Sorry (but since it was a prefect world and all). Maybe not the best starting point. I would think it depends on how fast you want it to get to a certain speed. Not really my forté(?), I’m not sure how to calculate this. I think it would be dependent on things like wheel radius too.
T = F * L (in my simple mind at least, also I found it is equal to angular acceleration * inertia).
F = m * a
T = Torque
L = arm length where force is applied
F = Force
a = acceleration
m = mass
a = F/m, up to a certain speed for your motor. Except minus some friction resistance, which is the big question as to how to get. Once you get that somehow, its probably just a matter to juggle the equations a bit to get a ballpark torque for your motor?
Or something like this. I’m sure a google could provide better answer. Or maybe a Wolfram Alpha
… and since this was interesting, I googled up Rolling resistance
According to this, it is:
F = Crr * Nf
F = Nf*b / r
b = Crr * r
C[sub]rr[/sub] is the dimensionless rolling resistance coefficient or coefficient of rolling friction (CRF)
N[sub]f[/sub] is the force normal to the surface.
F is the rolling resistance force
r is the wheel radius
b is the rolling resistance coefficient or coefficient of rolling friction with dimension of length
(The above basically taken from wikipedia.)
Now I don’t know anything about what kind of wheels you use, the radius or substance they roll against, so this is a guesstimate. According to the rolling friction table at the above link, I guess on a Crr of about 0.005 for your wheel thing.
It would then requre a force of:
5 lbs = 2.268 kg
F = 0.005 * 2.268 kg * 9.8 m/s/s = 0.111 N
This is just to be moving (rolling) horizontally. If you got 4 wheels I suppose they would add up to the same. Plus a bit for friction on the bearings.
That is part 1… Then part 2; how fast do you want to get up to a certain speed? Which is back to the F = m * a formula
Say 5 seconds to get to a speed of 1 m/s…just to pick some numbers. This is probably too slow an acceleration though.
Which indicates an acceleration of:
v = a * t
a = v/t = 1/5 m/s/s
v = speed
a = acceleration
t = time
requiring a force of
F = m * a = 2.268kg * 1/5 m/s/s = 0.454 N
Add this to the rolling resistance force required:
Ftot = 0.457N + 0.111N = 0.565 N
Now for a wheel radius of say 5 cm (just to pick another number…), you would need a torque of:
T = Ftot * L = 0.565N * 0.05m = 0.0283Nm
Seems like a pretty low number, but I also picked a pretty low acceleration. At least I think so.
Be warned: I got virtually no experience with motors and the like… I don’t even know if this is a practical number for torque, or indeed if this is correct-ish. But if it is, maybe it could be a “starting point” to fill in your actual numbers.