{"id":640,"date":"2016-07-15T20:59:20","date_gmt":"2016-07-16T00:59:20","guid":{"rendered":"http:\/\/www.tjkopena.com\/blogs\/outdoors\/?p=640"},"modified":"2018-03-07T02:02:33","modified_gmt":"2018-03-07T07:02:33","slug":"should-froome-run","status":"publish","type":"post","link":"https:\/\/www.tjkopena.com\/blogs\/outdoors\/2016\/07\/should-froome-run\/","title":{"rendered":"Should Froome Run?"},"content":{"rendered":"

Yesterday, Tour de France yellow jersey bearer Chris Froome was caught up in a crash approaching the end of\u00a0the monstrous finishing climb up Ventoux caused by the congestion of spectators. His bike broken but with no team or neutral support car in sight, he started running up the hill.<\/p>\n

Let’s set aside all questions of whether it matters or not that Froome broke a rule (UCI 12.12.14<\/a>: Attempt to be placed without having covered the entire course by bicycle), and the more important\u00a0question of why don’t the ASO and UCI do more to ensure safe and fair courses. Here’s a much\u00a0smaller\u00a0but still interesting question:\u00a0Did it\u00a0make sense for Froome to start running?<\/p>\n

I would argue that it doesn’t make sense from the perspective that\u00a0he took a big risk on slipping & falling, twisting an ankle, or any number of other problems by running in his cleats. But, purely from a time perspective, did it make sense?<\/p>\n

That turns out to be not as obvious as it might seem. A smart friend who’s an\u00a0experienced racer &\u00a0official made the reasonable point that you want the support car to catch up to you as quickly as possible. Being on a bike is much faster than being on foot, so\u00a0running away from the car and prolonging the time it takes to get a new bike doesn’t make sense.<\/p>\n

My argument was that if the car is blocked from getting to you quickly, you should continue moving forward. Once it clears any slowdown, i.e., the crash site, its speed will dwarf the distance you’ve gained, so you won’t be penalized by running from it. Therefore, in the interim, while the car is slowed or blocked, you should gain what ground you can. Otherwise you’d just have to cover that distance anyway, but after standing around waiting\u00a0and wasting time.<\/p>\n

Model<\/h2>\n

To investigate I wrote a simple simulation. The model works\u00a0as follows.<\/p>\n

\"Scenario
Scenario at T0.<\/figcaption><\/figure>\n

At time zero the racer\u00a0starts running or waiting patiently at distance zero, the crash site, while the support car is some distance behind.<\/p>\n

\"The
The car passes the crash site and starts moving at its full speed.<\/figcaption><\/figure>\n

The car moves at its blocked rate until it passes the crash site, at which point it starts moving at its free rate. The racer meanwhile moves at their running rate.<\/p>\n

\"The
The car catches the racer and gives them a new bike.<\/figcaption><\/figure>\n

Eventually the car catches up to the racer, who then switches to their new bike and a faster rate\u00a0of travel.<\/p>\n

\"The
The finish!<\/figcaption><\/figure>\n

The racer then eventually\u00a0pedals on to the finish some distance ahead.<\/p>\n

Simulation<\/h2>\n

A program implementing that model is very simple. I wrote one in Go:<\/p>\n

\"Screenshot_2016-07-15_18-18-20\"<\/p>\n

You can play with it yourself in your browser using this link<\/a>. Hit the Run button up top, and in a moment the output will show up at the bottom of the screen. You can change the scenario by altering the parameters starting on line 17:<\/p>\n