Braking distance on a decline when hauling a trailer

[Bolter Man]

Hello all, I'm new to the forum and have been searching for some help to a braking calculation. I'm looking at designing a machine that has a 5th wheel on it to haul trailers. I'm keep this simple as in do not account for driver reaction time and tires are assumed to be locked up. If I know (which will change from machine location) the decline (lets say 15 percent), the coefficient of friction (0.7), both axle weights (front is different than rear due to 5th wheel loading), brake torque available at tires, speed, and trailer weight (has no brakes); how would I calculate the braking distance when the tires lock up? I can do the calculations with the machine with no trailer but once you add a trailer pushing it and adding more weight to the rear axle, I struggle to find the proper way to calculate this. Any suggestions on how I should approach this?
Thanks,

 

[3DDave]

It's not going to be easy. Depending on the geometry all the axle load on the rear might be removed. But if the wheels are locked up there is a maximum amount of friction available, so assume the weight of the vehicle is all on the front tires, calculate the friction there, and use the energy equation F*deltaT = m*deltaV, where m is the total mass of the trailer and the vehicle. Then, assume the friction remains the same throughout and use d=1/2*a*t^2 where a = F/m.

This should ball-park it.

If you look at it there are limiting cases. For example, the friction on the front might, in combination with a high located 5th wheel, simply tip the vehicle up and over the front axle. Welcome to a rider on a bicycle catching a stick in the front wheel.

To get a better answer I'd make a program that looks at the force from the tires and the effect that has on 5th wheel height, noting that as the suspension deflects more load is heading forward, increasing the suspension deflection to some equilibrium point for that instant and try to converge on a solution.

 

[GregLocock]

You need to draw an FBD for the trailer and one for the tractor. The crude tire model is misleading due to tire load sensitivity, specifically you may run out of capacity on one axle or the other or both.

https://en.wikipedia.org/wiki/Tire_load_sensitivity

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[Bolter Man]

I have installed load cells on the rear axles so I can get an active read out on the weight from the 5th wheel load. We have built in measures that limit and or alert the operator of over loading but if I'm just going off of what should be the correct weights, then the front axle weight would be 33,880 lbs and the rear axle weight is 20,220 lbs (this is after the tongue weight is added). The trailer is 40,000 lbs sitting there but when hooked up to the 5th wheel 6,000 lbs of the 40,000 are added to the rear axle which amounts to 20,220 lbs on the rear.

 

[MintJulep]

You also need to work in the height of the attachment point above the pitch center of the tractor.

Typically that will tend to load the front axle and unload the rear.

 

[Bolter Man]

I suppose that I'm going to have to make some assumptions but you are correct, there are scenarios where the rear axle could become unloaded.
Thanks,