I lose more speed on turns in 300's than either 200's or 400's. Which makes sense because I hit the turn fastest in a 300.
I've read various things by famous sprint coaches about turns, but I haven't seen a good analysis of the mechanics. How much to lean, and so forth. So I thought up a few basics.
An object in circular motion is accelerated centripetally at a rate of
Ac = v^2/r
In lane 1, at 7 m/s (57 pace), this is approximately
7^2/35 = 1.4 m/s^2
The force needed to accelerate an 80kg body that much is 80x1.4 = 120N or about 26 pounds.
Leaning into the turn aligns the vertical plane of the body to include a centripetal component vector. The question is, how much lean translates the exact amount of force needed from forward running to sideways? I don't know any data about how much force is used to run forward at constant speed. But there is the wild-guess saying that the force of footstrike is 3 times body weight. Perhaps takeoff force is approximately the same. Deducting 1xbody weight, which is required simply to stand still, for a body of mass m this would mean a net takeoff force of
2x2.2m/.22 = 20m Newtons
with a net centripetal force required of 1.4m N, the optimal angle to achieve the turn with "forward" running would be
arccos(1.4/20) = 86 degrees, or a lean of 4 degrees
More generally, for a velocity v, the angle is
arccos(v^2/35/20) = arccos(v^2/700).
A Michael Johnson tearing around the 2nd turn at 9m/s would be optimal at 83 degrees or a 7 degree lean.
Judging from Kiprop at 7m/s
http://www.youtube.com/watch?v=6yOgsaatxTI
and MJ (outside lane 1) at 9m/s
http://www.youtube.com/watch?v=JQ9cBQANjiw
Kiprop seems to be leaning about 4 or 5 degrees while MJ is leaning 8 to 9 degrees. Meaning either
1) my original estimate of forward takeoff force is slightly too high
2) MJ is used to cornering at 10m/s rather than 9m/s
3) They are leaning too much
4) They are leaning extra to "accelerate off the turn"
or, most likely
5) something else at work that I haven't considered yet.
On the other hand, the human middle ear can detect the net acceleration vector and tell when it is parallel to the sagittal plane. So figuring the ideal angle may be a bit like calculating the trajectory of a baseball instead of just catching it. But I'm still getting killed by turns, so analyzing the physics is worth a shot.
Anyone know of some good science papers on turn running? Or how do you run them?