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[Phys-L] Re: Stopping Distance



My lab assistant is a retired brake engineer--here is his response:

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You are correct about the KE the brakes and drums have to convert into
heat and dissipate into the atmosphere. As temperature rises, the
coefficient of friction of the lining to the drum usually changes and
this is usually lower. The drum brakes used on the "big rigs" rely on
the lining mu to "energize" the brakes to produce higher torques through
the geometry of the brakes (i.e. simply stated: the friction force acts
like a lever to increase the normal force and hence, more torque for
more stopping force at the tires). When the mu decreases, so does the
torque and its created stopping force and usually not just a straight
line function (i.e. a 1% reduction in mu may yield a 5 to 10% reduction
in torque - numbers not real, but to make the point about not being
linear). At high speeds and large loads, this can be a factor even in
one stop. Multiple stops, or applications for slowing while going down
a long grade, does this as a rule and we call this "fade" (i.e. it takes
more force to stop or slow the vehicle as the lining "fades" - mu gets
lower). The brakes and drums cannot instantaneously absorb and
dissipate the heat so things get hotter!

Another consideration is the lag time (especially for air brake
vehicles). This can be considerable! The signal to apply the brakes is
controlled by the foot valve in the cab of the truck. This signal (an
amount of air pressure) has to travel considerable distance to activate
the brakes to another valve. Then the "air chambers" have to fill up
with relative high pressure air from storage tanks. This can take
several seconds. If you're going at 60 mph (88 fps) considerable
distance can be traveled while the stopping power (brake torque) is
being 'built up'.

Something else with air brakes (tractor - trailer rigs all have air
brakes because they can be easily disconnected from each other and use
the same power source; the air compressor driven by the tractor engine):
Most are applied by the "air chamber" (i.e. pressure over an area to
produce a force) to what is called a "slack adjuster" (it is adjusted to
compensate for lining wear). This is basically a lever that rotates
about a shaft which has a cam on the other end to activate the brake
shoes. For optimum force, you must have the force input at 90 degrees
to the rotating slack adjuster. Since the slack adjuster rotates
through an arc, there is only one position where it is really at 90
degrees to its actuating rod; maximum force input for the brakes. Small
changes in this may not be noticeable, but as the angle increases, the
"useable" actuating force gets smaller resulting in less available brake
torque. This is a maintenance item because the brakes must be adjusted.
They now have "automatic adjusting" slack adjusters and I imagine they
are coming into more use on the tractor-trailer vehicles on the road
today.

Also, there is the practical matter of usable space for the brakes and
drums. The big rigs use 20 to 22.5 inch diameter wheels. The brakes
have to fit into them. Therefore only so much mass and area for heat
conversion and dissipation will be able to be put into the brakes and
drums and only so much room will be available for the forces to generate
the brake torque. I don't have any numbers off hand, but I'm sure the
heavy truck 'Gross Axle Weight Rating' (GAWR) to wheel diameter would be
an order of magnitude to that of a passenger car and light truck. Then
there is another compromise, as you stated, and that has to do with the
considerably large difference between the loaded and unloaded wheel load
to the road of a heavy truck versus and car. If the brake engineer uses
sufficiently large forces to stop the heavy truck as fast as a car when
it is fully loaded, the force to stop it when empty or just lightly
loaded will be very difficult to control and then you get the wheels and
tire to very easily lock and this results in stability issues (i.e. the
"jackknife" or "bobtail tractor" problems). ABS helps this issue and
various systems have been available on the heavy trucks for some years
now. I don't know how many of the rigs on the road have this feature
and would imagine there are some that still do not.
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Message forwarded by Rick Tarara