7- AUTOMOTIVE AERODYNAMICS

Brian Paul Wiegand, B.M.E., P.E
2
When a body moves through a “fluid” a force opposite the direction
of motion is generated; this force is called “drag”. A force
orthogonal to the direction of motion may be generated as well; this
force is generally called “lift”. The study of such body–fluid
interactions is called “fluid mechanics”, and when the “fluid” of
interest is a gas such as air, then the dynamic area of study narrows
down to that subset of “fluid mechanics” called “aerodynamics”.
For aerodynamic drag to be generated there must be air present,
and there must be relative motion between the air and a body;
without air or motion there can be no drag or lift. The

3
Over the course of history a great many distinguished individuals
have contributed to the understanding of fluid mechanics; Newton,
Euler, Bernoulli, Navier, Stokes, and Reynolds to name just a few.
The ultimate model of fluid behavior, the Navier-Stokes Equations,
are so complex that a complete analytical solution can not be
found…

4
Such “indicators” make the complex study of Fluid Mechanics more
manageable as they indicate the presence of certain phases of fluid
flow behavior, and whether or not two different fluid flow situations
might be in the same phase and thus similar. This means that the
researcher can concentrate on just certain limited behavior as much
of the rest of the overwhelmingly complex nature of the situation
can be disregarded per the dimensionless parameter’s indication.
There are a number of such “dimensionless indicators”, a.k.a.
“similarity parameters”, “dimensionless parameters”; like the:
Reynolds Number, Mach Number, Froude Number, Weber
Number, Prandtl Number… Of all of these numbers we are
going to be the most concerned with just the first two…

5
For example, the Mach Number can indicate whether a gas flow is in
an incompressible flow phase or not; at Mach numbers less than 1
the flow is compressible, which means the designer need not yet be
concerned with the formation of shock waves and the associated
energy loss, and can focus on creating a body shape appropriate for
subsonic use.
Another example of the utility of a dimensionless indicator: wind
tunnel testing of the aerodynamic nature of a body design by use of
a scale model provides, this time of the Reynolds Number. Only
when the Reynolds Number of the wind tunnel experiment is
comparable in value to the Reynolds Number of the full size
design can the scale model wind tunnel results have any
relevance to the full scale situation.

6
George Gabriel Stokes (1819-1903) derived the Reynolds Number
from the Navier-Stokes Equations in 1851, but it took Osborne
Reynolds (1842-1912) to make its practical use apparent in 1883…*
The Reynolds Number
Where:
V is the maximum velocity of the object relative to the fluid (m/s, ft/s)
L is a characteristic linear dimension, travelled length of the fluid (m, ft)
μ is the dynamic viscosity of the fluid (kg/(m·s), lb-s/ft 2)
ν is the kinematic viscosity of the fluid: ν = μ/ρ (m2/s, ft2/s)
ρ is the density of the fluid (kg/m3, lb/ft3/g).
* “An Experimental Investigation of the Circumstances which Determine Whether the Motion of Water in
Parallel Channels shall be Direct or Sinuous and of the Law of Resistance in Parallel Channels”, 1883.

7
Austrian physicist and philosopher Ernst Mach (1838-1916)
published a paper in 1887 concerning the formation of “shock
waves” by projectiles traveling at speeds greater than the speed of
sound ( Vp/Vs > 1)…
The Mach Number
Where:
M is the Mach Number.
u is the local flow velocity.
c is the speed of sound in the fluid. For a gas
this is equal to (see next slide).

8
Where:
c is the “speed of sound” in a gas.
κ is the “specific heat ratio” of the gas.
R is the “specific gas constant”.
T is the “absolute temperature”.
c
So, an aircraft traveling at Mach 1 at 20°C (68°F) at sea level will
experience shock waves just like an aircraft traveling at Mach 1 at
11,000 m (36,000 ft) altitude at −50°C (−58°F), but despite being at the
same Mach Number the second aircraft is only traveling 87% as fast as
the first due to the fact that the ambient conditions are quite different.

9
c
TEMPERATURE CONVERSION:
ºR = ºC * 1.8000 + 491.67

10
Aircraft #1 traveling at Mach 1 at 20°C (527.67°R) at
sea level =
Aircraft #2 traveling at Mach 1 at −50°C (401.67°R) at
36,000 ft =
So the second aircraft is indeed only traveling 87%
as fast as the first aircraft…

11
It is because fluid behavior is so complex that most problems in fluid
mechanics are modeled as very limited and degenerate subsets of
the ultimate reality. This means that the resultant limitations of any
equations used must be borne in mind, that any exposition on fluid
mechanics or some aspect thereof must necessarily be somewhat
simplistic and misleading, and that any results obtained, whether by
“back of the envelop” calculation or by computerized fluid dynamics
(CFD) simulation, must still be subject to a thorough empirical
validation.
With that said, and the student now supposedly aware of the
consequent need for caution and the requirement for humility,
this segment of the Automotive Dynamics curriculum may
begin in earnest…

12
The most elemental explanation of “streamlines” is that such serves as an
attempt to visualize the fluid flow around a body. The use of smoke, yarn
tuffs, and ink in the wind tunnel as an attempt to find the streamlines is
common…Ideally a streamline is a path traced out by a “mass-less” particle
as it moves with the flow. Since the streamline is traced out by a moving
particle, at every point along the path the velocity is tangent to the path.
Since there is no normal component of the velocity along the path, mass
cannot cross a streamline. The mass contained between any two
streamlines remains the same throughout the flow field. We can
use Bernoulli’s Equation to relate the pressure and velocity along the
streamline. Since no mass passes through the surface of the body, the
surface of the body can also be a streamline.

13
Daniel Bernoulli (1700-1782), developing some earlier work by Leonhard
Euler (1707-1783), derived a simple but very useful equation regarding fluid
flow which he published by 1738 in his book Hydrodynamica. A version of
that equation may be expressed as:
½ ρ1 V1
2 + P1 = ½ ρ2 V2
2 + P2
This simple version of Bernoulli's equation is valid for incompressible
flows (liquids, plus gases moving at low Mach Number) where the density
“ρ” can be taken as constant. It can be used to help interpret the meaning
of streamlines realistically drawn about a body to denote the fluid flow.
Essentially it says how the velocity “V” and the pressure “P” at two
different points along a flow are related to each other, and that the
relationship between “V” and “P” is inverse.

14
Aerodynamic “drag” comes about through a number of different
mechanisms, but mainly as “Form Drag” and “Skin Drag”. To those
two add “Interference Drag” and the trio constitutes what is called
“parasitic drag”. Finally, there is also “Induced Drag”, “Ram Drag ”,
and “Wave Drag”. There are also a number of “drag effects” or
qualities which affect these drag types, like “ground effect”. The
total drag on a vehicle is the result of a very complicated interaction.
The natural simplistic assumption is that the total drag, reflected in
a value called the “Coefficient of Drag” or “Cd”, is merely the sum
of the individual drag components:
Cd = CdForm + CdSkin + CdInt + CdInd + CdRam + CdWav
However, this is very deceptive and conducive to error due
to the interaction (i.e., measured separately a 0.100 Cdform plus
a 0.005 Cdram might equal a total 0.130 Cd due to interaction).
Parasitic Drag

15
“Form drag” has to do the mass of air that is displaced as a body
moves through it due to the body’s shape and size. At the front of a
body moving at moderate speed the air tends to be compressed and
a high pressure area develops, with the highest pressure at a
location called the “stagnation point”, while at the rear of the body
the air tends to expand and a low pressure area develops. This
pressure differential times the body’s cross-sectional area
constitutes the essence of form drag (actually the summation of the
longitudinal pressure components over the surface area of the body
constitutes the total drag force).
Note in the figure on the next slide how the absolute “Cd” of
“force/area” becomes the relative and dimensionless “Cd”
of general familiarity when divided by the absolute “Cd” of
a flat plate…

16
The relative “form drag”, as measured by a quantity called the
“coefficient of drag” or “Cd”, of certain basic shapes may be
illustrated as follows:
(Weight Engineer’s Handbook, Society of Allied Weight Engineers; Chula Vista, CA; 1968-1986, pg.. 10.6)
*At Mach Numbers

17
There are other chart versions which use Reynolds Number to
express the limitation of applicability of the Cd values…
(Streeter, Victor L.; Fluid Mechanics, McGraw-Hill Book Co., NY,NY, 1966. pg. 246)

18
Then there are chart versions which are less than specific…
(NASA, “What Is Drag?”, www.grc.nasa.gov/WWW/K-12/airplane/drag1.html )
(F1 Engineer, “Science Behind F1 Aerodynamic Features”, www.f1-country.com
/f1-engineer/aeorodynamics/aerodynamics.html)

19
Form drag Cd can be very sensitive to slenderness ratio, speed realms…
Tree (C values from Munson et al., 1998)
A=Tree frontal area
C=0.43 if V=10 m/s (36.0 km/h, 22.4 mph)
C=0.26 if V=20 m/s (72.0 km/h, 44.7 mph)
C=0.20 if V=30 m/s (108 km/h, 67.1 mph)
Flag (C values from Munson et al., 1998)
A=DL
C=0.07 if L/D =1
C=0.12 if L/D= 2
C=0.15 if L/D= 3
Thin Rectangular Plate (C from Blevins,
2003) A=DL
C=1.05 if L/D= 1.0
C=1.10 if L/D= 2.0
C=1.12 if L/D= 4.0
C=1.20 if L/D= 8.0
C=1.22 if L/D=10.0
C=1.33 if L/D=17.8
C=1.90 if L/D= infinity

20
“Skin drag” has to do with the air in actual contact with the external
surface area of the moving body. The magnitude of the skin area
and the degree of its roughness are the primary factors in
determining the amount of skin drag present.
The layer or “lamina” in actual contact with the body’s skin tends to
slow down with respect to the body until it is actually moving along
with the body as an “entrained” or captive mass; i.e., the relative
velocity is zero. The next layer of air tends to slow down due to its
contact with the first layer, but will retain a velocity relative to the
body just short of zero. The layer after that will also
tend to slow, but to even a lesser degree, and so forth.

21
The total number of “lamina” in close proximity with the body’s skin that
has had its relative velocity affected by the body constitutes the “boundary
layer”; the lamina of this boundary layer present a characteristic velocity
profile such as shown in the figures on this slide.
Eventually there will be a point
reached where the boundary layer
“laminae” in closest proximity to
the body will have slowed down to
the extent that the affected air
mass has come to serve as an
obstacle to the flow from
upstream; this is called the
“separation point” where the
large scale turbulence of a “wake”
sets in…

22
“Induced drag” is a usually small (except in the case of high lift
forms such as wings) drag component resulting from the generation
of lift forces. The generation of drag and lift is always
interconnected.
“Interference drag” is the drag resulting from the interaction of aero
flows, like that around an exterior side-mounted rear-view mirror
conflicting with the flow around an automobile’s A-pillar. However,
there are many other examples of such drag, some being of such
particular interest as to constitute a particular type or “effect”…
“Wave drag“ is the result of a “shock wave” formation at supersonic
speeds.
“Ram drag” is the drag associated with induction of free
atmospheric air into a vehicle interior (for cooling, combustion,
etc.).

23
“Ram drag” is the drag associated with induction of free atmospheric
air into a vehicle interior (for cooling, combustion, etc.).
AIR INLETS AND OUTLETS OF THE PORSHE 956

24
(Hucho, Wolf-Heinrich; Aerodynamics of Road Vehicles, SAE R-177, Warrendale, PA, pg. 293
(small chart), pg. 201 (large figure).)

25
Bernoulli’s Equation says
when the air has to go
faster over the top than
under the bottom there
will less pressure at the
top than the bottom. The
pressure difference times
the planform area is the
resultant lift, which acts
orthogonal to the chord
“A-B”. Resolving this
resultant into its
components gives
us the Lift and the
Induced Drag…
a = Angle of Attack
Lift = LiftR Cos(a)
Induced Drag = LiftR Sin(a)

26
Note the minimum drag at
zero lift, which is not at α = 0;
airfoil drag also has a
minimum at some speed

27
Where:
D = the drag force (lb)
Cd = the drag coefficient (dimensionless)
Af = the frontal area (ft2)
V = the velocity (ft/sec)
If “V” is to be in mph, then the “841” factor should be “391”.

28
Where:
D = the drag force (lb).
Cd = the drag coefficient (dimensionless).
Af = the frontal area (ft2).
V = the velocity (ft/sec).
ρ = the air & vapor mass density (slugs/ft3):
Where:
ρ is the atmospheric pressure (lb/ft2).
Pv is the vapor pressure (lb/ft2).
g is the gravitational constant (32.172 ft/s2).
T is the temperature (°R).

29
Where:
L = the lift force (lb)
Cl = the lift coefficient (dimensionless)
Ap = the plan area (ft2)
V = the velocity (ft/sec)
If “V” is to be in mph, then the “841” factor should be “391”.
PLAN AREA FRONT AREA

30
Where:
L = the lift force (lb).
Cl = the lift coefficient (dimensionless).
Ap = the plan area (ft2).
V = the velocity (ft/sec).
ρ = the air & vapor mass density (slugs/ft3):
Where:
ρ is the atmospheric pressure (lb/ft2).
Pv is the vapor pressure (lb/ft2).
g is the gravitational constant (32.172 ft/s2).
T is the temperature (°R).

Brian Paul Wiegand, B.M.E., P.E.
31
Integrating the pressure times the surface area all around the body
surface determines the resultant aerodynamic force on the body. This
single force acts in effect through the average location of the pressure
on the surface of the object. This average location of the pressure forces
is termed the center of pressure (CP) in much the same way that the
average location of the gravitational forces on a body is termed
the center of gravity (CG), through which acts the resultant gravitational
force which is called the weight of the body. However, unlike that single
force, the resultant aerodynamic force must be resolved into two
component forces, lift and drag, both of which act through the center of
pressure. Another difference between the CG and the CP is that
the CP will move with variation in orientation and velocity of the
body with respect to the flow, whereas the CG is more fixed.

32
The aero forces acting through the CP affects automotive directional stability
in two ways. The lift and drag forces will modify the normal loads on the tires,
and thereby affect the directional stability “indirectly”. However, there is also
a more “direct” effect…
1969 Dodge Charger @
60 mph

33
The “direct” effect is what commonly comes to mind when the term
“aerodynamic directional stability” is used; it is the stability imparted to
arrows, missiles, and other such bodies moving through a fluid (air) without
benefit of ground contact… And that directional stability comes about when
the center of pressure is located aft of the center of gravity:
“If the vehicle becomes airborne, or if the track surface offers little traction,
the effect of the contact patches may suddenly disappear or be lessened.
In that case, ground vehicle stability, like aircraft stability, requires that the
center of pressure be located behind the center of mass. If the vehicle
develops a yaw or pitch angle, the aerodynamic forces acting at the center
of pressure will be a restoring force if located behind the center of mass,
but will tend to increase the yaw or pitch angle if located ahead of the
center of mass, possibly leading to a spin or flip. Thus it is highly desirable
to have the center of pressure located behind the center of mass.”
(Pater, Larry; “Aerodynamics: Drag, Lift, and Stability”, Design and Construction of a Land Speed Record
Streamliner, www.paterstreamliner.com, 2016)

34
However, from the same source as the previous quote the location of the CP
is said to be determined by:
“An approximate, much easier, method is to use the area centroid of the
projected body profile (Benson, NASA model rocketry website) as an
estimate of the location of the center of pressure. This works quite well for
long and thin bodies such as a streamliner body or model rocket (but
maybe not a roadster or other car) for which the pressure variations over
the surface are not large. This can be done mathematically by using area-
moments to determine the geometric area centroid. Mathematics can be
avoided by finding the balance point of a cardboard cutout of the projected
profile, which gives a non-mathematical estimate of the location of the area
centroid and thus the center of pressure...”
It’s good that the source acknowledged the possible lack of accuracy in
using the body profile area centroid as an estimate of the location of
the CP for “roadster or other car”; just consider the previous 1969
Dodge Charger example…

35
…the profile area centroid would seem to pretty far aft of the known CP
location; this “centroid CP” could be the CP location to use for determining
the effect of a side wind gust acting at a right angle to the longitudinal axis of
the vehicle, but for a strictly longitudinal air flow would be still located as
shown:
1969 Dodge Charger @
60 mph

36
The CP actually might vary in location between the illustrated location to the
centroid location depending on the magnitude and direction of the air flow
vector. This illustrates the fact that the CP location is a much more variable
parameter than the CG location, even though that too varies with loading, free
surface effect, etc. Having a CP well aft of the CG certainly promotes
directional stability for an arrow or other body totally dependent on aero
forces; but for a wheeled vehicle a lateral aero disturbance force would act
through the centroid location shown and, if tire/suspension characteristics
are the same all around, tend to cause larger slip angles at the rear than the
front. That would tend to make the vehicle turn towards the disturbance force
such that the resulting centrifugal reaction would be in the same direction as
the aero disturbance (!), but that centrifugal reaction would also tend to
even out the front-to-rear slip angle relationship thereby tending to
return the vehicle to straight ahead motion (!)…Consider the
consequences of a lateral aero disturbance for a number of
CG/CP relationships…

The conventional wisdom is that the CP should be aft of the CG; usually the
CP is not far from the CG so following two cases (fwd CG and aft CG) quite
naturally present themselves:
It would seem that, based on this “analysis”, the conventional wisdom
doesn‘t work out as well for an aft CG car as it does for a fwd CG car.
37

Now consider the exact opposite of the conventional wisdom, again for the
two cases of a fwd CG and an aft CG:
Neither of these two cases seem to work out very well with regard to
directional stability…However, what happens if the CG and CP are not so
closely coupled? Brian Paul Wiegand, B.M.E., P.E.
38

39
It is unlikely the CG and CP would ever be quite as divergent as depicted,
but to complete this “analysis” consider the two cases of a fwd and an aft
CG:
It would seem that a far aft CP doesn’t work out too badly for a fwd CG, but
a far fwd CP for an aft CG car works out very, very poorly.

As a final thought on the subject of automotive aerodynamic directional
stability consider the following quote:
“A vehicle in an airstream is the less stable
the better its shape is suited for low drag.”
Dr. Wunibald Kamm, 1933*
Of course, early aerodynamically shaped cars tended to be teardrop
shaped with a large blunt front end and long tapering tail which placed the
CP far forward. The engine tended to get placed far aft so that the air
intake and exhaust would have minimum affect on the flow over the body,
but this tended to result in a very aft CG location. That combination of CP
and CG location we have already seen as being very unstable…
40
(*Hucho, Wolf-Heinrich; Aerodynamics of Road Vehicles, SAE R-177, Warrendale, PA, 1988,
pg. 31.)

41
…is commonly depicted as a
rotating cylinder traveling
against an airstream such that
the rotation assists the flow
over the “top” and retards the
flow under the “bottom”. For
such a situation of high speed,
hence
low pressure, on top and low speed, hence high pressure, on bottom, the
classical Bernoulli result is one of lift. However, the obvious automotive
application differs from this in that the wheels rotate with respect to the air-
stream so as to cause “down-force”. At least the wheels would generate such
down-force if they were in a free stream as opposed to being in contact with
the ground plane. And if the wheels are partially enclosed
within wheel-wells, then the resultant behavior has precious little left to
do with the Magnus Effect…However, some people still seek to invoke it…

A 1996 paper presented by Pfadenhauer, Wickern, and Zwicker claims that the
wheels/tires/housings account for about 35% of the total vehicle Cd
1; BMW
aerodynamicist Karlheinz Ebbinghaus corroborated this estimate of the
wheels/tires/housings aero drag contribution: “Thirty to forty percent of a car’s
aerodynamic resistance is created in the wheels and housings”2. It would therefore
seem to be reasonable to use this figure as the basis for a crude estimation of the
wheels/tires/housings impact on the aerodynamics of the basic auto body form.
However, this applies only to most road cars with Cds of around 0.35 to 0.30 in
value. The more streamlined the basic body form (the lower its Cd) the bigger the
relative impact (+%) that the addition of tire/wheel/wheelwells will have (and
streamlined open wheel race cars with very wide wheels may be the most affected
of all3)….
42
1 Talamelli & Westin; “Aerodynamics of Cars, Drag Reduction”, Department of Mechanics Presentation, KTH Royal
Institute of Technology, Stockholm, Sweden, slide 31.
2 Zenlea, David; “First Drive BMW i8”, Automobile, pp. 12-14, November 2013, pg.14.
3 Such race cars also have open cockpits and are designed to generate large amounts of “down-force” or negative
lift, and such lift generation means a large induced drag contribution to the total drag. Total Cd values might be
around 0.7 to 1.3 for an F1 car depending on wing angle of attack settings, etc.!!

(Hucho, Wolf-Heinrich; Aerodynamics of Road Vehicles, SAE R-177, Warrendale, PA, 1988, pg. 182.)
43
Drag and Lift is reduced for a rotating
wheel on the ground with respect to a
stationary wheel just off the ground.
However, drag is still high due to three
pairs of trailing vortices.
Experiments with a wheel just
over a stationary ground plane
demonstrates how Cd and Cl
decrease with wheel rotation.
The benefit of using large
smooth (“Moon”) wheel covers
is also demonstrated.

44
Wheel housings further affect
the Drag and Lift effect of the
wheels; the smaller the housing
volume “VH“ with respect to the
wheel volume “VW“ the less the
Drag and Lift generated…
(Hucho, Wolf-Heinrich; Aerodynamics of Road Vehicles, SAE R-177, Warrendale, PA, 1988, pp. 185 and 180.)

45
(Dimitriadis, Greg; “Vehicle Aerodynamics, Lecture 4: Fast Cars”, Université de Liége, Aeroelasticity and
Experimental Aerodynamics Research Group (AEA), Department of Aerospace and Mechanical Engineering , 2014 )

In NASCAR racing a practice known as “drafting”, a.k.a. “slipstreaming”, wherein
one car follows closely in the wake of another, has long been known to reduce the
aerodynamic drag of both vehicles. The exact effect depends very much on the
aerodynamic sophistication of the vehicles involved, the relative size of those
vehicles, and the distance (proximity), measured in car lengths, between the
vehicles.
46
(Hucho, Wolf-Heinrich (Ed.); Aerodynamics of Road Vehicles, SAE R-177, Warrendale, PA, pg. 208.)

47
Whenever there is a pressure differential
generated by the passage of a body through a
fluid the tendency of nature to equalize that
differential results in some lateral flow around
the body causing swirling flow motions that
represent a large energy loss and further drag…

48
Although turbulence and vortices are generally something to be
avoided, ironically such can actually be used to reduce drag, but just
when used on a smaller scale. When airflow in the boundary layer
begins to slow down to the point of separation, small scale roughness
or, even more efficiently certain structures, can induce turbulent and/or
vortex flow within the boundary layer lamina. This transverse
flow serves to bring an influx of
energy to the layers nearest the body
surface, speeding those layers up and
delaying separation. This results in a
reduced wake and an overall
decrease in drag…at least in the
higher speed ranges:
(Shapiro, Archer H.; Shape and Flow, The Fluid Dynamics of
Drag, Doubleday & Co., Garden City, NY, 1961, pg. 170.)

49
1928
1967
Wings had been used early in automotive history to provide down-
force to ensure traction, but their most extensive and notable
automotive use came in the form of the huge “high wings” used in
racing during the 1960’s. The wings were mounted so high in an
attempt to move them up out of the disturbed air flow and thereby
increase their effectiveness.
For a wing, the total drag coefficient, Cd is
equal to the base drag coefficient at zero
lift, Cdo, plus the induced drag
coefficient Cdi:
Cd = Cdo + Cdi

50
Modern wing usage as in Formula 1 involve the use of a front wing and an
aft wing, spread apart as far as possible to maximize their effect as “tuning”
devices for longitudinal normal load distribution and CP location. Front
wings operate in an extreme ground effect situation and are readily affected
by vehicle pitch motions. The rear wing is often designed to act in symbiosis
with a device located in the rear underbelly called a “diffuser”.
CP
CP CP

51
Fences are just barriers intended to direct
airflow in desired directions. Endplates are
just big fences commonly found at wing
tips in an effort to impede trailing vortex
formation; it could be said that such are an
attempt to maintain a 2-dimensional flow.

There is a paper by a Prof. Debojyoti Mitra, of the Sir Padampat
Singhania University, which allows quantification of the relation between
ground clearance and Cd / CL as per the following charts; note an example
vehicle with a 102 inch wheelbase undergoing a 1 inch reduction in ground
clearance sees a Cd reduction of 183 counts and a CL increase of 319 counts:
52

53
Shawn Buckley of the University of California at Berkeley was an early
researcher of underside aerodynamics of vehicles. Buckley had been the
designer of the first high-mounted wing used on an Indy racer, the Jerry
Eisert “Bat Car” of 1966. By 1969 Buckley was investigating how, by
shaping a car's underside so that the air speed there would increase, the
pressure could be reduced generating a negative lift. His resulting test
vehicles had a venturi-shaped channel on the underside which was sealed
by flexible side skirts from intrusion by “outside” air flow. Buckley would
also investigate how flow separation on the undersurface channel was
influenced by boundary layer suction and underbody surface divergence.
Much of Buckley’s work would not only influence Lotus, but Chaparral (Jim
Hall), March (Robin Herd), Brabham (Gordon Murray),
and others. Later, as a mechanical engineering professor at MIT,
Buckley would work with Lotus on the development of the Lotus 78.

The Lotus 79 was developed as an attempt to get more effective
ground effect, now with the assistance of David Williams of the
Cranfield Institute of Technology. Williams helped set up
instrumented studies of the “ground effect” downforce in order to
discover the exact nature of the phenomenon that Lotus was trying
to tame.
The main problem at the time was that changes in vehicle
speed, attitude, and ground clearance would vary the pressure and
cause the CP to move about affecting vehicle behavior; these were
effects not observable in the more idealized environment of the
wind tunnel. The vertical fluctuations and increased down-load
required much stiffer springing, which in turn caused increased
shock and vibration resulting in structural failure and driver
discomfort. Brian Paul Wiegand, B.M.E., P.E.
54

55
Part of the vertical
fluctuation problem
stemmed from the
difficulty in maintaining
an adequate “seal”
with the side skirts due
to ground surface and
ride height variation.
Movable skirts that
could flex in response
to the track contour
were banned by the
FIA in 1981.

56
Current Formula 1 regulations require that the under-body between the
axle lines be absolutely flat, and that no side skirts be used to “seal off”
the under-side to prevent a lateral in-flow. This prevents the extensive
sculpting of the underside to generate negative pressure zones as had
been the case previous. However, this gave rise to the development of
what came to be known as a “diffuser” just aft of the rear axle line.
Diffusers constitute a shaping of the aft end such as to act as
an “extractor” sucking out the air from under the car and thereby
increasing velocity and lowering the pressure, resulting in “downforce”.

addition of the vertical ‘fences’ to the diffuser help to optimize the efficiency by
restoring smooth air flow.
57
Toyota TF109.
The role of the diffuser on a
racing car is to speed the
airflow up underneath the car,
reducing its pressure, creating
a greater difference in pressure
between the upper and lower
surfaces of the car.
The diffuser increases in volume along
its length, creating a void that has to be
filled by the air passing under the body.
The resulting venturi effect means that
the flow is accelerated through the throat
of the diffuser, creating the desired low
pressure, after which the flow is
gradually returned to the same velocity
at which it started. The angle or slope of
the diffuser is very important; the
diffuser must have a gradual slope to
avoid flow separation from its roof and
sides. The

58
For road cars a front spoiler is often positioned under, or integrated into,
the front bumper. In regular passenger vehicle use, the focus is often on
directing the airflow into the engine bay for cooling purposes. When used
in racing, the spoiler is designed to improve the drag coefficient of the
body and to generate down force, at least at the front axle, by diverting air
flow from going underneath the vehicle. For dedicated race cars, such as
Formula 1 vehicles, front end aerodynamics depend on front wings and
splitters in lieu of spoilers.
Rear spoilers tend to be found on road cars, or racing versions thereof,
and are generally situated on the aft end of the rear deck. The intent is to
alter the aft airflow mainly for the purpose of reducing rear axle lift.
However, sometimes the rear spoiler can also be used to reduce
drag as well, depending on the specific aerodynamic situation.

59
A splitter, like a front spoiler or air dam, is also located toward the front
leading edge of a vehicle body. However, it is on, and even constitutes,
the exact leading edge and is horizontal in orientation. The intent is
once again to direct more air up and over (and possibly into the
radiator) the vehicle as opposed to underneath. However, a splitter
tends to be effective only at relatively high speeds, and since it is so
low on the vehicle, and projecting forwards, it may pose a practical
problem for road vehicles (curbs,
bump stops, etc.)

60
The difference between an air flow dam
and a front spoiler is mainly that a dam
is larger and more vertical in orientation
than a front spoiler. Otherwise they are
pretty much the same in that their
function is to divert airflow so as to
minimize flow going under the vehicle,
thereby reducing drag and front end lift.
(Simanaitis, Dennis; “Our Day in the Tunnel: Dam the Wind, Full Speed Ahead”, Road & Track, August 1982, pp. 48-50.)

61
The history of automotive aerodynamics would have been of interest to
Georg Wilhelm Friedrich Hegel (1770-1831) as it constitutes a perfect
example of the historical dialectic wherein the spirit of man drives ever
onward in an uneven progress toward knowledge. The struggle involved
many steps forward, followed by a few steps back, as many individuals
contributed to the progress, even those whose efforts would seem
wasted, who turned left or right from the straight path and ran into dead
ends. Some of the contributors were rational and educated, others were
more driven by sheer imagination. Some were conservative and retiring,
and others were flamboyant and self-promoting. Some acquired the
recognition they deserve, others fell into obscurity. The following
constitutes just a few of the physical milestones that mark the irregular
progress of the science of automotive aerodynamics…

62
1899 La Jamais Content
By Camille Jenatzy

63
1906 “The Rocket” LSR
By Stanley Steamer Co.
1903
1907

64
1914 Alfa Romeo
For Count Ricotti

65
1923 Tropfenwagen
by Edmund Rumpler
Cd = 0.28

66
1922 North
-Lucas

67
1922-1936 Paul Jaray
Jaray's designs for Tatra, Fiat Balilla, Maybach and Audi
Cd = 0.29

68
1923 Automobilul
Aerodinamic Perfect by
Aurel Persu
Cd = 0.22

69
1926 Rear/Mid-Engine by
Emile Claveau
1956

70
1932 Bergholt Streamline
by Fred Bergholt

71
1934 Chrysler Airflow
By Carl Breer,
Fred Zeder, and
Owen Skelton
Cd = 0.50 to 0.55

72
1934 Dymaxion by
Buckminster Fuller
1933
*A Cd of 0.131 was obtained based on a simplified CAD model of the
Dymaxion car which contains no internal engine bay or HVAC flow. Also
absent are the suspension geometries and bodywork detail (hinges,
louvers etc). Other simplifications include basic wheels and wheel
arches.
Cd = 0.25*

73
1934 McQuay-Norris
“Tear Drop Test Car # 9”

74
1934-36 Tatra T77,
T77a, & T87 by Hans
Ledwinka
T87 Cd = 0.36
T77a
T77a Cd = 0.33
Erich Übelacker (1899-1977)

75
1935 Streamliner by
Robert Gougeon

76
1935 Rier-
McCaslin

77
1936 Stout Scarab

78
1936 Dolphin by André
Dubonnet
André Dubonnet at the wheel of the Dolphin. At his side, his
chief engineer Gustav Chedru.

79
1938 Lewis Aeromobile by Paul Lewis
1937

80
1938 Phantom Corsair
by Rust Heinz

81
1938-39 Kamm-Wagen K3 by Dr.
Wunibald Kamm
Cd = 0.37
K-3
K-1

82
1938 Xenia by André Dubonnet

83
1939
Schlörwagen by
Karl Schlör
Cd = 0.19

84
1947 TASCO by Gordon Buehrig

85
(Actually there
was a series of
twin-boom cars
with varying
types of tail fin
configurations
and different
engine sizes)
1948 TARF GILERA BY PIERRO TARUFFI

86
1953 BAT 5
Alfa Romeo by
Bertone
Cd = 0.23

87
1954 BAT 7
Alfa Romeo by
Bertone
Cd = 0.19

88
1955 BAT 9
Alfa Romeo by
Bertone

89
1956 Morelli M1000
by Alberto Morelli

90
Cd = 0.23
1960 Pinninfarina
X by Alberto
Morelli

91
1962 TVR Ultra Low
Drag by Frank Costin
1970 Amigo
1959 Marcos

92
1976 Pinninfarina
CNR/PF by
Alberto Morelli
Cd=0.20

93
1983 Aero 2002 by GM
Cd = 0.14

94
1996 General
Motors EV-1
Cd = 0.19
1990
“Impact”

95
2002 Volkswagen 1L
Cd= 0.159
2015
XL1

96
FIAT Production Cars

ALWAYS REMEMBER THAT IN AERODYNAMICS TWO PLUS TWO
SOMETIMES EQUALS FIVE, OR THREE, OR…AERODYNAMIC BEHAVIOR
IS COMPLEX AND REPLETE WITH SYNERGISTIC INTERACTIONS…
SUGGESTED FOR FURTHER STUDY…
*Streeter, Victor L.; Fluid Mechanics, McGraw-Hill Book Co., NY,NY, 1966.
*Morelli, Albert; “A New Aerodynamic Approach to Advanced Automobile Basic Shapes”,
SAE Paper 2000-01-0491, Warrendale, PA, 2000.
*Pershing, Bernard (Ed.); The Aerodynamics of Sports & Competition Automobiles,
Proceedings of the 1968 AIAA Symposium, Vol. 7, Western Periodicals, Hollywood, CA,
1969.
*Gleason, Mark, and Gary Romberg, Glen Scharpf; Automotive Aerodynamics, Progress in
Technology Series, Vol. 16, SAE PT-78/16, Warrendale, PA, 1978.
*Hucho, Wolf-Heinrich (Ed.); Aerodynamics of Road Vehicles, SAE R-177,
Warrendale, PA, 1998.
97

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