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. |