Bicycle Gear Ratio Simulator

This tool models the bicycle drivetrain from the relationship between gear teeth and wheel rotation. From the front teeth \(N_f\) and rear teeth \(N_r\) the gear ratio is defined as \(G = N_f / N_r\). The rear wheel turns \(G\) times for each pedal revolution, and using the wheel circumference \(L\) (derived from tyre size) the development (rollout) \(R\) is \(R = G \cdot L\). Speed \(v\) follows from cadence \(C\) (rpm) as \(v = \frac{C \cdot R}{60}\) in m/s. Climbing ability is estimated by assuming the required power \(P = m g v \sin\theta\) for gravity \(g\), total mass \(m\) (bike + rider) and grade \(\theta\), then back-solving the limiting grade from the maximum sustainable power. The animation at the top draws, in real time, the pedalled chainring driving the rear cog through the chain and the rear wheel spinning at \(G\) times the pedalling rate, connecting the equations directly to the physical motion.

Industrial use
Component makers such as Shimano and SRAM use this kind of calculation to validate new cranks and cassettes. When optimising the tooth layout of a road groupset like the 105 series, they simulate the speed range and gear jumps of a 50T front with an 11-34T cassette to assess baseline performance before road testing. Complete-bike makers tune gear ratios per model so that cross bikes and MTBs balance city riding against off-road performance.

Research and education
Mechanical engineering and sports-science departments use it as a teaching aid for drivetrain efficiency. Visualising the cadence-speed relationship helps students grasp the best shift timing intuitively. In environmental engineering courses, the energy change from different gear ratios is computed and applied to e-bike motor-control map design.

Position in the CAE workflow
The tool sits at the front of a CAE workflow: gear ratio and development are computed first to narrow the design space. The data then feeds chain-tension and frame-stress analysis in ANSYS or Abaqus. In MTB suspension design, the climbing-ability metric obtained here drives a parameter study to optimise rear-shock damping, cutting prototype iterations and shortening development.

It is tempting to think "a bigger gear ratio is always faster," but in reality the balance with pedalling efficiency, strength and endurance matters. Too high a ratio drops cadence drastically, loads the joints and muscles, and actually makes speed harder to hold. On climbs especially, a lighter ratio at high cadence is often more efficient — do not be misled by the number alone.

It is also a mistake to think "with the same front teeth, speed depends only on the rear." Tyre outer diameter (development) has a large effect too. For the same gear ratio, a 700C road bike and a 26-inch MTB travel different distances per revolution, so accurate wheel circumference is essential. Climbing ability depends not only on gear ratio but also on total weight (bike + rider) and grade — don't overlook the benefit of going lighter.