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Simple Machines · Question 11 of 20

Bicycle gears

Your bike cannot give you more power — nothing can. Gears just let you choose how to spend the power you have.

Plate XIV — The tooth market ω_wheel = ω_pedal × front/rear
Count the marker spokes' laps — teeth never lie.
pedals · 44twheel · 18twatch the two marker spokes — count their laps
FIG. XIV — THE TOOTH MARKET
Front chainring 44 teeth
Rear cog 18 teeth
Gear ratio
2.4:1
Speed @ 70 rpm
22km/h
Pedal effort
medium
Every pedal turn drags 44 chain links past, and the back cog only needs 18 links per lap — so the wheel spins 2.4 times per pedal stroke. Big number = fast but hard to push. Small number = slow but easy. That's the whole secret of gears.
The short answer

Gears let you choose your trade: an easy gear turns the wheel a little per pedal but feels light; a hard gear turns it a lot but takes more push.

What's actually happening

Every gear system on Earth sells the same product: a trade. Your legs produce a certain effort at a certain pedalling rhythm, and the gears convert that into a chosen blend of wheel-turning force versus wheel-turning speed. More of one always costs the other — the chain is a market with no free lunches.

The arithmetic lives in the teeth. Pedal a 50-tooth front chainring connected to a 25-tooth rear cog and every pedal revolution drags 50 links of chain past, spinning the rear cog — and the wheel — exactly twice. You've doubled speed and halved force. Swap to a 34-tooth front and a 34-tooth rear and one pedal turn is one wheel turn: all your force survives, but you crawl. That is the whole theory of the twenty-something gears on a modern bike: a menu of tooth ratios from about 1:1 (steep climbs) to 4:1 (flat-out descents).

Why does "spinning an easy gear" up a hill work? The hill demands a fixed amount of work to climb — weight times height, no negotiating. A low gear doesn't reduce the bill; it lets you pay in many small instalments (light pedal strokes) instead of a few crushing ones. Cars do exactly the same thing: first gear for pulling away with force, sixth for cruising with speed, and a lorry grinding up a motorway hill at 30 mph is just a cyclist in their granny gear, scaled up.

Try it at home Audit your own gears
  1. 1Flip a bike upside down. Count teeth on the biggest front chainring and the smallest rear cog (just count one and check the stamp on the other — they're usually marked).
  2. 2Predict the ratio: front teeth ÷ rear teeth = wheel turns per pedal turn.
  3. 3Turn the pedals exactly once by hand with a tape mark on the rear tyre, and count wheel revolutions. The teeth never lie.