[Phys-L] Re: Stopping Distance

[jsd at AV8N.COM (John Denker)]

Shapiro, Mark wrote:
> ... Partially loaded trucks typically have a large fraction
> of their weight on the forward 10 wheels, and much less on their rear
> eight wheels.  Thus there is a high propensity for the box to break
> loose and fishtail if the brakes are applied too hard.
>
> Truckers learn to compensate for this effect, but that leads (along with
> all the other factors mentioned) to longer stopping distances.

This is an interesting subtopic ... but I am mystified as to the alleged
_sign_ of the effect.

In every other example I can think of, a forward CM is conducive to
_enhanced_ stability during braking, OTBE. (This is, I assume, the
reason why truckers commonly load the box with a forward CM.)  Draw
the free-body diagram.

OTBE := Other Things Being Equal.

A well-known (in some quarters) example of the advantages of having a
CM forward of the brakes is the contrast between a taildragger type
aircraft and tricycle-gear aircraft.
   http://www.aerospaceweb.org/question/design/q0200.shtml

I wouldn't recommend it to an elementary class, but the easiest way
to draw the free-body diagram is to use the _accelerated_ reference
frame comoving with the truck.  Then you get an obvious torque due
to the force on the accelerated mass ("artificial gravity") acting
through a lever arm relative to the braking force.

========

If we look beyond the OTBE approximation, in *some* scenarios involving
antilock brakes, different wheels will develop different amounts of
braking force -- but this only goes as far as mimicking the weight
distribution, compensating (never overcompensating) for the stabilizing
effect of a forward CM.  So this at most a wash ... so I can say the
forward CM is never destabilizing in any scenario I can think of; it
is usual stabilizing but arguably sometimes only neutral.

Or am I missing something?  Please clarify.

Surely any brakes on the _tractor_ part of a big rig will be destabilizing.
Also any multi-trailer configuration will have "innnnteresting" stability
issues.

Here "innnnteresting" is used in the Chinese sense.