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

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    Force Formula
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Discussion Overview

The discussion revolves around a formula related to calculating the towing force between a truck and a trailer, specifically focusing on the factors involved in rolling resistance and friction. Participants seek to understand the derivation and validity of the formula in the context of physics applications.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents a formula for towing force that includes weight, friction coefficient, axle diameter, and wheel diameter, suggesting it is used to calculate tension force between a truck and a trailer.
  • Another participant notes that the formula resembles the equation for rolling resistance but does not find the axle diameter in standard sources, recommending a search for rolling resistance information.
  • A different participant emphasizes that the pulling force on a trailer on level ground is influenced more by rolling resistance and axle bearing friction rather than static or kinetic friction, suggesting the formula may be empirical.
  • One participant proposes that if "friction coefficient" refers to bearing friction, the formula could make sense, but also mentions the need to consider additional forces like rolling resistance and air drag.
  • Another participant explains the relationship between torques and forces involved in the system, suggesting that rearranging these relationships could lead back to the original formula.

Areas of Agreement / Disagreement

Participants express differing views on the validity and components of the formula, with no consensus reached regarding its derivation or application. Multiple competing perspectives on the factors influencing towing force are present.

Contextual Notes

There are unresolved assumptions regarding the definitions of terms used in the formula, and the discussion highlights the potential empirical nature of the formula without definitive sources or derivations provided.

AviationFanBoy
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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.
 
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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.
 
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.
 
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.
 
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.

(Faxle * Raxle) - (Fwheel * Rwheel) = 0

Likewise the linear forces must also sum to zero so

Ftowing - Fwheel = 0

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

Towing.jpg
 
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