[Phys-L] Re: race between car and airplane

["Folkerts, Timothy J" <FolkertsT@BARTONCCC.EDU>]

Granted, there are all sorts of refinements and clarifications that c=
ould be made.  Still the basic result that the car would go faster is=
 pretty clear over a wide variety of conditions and assumptions (as l=
ong as the functional form of the drag is similar for both vehicles).

As a simplification, one could compare a car and a plane first in no =
wind and then in a direct headwind.  That eliminates 1) much of the s=
elf-contradictory conditions and 2) any effects of cross-winds/change=
s in effective area/etc.  This is actually the gist of the problem (a=
t least as I saw it) - a car an plane are even until the headwind inc=
reases.  Then who will pull ahead?

In this case, the plane simply slows down by the amount of the headwi=
nd.  The car also slows down, but not as much (as long as the drag sc=
ales a some function greater than F =3Dkv).

Tim F

-----Original Message-----
=46rom: Forum for Physics Educators on behalf of Brian Whatcott
Sent: Fri 1/27/2006 6:01 PM
To: PHYS-L@LISTS.NAU.EDU
Subject: Re: race between car and airplane
=20
At 03:02 PM 1/27/2006, Tim Folkerts, you wrote:
> John,
> ///
> 1) Your 3rd assumption is in direct conflict with a section of the p=
roblem
> statement, but since the problem itself is not clear or consistent, =
that
>  is hard to avoid.  (The problem specifically states the car "in st=
ill air
>  goes 120 mph", but you are assuming it goes 120 mph with a 20 mph
> cross-wind as the plane flies above in the same crosswind).
>
> Tim Folkerts

Actually, all three of John's explicit assumptions are either in conf=
lict
  with the facts of the puzzle as asserted, or with the usual physica=
l
models of aerodynamic drag when viewed from different perspectives.

But that's just fine for a class of puzzles known as tech teasers,
sometimes  used on employment interviews.

For example, if we acknowledge that at some stage the car IS operatin=
g
  in still air, then turns (not necessarily by 90 degrees) into a hea=
dwind;
(say after penetrating a front) - how could we possibly come to a
similar conclusion to John's?    (though one smiles behind the hand
to suppose this or any other solution is at all exact.)

Easy! Two vehicles penetrating a headwind, and subject only to
aerodynamic drag can experience different drag forces at the same
"air" speed (obviously).  One is flying in free-field conditions, and=
 the
other is flying within a foot or so of the ground.
But the free field vehicle is smooth on the underside, as a matter
  of course, and (until quite recently at least) the other one has im=
mense
protuberances. Despite the fact that the car is subject to enhanced
viscous shear over the short range involved between floor and road.
  When the relative speed of the road to underbody changes,
you can expect aero drag  to change in a different way from that
  of the free field vehicle.

   This reminds me of the tale that you have probably heard about
   - i.e. it's not good enough to place a car in a  wind tunnel, with=
out
  attention to substrate motion.

There are other argumentations that could be aired....
  how about a person who offers a long-standing model of aero drag
force as  Fd =3D Cd.A. 1/2 .rho.V squared and then suggests that an
effective value for A,  the cross section area is augmented by
  sin 10 deg of the side area, if the car were operating in a
  quartering headwind?

This could be quite a drag increment if Fd really scaled with A...
You may be reminded that some cars offered lower drag values
going backwards than forwards, but I fancy there are still rather
few car shapes that don't at least increase drag when placed
  broadside to the wind....
       There are more debating points, I feel sure, but I have writte=
n
  enough.


Brian Whatcott    Altus OK    Eureka!
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