# how to calculate motor strength?

By maneuver

December 15, 2009

December 15, 2009

Is there a common formula for finding required motor strength?

If I know the total bot weight and wheel diameter, could I find out what kind of motor I need. I know that gearing will come into play, but I dont know anything about these physics thingys so I choose to phrase the question as vaguely as possible..

Like, what kind of specs would a motor for a scooter (with me on top of it), doing 35km/Hrs require

or, an offroader weighting 10K, doing 3km/Hrs with 10cm big wheels in rough terrain?

I guess there arent easy answers, but I was hoping that someone knowing more than me could be bothered giving a brief introduction to the subject.

## Power schmover

I was hoping to learn what kind of specs I should be looking for when hunting bargains on eBay.

like, what project will "hight torque 5500RPM 300watt brushless motor" (made up example) be enough for? Will it be able to run an old toyota with the right gearbox? probably not, but there probably is a way to find out. The online caclculator from RobotFreak was helpful.

## Well, let's have a look at

Well, let's have a look at your 5500RPM 300W brushless motor as an example.

[Power] = [Torque]*[Rotational Velocity] or P = τ*ω

P = 300W, ω = π*5500RPM/60s.min-¹ = 287.98 rad.s-¹

τ = P/ω = 300W/287.98 = 1.04N.m

Now, if you wanted to drive your Toyota Prius (~1254kg) up a slope of up to 10°, the resisting force (due to just self-weight, let's assume no air resistance) will be 1254kg*9.81m.s-²*sin(10°) = 2136.18N.

If the car has 15" tyres, then the radius is 15"*(25.4/1000)inch.m-¹ = 0.381m.

The total torque provided by the wheels must therefore be at least 2136.18N*0.381m = 813.89N.m.

Your motor falls short... by a factor of ~783. So in other words you'd need a gearbox that provides at least a 783:1 reduction, but in real life such a gearbox (and also the rest of the transmission) will have inefficiencies/losses, so the gear ratio would probably have to be closer to 2500:1. Which means your 5500RPM motor output converts to a wheel speed of only 5500RPM/2500 = 2.2RPM. We can then work out the maximum road speed with such a gearbox/motor config as 2*π*0.381m*2.2RPM = 5.27m.min-¹, which converts to 5.27m.min-¹*(60/1000)km.min/m.hr = 0.32km.hr-¹ or 0.2mph =D

So yeah, 0.2mph isn't much of a top speed, and 30% efficiency is probably pretty high for a 2500:1 gearbox, but at least this should give you an idea of how the basic calcs usually run.

## I cant afford a Prius, but

## Yes, I've had a very

## Always go bigger

When you say "power" which is in Watts that is not really usefull. Perhaps you should be looking at how much torque you need and at what speed.

I think the best way is to use the most powerfull motor you can find/fit/afford in your robot and then if it is too powerfull (like that will ever happen) then use PWM to reduce the power.

Note: motors using "rare earth magnets" (usually neodymium) will have lower speed, higher torque and will draw more current.

## Im using an online

Im using an online calculator for this:

http://translate.google.de/translate?u=http%3A%2F%2Fwww.roboternetz.de%2FphpBB2%2Fmotordrehmoment.php&sl=de&tl=en&hl=&ie=UTF-8

And here are some math formulas for calculating the motor strength:

http://translate.googleusercontent.com/translate_c?hl=de&ie=UTF-8&sl=de&tl=en&u=http://www.rn-wissen.de/index.php/Motorkraft_berechnen&rurl=translate.google.de&twu=1&usg=ALkJrhjbKvqSkO0Wr710Rnjm6iY_dLdKsQ

## hi

i have no idea, donload phun(google ''phun'' and dowloand, its open source, theres a pro version called algodoo, get the simple version)

its a physics simulator, make a square with the weight your scooter weighs, add a motor, and see how many nm it takes to move it...