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General Model
of Rider on Surface

  There are situations where we would like to model a rider following a arbitrary path on some arbitrary surface. Perhaps we would like to test a sprint tactic or an idea for a path for a flying 200. We have a model now that is general enough to do this.

Results show that selecting one path over another in a flying 200 can make a difference of four or five places in match sprint seeding at a national level competition.

In a pursuit context the model shows that times are different on different tracks. If one wanted to pick a track for a record attempt, one would want to analyze each of several tracts to see which one would be fastest. If one were setting qualification times one would want to compare the qualification venue to the competition venue.

The model takes into consideration lean in turns along a rider's path. A leaning rider's center of mass follows a different, shorter path than the path of the rider's wheel. An analysis of this is at "Analysis of Lean in Flying 200"

One of the first question posed was "Is there an advantage to riding wide in the straight in a pursuit?" An analysis can show when this is true and estimate the benefit.  "Riding Wide, Pursuit"

Most questions of this nature deal with small differences. We have done calculations for many situations, and it's clear that the answer depends on the surface, path, and rider. One must do the calculations or one is just guessing at what is best.

Applications for the model:
  • Best path for a flying 200. For an example see "How Should I Ride My Flying 200?"
  • Benefit from different patterns of power application (energy budget)
  • Quantify improvements from improved techniques and equipment
  • Match sprint tactics
  • Best track for records attempt
  • Selection of qualification times
  • Optimal path for exchange in team pursuit
  • Analysis of cadence along path
  • Finish of a criterium or road race
  • Best place to attack in criterium or road race
If you are a coach or rider or represent a federation or team that has an interest in applying this model in a competitive situation, please contact us.


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The model starts by defining a surface. A velodrome can be defined based on simple parameters such as the radius of turns, length of straights, and banking. Or it could be defined in greater detail by giving a list of points on a surface in terms of distance from a starting point, width, slope tangent to the direction of the surface, slope radial to the direction of the surface, and direction/angle of the measurement line. This approach allows many different surfaces to be defined including the finish of a criterium or an entire road course.

The first example is the finish of a road course with a long downhill through a long-radius sweeping turn to an uphill finish. The second example is of a velodrome.


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The model continues by defining the path of a rider on the surface. The path could be along the measurement line as in a pursuit or it could be a path along the rail with a dive to a start line as in a flying 200. It can be any arbitrary path that can be defined by a distance along a measurement line and a corresponding distance away from the measurement line as measured in the plain of the surface.

The first example is a Flying 200 path on 250m velodrome. The second path is a Flying 200 path on a 200m velodrome.


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The model uses standard equations for estimating forces on a rider due to air drag, rolling resistance, and slope. See the Glossary for more explanation.

 
Rider power can be any function of time. The shape of the power function for a sprint is often about the same. The parameters for maximum power and average power can be used to control the shape.

The model writes the differential equations of motion for the rider (sum of the forces equals mass multiplied by the acceleration of the mass). The equations take into consideration the instantaneous curvature of the rider's path and the rider's lean.

The model solves the differential equations for the displacement, velocity, and acceleration of the rider's center of mass and point of contact with the surface.

The model provides plots of elevation, grade, curvature, speed, cadence, and g-force along a rider's path. Plots also show the rider's lean in relationship to a rider's point of contact on the surface.
 
Example of table of output from an analysis of a flying 200. This was on a 200 meter track with steep turns. Notice that the center of mass travels less than the nominal 200 meters.
Length of Path relative to Measurement Line 285.00 m
Length of Path of wheel 297.50 m
Length of Path of center of mass 289.42 m
Fly 200 time 12.144 s
Total time to cover path of center of mass 19.343 s
Length of path of center of mass in final 200m 193.89 m
Average speed for center of mass in final 200m 15.97 m/s
Average speed for nominal measurement line distance in final 200m 16.47 m/s
Speed at 200m-to-go line 15.68 m/s
Total work from start of effort 11151. N m
Total work for Fly 200 4354. N m
Speed (m/s) along the path of a rider's center of mass. As a rider leans and the center of mass goes down, the rider increases speed just like a roller coaster, slow at the top, fast at the bottom. This feature is often ignored in models, but it is included in this model since we are looking for very small changes.
Lean of rider at points along path in relationship to position on surface.
Rider lean along path. This is on a track with 50 degree banking in the turns.
G-force on rider. This is on a track with 50 degree banking in the turns.
Copyright © 2000 Tom Compton All rights reserved.