Analytic Cycling Logo Pedaling Model

The Pedaling Model can be used to test the effects of changes in position, crank length, and shin length (heel up or down can effectively change "shin length"). It can be used to test the effects of different pedaling techniques and stronger muscle development. How do longer cranks change power output? How is power affected by changing seat position? Do people with shorter shins have an advantage? Different regions within the full range of muscle motion could yield different power outputs. 

The Pedaling Model is more fully described at How Pedaling Model Works. See Figure  1 below for nomenclature.

Pedaling Model Nomenclature

Input Form 

Thigh Length is the distance in centimeters from the point of rotation at hip to point of rotation of knee.  Shin Length is the distance in centimeters from the point of rotation of knee to center of pedal spindle.  Hip's Horizontal Distance is the horizontal distance from vertical line through bottom bracket to point of rotation of hip. Rear direction, positive, forward negative. 

Pedal Model Points is the number of divisions of a complete rotation of the pedals used in the model.  A value of 12 gives good results for most cases.  However, if the torque at the bottom bracket is all in a small portion of the pedal rotation, a larger value will give better results. 

A graphic is produced that shows geometric relationships, torques from the shin and thigh, and forces at the pedals.  Each of the positioned modeled by Pedal Model Plot points can be chosen as a position modeled by the graphic. Plot Position is the position to be plotted and can be any positive integer less than or equal to Pedal Model Points.  The first position is one position clockwise from top.

Thigh and Shin Extensor and Flexor Fit Points are lists of points that the Pedal Model uses to define the Thigh and Shin Extensor and Flexor strength functions. Such lists should be values spaced evenly over a range of motion and are in units of N m. 

Fit Points Example: 

          {0., 88., 200., 232., 240., 232., 200., 88., 0.} 

  • The list begins and ends with "curly braces, {}"
  • Each value must be separated by a comma.
  • The model requires at least four points.
  • Values can be zero; a "zero valued moment function." is {0,0,0,0}. 
    A number in front of the list has the effect of multiplying all the values in the list by this number, i.e., 2 {0., 88., 200., 232., 240., 232., 200., 88., 0.} would give the same result as {0.,166.,400.,464.,480.,464.,400.,164.,0.}. 

     

Sample Output 

Values calculated by the Pedal Model, the input values used for Fit Points, and a graphic are shown below.  The graphic shows the geometry, shin and thigh torques, and forces at the pedals at one position of a pedal rotation are shown below. 
 
Pedaling Model Output 
Length of Thigh  56.0  cm 
Length of Shin  44.5  cm 
Length of Crank  170.  mm 
Point of rotation of thigh at hip  { -30.0, 76.0}  cm 
Work of Revolution, one leg,  155.9  kg m2/s2</ sup> 
Work of back half of revolution, one leg,  29.3  kg m2/s2</ sup> 
Cadence  100.  rev/min 
Watts for two legs  519.7  kg m2/s3</ sup> 
Average pedal force for Watts  291.9  kg m/s2 
Minimum angle between shin and thigh, Theta5Min  22.  degrees 
Maximum angle between shin and thigh, Theta5Max  101.  degrees 
Range of angle between shin and thigh, Theta5Delta  79.  degrees 
Minimum angle between thigh and horizontal,Theta2Min  20.  degrees 
Maximum angle between thigh and horizontal, Theta2Max  60.  degrees 
Range of angle between thigh and horizontal, Theta2Delta  41.  degrees 
Angle of hips, Theta8  82.  degrees 
 
Pedaling Model Fit Points 
Hip Extensor Fit Points  { 0.0, 88.0, 200.0, 232.0, 240.0, 232.0, 200.0, 88.0, 0.0} 
Hip Flexor Fit Points  { 0.0, 12.5, 28.3, 32.9, 34.0, 32.9, 28.3, 12.5, 0.0} 
Shin Extensor Fit Points  { 0.0, 12.1, 27.5, 31.9, 33.0, 31.9, 27.5, 12.1, 0.0} 
Shin Flexor Fit Points  { 0.0, 7.7, 17.5, 20.3, 21.0, 20.3, 17.5, 7.7, 0.0} 

 

© 1997 Tom Compton