gearbox and speed prediction?

Question

i have a dc permanant magnet electric motor and want to use a gearbox to vary the speed of an electric vehicle.The vehicle weights about 200kg and have a maximum speed of 2m/s.

i just have only one choice of varying the speed(so i cant use a electronic controller), a step down gearbox which is:

http://www.thegreenreaper.co.uk/ShowDetails.asp?id=564

I am not sure why,but this gearbox have a maximum speed of 2000rpm for the motor input. The maximum gear ratio is 68:1 and the lowest is 17:1.

i know that to calculated the output speed is equal to:

rpm = speed/ 2*phi*r

since there is a limit on the input speed,the thing that i am confius about is:

How do you calculated the maximum speed that the motor could achieved(in this case is 2m/s), when the maximum input speed for the gearbox is 2000rpm(which is basically at the NO LOAD speed of a motor)....

Answer 1

Okay, 2000 rpm is 2000/60 rps. If there's a gear reduction of 17:1, then the axle rotation speed is 2000/(60*17) rps. Finally, the circumference of the specified maximum size wheel is (3.14)(0.505 m), so we multiply all of this together to get:

(2000 rps * 3.14 * 0.505 m) / (60 * 17) = 3.11 m/s

Remember, this is "no load" speed, so that perhaps a realistic maximum "load" speed is 2 m/s.