# Comparison of 20" and 26" bicycles uphill

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1. Nov 2, 2015

### fishwish

Let's say you've got two electric bicycles both powered by identical 250W motors. Both are fixed gear. Both weigh about the same and have riders of the same weight. Both riders contribute no force to pedalling - all the work is done by the motors. The only difference is the first bike has 20" wheels, the second has 26" wheels. Both bikes get up to 25kph on the flat, then they are faced with a long steep hill.
Do they perform differently going up the hill, and if so, why. Would one get up the hill more easily? Would one be faster than the other?

2. Nov 2, 2015

### Dr. Courtney

It depends on the gears and the rpm range at which the motors give the most torque.

3. Nov 2, 2015

### andrewkirk

Bicycles with different size wheels perform differently in a number of ways.

Large wheels ride over bumps more smoothly and will lose slightly less energy to frictional resistance in the bearings.

If the gears were the same on both bicycles then the motor on the large wheeled bicycle would fail earlier than that on the small wheeled one, because the torque needed to keep moving would be greater. However, gears are generally designed with the wheel size in mind, so that the large-wheeled bicycle would have lower gears, making the required torque the same.

There would also be differences in angular momentum, making one of the bicycles lose stability as velocity slowed, earlier than the other. I think the small-wheeled bike would be less stable, but haven't thought it through fully.

4. Nov 2, 2015

### billy_joule

Either bike could be faster.
What matters is power output. Power is the rate of doing work, electric motors output peak power at a specific point.
Which ever bike happens to be geared to maintain it's motor closer to the peak power output will win.

If both bikes go 25 km/hr max on the flat they are both producing the same power (motor power output = power to overcome drag).
There are two cases that could explain this - both motors are at the same RPM and gearing (this can be achieved even if they have different sized wheels)
or - the motors are producing the same power but are on different sides of the peak power point.
In the second case when one motor slows, it's power output will increase as the RPM moves towards the peak power point and the other motor will decrease power as it slows and the RPM moves further from the peak power.
Obviously the later bike will lose (but if the race were down a hill the later bike would win..)

5. Nov 2, 2015

### fishwish

Some more info: the gears are identical, the battery output is 36V 10Ah

6. Nov 2, 2015

### andrewkirk

To be absolutely certain, when you say they are identical, do you mean:
1. The distance travelled by the bicycle for one full revolution of the electric motor is the same between the two bikes; or
2. The angle of rotation of the bicycle rear wheel for one full revolution of the electric motor is the same between the two bikes.

Bicycle gears are traditionally quoted using method 1 (#teeth on chainring x #teeth on rear sprocket x radius of wheel in inches), but I am not sure that is the case for gearboxes of motor-driven vehicles.

7. Nov 3, 2015

### HowlerMonkey

Don't use your "cute q100" with a 26 inch wheel if it's the fast wind motor.

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