> Air in contact with the body of a vehicle creates drag in the form of friction
> which acts upon the vehicle as it moves through the air.
For a blunt shape (in practice, anything other than a slender airfoil) like
an automobile, the skin friction drag is small compared to the drag caused by
separation. The profile drag of an object can be spilt into two components:
Cd = Cdf + Cdp
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.
However, it is the skin friction that causes the flow to separate which leads
to the pressure drag. If a symmetric shape like a cylinder were frictionless,
it would have no drag. Back in the 19th century, when scientists were just
beginning to seriously 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
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 boundary 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
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 exposed spinning tires on F1 and Indy cars
are *huge* sources of drag.
> Paul Jaray developed streamlined car body work in the 1920s. His innovative
> body design featured a low-profile teardrop shape with a long tail to
> minimize the air resistance of passenger cars. The long tapering tail bent
> the air, it induced the air into following the gently tapering bodywork of
> the vehicle, thus preventing the formation of a negative pressure area
> behind the vehicle.
Hungarian engineer Paul Jaray was the first to promote the full-on
teardrop shape for an automobile. Jaray had designed a new series of
Zeppelins that featured the teardrop shape and applied his ideas to
automobiles, applying for a patent in 1922. Jaray tested a series of
streamlined automobiles in the Zeppelin work's wind-tunnel in
Friedrichshafen, achieving drag coefficients as low as 0.2. He went
on to design a variety of aerodynamic bodies for Tatra, BMW, Benz,
Adler, Mayback, Audi and Hanomag and influenced a number of others.
Chrysler was forced to pay royalties for the Airflow to Jaray, as was
Peugeot (for the 402). IIRC, the Tatra T87 was designed by Hans Ledwinka
with the body based upon proposals submitted by Jaray. Ledwinka's Tatras
were rear engined (the T87 was an OHC V8 and the T97 was a flat four) and
air cooled and the designs would heavily influence Ferdinand Porsche.
Jaray's patent was contested by another aeronautical engineer, Edmund
Rumpler but was ultimately upheld. Rumpler had debuted a mid-engined,
aerodynamic automobile (the Tropfen) at 1921 show in Berlin. Benz used
Rumpler's ideas in a 1923 race car but Rumpler returned to aviation.
Rumpler was later arrested by the Nazis because he was Jewish but was
protected by Goering who knew of his aircraft designs. Rumpler's
design was wind tunnel tested in the late 1970's at VW and recorded a
Cd of 0.28.
While aerodynamically efficient, the Jaray teardrops were long and not
always easily applied to practical shapes. Based upon experimental
research conducted on buses, Reinhard Koenig-Fachsenfeld applied for
a patent on the chopped tail as a practical alternative. At around the
same time, Professor Wunnibald Kamm (head of the Automotive Research
Institute at Stuttgart Technical College) published a textbook that
described a similar truncated tail. Fachsenfeld was persuaded to sell
his patent to the German state and Kamm was funded to develop the concept.
Another university professor, Everling was onto the same idea and his
design was among those tested by Kamm. Kamm's research showed that a
properly truncated Jaray tail had less drag than a shortened tapered
tail. The full length tear drop is still a lower drag shape, of course.
When fairing in and truncating the tail, you want to do it in a manner
that raises the base pressure (the pressure acting on the aft end of
the vehicle) while making the base area (where the pressure acts) as
small as possible. There's a point of diminishing returns where
increasing the tail length has progressively less effect. Kamm's
research led him to the conclusion that you should find the point where
the tail is half as wide as the maximum width of the vehicle and cut it
off there. This Kamm truncated tail is what Pete Brock applied to the
Cobra Daytona from above and from the side, you'll see it tapers in both
dimensions. Fairing in the Pantera sugar scoop will help in one dimension
only so will not be as effective as a true Kamm tail.
Somewhere around here I have a copy of "The Aerodynamics of Land Borne
Vehicles" which details some of the early wind tunnel research on cars,
trucks, and trains.