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some auto aerodynamics... was 4k conversion advice
Todd, force and inertia are easy to confuse when they are both acting on the
vehicle, but keep them separate. The addition of a wing out back affects
polar moment of inertia only through its weight... which is its mass times
gravity.... and it's distance from the center of gravity. The force that a
wing exerts affects only the static friction of the tires... which is the
sum of the weight on the tires plus the downforce of the wing, all times the
coefficient of friction between the tires and the surface on which they
roll.
The force which the wing exerts on the vehicle is divided between the two
axles in inverse proportion to the proximity to those axles. If the wing is
25% of the wheelbase length from the rear wheels then it exerts 75% of its
force on the rear. If the wing is located outside the wheel base then the
ratio becomes a direct proportion on the nearest axle with the remaining
force acting in a negative direction on the axle at the other end. I'll
never understand why the AA Fuel dragsters have their wings behind the rear
wheels as the downforce it generates acts to raise the front wheels. As the
front wheels don't raise, even at 300mph, then clearly the front wings
generate more downforce than the rear wings generate 'upforce'. The irony
is that if both their wings acted in harmony, i.e. the rear wing were in
front of the rear wheels, the angle of attack of the front wing could be
reduced and the overall drag of the vehicle would be reduced
significantly.... can you say 'increased top speed?' I've tried to tell
John Force and Eddie Hill the error of their ways but apparently screaming
at the television is not very effective.
Back to your question. Moving the wing back will not increase the force
which it generates but the leverage, actually moment arm, will make a
difference. For the purposes of illustration, one could move a wing to
great distances outside the wheelbase and discuss the moment arm effects but
soon the handling you are seeking to improve will change enormously as a
function of speed and the resultant forces on that moment arm and the
problem is out of bounds.
Regarding the aero forces on the F1 cars, recall that what is happening in
the tunnel is only half of what one needs to consider, the other half is
what is going over the car. (Just like the airplane wing where the goal is
to have the resultant force going 'up' though generating faster air over the
top of the wing than the bottom.... apply Bernoulli here and recall that in
this regard force is that which is measured perpendicular to the direction
of airflow and had nothing to do with the dynamic force of the air
molecules.) If the air under the F1 car is caused to accelerate such that
it is going faster than the air that is going over the top of the car then
the resultant force is down... and the car 'sticks' better. How does one
get that air to accelerate under the car? Create a more curved path for it
to follow than the air that is going over the top. (The law of Conservation
of Mass says that if you measure the volume of air in front of the F1 car
then it _will_ be the same volume as behind the car, which means that the
air did whatever it had to in order to get to get to that aft measuring
point.) So, if you constructed a tunnel with a fairly small opening and
then increased that area inside the tunnel then the air molecules would have
to increase in velocity in response to that increased area... and the
pressure under the vehicle would decrease. The pressure on the top of the
vehicle is high, relative to underneath, thus creating downforce.
One must consider the forces on the system, not just locally within the
tunnel.
Regards, Gross Scruggs
Date: Mon, 14 Dec 1998 13:12:32 -0800
From: Todd Phenneger <phen9461@uidaho.edu>
Subject: Re: 4000 turbo conversion advice
Damn Scott,
Nice reply. THanks. One question. On the downforce thing, if you
stick the wing out back then doesn't that effectively ALSO change the Polar
moment of inertia? ANd, if you take a 1000lb force wing at 100mph and put
it in back over rear axle it creates 1000lbs force. Move it 3 feet back
from axle and it is more, say maybe 2,000lbs effective force.. BUT, you
also put the same wing 3-feet in front of front axle then do they both but
2,000lbs effective force? I would think not as my *limited* physics tells
me this is impossible but I could be very wrong. Seems to me the leverage
would counteract and both would still be 1,000lb effective force.
BTW, I dont spose you now how the tunnels under a F1 car creat
downforce. I understand the tunnel that widens to created a vacuum thing
but dont they also sometimes make bottom bend toward pavement to speed up
air. While that speeds up molecules like on an airplane wing since they
have to go further, under a car wouldn't a vacuum be more effective. Or is
that much higher drag so they go the bent/wing method.
Thanks
Todd