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During ≈15 km uphill cycling on high mountain passes they cycle about 70 r/min. [1] Cyclists choose cadence to minimise muscular fatigue, and not metabolic demand, since oxygen consumption is lower at cadences 60-70 r/min. [2] While fast cadence is also referred to as "spinning", slow cadence is referred to as "mashing" or "grinding".
Signal-flow graph connecting the inputs x (left) to the outputs y that depend on them (right) for a "butterfly" step of a radix-2 Cooley–Tukey FFT. This diagram resembles a butterfly (as in the morpho butterfly shown for comparison), hence the name, although in some countries it is also called the hourglass diagram.
From a mechanical viewpoint, up to 99% of the mechanical energy delivered by the rider into the pedals is transmitted to the wheels (clean, lubricated new chain at 400 W), although the use of gearing mechanisms reduces this by 1–7% (clean, well-lubricated derailleurs and a straight chainline), 4–12% (chain with 3-speed hubs), or 10–20% (shaft drive with 3-speed hubs).
Track sprinters make a compromise by using particular gear ratios that allow them to reach race speeds at a relatively high cadence (pedalling), around 130-135 revolutions per minute (r/min). [7] Long-distance attempts such as the hour record sometimes use high gear combinations such as 52×12 or 55×14.
Different cyclists may have different preferences for cadence, riding position, and pedalling force. Prolonged exertion of too much force in too high a gear at too low a cadence can increase the chance of knee damage; [1] cadence above 100 rpm becomes less effective after short bursts, as during a sprint. [1]
In 1895, Curtis H. Veeder invented the Cyclometer. [1] [2] [3] The Cyclometer was a simple mechanical device that counted the number of rotations of a bicycle wheel.[4] [5] A cable transmitted the number of rotations of the wheel to an analog odometer visible to the rider, which converted the wheel rotations into the number of miles traveled according to a predetermined formula.
The stopping distance s is also shortest when acceleration a is at the highest possible value compatible with road conditions: the equation s=ut + 1/2 at 2 makes s low when a is high and t is low. How much braking force to apply to each wheel depends both on ground conditions and on the balance of weight on the wheels at each instant in time.
In graph theory, it is known as the circuit rank, cyclomatic number, or nullity of the graph. Combining this formula for the rank with the fact that the cycle space is a vector space over the two-element field shows that the total number of elements in the cycle space is exactly 2 m − n + c {\displaystyle 2^{m-n+c}} .