The performance of 250W mid-drive motors and hub motors compared by simulations

This article does not apply to the USA because there is no 250W limit for ebikes.

During the selection of a 250W motor for a new Maxun One solar bike, I found out that a mid-drive motor doesn't perform much better than a hub motor. It's not like I'm against mid-drive motors, but I want a very lightweight 12kg ebike. Most mid-drive ebikes are much heavier.

The question is why should you choose for a mid-drive motor, besides the fact that it looks more impressive?

Mid-drive motor drawbacks

• It is much heavier in weight.
• There is serious resistance when you ride without assistance, this is because the freewheel is not mounted directly on the crankshaft, which would be best, but inside the motor, behind one or more gearwheels. This cause extra friction. Only with the Specialized Turbo Creo (has no zero cadence support), this resistance is negligible.
• It is many times more expensive, €750 instead of €100 and repairs are not done, you have to buy a new one. 

Mid-drive motor benefits

• The software, together with a torque sensor, provides a more natural cycling feeling, which many people like. But I prefer a throttle because in most of the time, I don't have to pedal myself with my Maxun One solarbike.
• The wheel doesn't slip (what happens with front wheel hub motors).
• You can easily change wheels when repairing a flat tire.

What's better?

In practice there is no significant difference in performance of both kind motors with a power limit of 250W. You can clearly experience this yourself during test drives, I did this myself too. Because I wanted to know the cause, I researched this subject extensively. 

Below I have simulated a hub motor and a mid-drive motor with the same power at different speeds and road inclinations. The calculations and graphs are quite complicated and cannot be understood by most people. I hope that in any case I can convince you of my conclusion that there is no big difference between both motor types.

The conclusion is that the advantage of mid-drive motors is only noticeable on steep slopes while the cyclist pedals only a little or not, see the last example: a slope of 8% where we do not pedal.

Notes

• This article handles about ebikes up to 250W (which are allowed in many countries without a license). This is because by nature, all small permanent magnetic motors have equal characteristics.
• In the US, ebikes have motors of 750W and more. At this power there are serious differences in performance between both types of motors.
• This article is only about the motor itself, without the software. At mid drive motors, the software has a major influence on the motor behavior.
• Direct drive hub motors have not been tested in this article. By the way, these are outdated concepts and far too heavy.
• Driving in a headwind has the same effect as driving uphill.

Electricbikereview

I have created a thread on Electricbikereview. I would like the thank the forum members for their comments, these have been incorporated into this article.

Mid drive motor simulations

A mid drive motor has, as opposed to a wheel hub motor, an almost constant speed. Since a mid drive motor drives the crank, the motor speed is proportional to the cadence, which is the pedal speed. By switching between the gears, the cyclist achieves that the cadence is always optimal, for recreational cyclist this is about 80rpm. But note that many people on electric bicycles have a very low cadence. In the article "Permanent magnet DC electric motor tuning" we see that the efficiency of a motor increases with the speed. Since the speed of a mid drive motor can be high at all travel speeds, its efficiency is higher than a wheel hub motor. But as we will see later, the theoretical advantage of a hub motor is disappointing in practice. 

In this Excel sheet on GitHub, we can simulate a mid drive motor and a wheel hub motor. Take the worksheet tab "Efficiency mid drive η(kmh)".

This simulation is done with the Cute Q85-SX motor. This motor is used for both the hub motor and the mid-drive motor simulation, otherwise we cannot compare fairly. Note that de hubmotor is taken as a whole unit, for example the motor constant k applies to the entire motor. The motor has to have a higher speed than the bottom bracket because the motor is not designed for mid-drive of course, but that does not matter. This is now called the gear ratio (motor-n / cadence). The gear ratio should be chosen in such a way that the motor performs best over a wide range of speeds and slopes. I have figured out that in our case a gear ratio of 2 is optimal.

In the simulation, I assume the ideal situation, that the bicycle has an infinite number of gears. So, by switching, the mid drive motor speed remains constant at all travel speeds. These values must be entered into the Excel sheet:

• Cadence. Fill in your optimal cadence.
• Mid motor drive gear ratio. This determines the motor speed.

Try different gear ratios to get the best efficiency over a wide travel speed range. These graphs show the little higher efficiency of a mid drive motor:

In the next example, the cyclist pedals too; the Excel value "Assistance above" = 100W. Here, the wheel hub motor works in a range where its efficiency is higher; there is not much difference between the efficiency between both configurations:

Efficiency mid-drive motor vs hub motor 

Here we will see that the theoretical advantage of a hub motor is disappointing in practice. It is remarkable that a mid-drive motor has advantages only on steep slopes. 

These values are used in the Excel sheet:
Assistance above 50W
Cadence 70rpm

Slope 0%

Both graphs are practically the same.

Slope 4%

At a slope of 4%, the efficiency of a mid-drive motor is slightly better.

Slope 6%

Here is an example of a fairly steep slope of 6%. A hub motor performs well here if we pedal lightly with 50W:

At a input power of 300W, the hub motor goes 14.5km/h and the loss is 100W. The mid-drive motor goes 15.5km/h and the power loss is 80W. The difference is small.

Slope 8%

To properly show the advantage of a mid drive motor, we have to take an extreme situation; a slope of 8% where we do not pedal:

At a input power of 300W, the hub motor goes 4.5km/h and the loss is 200W. The mid-drive motor goes 10km/h and the power loss is just 80W. 

The conclusion is that the advantage of mid-drive motors is only noticeable on steep slopes while the cyclist pedals only a little or not.