{"id":782,"date":"2012-08-06T19:25:36","date_gmt":"2012-08-06T18:25:36","guid":{"rendered":"http:\/\/www.sungate.co.uk\/?p=782"},"modified":"2015-09-04T14:52:15","modified_gmt":"2015-09-04T13:52:15","slug":"thought-experiment-could-i-beat-usain-bolt-over-100m-on-my-bike","status":"publish","type":"post","link":"https:\/\/www.sungate.co.uk\/?p=782","title":{"rendered":"Could I beat Usain Bolt over 100m on my bike?"},"content":{"rendered":"<p>Question: Could I beat Usain Bolt over 100 metres, if he ran and I biked?<\/p>\n<p>First thoughts: it might be possible, but I need to do some calculations to get an idea of whether it&#8217;s feasible or not.  <\/p>\n<p><a href=\"https:\/\/www.sungate.co.uk\/wp-content\/uploads\/boltvbike.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.sungate.co.uk\/wp-content\/uploads\/boltvbike.jpg\" alt=\"Usain Bolt running, Chris Hoy cycling\" title=\"Usain Bolt v Bike?\" width=\"500\" height=\"200\" class=\"aligncenter size-full wp-image-813\" srcset=\"https:\/\/www.sungate.co.uk\/wp-content\/uploads\/boltvbike.jpg 500w, https:\/\/www.sungate.co.uk\/wp-content\/uploads\/boltvbike-300x120.jpg 300w, https:\/\/www.sungate.co.uk\/wp-content\/uploads\/boltvbike-150x60.jpg 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/p>\n<p>To win the Olympic Gold on Sunday, Bolt ran 100 metres in 9.63 seconds.  That&#8217;s an average speed of 10.37m\/s.  The first thing one needs to figure out is: can I bike that fast?  Because if I can&#8217;t even match his <em>average<\/em> speed, then I clearly can&#8217;t beat him.  The speed 10.37m\/s is equivalent to 37.34km\/h (23.2mph): I can certainly ride faster than that over short distances; I might be able to manage 50km\/h (31mph) at a stretch.  So, as the MythBusters say, we are at the &#8216;Plausible&#8217; stage thus far.<\/p>\n<p>The key to this will be to attain top speed as quickly as possible.  I can certainly bike faster than Usain Bolt can run <em>but only once I&#8217;ve reached top speed<\/em>.<\/p>\n<p>Let&#8217;s assume a simple mathematical model for this task.  For calculation purposes, consider the 100m race split into two sections: <\/p>\n<ol>\n<li>Accelerate smoothly from stationary to top speed, and then <\/li>\n<li>Continue at that top speed until the end of the race.<\/li>\n<\/ol>\n<p>It&#8217;s probably a reasonable model for cycling over a short distance.  With this model, we must make two assumptions to plug into our model:<\/p>\n<ul>\n<li>What is my top speed? (let&#8217;s call this <em>V_max<\/em> for &#8220;Velocity-max&#8221;)<\/li>\n<li>How quickly can I reach that top speed? (let&#8217;s call this <em>T_accel<\/em> for &#8220;Time to accelerate to max velocity&#8221;)<\/li>\n<\/ul>\n<p>Calculating one&#8217;s finishing time for 100 metres based on the above model works as follows.  Ignore this bit and skip to the table below if aren&#8217;t interested in the method and just want to see the results:<\/p>\n<ul>\n<li>Given <em>T_accel<\/em>, one must calculate the distance over which the acceleration takes place.  This is calculated as <em>(V_max*T_accel)\/2<\/em> &#8211; let&#8217;s call that distance <em>D_accel<\/em><\/li>\n<li>Assuming that we finish accelerating before we reach 100m, we then work out how long we take to finish the remaining <em>100-D_accel<\/em> metres, riding at our top speed of <em>V_max<\/em>.  Let&#8217;s call that time <em>T_steady<\/em>, beecause it&#8217;s the time we spend at our steady top speed: <em>T_steady = (100-D_accel)\/V_max<\/em><\/li>\n<li>Our finishing 100m time <em>T_finish<\/em> is therefore: <em>T_accel+T_steady<\/em><\/li>\n<\/ul>\n<p>To make everything work properly, units of measurement must be consistent.  Times must be measured in seconds, distances in metres and speeds in metres per second.  Conversion between &#8220;metres per second&#8221; and &#8220;kilometres per hour&#8221; is very simple: one metre per second is 3600 metres per hour, i.e. 3.6km per hour.  Let&#8217;s try running the numbers with <em>V_max<\/em> speeds of 12m\/s, 13m\/s and 14m\/s (equivalent to 43.2km\/h, 46.8km\/h and 50.4km\/h).  What about acceleration times?  I&#8217;m less sure of suitable values here, but let&#8217;s try 5 seconds, 7 seconds and 10 seconds.<\/p>\n<table>\n<tr>\n<th align=right>Top speed:<\/th>\n<td>12 m\/s<\/td>\n<td>13 m\/s<\/td>\n<td>14 m\/s<\/td>\n<\/tr>\n<tr>\n<th>Acceleration time:<\/th>\n<\/tr>\n<tr>\n<td>10 seconds<\/td>\n<td>13.33<\/td>\n<td>12.69<\/td>\n<td>12.14<\/td>\n<\/tr>\n<tr>\n<td>7 seconds<\/td>\n<td>11.83<\/td>\n<td>11.19<\/td>\n<td>10.64<\/td>\n<\/tr>\n<tr>\n<td>5 seconds<\/td>\n<td>10.83<\/td>\n<td>10.19<\/td>\n<td>9.64<\/td>\n<\/tr>\n<\/table>\n<p>Aha!  If I can get my speed up to 14m\/s (50.4km\/h or 31.3mph) in five seconds and hold that speed, I can finish in 9.64 seconds, just 0.01s behind Usain Bolt, based on Sunday&#8217;s performance!<\/p>\n<p>Is that possible, could I do that?  It sounds like an awfully tall order.  I can beat Bolt if I can go faster or accelerate quicker than above, of course, but realistically I think that&#8217;s beyond my capabilities.<\/p>\n<p>If <em>I<\/em> can&#8217;t do it, what about real cycling professionals?  Let&#8217;s apply the same sort of mathematical model to the recent Velodrome cycling at the Olympics, I see some sprint cyclists recorded &#8220;first lap&#8221; times of just over 17 seconds.  This is a distance of 250 metres from a standing start.  If one assumes a smooth acceleration over the entire lap I calculate that these cyclists pass 100 metres at around <strong>10.7 seconds<\/strong> (detailed calculations available on request) &#8211; Bolt still wins.  However, if the cyclist achieves top speed much earlier in the lap, they will reach 100m sooner.  Jason Kenny completed his gold-medal-winning sprint final 200m (not quite a full lap), presumably at his absolute top speed, in around 10 seconds: this is an incredibly quick 20m\/s (72km\/h or 45mph!). So how quickly would he be able to complete 100m, from a standing start?  Assuming a top speed of 20m\/s, to reproduce the 17 second first lap time, this would be a 9-second acceleration (covering 90m in that time) and a further 8.0 seconds to cover the remaining 160m at 20m\/s; as a side-effect that shows us that such a cyclist would cover 100m in approximately <strong>9.50 seconds<\/strong>.  This beats Bolt!<\/p>\n<p>To answer my own question: could <em>I<\/em> beat Usain Bolt over 100m on my bike?  <strong>No.<\/strong> Not a chance.<\/p>\n<p>Further question: could <em>any<\/em> cyclist beat Usain Bolt over 100m?  <strong>Possibly, just<\/strong>, although it might be very close.<\/p>\n<p>I wonder how fast I could actually bike 100 metres, though, from a standing start?  I think I should try timing it&#8230;<\/p>\n<p>And of course it goes without saying that I&#8217;d be able to beat the sprinters over <em>200m<\/em>, because I&#8217;d be up to top speed for longer \ud83d\ude42<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Question: Could I beat Usain Bolt over 100 metres, if he ran and I biked? First thoughts: it might be possible, but I need to do some calculations to get an idea of whether it&#8217;s feasible or not. To win the Olympic Gold on Sunday, Bolt ran 100 metres in 9.63 seconds. That&#8217;s an average&#8230;&nbsp;(<a href=\"https:\/\/www.sungate.co.uk\/?p=782\">read more<\/a>)<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-782","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/www.sungate.co.uk\/index.php?rest_route=\/wp\/v2\/posts\/782","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sungate.co.uk\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sungate.co.uk\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sungate.co.uk\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sungate.co.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=782"}],"version-history":[{"count":55,"href":"https:\/\/www.sungate.co.uk\/index.php?rest_route=\/wp\/v2\/posts\/782\/revisions"}],"predecessor-version":[{"id":1203,"href":"https:\/\/www.sungate.co.uk\/index.php?rest_route=\/wp\/v2\/posts\/782\/revisions\/1203"}],"wp:attachment":[{"href":"https:\/\/www.sungate.co.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=782"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sungate.co.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=782"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sungate.co.uk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=782"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}