# question about torque



## le blond (Jul 26, 2007)

hi everybody!

for my e-bike project i wanna put this motor http://secure.oatleyelectronics.com...d=192&osCsid=05595849759ae525e3a47affcd28e1fd on a 26" wheel with a 7 speed gear (biggest 28 tooth - smallest 14 tooth) the motor is running at 320 rpm an have a torque of 7.46 Nm, my question is: is the motor will have enough torque to propel the bicycle with me on it (140lbs) i'm good only in basic mechanics sciences when it's get more complicated i bust!

p.s: excuse me if my english is not perfect i'm french!

thanks!!


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## xrotaryguy (Jul 26, 2007)

Your English is very good. Better than my French! 

Since the motor is actually bigger than the legal limit, I would assume that it is capable of moving you quite well. The questions that need answered are "How quickly will it accelerate?" and "How fast will it go?"

Let's see how my high school physics skills are holding up. The motor can make 7.46Nm of torque. This torque is multiplied by the radius of the largest cog (28 tooth) on the wheel. That radius should be about 0.061 meters. (7.46Nm)(1.061)=7.915Nm Someone please tell me if I am doing the math wrong here. I don't think we even did any problems like this one when I took this class  Now, to determine the force that is actually being transmitted to the ground, the torque is divided by the radius of the wheel. I am assuming that you are using a road bike wheel which has a radius of about 0.343 meters. I may be off a tad here because I am converting from a wheel with 27 inch diameter. Forgive me, I am an American  ... 7.915Nm/0.343m=23.08N. The formula for acceleration is acceleration=Force/mass. Your bicycle should accelerate at a rate of .2815m/(s^2) if the combined mass of you, your bike and the bike's batteries are 82kg.

To calculate top speed you will need to know the bicycle's aerodynamic drag coefficient. Actually this calculation really needs calculus to be very accurate. The acceleration calculation should be done with calculus as well because the motor will not always produce the same torque, and because drag will increase with speed, but we are probably close enough.


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## le blond (Jul 26, 2007)

wow!

thank you wery well for your answer, very helpful !


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