As we did with the KOP (Knee Over Pedal) method we’d like to make our contribution and add some more light and exposure to the issue.
Still, we often listen the old magical sentence “a bigger crank length increases leverage and therefore power output”. The crank length is just one of the many levers within the transmission system. The leverage depends also on the chainring, cog and wheel diameter. Increasing leverage is as simple as shifting to a higher gear ratio, and as we all know that doesn’t increase power output per se.
WHAT IS POWER
We all look for it, but what is it exactly? In physics power is the amount of energy per unit of time. For example in the international system of units (SI) power is measured in watts (W) which is a Joule (energy) per second(time) or could also be a Newton (Force) applied at certain Speed (m/s).
So the power output doesn’t only depend on the amount of force applied to the pedal, but also on the speed of our foot.
P= F x v
So we can increase or power out either by increasing the force (tangential force) or the speed of the foot.
Still more suitable for cycling… We can say that power is torque multiplied by the cadence, which is basically the same as the formula above.
P= Torque x Cadence = F x Crank Length x Cadence
And here comes the key, increasing crank length by 25% would apparently increase power by that same amount, If that wouldn’t affect Force (F) or Cadence, which it does. Because we have certain ability to speed up our foot (which can be trained to improve as we do with the force), cadence will decrease indirectly proportional to crank length, this is, it will take us 25% more time for each pedal stroke. This means that increasing crank length decreases the cadence by the same amount (%) so no gain. Actually there is cons that we will see bellow.
Of course, the direction of the force is crucial as every force that isn’t tangent to the circle drawn by the pedal axle will not make any contribution to the motion. I.E: When the pedal is at its lowest position, a vertical force doesn’t make any contribution to the motion. It is just a waste of energy as long as the goal isn’t lengthening the crank! Here the importance of the pedaling technique.
NO RELATION BETWEEN CRANK LENGTH AND POWER OUTPUT
Among all the scientific literature on the matter, which is not little, there is no founded evidence of the effect of the crank length on performance. This is, looking solely at crank length there is no founded demonstration of any significant relation between crank length and performance. At least within a non-extreme range of 150-200mm crank length.
In other words this means that “Torque x Cadence” stays the same no matter the crank length. I.E: If we increase crank length by 50% obviously torque will increase 50% because it is proportional to crank length but cadence will drop 50% because the pedal draws a bigger circle, so with the same foot speed we achieve less spins per minute.
CRANK LENGTH DOES AFFECT THE POSITION
Crank length has a direct impact on the motion ranges and therefore on ergonomics and aerodynamics.
A longer crank requires a bigger knee and hip flexion because the pedal has a bigger range of movement. Unfortunately the flexion and extension of our joins is limited and over certain limits there is a negative impact on performance and integrity. Excessive flexion or extension is injurious and ineffective.
This is often the case for road, triathlon and TT positions where hip and knee flexion happen to be a limiting factor. The handlebar height is often limited by the hip flexion. In those cases if we like to reduce the flexion (open the gap between knees and chest) we can reduce saddle setback or crank length. While saddle setback reduction might have other implications as moving weight to the handlebars, we don’t know downsides for the crank shortening. Remember that there is no prove for impact in power output.
Summarizing, a shorter crank might help achieving a lower handlebar position, or simply gaining comfort on aggressive low handlebar positions. A shorter crank can improve aerodynamics and comfort, which translates in better performance.
If you like to improve your power output look at improving your force (F) and your foot speed (v) or cadence, as well as the pedaling technique, all the forces applies on a non tangential direction wont make any contribution to the motion (power output).
However performance is not only power output and a shorter crank can help to lower the chest and head improving aerodynamics and ergonomics, therefore performance.