[DeTomaso] Rear deck lid wanted
Daniel C Jones
daniel.c.jones2 at gmail.com
Thu Nov 2 19:15:27 EDT 2023
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> We are looking to acquire a stockish rear deck lid to do some aero
experiments
What sort of experiments are you looking at doing? You'll likely find that
flow separates at the trailing edge of the roof so any wing will need to be
well aft and/or raised substantially to be in clean air and produce any sort
of meaningful downforce. You may also find that better flow comes from
around
the sides of the car. It's easy enough to tape yarn tufts and film the car
at
speed to determine where flow is attached or separated. I'm an aerospace
engineer and a couple of friends here at work (then McDonnell Aircraft, now
Boeing), tufted a 1987 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 detachment 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
times 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. Another
engineer I knew, added a rear wing to the decklid of a Mustang coupe and
fitted a load cell. The extra "downforce" from the wing was all due to the
weight of the wing.
> I am being told that there was an exhaustive aero study done on the stock
Pantera
That might be the old Style Auto (Issue 29) article that detailed the wind
tunnel results for an early Pantera. Below, I've attached a few email reply
where I included some of the Style Auto results plus other aero related
replies.
Dan Jones
>> Aerodynamic research by Dr. Andrew Wortmen has evidenced poor aerodynamic
>> performance around the rear decklid exacerbated by the sugar scoop
design.
>> He champions that a tremendous improvement in Aero could be gained by a
>> cover that encloses it. He also supports the idea of a belly pan.
> Can you elaborate? Was this for Panteras or just in general?
It is a general principle that applies to the Pantera. If the pressure
on the aft end of the car were equal to the pressure on the front end of
the car, the vehicle would have no form drag. Unfortunately, the abrupt
step at the sugar scoop causes pressure separation which causes the
pressure on the aft face of the car to be very low, resulting in increased
drag. Fairing in the sugar scoop can forestall pressure separation and
reduce drag.
One of nature's best streamlined shapes is the tear drop shape that a
water droplet assumes as it falls under the pull of gravity. For subsonic
speeds, a teardrop is a very low drag shape and has a blunt, rounded,
leading edge with a long gently tapered, pointy, tail. 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 tear drop 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).
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 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.
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.
Be aware that aero is concerned with much more than just drag. A low
drag shape is of little use on an automobile if it is unstable or generates
too much lift (or not enough downforce) or doesn't allow for cooling.
The old Style Auto (Issue 29) wind tunnel results had data for both front
and rear lift:
Vehicle Speed Speed Lift Lift Lift Drag HP required
(KPH) (MPH) Front Rear Total (lb) due to drag
(lb) (lb) (lb)
-----------------------------------------------------------------
260 162 300 112 412 556 238
225 140 229 86 315 426 159
Pantera 190 118 170 62 232 313 100
160 99 115 49 164 218 58
130 81 75 33 108 139 30
-----------------------------------------------------------------
Notice that the front lift is nearly 3 times that of rear lift. Remember
that lift acts in conjunction with the weight of a car. Using Pantera
specification information from the August 1971 issue of Car and Driver
(curb weight = 3123 lbs, weight distribution = 40.9% front, 59.1% rear)
you'd have 1277.3 lbs of weight on the front and 1845.7 lbs on the rear.
At 162 MPH, subtract the aero lift and you'd have 977.3 lbs total on the
front and 1733.7 lbs total on the rear. Couple that with the angle of
attack changes that happen at the front when you crest a hill or encounter
a bump and it's not hard to see the front needs to be addressed first.
Several caveats apply here: we're using curb weight of a stock vehicle
without driver, the wind tunnel used a fixed ground plane and not a
rolling mat, and the numbers for 162 MPH were extrapolated from lower
speed data but I think the trend is still obvious. It should also be
obvious that ballasting the front can be as big a help as reducing lift.
Dan Jones
> Did you see my question about why the unlatched decklid lifts?
No, I missed that.
> Is it pushed from below or sucked from above?
The air separates over the decklid so that should be near static pressure
so I'd guess it's a pressure build up underneath.
> Current practice seems to be using diffusers at the rear - I assume
> to generate downforce -- what does this do in terms of drag?
The diffuser lowers pressure (via the area increase as the diffuser fans
out) under the car. Low pressure underneath and high above yields
downforce.
Off hand, I don't see why it would increase drag. There's an induced drag
but I would think it would be small and likely offset.
> A lot of folks doing LSR (land speed racing) add wt. - hundreds of pounds
> some times.
Think of it as downforce without drag.
> For a Pantera, any idea where the aero center might be?
For subsonic non-stalled wings, it's at 1/4 chord, so a rough guess would be
1/4 of the way back.
> Supposed to be in front of the c.g. for stability, correct?
Other way around. Think WWII fighter. The engine mass is ahead of the
wing.
> Do you know of the Wortman fellow?
Never met him.
Dan 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 unnecessary. If the flow is already fully
turbulent ahead of the point at which the flow detaches, 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 detachment 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 split 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 friction-less. 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 spheres 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 boundary 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
Also, Ford tested a Pantera in a wind tunnel and the results were published
in the Italian design magazine "Style Auto" (Issue #29). Front, rear and
total lift along with the total drag was presented for 5 speeds from 130 to
260 KPH. This info is also reproduced in the PI new member packet I just
got
from Paige Adler. If I did my SI unit conversions correctly, here's the
data
from the wind tunnel test published in Style Auto Issue 29:
Vehicle Speed Speed Lift Lift Lift Drag HP required
(KPH) (MPH) Front Rear Total (lb) due to drag
(lb) (lb) (lb)
-----------------------------------------------------------------
260 162 300 112 412 556 238
225 140 229 86 315 426 159
Pantera 190 118 170 62 232 313 100
160 99 115 49 164 218 58
130 81 75 33 108 139 30
-----------------------------------------------------------------
260 162 265 -31 234 509 217
225 140 203 -24 179 390 146
GT40 190 118 150 -18 132 287 92
160 99 97 -11 86 201 54
130 81 60 - 7 53 132 28
-----------------------------------------------------------------
260 162 560 -165 395 758 324
Mustang 225 140 428 -126 302 580 217
Boss 302 190 118 315 -93 222 426 137
160 99 218 -64 154 302 81
130 81 132 -42 90 196 42
-----------------------------------------------------------------
The article was about the Pantera and the photos show the original
pushbutton Pantera prototype sitting visually level.
> The information I have is from racers like Gary Hall, when he did race.
> I know that Gary used flexible ducting from the bat ears to the carb(s).
You do want to isolate the incoming air from the engine bay air for both
temperature and pressure reasons. Smooth tubing with a flexible coupling
will result in a lower pressure drop within the ducting.
> I think it was more of a cold air source than a ram air effect.
Yes, though at high speeds the ram air effect can be significant.
The conversion of dynamic to static pressure is a linear function of
density (which is itself a function of temperature) and a function of the
velocity squared. It's quite easy to calculate the static pressure rise.
Below 100 MPH, the ram effect is pretty small and the cooler air is the
stronger effect. As the speed goes above 100 MPH, the ram air effect
increases more rapidly and becomes dominant since it is a function of the
velocity squared. Glancing at the tables in my Gas Dynamics book, it looks
like a 2% pressure rise would be possible at around 112 knots which is
something like 129 MPH. On a 400 HP engine, you'd need over 190 MPH to see
a potential 20 HP (5%) increase. You have to balance this against the drag
penalty, of course.
If you ignore rolling resistance, the following easily derived formula
can be used to estimate a car's top speed:
/------------
15 / 1100 P
Vmax = ---- \ 3 / -------------
22 \ / Cd A rho
\/
where:
P = rear wheel power in horsepower
Cd = drag coefficient
A = frontal area in square feet
Vmax = drag limited speed in miles/hour
rho = density of air in slug/cu. ft.
= 0.002378 slug/cu ft. (at standard sea level density)
Note this only considers aerodynamic drag and not rolling resistance
and will underestimate the power required to go a given speed.
However, if you use coast-down times (at multiple speeds) to estimate
CdA, it will overestimate the required horsepower as rolling resistance
will be assumed to vary as speed squared when it actually varies to
the 1.X power. Using both calculations will allow you to bound the
power needed. Of course, this assumes optimal gearing such that
rear wheel torque peak occurs at the intersection of the drag/speed.
In general, aerodynamic drag dominates so the answer isn't that far
off.
If we assume Cd * A = 8.2035, we get a decent match to the HP required
numbers in Style Auto at 99, 118, 140, and 162 MPH. Plugging in
200 MPH and solving for HP required (at the rear wheels) indicates
447 HP:
Vehicle Speed Drag HP required Calculated
(MPH) (lb) from Style HP
Auto
-------------------------------------------------------------------------
200 -- --- 447
162 556 238 238
140 426 159 153
Pantera 118 313 100 92
99 218 58 54
81 139 30 30
Adding downforce through rake, wing, or diffuser will only increase
drag. wider wheels or tires, etc.
I used to have a NASA paper that characterized rolling resistance but
can't seem to find it. I searched a bit on the 'net and came up with
an equation of the form:
fr = fo + 3.24 * fs * (v_mph / 100)**2.5
where:
v_mph = speed (mph)
fo = basic coefficient
fs = Speed effect coefficient
Assuming the tires are rolling on clean concrete, warmed up and inflated
to proper pressure the following coefficients were suggested:
fo = 0.008
fs = 0.0018
Plug these back into the equation for rolling resistance:
fr = 0.008 + 3.24 * 0.0018 * (v_mph / 100)**2.5
For weight in pounds:
drag_rr = fr * weight
where:
drag_rr = drag due to rolling resistance
For velocity in ft/sec:
HP_reqd = drag_rr * v_fps / 550.0
where: HP_reqd = horsepower required to overcome rolling resistance for a
given speed and weight
V_fps = v_mph * 3600 / 5280
I wrote a little program and for the Pantera example used above:
Enter drag coefficient: 0.45
Enter frontal area in square feet: 18.23
Enter velocity in miles per hour: 200.
Enter vehicle weight (including driver and fluid weights): 3100.
It calculates the following:
Drag due to aerodynamic drag (pounds) = 838.8860086847279
Drag due to rolling resistance (pounds) = 127.0713993474226
Horsepower required due to aerodynamic drag = 447.4059065147985
Horsepower required w/rolling resistance = 515.1773209689964
If the assumptions are correct, it looks like a stock bodied '71 would
need on the order of 515 RWHP to turn 200 MPH on a level concrete surface.
Note that other sources show different values for Cd*A. One source had:
1972 Pantera Cd = 0.34 A (ft) = 18.23 Cd*A = 6.20
> Does anyone know the HP at 8000+ RPM the Bloomberg's Pantera delivered
> for their 209 MPH run at Bonneville?
Remember that land speed cars routinely tape seams, remove mirrors, lower
ride height and use ballast instead of wings for stability to reduce aero
drag.
Dan Jones
-------------- next part --------------
The reply below was formatted using a non-proportional font and an 80
character word wrap.A The forum software will screw up the formatting
so you may want to cut and paste into an editor to convert it back to a
non-proportional font.
> We are looking to acquire a stockish rear deck lid to do some aero
experiments
What sort of experiments are you looking at doing?A You'll likely find
that
flow separates at the trailing edge of the roof so any wing will need
to be
well aft and/or raised substantially to be in clean air and produce any
sort
of meaningful downforce.A You may also find that better flow comes
from around
the sides of the car.A It's easy enough to tape yarn tufts and film
the car at
speed to determine where flow is attached or separated.A I'm an
aerospace
engineer and a couple of friends here at work (then McDonnell Aircraft,
now
Boeing), tufted a 1987 Mustang LX hatchback from the center of the roof
to the
taillights.A They were trying to use vortex generators to to induce
turbulence
to trip the boundary layer, hoping to delay the flow detachment at the
hatch
so they could get cleaner air over the wing.A 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.A 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
times the boundary layer thickness).A They didn't see an improvement
in coast
down times, but the tufts did appear a little better behaved with the
vortex
generators.A They believe the turn at the back of the roof may be too
sharp
to permit attached flow.A They also noted that much of the clean flow
to
the wing appeared to be coming from around the sides of the car.A
Another
engineer I knew, added a rear wing to the decklid of a Mustang coupe
and
fitted a load cell.A The extra "downforce" from the wing was all due
to the
weight of the wing.
> I am being told that there was an exhaustive aero study done on the
stock Pantera
That might be the old Style Auto (Issue 29) article that detailed the
wind
tunnel results for an early Pantera.A Below, I've attached a few email
reply
where I included some of the Style Auto results plus other aero related
replies.
Dan Jones
>> Aerodynamic research by Dr. Andrew Wortmen has evidenced poor
aerodynamic
>> performance around the rear decklid exacerbated by the sugar scoop
design.
>> He champions that a tremendous improvement in Aero could be gained
by a
>> cover that encloses it.A He also supports the idea of a belly pan.
> Can you elaborate? Was this for Panteras or just in general?
It is a general principle that applies to the Pantera.A If the
pressure
on the aft end of the car were equal to the pressure on the front end
of
the car, the vehicle would have no form drag.A Unfortunately, the
abrupt
step at the sugar scoop causes pressure separation which causes the
pressure on the aft face of the car to be very low, resulting in
increased
drag.A Fairing in the sugar scoop can forestall pressure separation
and
reduce drag.
One of nature's best streamlined shapes is the tear drop shape that a
water droplet assumes as it falls under the pull of gravity.A For
subsonic
speeds, a teardrop is a very low drag shape and has a blunt, rounded,
leading edge with a long gently tapered, pointy, tail.A Hungarian
engineer
Paul Jaray was the first to promote the full-on teardrop shape for an
automobile.A Jaray had designed a new series of Zeppelins that
featured
the tear drop shape and applied his ideas to automobiles, applying for
a
patent in 1922.A Jaray tested a series of streamlined automobiles in
the
Zeppelin work's wind-tunnel in Friedrichshafen, achieving drag
coefficients
as low as 0.2.A 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.A Chrysler was forced to pay royalties for the Airflow to
Jaray,
as was Peugeot (for the 402).
Jaray's patent was contested by another aeronautical engineer, Edmund
Rumpler but was ultimately upheld.A Rumpler had debuted a mid-engined,
aerodynamic automobile (the Tropfen) at 1921 show in Berlin.A 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.A 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.A Based upon experimental
research conducted on buses, Reinhard Koenig-Fachsenfeld applied for
a patent on the chopped tail as a practical alternative.A 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.A Fachsenfeld was persuaded to sell
his patent to the 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.A Kamm's research showed that a
properly truncated Jaray tail had less drag than a shortened tapered
tail.
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.A There's a point of diminishing returns where
increasing the tail length has progressively less effect.A 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.A 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.A Fairing in the Pantera sugar scoop will help in one
dimension
only so will not be as effective as a true Kamm tail.
Be aware that aero is concerned with much more than just drag.A A low
drag shape is of little use on an automobile if it is unstable or
generates
too much lift (or not enough downforce) or doesn't allow for cooling.
The old Style Auto (Issue 29) wind tunnel results had data for both
front
and rear lift:
Vehicle A A A Speed A A Speed A Lift A A Lift A A Lift A Drag A
A HP required
A A A A A A A (KPH) A A (MPH) A Front A Rear A A Total A (lb)
A A due to drag
A A A A A A A A A A A A A A A (lb) A A (lb) A A (lb)
-----------------------------------------------------------------
A A A A A A A 260 A A A 162 A A 300 A A 112 A A 412 A A
556 A A 238
A A A A A A A 225 A A A 140 A A 229 A A A 86 A A 315 A
A 426 A A 159
Pantera A A A 190 A A A 118 A A 170 A A A 62 A A 232 A A
313 A A 100
A A A A A A A 160 A A A 99 A A 115 A A A 49 A A 164 A
A 218 A A A 58
A A A A A A A 130 A A A 81 A A A 75 A A A 33 A A 108 A
A 139 A A A 30
-----------------------------------------------------------------
Notice that the front lift is nearly 3 times that of rear lift.A
Remember
that lift acts in conjunction with the weight of a car.A Using Pantera
specification information from the August 1971 issue of Car and Driver
(curb weight = 3123 lbs, weight distribution = 40.9% front, 59.1% rear)
you'd have 1277.3 lbs of weight on the front and 1845.7 lbs on the
rear.
At 162 MPH, subtract the aero lift and you'd have 977.3 lbs total on
the
front and 1733.7 lbs total on the rear.A Couple that with the angle of
attack changes that happen at the front when you crest a hill or
encounter
a bump and it's not hard to see the front needs to be addressed first.
Several caveats apply here: we're using curb weight of a stock vehicle
without driver, the wind tunnel used a fixed ground plane and not a
rolling mat, and the numbers for 162 MPH were extrapolated from lower
speed data but I think the trend is still obvious.A It should also be
obvious that ballasting the front can be as big a help as reducing
lift.
Dan Jones
> Did you see my question about why the unlatched decklid lifts?
No, I missed that.
> Is it pushed from below or sucked from above?
The air separates over the decklid so that should be near static
pressure
so I'd guess it's a pressure build up underneath.
> Current practice seems to be using diffusers at the rear - I assume
> to generate downforce -- what does this do in terms of drag?
The diffuser lowers pressure (via the area increase as the diffuser
fans
out) under the car.A Low pressure underneath and high above yields
downforce.
Off hand, I don't see why it would increase drag.A There's an induced
drag
but I would think it would be small and likely offset.
> A lot of folks doing LSR (land speed racing) add wt. - hundreds of
pounds
> some times.
Think of it as downforce without drag.
> For a Pantera, any idea where the aero center might be?
For subsonic non-stalled wings, it's at 1/4 chord, so a rough guess
would be
1/4 of the way back.
> Supposed to be in front of the c.g. for stability, correct?
Other way around.A Think WWII fighter.A The engine mass is ahead of
the wing.
> Do you know of the Wortman fellow?
Never met him.
Dan Jones
The dimples on a golf ball decrease drag by inducing a turbulent
boundary
layer to delay the drag increase associated with separated flow.A The
least
drag is achieved when the boundary layer is laminar and the flow stays
attached to the surface contour.A In practice, this only occurs
passively
for slender shapes, like air foils) and then only sometimes.A For most
practical shapes, laminar flow boundary layers will separate from the
surface.A This separation causes a large drag increase.A In cases
like
that, a turbulent boundary layer stays attached to the surface longer,
resulting in less overall drag.A 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.A The location along the body at which the flow
transitions from laminar to turbulent determines the critical Reynolds
number.A Below this number, the flow is laminar, above it's turbulent.
The Reynolds number is a linear function of velocity.A The faster you
go, the farther forward the transition point moves.A You don't have to
rely on high speeds to cause the boundary layer to "trip" from laminar
to turbulent.A Small disturbances in the flow path can do the same
thing.
That's why golf balls have dimples.A A better approach for a Pantera
would boundary layer trip strips or vortex generators to do the same
thing.A However it may be unnecessary.A If the flow is already fully
turbulent ahead of the point at which the flow detaches, introducing
additional turbulence will not have a beneficial effect.A Also, the
body needs to have a gradual slope for even a turbulent boundary layer
to stay attached.A 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.A They were trying to
use
vortex generators to to induce turbulence to trip the boundary layer,
hoping to delay the flow detachment at the hatch so they could get
cleaner
air over the wing.A 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.A 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).A They didn't see an improvement in coast
down
times, but the tufts did appear a little better behaved with the vortex
generators.A They believe the turn at the back of the roof may be too
sharp
to permit attached flow.A 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 split into two components:
A A Cd = Cdf + Cdp
A where
A A Cd A = profile drag coefficient
A A Cdp = pressure drag coefficient due to flow separation
A A Cdf = skin friction drag coefficient due to surface roughness
A A A A A 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 A
smooth
surface will have a low Cdf.A Also, the Cdf is lower for laminar flow
and
higher for turbulent flow.A Cdp, on the other hand, is caused by the
fore-and-aft pressure differential created by flow separation.A
Usually,
Cdp is lower for turbulent flow and higher for laminar flow.A In many
cases,
inducing turbulence will dramatically decrease the pressure drag
component,
decreasing the overall drag.A 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.A Since a cylinder is symmetric front-to-back
(and
top-to-bottom), their early theories predicted it should have no drag
(or
lift).A 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.A 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.A This difference between predicted and observed
drag
over a cylinder was particularly bothersome to early aerodynamicists
who
termed the phenomenon d'Alembert's paradox.A 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.A 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 friction-less.A The boundary layer can be further characterized as
either laminar or turbulent.A Under laminar conditions, the flow moves
smoothly and follows the general contours of the body.A Under
turbulent
conditions, the flow becomes chaotic and random.
It turns out that a cylinder is a very high drag shape.A At the speeds
we're talking about, a cylinder has a drag Cd of approximately 0.4.A
By
comparison, an infinite flat plate would have a Cd of 1.0.A Note that
this is not a theoretical limit.A A rectangular beam will exhibit flow
separation at each corner and can have a Cd in the range of 2.0.A 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.A
Think
about what this means.A 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.A 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.A The reason lies in different effects laminar and turbulent
boundary
layers have on flow separation.A Laminar boundary layers separate
(detach
from the body) much more easily than turbulent ones.A 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.A As the air flow speed is increased, the transition from laminar
to
turbulent takes place on the front face.A The turbulent boundary layer
stays
attached longer so the separation point moves rearward, resulting in a
smaller wake and lower drag.A 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.A With a turbulent boundary layer, flow can stay
attached
to around 120 degrees, resulting in a decrease in drag of Cd=0.3.A The
same
effect occurs for similarly sized spheres 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.A Below this number,
the
flow is laminar, above it's turbulent.A The Reynolds number is defined
as:
A A Re_x = (Rho * V * X)/Mu
A where:
A A Re_x = Reynolds number at location x (a dimensionless quantity)
A A Rho A = freestream air density
A A V A A = freestream flow velocity
A A x A A = distance from the leading edge
A A Mu A = freestream viscosity, a physical property of the gas (or
liquid)
A A A A A involved, varies with temperature, at standard
conditions mu is
A A A A A 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.A At cruising speed on a typical jet airliner, only a
small region
near the leading edge may be laminar.A 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.A Laminar flow is desirable
when
there is no pressure separation.
You don't have to rely on high speeds to cause the boundary layer to
"trip"
from laminar to turbulent.A Small disturbances in the flow path can do
the
same thing.A A golf ball is a classic example.A The dimples on a golf
ball
are designed to promote turbulence and thus reduce drag on the ball in
flight.A If a golf ball were smooth like a ping pong ball, it would
have
much more drag.A If you look closely, you'll notice that some Indy and
F1
helmets have a boundary layer trip strip to reduce buffeting.A 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.A 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.A I think this phenomenon is
known
as the Magnus effect.A BTW, the spinning tires on F1 and Indy cars are
*huge*
sources of drag.
Dan Jones
Also, Ford tested a Pantera in a wind tunnel and the results were
published
in the Italian design magazine "Style Auto" (Issue #29).A Front, rear
and
total lift along with the total drag was presented for 5 speeds from
130 to
260 KPH.A This info is also reproduced in the PI new member packet I
just got
from Paige Adler.A If I did my SI unit conversions correctly, here's
the data
from the wind tunnel test published in Style Auto Issue 29:
Vehicle A A A Speed A A Speed A Lift A A Lift A A Lift A Drag A
A HP required
A A A A A A A (KPH) A A (MPH) A Front A Rear A A Total A (lb)
A A due to drag
A A A A A A A A A A A A A A A (lb) A A (lb) A A (lb)
-----------------------------------------------------------------
A A A A A A A 260 A A A 162 A A 300 A A 112 A A 412 A A
556 A A 238
A A A A A A A 225 A A A 140 A A 229 A A A 86 A A 315 A
A 426 A A 159
Pantera A A A 190 A A A 118 A A 170 A A A 62 A A 232 A A
313 A A 100
A A A A A A A 160 A A A 99 A A 115 A A A 49 A A 164 A
A 218 A A A 58
A A A A A A A 130 A A A 81 A A A 75 A A A 33 A A 108 A
A 139 A A A 30
-----------------------------------------------------------------
A A A A A A A 260 A A A 162 A A 265 A A -31 A A 234 A A
509 A A 217
A A A A A A A 225 A A A 140 A A 203 A A -24 A A 179 A A
390 A A 146
GT40 A A A A 190 A A A 118 A A 150 A A -18 A A 132 A A
287 A A A 92
A A A A A A A 160 A A A 99 A A A 97 A A -11 A A A 86 A
A 201 A A A 54
A A A A A A A 130 A A A 81 A A A 60 A A - 7 A A A 53 A
A 132 A A A 28
-----------------------------------------------------------------
A A A A A A A 260 A A A 162 A A 560 A A -165 A A 395 A A
758 A A 324
Mustang A A A 225 A A A 140 A A 428 A A -126 A A 302 A A 580
A A 217
Boss 302 A A 190 A A A 118 A A 315 A A -93 A A 222 A A 426
A A 137
A A A A A A A 160 A A A 99 A A 218 A A -64 A A 154 A A
302 A A A 81
A A A A A A A 130 A A A 81 A A 132 A A -42 A A A 90 A
A 196 A A A 42
-----------------------------------------------------------------
The article was about the Pantera and the photos show the original
pushbutton Pantera prototype sitting visually level.
> The information I have is from racers like Gary Hall, when he did
race.
> I know that Gary used flexible ducting from the bat ears to the
carb(s).
You do want to isolate the incoming air from the engine bay air for
both
temperature and pressure reasons.A Smooth tubing with a flexible
coupling
will result in a lower pressure drop within the ducting.
> I think it was more of a cold air source than a ram air effect.
Yes, though at high speeds the ram air effect can be significant.
The conversion of dynamic to static pressure is a linear function of
density (which is itself a function of temperature) and a function of
the
velocity squared.A It's quite easy to calculate the static pressure
rise.
Below 100 MPH, the ram effect is pretty small and the cooler air is the
stronger effect.A As the speed goes above 100 MPH, the ram air effect
increases more rapidly and becomes dominant since it is a function of
the
velocity squared.A Glancing at the tables in my Gas Dynamics book, it
looks
like a 2% pressure rise would be possible at around 112 knots which is
something like 129 MPH.A On a 400 HP engine, you'd need over 190 MPH
to see
a potential 20 HP (5%) increase.A You have to balance this against the
drag
penalty, of course.
If you ignore rolling resistance, the following easily derived formula
can be used to estimate a car's top speed:
A A A A A A A A A A A /------------
A A A A A A 15 A A A A / A 1100 P
A Vmax = A ---- \ 3 A / -------------
A A A A A A 22 A \ A / A Cd A rho
A A A A A A A A A \/
where:
A P A A = rear wheel power in horsepower
A Cd A = drag coefficient
A A A A = frontal area in square feet
A Vmax = drag limited speed in miles/hour
A rho A = density of air in slug/cu. ft.
A A A A = 0.002378 slug/cu ft. (at standard sea level density)
Note this only considers aerodynamic drag and not rolling resistance
and will underestimate the power required to go a given speed.
However, if you use coast-down times (at multiple speeds) to estimate
CdA, it will overestimate the required horsepower as rolling resistance
will be assumed to vary as speed squared when it actually varies to
the 1.X power.A Using both calculations will allow you to bound the
power needed.A Of course, this assumes optimal gearing such that
rear wheel torque peak occurs at the intersection of the drag/speed.
In general, aerodynamic drag dominates so the answer isn't that far
off.
If we assume Cd * A = 8.2035, we get a decent match to the HP required
numbers in Style Auto at 99, 118, 140, and 162 MPH.A Plugging in
200 MPH and solving for HP required (at the rear wheels) indicates
447 HP:
Vehicle A A A Speed A Drag A A HP required A Calculated
A A A A A A A (MPH) A (lb) A A from Style A A HP
A A A A A A A A A A A A A A A Auto
-----------------------------------------------------------------------
--
A A A A A A A 200 A A -- A A A A --- A A A A A 447
A A A A A A A 162 A A 556 A A A 238 A A A A A 238
A A A A A A A 140 A A 426 A A A 159 A A A A A 153
Pantera A A A 118 A A 313 A A A 100 A A A A A 92
A A A A A A A 99 A A 218 A A A A 58 A A A A A 54
A A A A A A A 81 A A 139 A A A A 30 A A A A A 30
Adding downforce through rake, wing, or diffuser will only increase
drag. wider wheels or tires, etc.
I used to have a NASA paper that characterized rolling resistance but
can't seem to find it.A I searched a bit on the 'net and came up with
an equation of the form:
A fr = fo + 3.24 * fs * (v_mph / 100)**2.5
where:
A v_mph = speed (mph)
A fo = basic coefficient
A fs = Speed effect coefficient
Assuming the tires are rolling on clean concrete, warmed up and
inflated
to proper pressure the following coefficients were suggested:
A fo = 0.008
A fs = 0.0018
Plug these back into the equation for rolling resistance:
A fr = 0.008 + 3.24 * 0.0018 * (v_mph / 100)**2.5
For weight in pounds:
A drag_rr = fr * weight
where:
A drag_rr = drag due to rolling resistance
For velocity in ft/sec:
A HP_reqd = drag_rr * v_fps / 550.0
where: A HP_reqd = horsepower required to overcome rolling resistance
for a
A A A A A A given speed and weight
A V_fps = v_mph * 3600 / 5280
I wrote a little program and for the Pantera example used above:
A Enter drag coefficient: 0.45
A Enter frontal area in square feet: 18.23
A Enter velocity in miles per hour: 200.
A Enter vehicle weight (including driver and fluid weights): 3100.
It calculates the following:
A Drag due to aerodynamic drag (pounds) = 838.8860086847279
A Drag due to rolling resistance (pounds) = 127.0713993474226
A Horsepower required due to aerodynamic drag = 447.4059065147985
A Horsepower required w/rolling resistance = 515.1773209689964
If the assumptions are correct, it looks like a stock bodied '71 would
need on the order of 515 RWHP to turn 200 MPH on a level concrete
surface.
Note that other sources show different values for Cd*A.A One source
had:
A 1972 Pantera Cd = 0.34 A A (ft) = 18.23 A Cd*A = 6.20
> Does anyone know the HP at 8000+ RPM the Bloomberg's Pantera
delivered
> for their 209 MPH run at Bonneville?
Remember that land speed cars routinely tape seams, remove mirrors,
lower
ride height and use ballast instead of wings for stability to reduce
aero
drag.
Dan Jones
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