Where can i get more info on this formula? (trailer towing force)

[AviationFanBoy]

I need to use this formula for a physics prac (my dad an engineer told me it).
F = Weight (normal) x friction coefficient x diatmer of axle)/diamter of wheel
x4 cause the trailer has 4 wheels.

Can anybody point me towards a source of info on it, in particular the derivation.
I use it to calculate the tension force acting between a truck and a trailer.

 

[Drakkith]

That looks similar to the equation for rolling resistance, but I'm not seeing the diameter of the axle in the equation in any of the sources I've looked at. You could try searching google for rolling resistance and see if you can find something I missed.

 

[PhanthomJay]

I have not seen that formula either, but I want to point out that if the trailer is being pulled by a truck on level ground, the pulling force on the trailer without slippage of the tires does not depend directly on static or kinetic friction but rather on rolling resistance and axle bearing friction. The formula your dad sites might be an empirical formula based on tests. For example, if the diameter ratio is 1/12 and static friction coefficient rubber on pavement is 0.6, then equivalent resistance coefficient is 0.05 which might be in the ballpark, and the pull force at constant speed is 0.05 W times 4, where W is the weight on each tire. Of course, if you had my old Columbia bike with lousy tires and worn bearings, that value would go way up. Just guessing here, though.

 

[CWatters]

I think the formulae makes sense if "friction coefficient" refers to the bearing friction. I think that would explain the inclusion of the ratio axel/wheel diameter.

However to that force you also need to add other forces such as that due to rolling resistance and air drag.

 

[CWatters]

Just to explain what I mean...

If you assume constant angular velocity then the net torque sums to zero. So if the bearing or axle friction acts clockwise then friction between wheel and ground must act anticlockwise. These two torques must sum to zero.

(F_axle * R_axle) - (F_wheel * R_wheel) = 0

Likewise the linear forces must also sum to zero so

F_towing - F_wheel = 0

If you rearrange that lot you should get the original equation.