# Horsepower achieved with multiple motors

Scenario

I'm planning to build an electric motor for fun (not for any practical purpose). I recently purchased a shapeoko CNC mill kit and intend to manufacture most of the parts housing, stator etc. I'm currently in the planning stage and would like to plan/build this intelligently vs trial and error.

Goals move 200lb (including the motors) at about 5-10mph (faster end of that if possible)

Questions

1. How do you calculate the torque/hp that a motor will produce?
2. If I put 4 smaller motors (instead of 1 powering the entire drive train) on the job can each produce less torque/hp and still achieve my goals?

I understand the basics of building an electric brushless motor, I'm more interested on how to plan a motor for a specific output.

# EDIT

After some more research it seems that 1 HP = 745.699872 watts

so to move 200lb at 5 mph

• I need a 0.0019511579888525 horsepower motor.
• I need to provide 1.4549782617235 watts to the motor.

AND to move 200lb at 10mph

• I need a 0.01560926391082 horsepower motor.
• I need to provide 11.639826093788 watts to the motor.

I still need to figure out how Question 2 factors into my calculations.

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Are you moving horizontally opposing friction, or vertically opposing gravity, or both? Note that power is $W=F\cdot V$ without any exponents as stated in the question. I calculate about 4000 Watts, which makes more sense given the requirements. – ja72 Sep 6 '12 at 18:53
horizontally opposing friction, where did my math go wrong? should i not calculate W off of horsepower? – Francis Yaconiello Sep 6 '12 at 19:16

If the weight is $F$ in pounds, the coefficient of friction $\mu$ and the speed of $v$ in mph then the power $W$ required to maintain this motion in Watts is
$$W \approx 2.0 \mu \cdot F \cdot v$$
The coefficient of $2.0$ comes from the conversion into metric units. To move 200 lbs at 10 mph with a coefficient of friction of $\mu=0.4$ is
$$W \approx 2.0 (0.4) (200\; {\rm lbf}) (10\; {\rm mph}) = 1600 \; {\rm Watt} = 2.15 \;{\rm hp}$$
This power comes from $W=I\,V$ where $I$ is current and $V$ is voltage, without losses or a fraction of this product with losses. I guess you can get the details from wikipedia. An online calculator is also here.