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Analysis:
"Riding Wide, Pursuit"

Riders of pursuits have been observed deliberately riding wide in the straights. Does this have any advantage?

Some velodromes, while they appear to be level all the way around, have turns that are at higher elevations than the centers of the straights. This means that riders have to ride downhill and back up between turns. Riding wide on these velodromes would have the effect of avoiding the "valleys" at the expense of riding further. However, we also see riders doing the same thing in velodromes that are at the same elevation all the way around.

In this analysis we setup two velodromes, one with a measurement line that is level all the way around and one with some slope in the straights. Then we test different paths. The rider has the same characteristics and same power in all cases.

Conclusions:
  • Ride the measurement line on velodromes where the measurement line is level all the way around.
  • Ride a level path on velodromes where the measurement line is not level all the way around.
  • If the ride is really important and small differences matter, do an analysis for each case of interest based on a specific velodrome, path, and rider. Velodromes with different configurations could lead to different conclusions.
Is the time difference significant? The differences shown are of the magnitude of 0.1 to 0.2 seconds at the end of a 4k pursuit. This is a small difference. At the 2000 US Olympic trails it would not have made a difference in the outcome. However, 0.2 seconds at 14 m/s is 2.8 meters; pursuits have been won by less. The numbers below represent accurate values based in the physics and the numerics of the computation.

The Model. The model on which this analysis is based starts by defining a velodrome surface. This can model any velodrome of any complexity. It continues by defining a path to be ridden. The path can be any path a rider can ride on the surface. It continues by writing and solving the differential equations of motion for the rider while the rider rides the path. The differential equations take into account the rider's lean in the turns (a function of speed of the rider's center of mass and the radius of the turn). Lean in the turns causes rides to actually ride less distance. The solution gives distance, speed, and acceleration of the rider's center of mass as a function of time while the rider's wheel traces the path on the velodrome surface.
  Mea Line Wide Path Level Path
Velodrome type Level Slope Level Slope Level Slope
Plots more more more more more more
Nominal path Length (m) 4000.00 4000.00 4000.00 4000.00 4000.00 4000.00
Calculated wheel path Length (m) 3999.84 3999.86 4000.42 4000.26 3999.84 3999.94
Time for pursuit, min:sec 4:42.37 4:42.35 4:42.43 4:42.23 4:42.37 4:42.27
Average speed for pursuit (m/s) 14.17 14.17 14.16 14.17 14.17 14.17
Length of path of center of mass (m) 3922.97 3921.21 3924.41 3922.03 3922.97 3921.46
Average speed for center of mass (m/s) 13.89 13.89 13.90 13.90 13.89 13.89
A rendering of the Adelaide velodrome, a 250m track with a level measurement line. This was used as the model for the level velodrome.

  • Length of straight = 43m,
  • Radius of turn = 82m / Pi,
  • Track Width = 7m,
  • Distance from center of straight to start line = 10m,
  • Slope at center of straight = 12.5,
  • Slope in turn = 43,
A rendering of 250m velodrome with a slope in the straights of 0.6%. This was used as the model for a velodrome with slope.

  • Length of straight = 46.46m,
  • Radius of turn = 25m,
  • Track Width = 7m,
  • Distance from center of straight to start line = 20m,
  • Slope at center of straight = 28,
  • Slope in turn = 42,
  • Slope in straight = 0.6%,
Copyright © 2000 Tom Compton All rights reserved.