Average Lap Distance

[Bongle]

I computed a version of the 'fastest possible lap' yesterday, and found that a lap with semicircles at each end and lines for the straights has length:
2(pi*r + 27 - 2r).
and that your best possible time per lap given radius r and friction coefficient u was:
t_total(u,r) = 2*pi*r / sqrt(9.8ur) + 4*sqrt( [27-r]/[4.8u] )

Note that there are many assumptions I made in order to get 'ideal' lap
-Robots are points
-Robots are powerful enough that their acceleration is friction-limited

I think if you steered a 13ft radius corner at each end, thus carrying maximum speed out of each corner, a 5-6 second lap might be possible with a robot that dispenses with all other goals except speed. The best possible time for a friction-limited lap with u = 1.3 that does a 13ft corner at each end is 4.1 seconds. You can go much faster if you do a tight corner, but that's only because we're dealing with 1.3g acceleration along the straight.