# Choose a DC Motor for a skateboard

My body weight and that of the skateboard is $M = 90\text{ kg}$

I want to move 10 meters in 4 seconds.

\begin{align} x(t) &= (at^2)/2 \\ x(4) &= (a\cdot4^2)/2 = 10 \\ &= a\cdot16/2 = a\cdot8 = 10 \\ \therefore a &= 10/8 = 1.25\text{ m/s}^2 \end{align}

The wheels of the skateboard have a radius $r = 0.027\text{ m}$. I want a maximum velocity of $v = 30\text{ km/h} = 8.333\text{ m/s}$.

$$\omega = \dfrac{V}{r} = \dfrac{8.333}{0.027} = 308\text{ rad/s} = 2941\text{ rpm}$$

$$F = ma = 1.25\cdot90 = 112.5\text{ N}$$

The torque needed $C = Fr = 112.5\cdot0.027 = 3.03\text{ Nm}$.

Therefore the power $P = C\omega = 933\text{ W}$.

But I'm not really sure if it is correct because I only need 3.03 Nm when I start moving, same for 2941 rpm is just the maximum velocity.

$C\omega = P$ but I'm not sure that it is the torque at start multiplied by $\omega_{max}$.

If I am right I need then to buy a DC Motor with 933 W and at least 3.03 Nm and at least 2941 rpm?

• Clearly you don't need enough power to still be accelerating at $1.25m/s^2$ while also at top speed! The thing is, you won't get a constant acceleration... Sorry I don't have time for a full answer now - I'll come back to this if nobody else provides a good answer. In the mean time, have a look at this: vias.org/kimberlyee/ee_15_04.html consider how fast you will be going after 10m (since this is what you based your acceleration requirement on), and consider how much power will be required to overcome air resistance and keep you moving at a constant $30km/h$ Feb 20 '18 at 19:47
• 933W is sure enough to get you going 30km/h. Older mopeds had barely that, and they get you 50km/h easily. To prevent future failure moments and save time, I'd advice you to design a set-up first and show that here. It matters a lot how your set-up is configured for how much power you need. With set-up, I mean an idea, a coarse drawing of the technicals(gearing etc.), and how you plan to take a battery with you, what kind of battery etc.
– Bart
Feb 20 '18 at 21:04
• Fastest move is not a constant acceleration but trapezoidal velocity curve. Feb 22 '18 at 14:19