[DeTomaso] Other Aero Issues

[Daniel C Jones]

The dimples on a golf ball decrease drag by inducing a turbulent boundary
layer to delay the drag increase associated with separated flow.  The least
drag is achieved when the boundary layer is laminar and the flow stays
attached to the surface contour.  In practice, this only occurs passively
for slender shapes, like air foils) and then only sometimes.  For most
practical shapes, laminar flow boundary layers will separate from the
surface.  This separation causes a large drag increase.  In cases like
that, a turbulent boundary layer stays attached to the surface longer,
resulting in less overall drag.  It takes a fair bit of math to prove
this but it comes down to the fact that a turbulent boundary layer is
more energetic than a laminar one and requires a larger adverse pressure
gradient to detach.  The location along the body at which the flow
transitions from laminar to turbulent determines the critical Reynolds
number.  Below this number, the flow is laminar, above it's turbulent.
The Reynolds number is a linear function of velocity.  The faster you
go, the farther forward the transition point moves.  You don't have to
rely on high speeds to cause the boundary layer to "trip" from laminar
to turbulent.  Small disturbances in the flow path can do the same thing.
That's why golf balls have dimples.  A better approach for a Pantera
would boundary layer trip strips or vortex generators to do the same
thing.  However it may be unnecesary.  If the flow is already fully
turbulent ahead of the point at which the flow deaches, introducing
additional turbulence will not have a beneficial effect.  Also, the
body needs to have a gradual slope for even a turbulent boundary layer
to stay attached.  Flow will detach at the pronounced step at the sugar
scoop.

A couple of guys here at work (Boeing), tufted an '87 Mustang LX hatchback
from the center of the roof to the taillights.  They were trying to use
vortex generators to to induce turbulence to trip the boundary layer,
hoping to delay the flow dettachment at the hatch so they could get cleaner
air over the wing.  Their vortex generators were based on aircraft designs
and they used a hang glider airspeed indicator on a pole to measure the
boundary layer thickness across the roof.  They made the vortex generators
two inches tall to be conservative (the boundary layer was approximately
one inch thick and a rule of thumb is to make the generators 1.5 time the
boundary layer thickness).  They didn't see an improvement in coast down
times, but the tufts did appear a little better behaved with the vortex
generators.  They believe the turn at the back of the roof may be too sharp
to permit attached flow.  They also noted that much of the clean flow to
the wing appeared to be coming from around the sides of the car.

More on boundary layers follows...

The profile drag of an object can be spilt into two components:

    Cd = Cdf + Cdp

  where

    Cd  = profile drag coefficient
    Cdp = pressure drag coefficient due to flow separation
    Cdf = skin friction drag coefficient due to surface roughness
          in the presence of laminar/turbulent flow

The drag which comprises the Cdf component is caused by the shear stress
induced when air molecules collide with the surface of a body.  A smooth
surface will have a low Cdf.  Also, the Cdf is lower for laminar flow and
higher for turbulent flow.  Cdp, on the other hand, is caused by the
fore-and-aft pressure differential created by flow separation.  Usually,
Cdp is lower for turbulent flow and higher for laminar flow.  In many cases,
inducing turbulence will dramatically decrease the pressure drag component,
decreasing the overall drag.  Airplanes use this trick all the time.

Back in the 19th century, when scientists were just beginning to study the
field of aerodynamics, an interesting observation was made with respect to
the drag of a cylinder.  Since a cylinder is symmetric front-to-back (and
top-to-bottom), their early theories predicted it should have no drag (or
lift).  If you plot the (theoretical) pressure distribution along the
surface of the cylinder (remembering that pressure acts perpendicular to a
surface) and decompose it into horizontal (drag) and vertical (lift)
components, you'll find that the pressure on the front face of the cylinder
(from -90 to +90 degrees) and the pressure on the rear face ( from +90 to
+270 degrees) are equal in magnitude but opposite in direction, exactly
cancelling each other out.  Therefore, there should be no drag (or lift).

However, if you actually measure the pressure distribution, you'll find
there are considerably lower pressures on the rear face, resulting in
considerable drag.  This difference between predicted and observed drag
over a cylinder was particularly bothersome to early aerodynamicists who
termed the phenomenon d'Alembert's paradox.  The problem was due to the
fact that the original analysis did not include the effects of skin
friction at the surface of the cylinder.  When air flow comes in contact
with a surface, the flow adheres to the surface, altering its dynamics.
Conceptually, aerodynamicists split airflow up into two separate regions,
a region close to the surface where skin friction is important (termed the
boundary layer), and the area outside the boundary layer which is treated
as frictionless.  The boundary layer can be further characterized as
either laminar or turbulent.  Under laminar conditions, the flow moves
smoothly and follows the general contours of the body.  Under turbulent
conditions, the flow becomes chaotic and random.

It turns out that a cylinder is a very high drag shape.  At the speeds
we're talking about, a cylinder has a drag Cd of approximately 0.4.  By
comparison, an infinite flat plate would have a Cd of 1.0.  Note that
this is not a theoretical limit.  A rectangular beam will exhibit flow
separation at each corner and can have a Cd in the range of 2.0.  An
efficient shape like an airfoil (that is aligned with the airflow, i.e.
is at 0 degrees angle of attack) may have a Cd of 0.005 to 0.01.  Think
about what this means.  An airfoil that is 40 to 80 inches tall may have
approximately the same drag as a 1 inch diameter cylinder.

Luckily, there are easy ways of reducing a cylinder's drag.  Another thing
the early aerodynamicists noticed was that as you increased the speed of
the air flowing over a cylinder, eventually there was a drastic decrease in
drag.  The reason lies in different effects laminar and turbulent boundary
layers have on flow separation.  Laminar boundary layers separate (detach
from the body) much more easily than turbulent ones.  In the case of the
cylinder, when the flow is laminar, the boundary layer separates earlier,
resulting in flow that is totally separated from the rear face and a large
wake.  As the air flow speed is increased, the transition from laminar to
turbulent takes place on the front face.  The turbulent bundary layer stays
attached longer so the separation point moves rearward, resulting in a
smaller wake and lower drag.  For a cylinder, laminar flow separation may
occur at 82 degrees (with the leading edge of the cylinder at 0 degrees)
and yield a Cd=1.2.  With a turbulent boundary layer, flow can stay attached
to around 120 degrees, resulting in a decrease in drag of Cd=0.3.  The same
effect occurs for similarly sized sphere which can have a Cd=0.5 under
laminar conditions and a Cd=0.2 under turbulent conditions.

The location along the body at which the flow transitions from laminar to
turbulent determines the critical Reynolds number.  Below this number, the
flow is laminar, above it's turbulent.  The Reynolds number is defined as:

   Re_x = (Rho * V * X)/Mu

 where:

   Re_x = Reynolds number at location x (a dimensionless quantity)
   Rho  = freestream air density
   V    = freestream flow velocity
   x    = distance from the leading edge
   Mu   = freestream viscosity, a physical property of the gas (or liquid)
          involved, varies with temperature, at standard conditions mu is
          approximately 3.7373x10E-07 slug/(ft*sec) for air.

Since the Reynolds number varies linearly with the location along the body
and with velocity, the faster you go, the farther forward the transition
point moves.  At cruising speed on a typical jet airliner, only a small region
near the leading edge may be laminar.  Slow speed gliders with very slender
(but still with rounded, blunt, leading edges) may maintain laminar flow over
most of the wing surface but this is not the case for most practical aircraft.
Note that glider wings are typically designed with very short chord lengths
(x distances) to help promote laminar flow.  Laminar flow is desirable when
there is no pressure separation.

You don't have to rely on high speeds to cause the bondary layer to "trip"
from laminar to turbulent.  Small disturbances in the flow path can do the
same thing.  A golf ball is a classic example.  The dimples on a golf ball
are designed to promote turbulence and thus reduce drag on the ball in
flight.  If a golf ball were smooth like a ping pong ball, it would have
much more drag.  If you look closely, you'll notice that some Indy and F1
helmets have a boundary layer trip strip to reduce buffeting.  It seems odd
but promoting turbulence can reduce buffeting by producing a smaller wake.

Another consequence of skin friction on a cylinder is that you can generate
substantial lift with a spinning cylinder.  By spinning a cylinder you can
speed up the flow over the top and slow down flow under the bottom, resulting
in a lift producing pressure differential.  I think this phenomenon is known
as the Magnus effect.  BTW, the spinning tires on F1 and Indy cars are *huge*
sources of drag.

Dan Jones