Wednesday, May 20, 2015

sprinter speeds crossing the finish at the final stage of the 2015 Amgen Tour of California

Here's a finish line photo of the final stage of the 2015 Amgen Tour of California:

ATOC photo finish

I love photo finish images because the "x-axis" which is usually position in most photographs, is time instead. There's only one spatial dimension. The camera records a slit image of what is crossing the finish line at a given time. So if you measure the "width" of a bike crossing the line, that's how much time it takes for the bike to cross the line. If I assume all bikes are the same length, then speed is inversely proportional to the amount of time taken to cross the finish.

Here's a typical bike geometry chart, in this case for Trek's racing bikes, which have "H1" and "H2" geometry. Note the wheelbases vary from 97.4 to 101.8 mm, a range of 4.5%.

In contrast the Specialized Tarmac goes from 970 mm to 1013 mm, a very similar range.

Cannondale: 962 mm to 1012 mm.

In all, wheelbases seem to vary by around 5% among bikes across the full size range. To get total bike length you need to add on a wheel diameter, and those are very similar (basically all the pro riders @ ATOC were on similar 25 mm tires. I saw only one team on 23 mm). But the sizes vary less between manufacturers than they do between sizes. So generally larger bikes will have longer wheelbase than smaller bikes.

I counted the number of pixels on the full-resolution image of each rider from the front of his front wheel to the back of his rear wheel. Stage results are here. Here's the pixel counts:

place  rider           team              pixels
1      Mark Cavendish  Etixx-Quickstep   262
2      Wouter Wippert  Drapec            265
3      Peter Sagan     Tinkof-Saxo       251
4      Tyler Farrar    MTN-Quibeka       255
5      Tom Van Asbroek Lotto-Jumbo       266

The interesting thing here is that Mark Cavendish was pretty fast, not the fastest but still pretty fast, despite crossing the line in a very unaerodynamic position: a full victory salute. He'd obviously lost some speed by this point.

But there is the issue of the 5% variation in wheelbase, which is around 13 pixels. That's a big source of uncertainty, although I could correct for it by looking up the specific wheelbase of each rider's model and size of bike. But I can also measure just the front wheel length crossing the finish line. Front tires, as I said, should all be essentially the same size with the standardization to 25 mm tires:

place  rider           team              pixels
1      Mark Cavendish  Etixx-Quickstep   107
2      Wouter Wippert  Drapec            107
3      Peter Sagan     Tinkof-Saxo       102
4      Tyler Farrar    MTN-Quibeka       105
5      Tom Van Asbroek Lotto-Jumbo       ???

The result is similar. Sagan was fastest, Farrar next, and Cavendish and Wippert slower but not as slower as you might expect from the parachute-like victory salute. If he's that fast in the salute, how fast was he going before that?

Here's a video of that sprint from Wouter Wippert's bike cam:

That's simply amazing.

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