Hello Physics Forums,(adsbygoogle = window.adsbygoogle || []).push({});

I've been looking around on these forums for help with trying to calculate the max velocity of an electric longboard my group of friends are making. After reading a few posts, you guys have helped me understand these calculation a lot better.

Right now we have a gear we are thinking about using, but we are considering getting a new gear depending on a maximum speed calculation.

This longboard is powered by one electric motor with a pulley belt going from the motor shaft pulley to a pulley on a wheel of the longboard.

Like this:

I am aware that the maximum speed of the longboard can be can be calculated from rpm of the wheel times the circumference:

Velocity = rpm shaft * gear ratio * 2 * PI * radius wheel

(gear ratio = shaft pulley / wheel pulley)

(rpm shaft = Battery Volts * Kv Motor)

But it we wanted to use a different calculation because this equation didn't take into consideration other forces acting on the longboard.

Therefore we used the equations below that uses rolling friction, drag, and the force at the wheel of the longboard from the power and torque supplied by the motor.

Free body diagrams:

https://docs.google.com/presentation/d/1AQB0hobkEDjml_ogeAiS_b97AHGMdfuXgTlEd_Qzw64/edit?usp=sharing

Google sheets calculations using the equations below:

https://docs.google.com/spreadsheets/d/1_gZbtuwIs4DpJcVSWQHrwEuCpFddRLJ7mRFlSEbtPy0/edit?usp=sharing

Power shaft = Torque shaft * Angular Velocity

Power shaft = Voltage * Current

Angular Velocity shaft = rpm shaft * (1/60) * (2*PI / revolution)

Torque shaft = Power shaft / Angular Velocity shaft

Force Pulley Belt = Torque shaft / radius shaft pulley

Torque Wheel = Force Pulley Belt * Radius Wheel Pulley

Force Wheel = Torque Wheel / radius wheel

The only issue is that as the wheel pulley gets larger, the Force Wheel and maximum velocity of the longboard increases. Furthermore, if the wheel pulley gets smaller, the Force Wheel and maximum velocity of the longboard decreases. This doesn't make sense because a smaller pulley would be spinning much faster than a bigger pulley and should go faster.

So we were wondering if there is something we are missing with our calculations that would account for the rpm of the wheel. Or does anyone have another suggestion for calculating max velocity?

I saw people using:

Power = Force*Velocity

And "jack action" has the HP Wizard website that has the max velocity equation displayed here:

http://hpwizard.com/accelerating-power-limit.html

But I think I might run into the same problem as I did before because it doesn't account for rpm. Do you guys have any ideas?

Thanks for your time.

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# Calculating Maximum Velocity Electric Longboard

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