Wednesday, September 14, 2011

Mathlete Takes a Tumble, But How?




My blogger name is "Mathlete" because in my spare time I'm a triathlete. There is a whole lot of physics in swimming, biking and running. I learned this past weekend there is also a lot of physics in crashing. I was racing in the Mighty Hamptons Olympic Distance triathlon (1 mile swim, 24 mile bike, 6.2 mile run) on Sunday and about half way through the bike section, my back wheel stopped rotating and I ended up falling (for gross pictures, see below). After getting over the shock, I looked to see why my wheel had stopped. I have spent 3 days trying to use physics to explain what I saw and simply have not been able to. Can you guys help?


When I looked at my back wheel, I saw that a water bottle, 2/3 full of gatorade, had lodged itself half between my spokes. The bottle was about half way through, parallel to the axis of rotation of the wheel. I have a fancy dancy Cervelo P3 (affectionately named Firebolt) with an airplane wing frame so for aerodynamic reasons, I have the water bottle cages behind my saddle instead of on the frame. That is the problem set up, a water bottle launching and ending up in the spokes. So, hmm...




The way I see it, when I hit a bump the bottle got enough upward momentum to launch out of the cage. The cage is tilted slightly back so the bottle trajectory should be up and back. Because of the weight of the bottle due to the gatorade, I will neglect air resistance. At the same time the bottle is launched, the back wheel is turning counterclockwise and the whole wheel is moving forward at, lets say, 18 mph. One would expect the trajectory of the bottle to take it far beyond my wheel and if anything, cause trouble for the cyclist behind me. With the wheel moving forward and the bottle moving backward, this seems more than reasonable. about 5 minutes before the "incident" I had taken a drink of gatorade so I know the bottle was firmly in the cage.

But that is not what it did. Somehow its path took it up and out in a direction parallel to my forward motion and also in a direction perpendicular to my direction of motion. One I understand, one I do not. Where did the momentum in the perpendicular direction come from? How did it turn and lodge itself squarely in my wheel, jamming itself right through the spokes?Does anyone have any ideas? There were three physicists looking at my bike set up and for the life of us we couldn't figure it out. Here are some things to think about. Might I have a problem in the way I'm looking at the problem? Are the assumptions I'm making about the initial bottle trajectory correct? I was in the process of passing someone so in reality probably going above 18mph, and I hit a really rough patch of road with four or five good potholes in a row. Any suggestions welcome.


If you are interested, the Firebolt is ok, but broke a spoke. I finished the race though the second half of the bike section wasn't so good as I was riding a fairly broken bike. The run section was survivable and once I realized I could run on my leg, I picked up speed, though my time was still pretty bad. Hopefully the physics involved in my next race will push me forward fast and not let me end up with my wheels in the air and rear on the pavement. At least the swim was good!


WARNING, GROSS PICTURE BELOW!!!!!!!













2 comments:

  1. Even though the bottle came out of its cage, it is still moving at 18 mph along with you and your bike. The bottle does not immediately stop when it becomes disconnected, but does slow down because of air resistance. In the short time the bottle has to fall from your saddle to the wheel, the bottle probably does not slow down much.

    Think about it as if your bike was stationary and the bottle was jolted out. The bike would stay put and the bottle would land right on top of the rear wheel. Ignoring air resistance, the bottle would follow the same path whether the bike was still, moving at 18 mph, or moving at 100 mph.

    As far as the rotation, the bottle probably did not come out of its cage cleanly and it had some rotation motion to it.

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  2. I think you deserve a Black (& Blue) Knee, the biking equivalent of the military's Purple Heart.
    I was a firefighter / EMT once. As I would have said had I been there, "It's a long way from the heart. You're gonna live."

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