Analytic Cycling Logo Optimal Crank Length

Longer or shorter cranks can change the geometry and range of motion of muscles.  How does this affect power?

Say a rider is contemplating changing crank length.  What does the Pedaling Model say about different crank lengths and power?  For example, say a rider contemplates that shorter cranks would allow a quicker cadence.  A rider can make assumptions regarding how shorter cranks change the Strength Functions and test the effect on Power using the Pedaling Model, all without having to learn to pedal differently just to see if power improves. 

Thigh and Shin Strength Functions depend on cadence and range of motion. A change in crank length changes the geometry and hence changes this range of motion. If it is assumed that, while geometry changes, the magnitude of the Strength Functions stay the same over the new range (a reasonable assumption for relatively small changes in range of motion), how does this affect Power output? The following table shows the power for different Crank Lengths.   

Power vs. Crank Length

It may be that a different range of motion does change the magnitude of the Thigh and Shin Strength Functions. Questions such as this can be tested here.  Of course, there are other considerations as well such as appropriateness of the range of motion considering a riders size and what may or may not be comfortable. 

Sprint Strength Function Plot

Figure 3.  A "Sprint" Crank Length

In a sprint context force to the pedals tends to be applied as "impulses." That is to say that the Thigh and Shin Strength Functions are "narrow and pointed," much as shown in Figure 3. What happens if a rider changes the Crank Length while using such Thigh and Shin Strength Functions?  

Using "narrower and high" Fit Points (Thigh Extensor Fit Points of {0.,20.,60,300.,1000, 300.,60,20.,0.} and Shin Extensor Fit points of {0.,2.8,8.4,42.,140.,42.,8.4,2.8,0.} and default values for other Fit Points) gives the  
results in the following table:

Sprint Power vs Crank Length

Other considerations may affect choice of crank lengths.  Cranks lengths in track tend to be short due to limits imposed by track banking and minimum speeds. 

The numbers in the above examples were selected for illustrative purposes; your values could be very different. 

Pedaling Model Nomenclature   

Sample Output:

The table below shows examples of range motion for different crank lengths (refer to Figure 1 for nomenclature):

Power & Range of Motion for Crank Lengths

© 1997 Tom Compton