🚲Bicycle Physics Calculator - Gears, Power & Speed, Climbs, Self-Stability, Braking

How to use Bicycle Physics Calculator

1. 1In Gears & cadence pick a drivetrain or type the teeth, choose a tyre and cadence, and click a row to shift the animated bike
2. 2In Power & speed set mass, position, surface, grade and wind, then solve speed from power or power from speed
3. 3In Climbing pick a climb and a power-to-weight ratio to see the time and VAM
4. 4In Self-stability adjust head angle, fork offset and speed to see the eigenvalues and the hands-off lean response
5. 5In Braking set the centre-of-mass position and friction to compare front, rear and combined braking

FAQ

Why are there fewer usable gears than rings × cogs?

Many big-ring and small-ring combinations give nearly the same ratio, for example 50×21 ≈ 34×14. These duplicates (flagged when within 3%) add no new ratios, and the cross-chained combinations bend the chain badly. A 2×12 road groupset ends up with roughly 15 distinct gears, which is one reason single-ring drivetrains with wide cassettes are popular on gravel and mountain bikes.

Why does riding a little faster take so much more effort?

Air drag grows roughly with the square of speed, so the power to overcome it grows with the cube. Above about 30 km/h on the flat, more than 80% of your power goes into pushing air aside, and 10% more speed needs about 33% more power. Reducing drag by tucking down, using aero bars or drafting pays off more than a little extra strength. Uphill the speed is low, drag matters less and power-to-weight decides.

Why can a bicycle balance itself without a rider steering?

When the bike starts to fall to one side, the front wheel steers into the fall and brings the wheels back under the frame. This comes from the steering geometry (trail and steer-axis tilt) and the front wheel’s gyroscopic effect. The linearized Whipple model captures both: too slow and the correction comes too late, giving a growing wobble (weave); too fast and it is too weak, so the bike slowly topples (capsize). The benchmark bike is self-stable between about 4.3 and 6.0 m/s.

Does more trail always mean more stability?

Trail is the distance from where the steering axis meets the ground back to the tyre contact point; it makes the front wheel self-centre like a caster. More trail generally gives calmer steering, but self-stability also depends on head angle, mass distribution and front-wheel inertia, so more is not always better. Researchers have even built a self-stable bicycle with zero trail and no gyroscopic effect. Changing the head angle and fork offset in the tool shows the stable range shifting or vanishing.

Can the front brake alone throw me over the bars?

Hard braking shifts weight to the front wheel, so the front brake can stop you far harder than the rear. On dry roads its limit is usually not skidding but pitching over: at a deceleration of g × b/h (b is the horizontal distance from the centre of mass to the front contact, h its height) the rear wheel lifts. That is about 0.5–0.6 g for a typical road bike. Sliding your body back and staying low raises the limit; on slippery roads the tyre skids first.