Question

Consider rider on a typical bicycle pedalling up a hill. Specifically, the case when the cyclist is using their body weight alone to apply the pedalling force. Draw a diagram of the situation that you can analyse the system and answer the following questions:

a) Does the mass of the rider affect the acceleration of the bike (and rider) up the hill?

b) Is there an optimum ratio from pedal crank radius to rear wheel (including the chain drive ratio) that will maximise the acceleration?

c) Is there a maximum angle that the bike and rider could ride up?

d) How does the angle of the pedal affect the acceleration (if at all)?

e) What coefficient of the friction is needed between the tire and the wheel to ensure no slipping?

Ignore air resistance and friction losses within the bike.

Answer 1

Friction is a great thing in brakes and tires—but it's less welcome in another form: as air resistance that slows you down. The faster you go, the more drag becomes a problem. At high speeds, racing a bicycle can feel like swimming through water: you can really feel the air pushing against you and (as we've already seen) you use around 80 percent of your energy overcoming drag. Now a bicycle is pretty thin and streamlined, but a cyclist's body is much fatter and wider. In practice, a cyclist's bodycreates twice as much drag as their bicycle. That's why cyclists wear tight neoprene clothing and pointed helmets to streamline themselves and minimize energy losses.

Photo: Racing bicycles have two sets of handlebars. Inner handlebars let riders reduce air resistance by keeping their elbows closer together. Photo by Ben A. Gonzales courtesy of US Navy.

You might not have noticed, but the handlebars of a bicycle are levers too: longer handlebars provide leverage that makes it easier to swivel the front wheel. But the wider you space your arms, the more air resistance you create. That's why racing bicycles have two sets of handlebars to help the cyclist adopt the best, most streamlined position. There are conventional, outer handlebars for steering and inner ones for holding onto on the straight. Using these inner handlebars forces the cyclist's arms into a much tighter, more streamlined position. Most cyclists now wear helmets, both for safety reasons and improved aerodynamics.