# Powerpedal

engineering and biomechanics in cycling

## Force - Power measurement pedals

In order to increase the effectiveness while pedaling (Gross Efficiency) we have to increase the efficiency of the pedaling.
This is basically impossible without measurement technology and visualization. In collaboration with SRM we have designed a SPD-R compatible pedal - software product that measures and displays the effect of the legs' stroke. The aim is to maximize the tangential forces (Ft) on the crank, as only these are involved in propulsion. The radial forces (Fr) are dissipation forces that do not contribute to the pedaling motion. The graphic illustrates the kinematic connection between pedal and pedal crank forces. The magnitude of the normal pedal force (Fn is perpendicular to the pedal surface) depends on the direction of the total force. And this is based on the one hand by the contact points with the bike (hip/saddle and foot/pedal) and on the other hand by the dorsal an plantar flexion of the ankle. In English we say 'ankling' for this.

Due to the fixed distance with the crank the pedal moves in a circular path around the bottom bracket. If we could apply the force perpendicularly (tangentially) to this circular path we would use the maximum possible lever length (crank length). A machine might be able to do that but not humans with their limited anatomical abilities.

In order to describe the path of the pedal mathematically, one uses the conversion from polar to Cartesian coordinates. This creates a so-called sinusuid (blue graph). It is almost the ideal of a circular motion. If our ankle could move so flexibly, we could achieve this as an ideal function, i.e. transfer the maximum possible force to the pedal. But the nature has set us limits here. We can therefore only work with the maximum and minimum possible ankle angles. We have packed the problem into a mathematical equation to calculate the trajectory of the ankle with the maximum and minimum possible joint angles in order to achieve an optimum (green graph) following a sinusuid function. This would be the optimal 'ankling'. The circular plot clearly shows how big the difference good pedaling technique can be. And that is expressed directly in the speed driven with the same energetic effort. And this can definitely mean the difference between victory and defeat in a time trial.