Analytic Cycling Logo Example

Quantifying potential improvements allows a rider to focus on the ones with the most potential.  Here is a list of possible improvements and what they are worth for a hypothetical rider, an example of the use of the tools presented. This example shows how a hypothetical rider could use the tools presented to improve a an up-hill time-trial time from 36:47 to 29:17 minutes. 

Steady-State Power 

Estimate your steady-state power. You know that on a calm day on flat terrain you can ride at 38 kph (10.55 m/s).  Make some assumptions about your frontal area:  you are big so .6 m2 would be a good estimate.  Supply additional data for Power, Given Speed, and let it calculate your steady-state power, giving 257.3 watts. 

Forces On Rider 
Frontal Area  0.60  m2 
Coefficient Wind Drag  0.50  dimensionless 
Air Density  1.226  kg/m3 
Weight  100.0  kg 
Coefficient of Rolling  0.004  dimensionless 
Grade  0.000  decimal 
Wind Resistance  20.5  kg m/s2 
Rolling Resistance  3.9  kg m/s2 
Slope Force  0.0  kg m/s2 
Cadence  100.  rev/min 
Crank Length  170.  mm 
Pedal Speed  1.78  m/s 
Average Pedal Force  144.5  kg m/s2 
Effective Pedaling Range  70.  degree 
Effective Pedal Force  371.7  kg m/s2 
Speed  10.55  m/s 
Power  257.3  watts 

Speed For Given Power 

Now suppose that you are going to do a hill climb time trial.  The course is a constant grade of 5% for 10 kilometers.  What speed can you expect based on your steady-state power? Speed, Given Power gives a  speed of 4.53 m/s. 

Speed For Given Power 
Speed For These Parameters  4.53  m/s 
Power  257.3  watts 
Frontal Area  0.6  m2 
Coefficient Wind Drag  0.5  Dimensionless 
Air Density  1.226  kg/m3 
Weight Rider & Bike  100  kg 
Coefficient of Rolling  0.004  Dimensionless 
Slope of Hill  0.05  decimal 

Speed Improvement From Less Weight 

Your estimated time for the time trial of 10, 000 m/4.53 m/s or 36:47 (2207 seconds) is not fast enough to suit you.  You are contemplating going on a diet in which you think you can loose 5 kg.  How much difference will this make?  Less Weight on Hill calculates the speed change for the given weight change.  This gives a new time of 35:17 (2207 seconds - 90.11 seconds = 2134 seconds ). 

Benefit From Less Weight 

This Much Less Weight  5  kg 
Over This Distance  10000  meters 
On Hill of Slope  0.05  Decimal 
Faster by  90.11  s 
Ahead by  408.66  m 
Frontal Area  0.6  m^2 
Coefficient Wind Drag  0.5  Dimensionless 
Air Density  1.226  kg/m^3 
Weight Rider & Bike  100  kg 
Rolling Coefficient  0.004  Dimensionless 
Power  257.3  watts 

Speed Improvement From Weight Training 

You have noticed some weakness in your pedal stroke from last season.  It's early, so you are going to the gym to do some lifting.  Suppose you improve the force developed by your legs by 10%.  How much additional power can you expect?  You have taken the measurements for the Pedal Model and before training it gave the following results (see Figure 1 for nomenclature): 
 
Pedal 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,  77.2  kg m2/s2 
Work of back half of revolution, one leg,  14.5  kg m2/s2 
Cadence  100.  rev/min 
Watts for two legs  257.3  kg m2/s3 
Average pedal force for Watts  144.5  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 
 
Pedal Model Fit Points
Hip Extensor Fit Points  { 0.0, 43.6, 99.0, 114.8, 118.8, 114.8, 99.0, 43.6, 0.0} 
Hip Flexor Fit Points  { 0.0, 6.2, 14.0, 16.3, 16.8, 16.3, 14.0, 6.2, 0.0} 
Shin Extensor Fit Points  { 0.0, 6.0, 13.6, 15.8, 16.3, 15.8, 13.6, 6.0, 0.0} 
Shin Flexor Fit Points  { 0.0, 3.8, 8.7, 10.0, 10.4, 10.0, 8.7, 3.8, 0.0} 
 

The Pedal Model says that your 10% improvements would be worth: 
 
Pedal 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,  83.5  kg m2/s2 
Work of back half of revolution, one leg,  14.5  kg m2/s2 
Cadence  100.  rev/min 
Watts for two legs  278.2  kg m2/s3 
Average pedal force for Watts  156.3  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 
 
Pedal Model Fit Points
Hip Extensor Fit Points  { 0.0, 47.9, 108.9, 126.3, 130.7, 126.3, 108.9, 47.9, 0.0} 
Hip Flexor Fit Points  { 0.0, 6.2, 14.0, 16.3, 16.8, 16.3, 14.0, 6.2, 0.0} 
Shin Extensor Fit Points  { 0.0, 6.6, 15.0, 17.4, 18.0, 17.4, 15.0, 6.6, 0.0} 
Shin Flexor Fit Points  { 0.0, 3.8, 8.7, 10.0, 10.4, 10.0, 8.7, 3.8, 0.0} 
This is about a 8% gain, not as much as you expected.  (In this example the Thigh Extensors and Shin Extensors were trained, but Thigh Flexors Shin Flexors were neglected.)  The improvements so far (less weight, and more power) have increased speed to 5.06 m/s or a new time of 32:56 (1976 seconds).  (Speed, Given Power with power of 278.2 and weight of 100-5 kg.)   

Speed For Given Power 
Speed For These Parameters  5.06  m/s 
Power  278.2  watts 
Frontal Area  0.6  m2 
Coefficient Wind Drag  0.5  Dimensionless 
Air Density  1.226  kg/m3 
Weight Rider & Bike  95  kg 
Coefficient of Rolling  0.004  Dimensionless 
Slope of Hill  0.05  decimal 

Speed Improvement From Change in Position 

There may be some inefficiencies in your bike setup.  What happens if we look at saddle height?  Optimal Seat Height shows how power is affected by changing saddle height.  The plot below shows that power could be improved by raising your saddle.  Power would improve from 287.2 watts to 320 watts.  (This is extreme, most riders are usually much closer to optimum.)  Your time can be expected to improve to 5.69 m/s or a new time of 29:17 (1757 s). 

 

Summary 

This approach identifies areas for improvement and quantifies them so a rider can focus on areas that have the most potential.  Always keep in mind that your results may be very different from the ones in this example.  

 ©1997 Tom Compton