Definition
Any material which flows, such as air or water, can
be referred to as a fluid; dynamics simply means
moving and computational is about calculations.
Aerodynamics was for many years about observing
the air flow over a vehicle, with sample calculations
for specific areas of the car; the advent of
computers meant that calculations could be done
many times faster than by long hand. So, it became
possible to carry out calculations for large sections
of the car very quickly.
In the 1970s engineers became interested in
the aerodynamics which were taking place both
underneath and inside the car, places which
could not be seen. More recently software has
been developed, such as AutoCAD, 3D Studio
and Pro/ENGINEER, which allows solid modelling
and the facility to virtually walk through a
40% overlap = 40% of the
width of the widest part of the
car (not including wing mirrors)
540 mm
1000 mm
64 kph (40 mph)
40%
overlap
500 mm
1500 mm
50 kph (30 mph)
R-Point
R-Point = hip point for a 95th
(a) Frontal impact test percentile male
(b) Side impact test
(c) Pole test (d) Pedestrain impact test
Child
head
Adult
head
Upper
leg
Leg
29 kph (17 mph)
Pole Diameter = 254 mm
The history, development and construction of the car body 31
design. This means that there is now no longer
a need to make a buck, or a mock-up, of a car to
be able to visualize the design. As an example,
vehicle body engineers used to use a wooden
buck of an engine to help them to design the
body work, and see if it could be fitted to and
removed from the initial body design. The Rover
75 is the first car to be designed without this; a
solid modelling package was used for a virtual
engine and body design, allowing an onscreen
test fit.
Having designed the virtual car it is possible to
observe it in a virtual wind tunnel and carry out
calculations both internally and externally, this is
what computational fluid dynamics (CFD) is all
about. As you can appreciate, the cost of a virtual
design and aerodynamic testing without a wind
tunnel is only a fraction of the cost of building a
buck and using a real wind tunnel.
The calculations
The following are some of the calculations which
an aerodynamist may be concerned with; it
should be remembered that these calculations are
often carried out on about 10 000 000 (ten million)
individual grid squares, or cells, on the car
body, a slight change of design will need a new
set of calculations. Even using the latest computer
software, the slightest change may take several
days; without CFD it would take months, and the
level of accuracy would be much less. If you
choose to use any of these formulae, remember to
use SI units, metres, newtons and seconds where
appropriate.
Dynamic pressure, which is also a kinetic energy
of unit volume in terms of cubic metres, comes
from the Bernoulli equations. Bernoulli was a scientist
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whose fluid flow theories were first used in
the design of ships hulls.
Dynamic pressure
_ 1/2 _ air density _ vehicle velocity squared
_ 1/2 _ V 2
As you can see, the speed (velocity) of the vehicle
is important for these calculations. Of course
velocity is a vector quantity, it is related to the
direction of the wind. Wind is very rarely a
straight-on head wind, so calculations can be done
for any of the 360 degree possible wind directions
for each of the ten million grid squares. Yes, that is
3.6 billion calculations for each speed and of
course the air density varies with altitude; at sea
level the value is 1.226 kilogrammes per cubic
metre.
Reynolds Number is a ratio which gives a good
guide to the air flow pattern and is an important
consideration of what is called scale effect.
Reynolds Number
_ air density _ air velocity
_ length of flow/air Viscosity
Re _ __ l __
Drag is the aerodynamic resistance of the vehicle,
its resistance to pass through air. Drag in newtons
force is found by the formula:
Drag _ 1/2 air density _ velocity squared
_ frontal area _ coefficient of drag
_ 1/2_ V 2 AC D
You will see that part of the formula is familiar,
and part of it is the same as dynamic pressure,
therefore:
Drag _ dynamic pressure _ frontal area
_ coefficient of drag
The coefficient of drag is a number which indicates
the resistance of the car to pass through the air,
typical values are between 0.25 and 0.35.
Lift is the force generated by an aerofoil section
normal to the direction of fluid flow. In other
words it is the upward lifting force which is generated
when passing horizontally through air. For
road vehicles wings are used to hold a vehicle on
to the road, this can be called downthrust or negative
lift.
Lift _ dynamic pressure _ wing area
_ coefficient of lift
When working with road vehicles the frontal area is
often used for the wing area figure. On aircraft, the
wing plan area is more appropriate. With advanced
aerodynamic work the plan area is related to a
reference area. For most road vehicles the frontal
area and the plan area are proportional; also the
coefficient of lift and the coefficient of drag are also
proportional.
Lift _1/2_ V 2 AC L
32 Repair of Vehicle Bodies
Grid system
The vehicle body shape is broken into grid squares,
or cells, see Figure 1.29. Depending on the shape
of the panel, the grid cells may be of different
shapes between square and oblong.
The squares are then considered as imaginary
cube shapes, see Figure 1.30. A set of calculations
called the NavierStokes equations gives a relationship
between pressure, momentum and viscous
forces in three-dimensional space. There is also a
similar set called the Euler equations. The above
calculations covered some of these concepts. The
computer is used to calculate the amount of energy
which is entering each cube and in turn leaving it.
Obviously the two figures should balance and there
will be flow between adjacent cubes.
Ahmed model
For benchmark testing of CFD systems the simplified
vehicle shape, known as the Ahmed model, is
used, see Figure 1.31. This is a simplified model of
a hatchback car. The Ahmed model can be made
from a wooden block and used in any wind tunnel.
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1.3 Methods of construction
The steel body can be divided into two main types:
those which are mounted on a separate chassis
frame, and those in which the underframe or floor
forms an integral part of the body. The construction
of todays mass-produced motor car has
changed almost completely from the composite,
that is conventional separate chassis and body, to
the integral or mono unit. This change is the result
of the need to reduce body weight and cost per unit
of the total vehicle.
Composite construction
(conventional separate chassis)
The chassis and body are built as two separate
units (Figure 1.32). The body is then assembled
on to the chassis with mounting brackets, which
Figure 1.30 One cube shape in a grid cell, the CFD
calculates the energy of entering and leaving each
cube (Dr Barnard 1996)
Figure 1.29 Grid of cells on a Volvo car (Dr Ramnefors 1994)
The history, development and construction of the car body 33
Figure 1.31 The Ahmed Model, a simplified shape of a hatchback vehicle (Dr Ahmed 1984)
Figure 1.32 Composite construction (conventional separate chassis)
34 Repair of Vehicle Bodies
Figure 1.33 Composite construction showing a Lotus Elan chassis before fitting the body (Lotus Engineering)
have rubber-bushed bolts to hold the body to
the rigid chassis. These flexible mountings allow
the body to move slightly when the car is in
motion. This means that the car can be dismantled
into the two units of the body and chassis.
The chassis assembly is built up of engine,
wheels, springs and transmission. On to this
assembly is added the body, which has been preassembled
in units to form a complete body shell
(Figure 1.33).
Integral (mono or unity)
Construction
Integral body construction employs the same
principles of design that have been used for years
in the aircraft industry. The main aim is to
strengthen without unnecessary weight, and the
construction does not employ a conventional separate
chassis frame for attachment of suspension,
engine and other chassis and transmission components
(Figure 1.34). The major difference between
composite and integral construction is hence the
design and construction of the floor (Figure 1.35).
In integral bodies the floor pan area is generally
called the underbody. The underbody is made up of
formed floor sections, channels, boxed sections,
formed rails and numerous reinforcements. In most
integral underbodies a suspension member is
incorporated in both the front and rear of the body.
The suspension members have very much the same
appearance as the conventional chassis frame from
the underside, but the front suspension members
end at the cowl or bulkhead and the rear suspension
members end just forward of the rear boot
floor. With the floor pan, side rails and reinforcements
welded to them, the suspension members
become an integral part of the underbody, and
they form the supports for engine, front and rear
suspension units and other chassis components. In
the integral body the floor pan area is usually of
heavier gauge metal than in the composite body,
and has one or more box sections and several channel
sections which may run across the floor either
from side to side or from front to rear; this variety
of underbody construction is due largely to the
difference in wheelbase, length and weight of the
car involved. A typical upper body for an integral
constructed car is very much the same as the
conventional composite body shell; the major
differences lie in the rear seat area and the construction
which joins the front wings to the front
The history, development and construction of the car body 35
bulkhead or cowl assembly. The construction in the
area to the rear of the back seat is much heavier in
an integral body than in a composite body. The
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same is true of the attaching members for the front
wings, front bulkhead and floor assembly, as these
constructions give great strength and stability to
the overall body structure.
Semi-integral methods of
Construction
In some forms of integral or mono assemblies, the
entire front end or subframe forward of the bulkhead
is joined to the cowl assembly with bolts. With this
construction, the bolts can be easily removed and the
entire front (or in some cases rear) subframe can be
replaced as one assembly in the event of extensive
damage.
Glass fibre composite
Construction
This method of producing complex shapes involves
applying layers of glass fibre and resin in a prepared
mould. After hardening, a strong moulding is
produced with a smooth outer surface requiring little
maintenance. Among the many shapes available
in this composite material are lorry cabs, bus front
canopies, container vehicles, and the bodies of cars
such as the Reliant Scimitar. The Italian designer,
Michelotti, styled the Scimitar body so that separately
moulded body panels could be used and
overlapped to hide the attachment points. This
allows the panels to be bolted directly to the supporting
square-section steel tube armatures located
on the main chassis frame. The inner body, which
rests directly on the chassis frame and which forms
the base for all internal trim equipment, is a complex
GRP moulding. The windscreen aperture is
moulded as a part of the inner body, and incorporates
steel reinforcing hoops which are braced
directly to the chassis. The boot compartment is
also a separate hand-laid GRP moulding, as are the
doors and some of the other panels. Most of the
body panels are secured by self-tapping bolts which
offer very positive location and a useful saving in
assembly time (see Figures 1.36 and 1.37).
