Gears

Shift your bike into the lowest gear and the steepest climb becomes doable, shift into the highest and you fly across the flat. Between your legs and the rear wheel sits the same machine either way: a pair of gears joined by a chain. Gears are the translators of engineering, they negotiate between fast and strong, and their language is nothing but teeth.

Counting teeth: the gear ratio

When two gears mesh, their teeth move in lockstep: for every tooth passing on one wheel, one passes on the other. Everything else follows from that. If a 20 tooth wheel drives a 60 tooth wheel, the big one turns only a third as fast, because it needs 60 teeth for a full revolution. The gear ratio is the ratio of the tooth counts: $i = z_2 / z_1$, where $z_1$ belongs to the driving wheel and $z_2$ to the driven one. Here $i = 3$.

Torque versus speed

What force and distance are for the lever, torque and speed are for the gear. Torque is the twisting effect at the shaft, force times lever arm, measured in newton metres (Nm). The rotational speed counts the revolutions per minute. The golden rule of mechanics applies to rotation as well: whatever you gain in torque you pay for in speed. If the big wheel turns three times slower, it turns with three times the torque. That is why you pick the large rear sprocket on a climb: the wheel turns more slowly but pushes harder. On the flat you pick the small sprocket and trade torque back for speed.

The direction flips

Two meshing gears always turn in opposite directions: one clockwise, the other against it. If the direction must be kept, engineers insert an idler gear. It changes nothing about the ratio, since its tooth count cancels out, it merely flips the rotation back. A car's reverse gear does exactly that: an extra wheel slides into the drivetrain and the car rolls backwards.

Gearboxes: stages in a row

A single gear pair rarely manages a ratio beyond about 5, otherwise the small wheel would become tiny and weak. Gearboxes therefore chain stages together, and the ratios multiply: two stages of 3 each give 9 in total. That is how a wind turbine's gearbox turns a leisurely 15 rotor revolutions per minute into about 1500 at the generator, and how a cordless screwdriver turns its motor's fast, weak spin into slow, forceful driving.