Usually when I get on my bike, I tend to just ride, without wondering of the technique like gear ratio or position etc.. Perhaps the body adjusts itself and its optimum can be relied on natural law. But the local optimum found by the body by trial and error is not necessarily a global optimum. The task of finding such points belong to doctors and physicists. Their academic achievements translate into sporting achievements of their clients .
Initially, it is worth mentioning that from the standpoint of physics, work is force (F) multiplied by the displacement (S), while the power is work (W) divided by time, ie the product of force and velocity (V).
P = W / t = F * S / t = F * V
Pedaling cadence must be optimal if it is too low or too high, the muscles will function with large losses, which means severe fatigue and low speed! As can be seen for longer crank arms, pedaling frequency should be lower than for shorterones (the product of angular velocity and radius should remain constant).
In the past, Hill dealt with experiments on muscle contraction. In practice, Hill's muscle model does not reflect the 100% real muscle, nor contractions are not perfectly isotonic. From this experience, however, comes a crucial and practical application. Muscles are most effective when working at a load equal to about 30% of maximum force generated.
Linear velocity of muscle contractions is the product of the angular velocity (omega) and the length of an crank arm (radius, r), thus :
P = F * omega * r = M * omega
The cross product of crank arm position and force delivered to the pedal is torque (M). Simplifying we can just multiply force acting effectively ( 90* to the current crank position) by length of crank arm which is radius (r). The notation is often used in mechanical engineering. Depending on the position of leg, defined by an angle, effective force has a different value and it’s delivered by different muscle groups.
On the first picture one can see 3 reference curves. The red curve represents the power generated in the short term. And here you can see, the maximum force falls to the low frequency of pedaling. However, this type of movement is far from optimal. As mentioned above, we try to find not the highest generated force, but power instead, and not the short term, but long term power, associated with optimal movement pattern.
Practical conclusion? Do not choose low cadence, this causes inefficient muscle operation, rapid fatigue, and damage to cartilage and ligamentous elements, increased sensitivity to the incorrect angle of spinning legs while pedaling. The problem of maintaining high cadence is not in the muscle itself, but in the mind, that must be properly trained to generate correct movement pattern. As seen in other curves - white and yellow, professional cyclists generate the greatest long-term power, with high pedaling cadence.
By generated long-term power, I mean power generated during aerobic work, for time greatest than 21 minutes. As can be seen, for very slow rotation, the values of power are low. It is associated with physiological feature of the blood vessels to collapse under pressure from the outside. Ischemic muscle, quickly ceases to generate power efficiently, accumulate in the lactate, decreasing the pH (acidosis). Increasing the frequency of rotation improves circulation by usage of muscle pump and muscle can longer perform high power generation. Unfortunately there may be an additional load on the cardio – vascular system due to peripheral resistance decrease, as more blood flows through the muscles and we can feel shortness of breath. We probably will note higher pulse rate to maintain perfusion pressure.
On the second graph I drew a curve of power generated against the amount of crank revolutions per minute (rpm - revolutions per minute). The maximum force generated for a long time falls for a much lower term - about 50 to 100 per minute, then rapidly decreases. Scientists say the optimum is to ride a 100-120 RPM, and some riders prefer the even moments to 150RPM. Power, is the product of force and speed, this means that the maximum power falls to a higher cadence than the maximum strength.
Last graph takes into account the power dependence on speed. We know that for each of the gears, for a given cadence, it translates into speed of the bicycle ride. One should choose the gear, to maintain steady and comfortable cadence, independent of bike speed. If road gets steep, the wind starts to blow, we get tired, gear ratio should be reduced so as to always operate at maximum limit our effectiveness, and steady pedaling rate.
"If your legs hurt more than your Lungs, Increase cadence. If your Lungs hurt more than your legs, use lower cadence. “