View Full Version : Math to determine motor requirements?

07 January 2014, 0919
Hi all,

We're new to this forum. We're a group of high school students converting an ICE motorcycle to electric.

We're having trouble finding the formulas necessary to determine the RPMs, torque, etc. needed by our motor. We've found a few "studies" (if you can call them that) that suggest nominal system voltages. We've decided on a 36V to 48V system to achieve a max speed of 35 mph and a range of about 25 miles (for our project, we had to do statistical analysis of drivers in our area to determine numerical requirements for the motorcycle).

Obviously there are many many suggestions as to what motor/controller to pick. We can't find much math though, and we need to justify our choice with math. Please can someone help us out?

IHS Electric Motorcycle

07 January 2014, 1046
I imagine that since you are a high school, doing the math is part of the stuff you want to learn, so here it is:

First, figure out how much force you will need at a given speed. I have found that in this equation is pretty accurate

Force = 60 + 0.0265*Speed*Speed (Force is Newtons, Speed is kph )

To turn a force into a torque use this equation:
Torque = Force * Length (Torque is Newton Meters, Force is Newtons, Length s Meters),

you can use that first equation for force at a given speed, and the rolling radius of a tire, which is circumference / (2 * pi), for a 17" wheel that is about 0.3m, as the length to figure out what wheel torque is required

If you are planning on running a hub motor (and certainly a hub motor will be able to get you up to 35mph) you don't need to calculate any gear ratios to figure out motor torque (motor torque = wheel torque), but if you want to have a chain drive, here are the equations for that

Wheel Torque = motor torque * rear sprocket size / front sprocket size
Wheel RPM = motor RPM * front sprocket size / rear sprocket size

If you consider gear ratio being rear sprocket size / front sprocket size, you can write those same equations as

Wheel torque = motor torque * gear ratio
Wheel RPM = motor RPM / gear ratio

If you want some more equations to determine power and give you other paths to come up with the same required wheel torque, here are some more equations for you.
To turn a force into a power use this equation

Power = Force * Speed (Power is Watts, Force is Newtons, Speed is meters per second)

To turn a power into a torque use this equation

Power = 2*pi*RPM/60 * torque (Power is in Watts, Torque is in Newton Meters, RPM is RPM)

To get RPM of a wheel from a speed, assume the tire circumfrence is 1.9m (which are just about true for a 17" street tire), here is an example conversion
35mph in RPM
Option 1) Paste this in a google search (just the stuff between the quotes) "35miles per hour / 1.9meters * 60 seconds" (isn't google search amazing?)
Option 2) 35mph * 1.6kph / mph / 1.9 meters / rotation * 1000meters / km / 60 minutes / hour = 491 rotations per minute

That should give you all you need. Let me know if I got some of that math doesn't work out, It is entirely possible that I made a mistake.

07 January 2014, 1128
Wow, this is really helpful!

So, it seems easy to determine the RPM rating for our motor. But we're still not quite sure how to determine the torque rating. From what we have learned, torque is linked to acceleration. A greater torque yields a greater acceleration. it takes little to keep a vehicle traveling at a speed, but it takes a lot of power to get it to that speed, right? So, how do we decide how much power/torque we need?

IHS Electric Motorcycle

07 January 2014, 1403
Probably the easiest way to determine the power/torque you need is to estimate the total mass of the bike (with rider). This will allow you to find the kinetic energy of the system. If you have a particular number in mind for the time you want it to take to reach 35mph, just use: Time = (Kinetic Energy)/Power
This will allow you to solve for power and from there torque by basically using the time it takes to build up to that energy level with a particular power input. It does not account for air or rolling resistance but at 35mph and lower the error probably won't be too large for your purpose.

07 January 2014, 1426
It is pretty straight forward to calculate required torque from acceleration.

Physics tells you Force = Mass * acceleration (Force is Newtons, Mass is kg and acceleration is m/s^2)

It is a safe assumption that a motorbike capable of only 35mph and have limited range will weigh 100kg or less, so with rider it should not be over 200kg.

here is an example calculation:
if you want to accelerate up to 35mph (about 16meters / second) in 4 seconds, that is an acceleration of 16m/s / 4 seconds = 4m/s^s

So put that together and you get a force of 200*4 = 800N

Convert that to torque at the rear wheel (0.3m tire radius) and you get 240Nm of torque at the rear wheel

if you have a hub motor it would need 240Nm of torque. If you have chain drive with a ratio of around 4:1, you motor would therefore need about 1/4 of that or about 60Nm of torque.

That is all theoretical, and will work pretty well at speeds less than 40mph. To calculate acceleration, especially once you get into higher speeds you need to factor in the force required to travel at that speed, and if you want to accelerate up a slope that needs to be factored in too, so you need to do a bit of calculus, which gets a little tricky, and since there are so many things that affect those forces it isn't going to be all that accurate any ways.

11 January 2014, 0041
Biff, I only browsed it, but did you take 200kg for 200N instead of 2000?

11 January 2014, 0940
Lots of good physics going on here.

For acceleration, you use torque like others said.

If you want to know the power needed to go a constant speed, you need to calculate the rolling resistance and air drag.

F_drag = 1/2 * p * v^2 * CdA

p = mass density of air (about 1.2 kg / m^3...actually, it's the Greek leter "rho", but it looks like p)
v = velocity
CdA = drag coefficient*area, for a motorcycle CdA is typically 0.3-0.7. A naked bike is on the higher end, 0.5 is a good number to use.

Then like Biff said, P = F_drag * v

For rolling resistance, use

F_rolling = C_rr * m * g

C_rr = is the rolling resistance coefficient (about 0.02)
m = mass (in kg)
g = gravitational acceleration (9.8 m/s^2)

Then same thing, P = F_rolling * v

So total power is:

P_total = P_drag + P_rolling = v * (1/2 * p * v^2 * CdA + C_rr * m * g)

That's the *continuous* motor power you need. Make sure it's continuous, not the peak rating. If you use peak, your motor will overheat.

Good luck!