# Bicycle gears, energy, work and power?

1. Dec 11, 2008

### many_atoms

Bicycle gears, energy, work and power??

hi everyone,

let's say you're riding a bicycle, and as you approach a hill, you shift to a lower gear. You pedal at the same rate, however. Does the power increase, decrease or stay the same? An explanation would be helpful. I've been trying to reason through this all day. I know that changing to a lower gear increases the amount of power, but what about the case of pedaling at the same rate?

Thanks!

2. Dec 11, 2008

### TVP45

Re: Bicycle gears, energy, work and power??

There should not be an increase in power because of the gear shift. You will be doing work because of the hill, but you'll be going slower. If you were to find the exact right gear, power would remain constant.

3. Dec 11, 2008

### Gnosis

Re: Bicycle gears, energy, work and power??

Changes made by gearing are conversions of mechanical output speed verses mechanical input speed. When you shift to a lower gear (for instance, drop from 1:1 to 2:1 gearing), per the same input pedal speed, the output speed is now only half of its previous output speed. Your legs are therefore only moving the bicycle half the distance per the same input pedal speed, so they are only working half as hard to perform the work of moving the bicycle however, they will have to move twice as many times to perform the same work as when pedaling using 1:1 gearing.

The reduced gearing (now 2:1 from the previous 1:1 gearing) has the advantage of doubling the torque applied to the output sprocket at the same time introduces the disadvantage of only half the output speed as the previous 1:1 gearing. Don't confuse the doubling of torque with the doubling of power, as they are entirely different from one another.

Via gearing changes, nothing is gained nor lost power-wise. You are simply better matching the available power per the RPM in which that power is produced to perform the work required to move the bicycle.