Reply to "rear wing aerodynamics"

The generation of lift occurs when a flow stream is turned. This is
consistent with Newton's 3rd Law of Equal and Opposite Action. When
an airfoil turns the flow, an equal and opposite reaction occurs which
imparts a force to the airfoil. The lift and drag components of this
force can be determined by integrating the pressure distribution over
the airfoil surface. Without going in to a lot of detail, let me state
that a proper theory of lift can not be arrived at without considering
the considerable effects of viscosity which introduce friction into the
flow. It is viscosity that introduces circulation into the flow. This
circulation reaches an equilibrium when the stagnation point reaches the
trailing edge. This is known as the Kutta condition (see the
Kutta-Joukowski theorem) and is why the flow over the top and bottom
meet at the trailing edge (nature abhors a vacuum).

>We're dealing in semantics, here. I came from the school that
>presupposes that if there is airflow toward an airfoil, then there
>is an angle which it approaches the chord of that airfoil, hence
>the definition of angle of attack, even if zero.

In every aerodynamics text book I've ever seen, the definition of
geometric angle of attack is the angle from the chord line to the
undisturbed freestream velocity vector. This is the definition that
all the NACA/NASA airfoil data assumes. Perhaps you are refering to
induced angle of attack, which is a consequence of wing finiteness?
For three-dimensional wings, downwash, induced by trailing wingtip
vortices, alters the local flowfield, resulting in an effective
angle of attack which is less than the geometric angle of attack.
The difference between the geometric and effective angles of attack
is termed the induced angle of attack:

AOAi = AOA - AOAeff

where:

AOA = geometric angle of attack
AOAi = induced angle of attack
AOAeff = effective angle of attack

For an elliptical lift distribution, the induced angle of attack
can be calculated as

AOAi = Cl/(pi*AR)

This occurs in both symmeric and cambered airfoils, and is a three-
dimensional effect. Air foil sections are two-dimensional and therefore
the geometric and effective angle of attacks are the same (i.e. the
induced angle of attack is zero). Even for 2-D airfoil sections, in
general, there is a non-zero lift component at zero angle of attack
for cambered airfoils. See the NACA air foil section 2408 I mentioned
previously for one example. Note that air foil data can be applied to
finite wings since flow over an inifinite wing at geometric angle
of attack is similar to a finite wing at effective angle of attack.
Also, since it can be measured directly, wind tunnel data for finite
wings is generally taken at the geometric angle of attack.

> 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.

> I do remember a drag coefficient being quoted for the Pantera of .29.
> Was it from this test? That's an impressive number even today.

I don't think that number was quoted in the Style Auto test.
I have one reference that shows a 1972 Pantera Pre-L as having:

Cd = 0.34
A = 18.23 square feet
Cd * A = 6.20

Assuming they ignored rolling resistance, I can get a decent match to
the HP required numbers in Style Auto for a value of Cd * A = 8.2035.
It may be the case they figured in a rolling resistance in the data.
I think the frontal area is in right ballpark. We can bracket the
frontal area on the high end by width times height and on the low end
by track times height. Using the specs on Pantera Place (from an August
1971 Car and Driver article):

A = 43.4 inches * 58 inches = 17.48 sq ft
A = 43.4 inches * 67 inches = 20.19 sq ft

Averaging the two numbers yields 18.835 which is close to the referenced
18.23 value. That area value would imply the coefficient of drag is 0.45
for the Style Auto data. That's relatively high so I wonder if they figured
in some sort of rolling resistance.

The Pre-L Pamteras had the chrome bumperettes and narrow tires. The later
L models had the rubber safety bumpers and may have been a bit slicker.
GT5-S had the Countach-like wings and flares. Those would have considerably
higher drag as well as larger frontal area.

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 resitance
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:

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:

Speed Drag HP required Calculated
(MPH) (lb) from Style HP
Auto
------------------------------------------
200 -- --- 447
162 556 238 238
140 426 159 153
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 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 concreter, 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 coeficient: 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.

> Does anyone know the HP at 8000+ RPM the Bloomberg's Pantera delivered
> for their 209MPH 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

> If the issue is that droppong the nose creates increased frontal area, air
> dams would also be bad. I thought that keeping air from getting under the
> car is a good thing. I thought a lot of new cars have air dams just for
> that reason..

Somewhere in the database, I have some info on 76 individual wind tunnel
tests that were carried out in the Maryland University wind tunnel on
a 3/8 scale model to arrive at the original GT40 MKI body shape. Based
upon those tests, a full-size model was built and tested at Ford's own
wind tunnel in Dearborn. Ford used the Lola GT as a baseline, comparing
it to various revisions of the baseline GT40 shape. Some results are
presented below:

Vehicle Yaw Speed Lift Lift Lift Drag
(MPH) Front Rear Total (lb)
(lb) (lb) (lb)

-----------------------------------------------------------------
Lola GT 0 200 528 168 696 503
15 200 768 384 1152
-----------------------------------------------------------------
GT40 with 0 200 540 108 648 519
High Nose 15 200 844 362 1206 614
-----------------------------------------------------------------
GT40 with 0 200 445 199 644 507
Low Nose 15 200 704 422 1126 596
-----------------------------------------------------------------
Front Spoiler 0 200 326 266 592 513
#1
-----------------------------------------------------------------
Front Spoiler - 200 --- --- --- 531
#2
-----------------------------------------------------------------
Front Spoiler 0 200 236 272 508 488
#3 15 200 309 343 652 591
-----------------------------------------------------------------

Front spoiler #1 was 2.67 tall and was added below nose, behind the
air intake. Front spoiler #2 was in the same location but twice as
tall. It reduced lift but was deemed to not have enough ground
clearance. Front spoiler #3 was 3 1/2" tall and faired in. Recessed
headlights were chosen as raised headlights resulted in "marked increases
in lift and drag".

Many of the tests were directed towards trying to find the lowest drag
way to provide air flow for the cooling system, the induction, engine
compartment ventilation, interior ventilation, and brake and shock
absorber cooling air. The designers originally wanted to use twin side
radiators mounted in the engine compartment but tests on the full scale
wind tunnel model indicated 8000 CFM would be required which was deemed
not possible with the side intake duct layout. A conventional front
mounted radiator with intake and outlet beneath the nose was a little
better. The final solution was to take air in at the high pressure
region below the nose, let it flow past an angled radiator and exhaust
out the low pressure region at the top of the nose bodywork. Anti-dive
and squat were designed into the suspension to keep the cars more level
so as to not upset the aerodynamics.

Even with all the wind tunnel work, Ford was learning as they went and
the GT40's airflow management proved insufficient once the cars got out
in the field. The wind tunnel models were not fitted with the internal
ducting so it was only later discovered that 76 horsepower were being
consumed up just trying to ram air through the car at high speed. The
cars were modified in the field to fix one problem like cooling only
to change another, like the aerodynamic balance resulting in yet another
problem. Ken Miles spoke of the problem:

"The aerodynamic problems we've had with the car were essentially ones of
air flow within the car being affected by external details. For example
we were getting very little air flow to the brakes, although they had huge
ducts ostensibly directing vast quantities of air at them. In fact, the
brakes were overheating badly. The engine was getting too hot. The
engine compartment itself was getting too hot. The cooling water was
getting too hot. The engine and gearbox oil was gettting too hot. All
this in spite of a large number of aperatures which should have supplied
them with more than enough air. We discovered that what was happening was
that due to design changes that had been made over a period of time,
probably without reference to the original specifications practically all
of the ductwork was at a "stall " condition" i.e. no air was moving in the
ducts".

Ford's aeronspace division Aeronutronics was brought in to instrument a
GT40 with pressure and temerature sensors on various parts of the body
(externally and inside the ducts). From this data, the Shelby team was
able to modify the cars properly. Even when the MKII's appeared, Ford
still had some aerodynamic lessons to learn. Phil Hill wrote "The second
year at LeMans we were in deep trouble when we first arrived, thanks
to a diabolical instability that had been supposedly eliminated in
stateside testing. The MKII's were simply terrifying down the Mulsanne
Straight. We ended up tacking on little eyebrow spoilers as well as an
additional little spoiler across the back to solve the problem. I also
remember early Ferraris with so much front end lift that the steering
became progressively lighter as speed climbed until finally the rebound
stops were a factor... we could have called it up-force."