Why does changing gear make pedaling easier?

Why do we shift before a climb? Forget the formula for a moment. Follow the gold link: your foot turns the chainring, the chain pulls the rear sprocket, and the rear axle drives the wheel.

Move closer. Each tooth must meet a matching link, so their spacing is not arbitrary. The chain wraps both sprockets and returns along the other side. A continuous loop makes continuous transmission possible.

Count one turn of the chainring. Thirty-four teeth advance thirty-four chain pitches. The rear sprocket has twenty-four teeth, so receiving that chain takes more than one revolution. That is where the speed ratio comes from.

The ratio below is thirty-four divided by twenty-four, about one point four two. One pedal revolution produces that many rear revolutions. This two-axle teaching rig makes the relationship easy to see.

Switch to the twelve-tooth rear sprocket. The pedals keep their rhythm, but the rear axle speeds up. The chain advances at the same rate; the smaller sprocket must turn more times to receive it.

Why can that faster gear feel harder? Chain pull acts at a smaller radius, producing less torque at the rear axle. To overcome the same resistance, you generally need to push harder on the pedals.

Now choose thirty-two teeth. The rear axle slows, but the chain acts at a larger radius. The lower ratio makes the load easier to turn, which is why a larger rear sprocket often helps on a steep climb.

Raise the road. Alongside rolling resistance and drag, you must now overcome a larger downhill component of gravity. Watch the required pedal force rise. Gearing changes how you supply effort; it cannot remove the hill.

Keep the gears fixed and vary the pedaling rhythm. Chain speed and rear speed change together. The gear ratio sets their relationship; cadence sets the pace. Those are two different controls over the ride.

An easier push does not create energy. Climbing the same height still requires a gain in gravitational potential energy. A lower gear usually takes more pedal turns and, at the same cadence, moves you more slowly.

Check the power readout. The model calculates what maintaining your chosen cadence would require, not what a rider can necessarily deliver. It includes slope, rolling resistance and drag, while leaving out the transient shifting mechanism.

Compare the gears once more. Lower the front-to-rear ratio for an easier climb; raise it for more speed at a given cadence. Following the chain gives you a more reliable rule than simply calling one gear large or small.