Low rpm, high power calculations help

Question

Im trying to build an electric wheelchair with mecanum wheels, and as you might know, each of its 4 wheels has to be independently powered for the chair to have holonomic motion.

With my desired speed to be around (brisk) walking speed only, say 1.15 m/s, and my mecanum wheels sized with a 4-inch radius, I know that I'm going to need a very low RPM (by my computations, ~110 rpm).

However, my computed power draw per wheel is around 300W, which is way large, that Im not sure if Im on the right track? My load capacity is somewhere around 136 kg, btw.

This brings me to my question: are my torque/rpm/power calculations correct?? (code-blocking it up for clarity)

per wheel:
r = wheel radius = 4 inches = 0.1016 m
circumference = 2pi(r) = 0.638 m
v = (max) running velocity = 1.25m/s
rpm = v(60/circumference) = 117.48 rpm

the chair:
u = coefficient of friction = ~0.7
N = normal force = mg
m = total mass (136 kg)
g = 9.81 m/(s^2)
vi = 0 (rest)
t = time to accelerate, say 2 s
a = acceleration = (v-vi)/t = 1.25/2 = 0.625 m/(s^2)

Finally:
Ftotal = uN + ma = m*(uN+a)
Fwheel = Ftotal/4 = 255. 248 N
Twheel = (Fwheel)(r) = 25.93 Nm

Pwheel = (Twheel)(rpm)(2pi/60) = 319 W

Is the power really supposed to be this large and my RPM that low?? Have I missed something?

Help/corrections would be very much appreciated!!

Answer 1

Here's a simple (frictionless) check: -

Force = mass x acceleration - with an acceleration of 0.625 m/s/s and a mass of 136 kg, that's a force of 85 newtons.

Work done in accelerating up to speed (1.25 m/s) is force x distance.

Distance covered is average speed in that 2 second time period x 2 seconds so that's 0.625 m/s x 2 seconds = 1.25 m.

Energy inputted (work done) is therefore 85 newtons x 1.25 m = 106.25 joules.

This can be converted to power by dividing by time (2 seconds) = 53.125 watts.

So it looks like something is wrong in your calculations (or mine, god forbid!).