HP requirements

[buzzp]

I have forgot all my physics and have the need to calculate the HP required to accelerate a vehicle up an 8% grade and I know the gear ratios and the weight. The final speed will be 2mph(yes, 2mph)?. What is the HP and time required to reach this speed? A generic formula would be best(all variables, weight, time, ratios, etc). Any help would be appreciated, Thanks Buzzp

 

[GregLocock]

Well I hope you haven't forgotten your maths. I'm ignoring all the losses in the following, and it's all in SI units.

The force required to accelerate the vehicle is m*(a+g*sin(theta))

The force from the motor is power divided by the vehicle speed.

So just set up a spreadsheet that integrates acceleration to velocity to distance, drop in your motor speed as a function of vehicle speed (ie your gear ratios and change speeds), and motor power as a function of motor speed, and bob's your uncle.

I am being slightly perverse, but there is no generic formula once you start to consider real things like torque vs speed for the motor, or gear ratios.
Cheers

Greg Locock