Physics and the track banking

Since we had a brief conversation about this tonight related to the 500m, here's some science to explain why at race pace you need to actively think "LEAN INTO THE TURN!"

Let's pretend there's no friction, no air resistance etc.. When you go around a turn, you're body feels like it is pushed in the opposite direction. This is why, when going fast, you feel like you're pressed into the bike. This force is equal to mV^2/R where m is your mass, V is the velocity, and R is the radius of the turn.

When you're on an incline, like the banking of the turn, you have a force perpendicular to the track. The part of this force that pushes towards the center of the turn (meaning opposite of the force we talked about above) is mgcos(theta) where m is your mass, g is the acceleration due to gravity, and theta is the angle of the track surface.

So, when these two forces are exactly in balance, you will not have any tendency to move up or down track -- you'll just follow the line and your bike will be exactly perpendicular to the track.

This means:

mV^2/R = mgcos(theta) => V = sqrt(Rgcos(theta))

The mass of the rider is no longer important! So it doesn't matter if you are 100 pounds or 1000, the result is the same. Using some geeky methods (as if this wasn't geeky enough), the radius of turns 3 and 4 is about 25m. If the banking is 33 degrees, this gives a speed of about 32 mph as the "neutral" speed.

So, if you are going faster than 32 mph, you will need to actively lean or turn while in turns 3 and 4 to keep the same line. If you are going less than that, you will not be perpendicular to the track (like when you ride really slow). For reference, 32 mph average over 200m will give you a 13.9 time.

There are some other forces that come into play in reality, like friction. But, neglecting that, you get a pretty good estimate of why you really need to work on actively leaning at speed in the turns.

There's other fun physics I could give you, but that's enough to digest for now!

Tim