# Calculating the speed taking into account the weight of a person

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1. Dec 22, 2015

### Rafn97

I need to buy a DC motor for an electric skateboard project. I need to calculate the speed at which it can travel with a person on top. I can calculate the speed at which the skateboard can go but is does not account for the weight of a person as that will surely decrease the speed. What formula can be used to calculate the speed with for say a 120kg person standing on the skateboard. The skateboard can go at a speed of 21mph how much will it decrease due to a person's weight? Any known formulas?

Also, what formula can I use to calculate the speed on an incline?

2. Dec 22, 2015

### Staff: Mentor

You need enough power and torque to overcome friction. The force from friction is something you probably have to test.
On an incline, you get an additional force component from gravity. Inclined plane problems can be found in literally every textbook on introductory mechanics.

3. Dec 22, 2015

### Rafn97

Thanks for your reply. Can you provide some formulas to calculate torque?

4. Dec 22, 2015

### Jeff Rosenbury

I think torque will be a measured quantity (unless you are building your own motor). Read it from the data sheet.

5. Dec 22, 2015

### Vedward

You are skipping several steps that need to be worked out to determine the motor characteristics.
First: establish the requirements - accelerate a mass of 120 kg from 0 to 36 km/hr in 30 seconds
Second: determine the force needed - F=MA. M is 120 kg. A is 36 km/hr divided by 30 seconds (convert units)
Third: from force F determine torque based on wheel size. T=Fr where r is wheel radius.
Fourth: change requirements if needed to match motor specifications.

I've left out some calculations - please review basic physics design requirements and there are some stiction (static friction) considerations for where the wheels touch the ground not covered. Also not covered are motor speed vs torque needed.

6. Dec 22, 2015

### meBigGuy

The weight of a person on a frictionless skateboad on a flat surface will not affect the speed. It will affect the rate of acceleration. As described above, F=ma.

The weight of a person will affect the friction (bearings and wheels-to-pavement). The size of a person will affect the wind resistance. Those will affect the top speed that can be maintained with a given motor/power system. I think there are plenty of web pages that will have calculators for those effects.

http://www.engineeringtoolbox.com/rolling-friction-resistance-d_1303.html is a good place to start.

So, a skateboard that can go 21mph with a person of weight X will go slower with an identically sized person of weight Y only because of increased wheel and bearing friction. It will also take a bit longer to get to that top speed.