[Phys-L] Re: Stopping Distance

[jsd at AV8N.COM (John Denker)]

Hi --

I think this is an excellent thread.
  -- It is important.  Understanding stopping distance is literally
   a life-and-death issue sometimes.
  -- When I talk to my non-scientist relatives, I sometimes ask them
   what they wish had (and hadn't) been covered in high-school physics.
   The most common answer is a request for more discussion of things
   like braking and cornering, i.e. stuff that directly affects their
   lives.
  -- The "information" in typical Drivers' Ed publications is provably
   wrong.
  -- The "information" I found on the web doesn't pass the giggle test.
  -- Some good information has appeared in this thread.


Let me clarify one of my earlier remarks:

> > It's just physics ... but it is not trivial one-parameter plug-and-chug
> > physics.

I overstated it when I said "just" physics.  There are a lot of
engineering tradeoffs involved, plus some outright arbitrariness,
so the right answer(s) cannot be obtained from fundamental physics
alone.


Rick Tarara wrote:
> My lab assistant is a retired brake engineer--here is his response:
...
> Another consideration is the lag time (especially for air brake
> vehicles).  ...  This can take
> several seconds.

I find that hard to believe.

> f you're going at 60 mph (88 fps) considerable
> distance can be traveled while the stopping power (brake torque) is
> being 'built up'.

Let's see:  five seconds times 88 fps is 440 feet, i.e. about 30 carlengths.
Not credible.

> 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.

That's an example of a non-physics consideration.  It's true, but not
derivable from fundamental physics.  They could make more space for
the brakes if they wanted to.  They could also provide better ventilation
for the brakes if they wanted to.

> 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.

Yeah, but have you ever seen the brakes on a DC-10?  They're pretty
impressive.  Here are the comparative statistics:
    DC-10                         big rig
   100 tons                      40 tons at most
   140 mph                       70 mph
   4 main brakes                 6 brakes on the box alone
   490,000 E units per brake     32,666 E units per brake
   triply redundant actuation    n/a

So the aircraft brake's job is at least 15X harder than the truck brake's job.
If they were built using comparable technology (which they aren't), the truck
brake could be an order of magnitude smaller.

The brake energy issue is not to be sneezed at.  Aircraft like the DC-10 have
brake temperature monitoring systems.  If you use the brakes unusually
heavily, you will most likely need to wait awhile before attempting the next
takeoff, so that the brake energy can drop to acceptable levels.  Usually you
slow the aircraft down most of the way using thrust reversers, but that is not
always an option, so it's nice to know there is enough energy capacity in the
brakes to stop the aircraft from full speed using brakes alone.  You can do
that once ... but not twice in quick succession.

Trucks face additional considerations:  they "should" have a steady-state
brake power budget (for stop-and-go driving), in addition to a peak energy
budgent (for one big sudden stop from high speed).  But anecdotal evidence
suggests that what trucks "should" have is not what they actually have:
   http://www.heavydutytrucking.com/2004/01/074a0401.asp
although undoubtedly some trucks are better than others.

>   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

I reckon that's commonly true ... but again it's not based on any physics
principles;  it doesn't need to be true.  It wouldn't be hard to implement
an adjustable sensitivity factor in the brake system ... either automatic
according to load, or simply a manual fudge-factor.

More generally:  It would be nice if stopping distance were limited by the
physics of the situation, but commonly it is much, much worse than that.