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How to select motor and gear ratio for mid-drive?

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How to select motor and gear ratio for mid-drive?

Old 07-09-19, 05:38 AM
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How to select motor and gear ratio for mid-drive?

Hey all!

I am working on my first ebike build and posted a question about friction drives earlier. Now, I have decided to go with a Mid-drive. I made calculations and found out the torque and rpm required for the build. But I am having difficulty find the right motor and gear ratio. I am trying to build something like the Brose S Mag, the size of the drive is so small but the power it delivers is insane. It delivers a torque of 90Nm. They said they use a planetary gear box. As per my understanding, they have used a high rpm motor and geared it to achieve the required torque and RPM. The place I live has a legal power limit of 250W and speed limit of 25Kmh for ebikes.

These are the specs of my bike:
GVW= 105kg
Wheel radius = 330mm
Max Speed = 25kmh

I calculated the air resistance using the formula:

RA = rhoCdAV^2/2 where rho is density of air, Cd is the drag coefficient(0.88), A is area of contact in m^2(0.4) and v is velocity in m/s(6.94)
RA = 10.38N

I calculated rolling resistance using the formula:

RR = GVW*Crr where GVW is total vehicle weight(105Kgs) and Crr is rolling resistance of tire on asphalt road(0.004)
RR = 4.12N

I calculated grade resistance using the formula:

RG = GVW*sin theta where sin theta = 0.196 for 20% gradeablity
RR = 202.09N
The acceleration force required for 25kmh in 5 secs is 145.74N

The torque required when considering grade resistance is 83.6Nm
The torque required on flat roads is 37.15Nm
The RPM required for 25kmh with a wheel dia of 26" is 240 after including a fudge factor of 20%

I should now select a motor that can achieve the above figures and the rated power has to be below 250W and size of motor should be really small. I think using a high rpm motor with planetary gear reduction can help me achieve these numbers. I am planning to use a 36V 10A controller so the peak power can be till 306W assuming a 85% efficiency of the motor.
Idk what motor should I choose and what gear ratio I should use. Will RC motors work as they provide very high rpms and are small too?

A user on the other forum told me that I would have to design a gearbox such the peak power of the motor is delivered at 60RPM since the bicycle drivetrains are built for the average human rpm which is around 60. But when I look for motors online, manufactures aren't giving the peak power inform. How do I find the rpm and torque at the peak power? I should build a gear to reduce it to 60 RPM? What should be the ideal torque or RPM values before reduction? If I reduce the RPM to 60 will still be able to achieve 25Kmh?
Should I design it such that it exceeds the 83.6Nm torque at the highest gear?

Please do let me know if my calculations are right.

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Old 07-11-19, 04:28 AM
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Most of the mid drive ebike motor kits do not have advanced pedal assist with a torque sensor. Here is one that has a torque sensor
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Old 07-11-19, 07:19 AM
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Dang. IF you are going to geek out on us – well, ebike.ca has done all the work for you. You can enter weight, speed, resistance (ohms), Cr, CdA, Volts, Amps, etc….

Play with this. https://www.ebikes.ca/tools/simulator.html That will tell you if your calculations are right/

If you want to play with resistance variables without a motor, most people use this: Bicycle Speed (Velocity) And Power Calculator

FYI, ebike motors and bicyclists both use Watts – so that is going to be the power term most people relate to easiest.

And for the rest – yeah, your average guy off the street (or the average 250lb ebike builder) probably pedals at 60rpm. Your average 150lb lycra dude here pedals about 100 rpm. Where do you fall on that scale? I think most mid drives are around 70-80, but I’m not sure. Mid drives give good power and range of terrain (flat to steep).

If you only need 250 watts – well you’re going to have to pedal a lot (or be very patient or very slow). But if that is really what you want you would be better served with a small hub motor (or even friction drive). It can be a lot cheaper, lighter, and less maintenance.
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