Why Does a Bicycle Have Gears? Trading Force Against Speed

Two meshed gears turn together, and because their teeth engage one for one, the smaller wheel completes more revolutions than the larger one in the same time, in proportion to the ratio of their sizes. Turning force goes the other way, so the larger wheel turns more slowly and with correspondingly more force. The product of force and speed is what the input supplies, and the gear pair redistributes it rather than creating anything, with a few per cent lost to friction. That is the whole principle, and everything a gearbox does follows from selecting which ratio is in use. The direction of rotation reverses between two meshed gears, which is why an intermediate idler gear is inserted where the direction must be preserved.

The selection follows from what the machine needs at that moment:

• •Starting a vehicle from rest needs force rather than speed, hence a low gear
• •Cruising needs speed with modest force, hence a high gear
• •An engine or a rider produces useful power over a narrow range, so gears keep it there
• •A climb needs force and a descent does not, which is the whole point of bicycle gearing
• •Clocks use large ratios to drive hands at very different rates from one movement
• •Reduction gearboxes let a small fast motor move something large and slow

Bicycle marketing counts gears and the useful measure is different. What determines whether a rider can climb a given hill and pedal comfortably at speed is the ratio of the lowest gear to the highest, meaning the range, together with how evenly the intermediate steps are spaced. A bicycle advertised as having a large number of gears may duplicate ratios between front and rear combinations, so the number of distinct usable ratios is substantially lower than the count. Very large steps between gears force a rider to pedal too fast or too slowly between them. Modern designs have moved towards a single front ring and a wide rear cassette, which reduces duplication and mechanical complexity while achieving comparable range, which is a clearer expression of what the rider actually needs.

Gear teeth are not arbitrary shapes and the curve used is chosen for a specific reason. If two gears mesh with badly shaped teeth, the ratio between their speeds varies slightly through each tooth engagement, which produces vibration, noise and wear. The involute curve, generated by tracing the end of a taut string unwound from a circle, has the property that the ratio stays exactly constant throughout the engagement regardless of small errors in the distance between the shafts, which is why almost every gear made uses it. That tolerance for imprecise centre distance is what makes gears manufacturable, since perfect alignment is impossible. Helical teeth, cut at an angle rather than straight across, engage gradually rather than all at once and are therefore quieter, at the cost of generating a force along the shaft that the bearings must take.

Several devices achieve the same exchange differently and each has its place. Belt and chain drives connect distant shafts with the ratio set by the pulley or sprocket sizes, which is what a bicycle chain does. Worm drives give very large reductions in one stage and generally cannot be driven backwards, which is useful where a load must not run away. Planetary gearsets fit several ratios into a compact package by holding different elements stationary, which is how automatic transmissions and hub gears work. Continuously variable transmissions change ratio smoothly rather than in steps, keeping an engine at its most efficient speed regardless of road speed. Differential gears split drive between two wheels while allowing them to turn at different rates, which is what lets a vehicle corner without dragging a tyre.

Meshed gears exchange turning force for rotation speed in proportion to their sizes, redistributing what the input supplies rather than creating anything. Low gears give force for starting and climbing, high gears give speed for cruising, and the purpose is keeping an engine or rider in its useful range. Range between lowest and highest matters more than the number of gears.