Optimum wheel diameter for e-bikes

[PaulM24]

As an owner of a not too old Benelli Classica 26 inch wheel front hub drive bike, I was surprised how responsive a 20 inch rear hub drive folding bike felt in comparison, especially going up hill. The folder wasn't that much lighter either and both bikes have cadence sensors only.

I have heard it said that smaller wheel e-bikes 'provide more torque', although I am not sure of the maths behind this statement. If it is true, would the efficiency and hence range of road going e-bikes actually benefit from having smaller wheels, accepting that there would have to be suspension and/or chunky tyres to deal with rough road surfaces.

Although there are a limited number of smaller wheel non-folding e-bikes for sale (like the Cube Compact Hybrid), is the overwhelmingly common use of 26 inch plus wheels down to the aesthetics of what we all used to seeing, rather than efficiency?

 

[Woosh]

small wheels are good on steep gradient because the motor yield gradually worsens when your speed drops to near stalling.
What people need to be aware is that your motor is far from perfect. When you ride at its optimal speed, the motor converts about 85% of electrical energy into mechanical energy. When you stall, the motor does not produce anything, its yield is zero, all electric input is turned into heat which is not good.
For geared hub motors, the minimum useable rotational speed is about 60 RPM or one rev/second.
Between the optimal speed and stalling the motor yield gradually drops. However, for the same speed, smaller 20" wheels rotate more rapidly than larger 26" or 700C wheels, its yield remains useable longer on lower speed, enabling you to climb steeper gradient albeit at slower speed.
Mathematically, for the same power, you use this formula:
power = input power * yield = torque * rotational speed = F * wheel diameter * pi * RPM /60
To calculate the maximum climbing gradient, substitute input power = battery voltage * controller's maximum Amp rating, use 60 for RPM. For yield, consult manufacturer's motor performance test chart.
As for optimum wheel diameter for climbing, there is no hard and fast rule. Designers will choose the best combination of motor, frame, wheels and tyres for their target market.

 

[sjpt]

If you put exactly the same motor in a 26" wheel or 20" wheel you will get more torque and better hill climbing from the 20". However, you will get less assistance at speed.

Often motors with slightly different winding details will be used for the different wheel sizes so both give similar hill climbing and speed performance.

When a crank drive is used (as in Cube Compact) it will depend on the gearing between the cranks and wheel, again that will generally be set to give similar results with both wheel sizes.

 

[vfr400]

The same motor will make more torque and less speed in a small wheel than a big one. It's the same as changing down a gear in a car.

The manufacturers normally use motors with internal differences depending on what size wheel it goes in. So that they don't lose too much speed in a small wheel, they change the windings to make the motor spin faster than the one that goes in a big wheel. This change doesn't reduce the torque much, so a fast motor in a small wheel will normally produce more torque than a slow motor in a big wheel. It will also make more power because it's spinning faster with the same torque.

The motor's torque is more or less directly proportional to the current you give it. I'm assuming that the manufacturers use the same controller in both cases of wheel size, but you often see 20" bikes with 12, 13 or 14 amp controllers compared with 15 being more normal for 26" wheeled ones.

All motors have a maximum rotation speed that depends on their windings and the battery voltage. Designers aim to have the motor spinning at around 75% of its max rpm when the bike is travelling at its modal speed. That's where it produces most power and has the best efficiency. If the motor spins at less than 50% of its maximum rpm, it's efficiency accelerates downwards the further it goes below that speed.

To summarise, for a motor to have the same efficiency and speed characteristics in 20" and 26" wheels, it would have to have windings that allow it to spin 30% faster. In the small wheel, it'll always make more torque.

You will often see motors labeled as around 180 rpm for 700c wheels, 201 rpm for 26" wheels and 320 rpm for 20" ones. The motor rpm is a critical characteristic. It needs to be right for the type of bike and the way you ride.

 

[PaulM24]

Thank you for the detailed replies. I can also see that I have been making a fundamental error in my riding technique going uphill, where I have been tending to keep in a higher gear for too long and letting the cadence get too low, hence running the motor at low efficiency. From now on I will try to use a lower gear for hill climbing more appropriately.

Is the trade off between hill climbing torque at say 10 mph versus assistance at speed that great, when power output is taken out at about 15.5 mph anyway due to legislation?

 

[PaulM24]

Sorry, just realised that my last statement was rubbish, the cadence would only apply to a crank geared bike.

 

[vfr400]

It doesn't matter what gear you're in with a hub-motor. Only the speed matters. try not to let it go below 5 mph.

The gear you're in affects how much power you can give to assist the motor. You get more power by using a lower gear and spinning the pedals fast.

 

[flecc]

is the overwhelmingly common use of 26 inch plus wheels down to the aesthetics of what we all used to seeing, rather than efficiency?

On all bikes, assisted or not, a major factor in wheel size choice is gearing, especially with derailleur gears. The smaller the rear wheel, the more difficult it becomes to achieve high enough top gears to avoid spinning out when pedalling, due to the restraints on rear sprocket and chainwheel sizes.
.

 

[Sturmey]

As an owner of a not too old Benelli Classica 26 inch wheel front hub drive bike, I was surprised how responsive a 20 inch rear hub drive folding bike felt in comparison, especially going up hill. The folder wasn't that much lighter either and both bikes have cadence sensors only.

I have heard it said that smaller wheel e-bikes 'provide more torque', although I am not sure of the maths behind this statement. If it is true, would the efficiency and hence range of road going e-bikes actually benefit from having smaller wheels, accepting that there would have to be suspension and/or chunky tyres to deal with rough road surfaces.

Although there are a limited number of smaller wheel non-folding e-bikes for sale (like the Cube Compact Hybrid), is the overwhelmingly common use of 26 inch plus wheels down to the aesthetics of what we all used to seeing, rather than efficiency?

 

[Sturmey]

I have heard it said that smaller wheel e-bikes 'provide more torque', although I am not sure of the maths behind this statement.

Strictly (mathmatically) speaking, a smaller wheel does not increase the torque. However, it does increase the thrust (horizontal pushing power) substantially, so going from 26 to 20 inch gives 30% more 'thrust' at the expense of about 30% less speed.
e.g. and notice that blue line below refers to 'thrust' in lbs.

Motor Simulator - Tools

Our ebike motor simulator allows you to easily simulate the different performance characteristics of different ebike setups - with a wide selection of hub motors modeled, and the ability to add custom batteries and controllers and set a wide variety of vehicle parameters you'll be able to see...

www.ebikes.ca

 

[BazP]

is the overwhelmingly common use of 26 inch plus wheels down to the aesthetics of what we all used to seeing, rather than efficiency?

If you are doing rough off road stuff then it’s definitely down to efficiency. On steep terrain over rocks I find the 29” wheels roll a lot better than 27.5”. I wouldn’t attempt some of the routes I do on 20” wheels.