Beatrix is ~67. Her claim was to be able to run a half marathon in the time it takes Paula to run a full one. Now Paula is not currently in peak shape - so let's assume Beatrix knows this - and go with a time of 2:20. This would give Beatrix an age-graded performance of ~70% making her a very decent Club-level runner. She must have done some training to be able to achieve this level. It is roughly the same performance level - if extended to marathon distance - that would get her good for age entry to many marathons (including London).<br />
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So, what is the evidence that over longer distance Men are trounced by Women? The 50 km road record for Women is 25 minutes slower than for Men. OK, may be that isn't long enough - not beyond the fatigue, burn, horror point. At 100 km things look like they might be closing with the Women's record only 20 mins slower. But, at 160 km (100 miles) on road Women have dropped back to 2 hours slower than Men and on the track at 160 km Women are almost 3 hours slower. The 24 hour records are similar with Men covering 43 km more than Women.<br />
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So, what might explain this? One possibility is that Beatrix is right, and that we are not comparing like-for-like athletes. Because more Men run than Women, the World Records for Men are closer to the limit than for Women - i.e. we still have not had the 'Paula Radcliffe' type of Woman do the race that goes beyond the fatigue, burn, horror point. But, even if that is true the wonderful powers that Women have that Men don't must be a very minor one. Whilst the predictions were that Women would be beating Men by around the year 2060 things have <i>not</i> got off to a good start over the past 10 years. We have seen a gradual improvement in Men's marathon times - whilst the Women's record is stuck at Paula's record in 2003. Indeed, very few Women have even got close to this level of performance. Something will have to radically change for the 2060 prediction to come true.<br />
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The simple fact here is that Men's physiological/anatomical make-up is different from Women. The hormonal background and anatomical structures put Women at a disadvantage. There are many differences, but the most obvious two are that training in Women does not induce as much muscle mass (there is a particular steroid to blame) and Women, even athletic Women, have larger breasts than Men. As far as running performance is concerned these represent performance 'barriers'. This is not sexism, it is just a difference.<br />
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I think the critical point here is that there are very few male club runners who have not been 'chicked' at some point. In fact most men in my club - including me - are 'chicked' in every race if one of a dozen female's turn-up. They are awesome. Do I care whether they can beat the fastest Man? No. They are beating not only me (and I take things pretty seriously) but also other Men who I aspire to beat one day.<br />
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It is time to stop looking at times, and start looking at age/sex graded performance. At 70% Beatrix I am willing to race you. You <i>will</i> finish behind me (I am a younger male) but you might win!Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2980004124283593961.post-50711127717050474882014-10-09T10:13:00.002+01:002016-01-28T17:45:15.302+00:00How much do I want that Snickers?I was just mulling over one particular 'theoretical' benefit that might
be gained by slow long runs. In my current case it is in the early taper stage before a marathon, but it applies to just about any time. One aspect that I
thought would be interesting to guesstimate is what might the 'weight-loss'
benefit to marathon improvement time be of a single run, since I don't have a 'ball-park' figure in my brain.<br />
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For me - at my last fast marathon I was roughly 60kg and ran 3:05 (to a
first approximation). Assuming I maintain the same aerobic ability and
just got rid of some 'mass' (which for the sake of this calculation we will assume is fat) then one source claims roughly 2.5 mins per
kg lost (with all the usual 'ifs and buts'). I am fairly confident that this <i>could</i> apply to me since I still have a good deal of abdominal fat. <b>If you are skinny as a rake - don't read this: it does not apply to you - go look for improvements elsewhere!</b><br />
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Fat has an approximate energy content of 9 Cal/g and for my normally-clad training run (multiple layers and heavy shoes) 1 km uses
roughly 70 Cal. So (big 'if' here) one was to fuel all of the run with fat
that would equate to ~8g of fat lost per km. Putting that weight loss
into the '2.5 mins per kg faster' gives ~1.2s improvement. Or, for a
20km run the 160g of fat that <i>might (immediately or eventually) </i>be used gives 24s improvement in
time.....<br />
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I know there are many 'ifs and buts', but I would not have 'ball-parked'
the theoretical number for the 'potential single-run induced
weight-loss related improvement' anywhere near that. If forced to guess I
would have said something about ten times lower.....<br />
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Of the 'ifs and buts' the critical one is to avoid consuming more
calories as a result of the longer run - that would stuff it completely.
Very slow running would take the maximum from fat whilst running and
preserve more of the carbo stores such that eating normally would top
them up again. Going faster would mean achieving only a partial
refilling of carbo stores after the run - i.e. one would gradually
pull-down the carbo store and be living generally on empty....Either way
the fat gets burnt - during the run or generally after the run (except possibly with a weaker, more hungry feeling...).<br />
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I like the idea of generating the marathon-time cost of foods. For me a
Snickers costs at most 4s (this is an 'at worst'-calculation predicated on the basis that a Snickers contains no useful nutrients and just gets turned into fat).....<br />
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For me the cost of a treat is, currently, not measured in £ and p but in seconds! This really is a 'First World' problem....Unknownnoreply@blogger.com2