AUTOMOTIVE aerodynamics, the study of airflow around vehicle bodies, has become more important in the last 20 years as designers try to make vehicles more slippery. The fact is that the total resistance to motion at any speed is the sum of the resistance due to drivetrain friction, tyre/road friction and friction between the body and the air flowing past it. At very low speed the first two forces are dominant, but by the time a car reaches 30 km/h the air resistance starts to climb, and thereafter plays a major role because it grows as the square of the speed, as we shall see later.
The major research thrust has been to reduce the drag coefficient, which is a shape factor. Other factors, such as the frontal area, are more difficult to minimise because most cars have to carry at least four people.
There is also a definite relationship between maximum speed and the total drag, because the maximum speed occurs when the total drag is exactly equal to the engine’s power output. Expressed as forces, these two act in opposite directions so that the resultant force on the car is zero, and according to Newton’s laws of motion, this implies that the acceleration is zero, ie the car cannot go any faster.
AERODYNAMIC HISTORY
In the first 20 years of the last century various crude experiments at streamlining cars were mainly confined to racing cars or land speed record attempts. Most engineers believed that ordinary cars were not fast enough to benefit from streamlining, despite the fact that a number of sporting cars could exceed 145 km/h from as early as 1910.
The first serious interest in streamlining started in Germany just after WW1. Edmund Rumpler, who invented the swing axle while with Adler in 1903, caused a sensation at the 1921 Berlin Motor Show by exhibiting a very advanced car bearing his own name, based on patents he’d taken out in 1919. The wheels were open, except for little wings above them, but the interior and most of the components were enclosed in a metal tub.
The underbelly was also enclosed and a birds-eye view showed a teardrop-shape.
The engine was a W6, having three banks of two cylinders each. Production only lasted for five years, and about 100 cars were built. It was too advanced for its day, but the Benz motor company bought one to study, and some of Benz’s later racing and sportscars showed a Rumpler influence.
Engineers only discovered how remarkable these cars were in 1979 when Volkswagen tested an example from a museum in its wind tunnel, and found the drag coefficient to be 0,28! This is better than the claimed figure for many modern cars. An even bigger mystery is the fact that there were no full-scale wind tunnels when the car was designed, so how did Rumpler manage to design such a slippery car?
Next on the scene was Paul Jaray. He was a Hungarian, born in Vienna, but he lived most of his life in Switzerland. He experimented with automobile bodies in the Zeppelin airship wind tunnel, and subsequently designed special bodies for a number of German manufacturers, but the only production cars he had a hand in were made by Tatra and Adler. The Chrysler Airflow and Peugeot 402 were considered close enough copies to enable Jaray to win a court case and the manufacturers were obliged to pay him royalties. Adler entered some very smooth racing sportscars at Le Mans in the late -’30s. They had very long tails, which was a Jaray trade mark, and were competitive in the smaller classes, despite having side-valve engines.
However, the most important result of pre-war research was the development of the Kamm tail, which can be seen on many modern cars. The appreciation that a long tail can be cut off at a certain point without destroying the aerodynamic profile occurred almost simultaneously to Baron von Koenig-Fachsenfeld and Professor Wunibald Kamm,head of the Automotive Research Institute at the Stuttgart Technical College. Together, they experimented with the shape in a wind tunnel, and aroused BMW’s interest. The latter then built a number of experimental cars that proved the idea’s merit.
The first well-known production car to have its shape developed in a wind tunnel was the Volkswagen Beetle. It had a drag coefficient of 0,4 at a time when most cars were closer to 0,6. Its body was developed by Erwin Komenda and Josef Mickl. The former stayed with Porsche from 1931 to 1966, and is famous for creating the body shape of the 356 and heading the design team that produced the immortal 911.
After the war, most European companies invested in some aerodynamic expertise, so by the time the energy crisis started they were able to produce designs with low drag coefficients.
BASICS
Air particles can interact in a number of ways, depending on the way the air moves around a body:
- Away from the body, the air particles flow smoothly at the free stream velocity, giving rise to what is known as laminar flow. This kind of flow can be seen on smoke photos of the paths of successive air particles in steady flow. These paths are called streamlines, and here most of the particles collide with each other without sliding. This produces what is called pressure or inertia forces, and in most of the air that flows around a body these forces predominate.
- Air particles close to the body stick to the surface, but the particles further away move at the free stream velocity. Between these regions is the boundary layer. Here the velocity can be anything between zero and the free stream velocity. Note that the term velocity covers speed as well as direction, so if the speed remains constant but the direction changes, it represents a change in velocity. Here most of the particles slide past each other, producing what are called tangential or shear forces.
- Sometimes the two types of flow separate, giving rise to turbulent flow or even a stalled condition. This results in high drag, or loss of lift. This can arise only from shear forces. In most practical situations the relative contribution of each kind of flow to the total effect depends on the size of the areas concerned.
A collection of streamlines is called a stream tube, and is used as an idealised concept to make the study of airflow easier. The tube is assumed to be isolated ie having an impenetrable boundary, and the air in the tube is assumed to be frictionless and incompressible so that the cross-sectional area is assumed to change as the pressure changes, as if the tube were elastic.
Inside the tube the total energy remains constant, and under these conditions the interchange of energy can be calculated by using an equation developed by Daniel Bernoulli, a mathematician and pioneer in fluid dynamics, and published in 1738 in his book entitled Hydrodynamica. Commonly known as Bernoulli’s equation, it can be expressed in two forms:
- The energy form states that the total energy is equal to the sum of the pressure energy and the kinetic energy.
- The pressure form states that for a unit volume the total pressure is equal to the sum of the pressure in the air stream (the static pressure), and the pressure that would be realised if the particles of air were brought to a complete stop, such as would occur if a large flat plate were inserted into the air stream (the dynamic pressure).
In summary: The total pressure in an air stream is equal to the static pressure plus the dynamic pressure.
DRAG EQUATION
The aerodynamic drag force experienced by a body in an air stream is given by the following formula:
F = 0,5pCdAV2 where
F= force in newtons p(Greek letter rho) = air density in kg per m3
Cd = drag coefficient
A = frontal area in m2
V = air speed in m/s
For a ball, the frontal area is the projected area, ie the area of the circular hole the ball will just fit into. For a car it is the area that can be seen on a photograph taken square onto the front of the car.
DRAG COEFFICIENT
The drag coefficient is a dimensionless number that can only be measured accurately in a wind tunnel. It can be thought of as a form factor, because its value depends on the form drag and the skin friction. In most cases a particular body will have a low drag coefficient if the boundary layer remains attached to the surface for as long as possible, giving a thin wake. This will happen if the flow becomes turbulent before separation from the body.
This effect can be illustrated by looking at the flow around a smooth golf ball, as shown on the opposite page. The laminar flow causes the main stream to separate from the surface of the ball well before the maximum diameter is reached, causing a broad wake. This results in a high drag coefficient because the wake is an area of low pressure that retards the flight of the ball. These sketches show why golf balls are dimpled. The dimples cause a turbulent boundary layer that retards the separation until well after the maximum diameter, resulting in a narrow wake, and consequently a lower drag coefficient. The result is that a dimpled ball travels further.
Unfortunately, not all shapes can be analysed so easily, because the above theory is only completely true for an ideal fluid moving over smooth body shapes. In practice, air does not always behave like a perfect fluid, and few cars have shapes that are smooth everywhere. Boundary layers usually tend to thicken as they get longer, and they eventually become turbulent, so if the object is long enough a stage is eventually reached where the boundary layer is so thick that flow separation occurs. Close to the surface the flow may even reverse. This often happens towards the rear of automotive body shapes where the flow separates and breaks down into a disturbed wake. This becomes an area of low pressure that has to be dragged along by the car using energy that comes from the engine. Separated flow is usually undesirable, but not always, so it’s risky to make general statements about airflow around complicated objects.
WIND TUNNEL TESTING
Modern high-speed computers have led to the rise of computational fluid dynamics, which allows most shapes to be analysed using mathematical models, although most shapes still have to be fine-tuned in wind tunnels. Ideally, cars should be tested in fullscale wind tunnels, but this is not always possible. Such tunnels are not only few and far between, but also extremely costly to build. Most cars are tested in half-scale tunnels, or even smaller-scale units, but this introduces the complication of making sure that the results can be applied to full size cars. Luckily, Osborne Reynolds (1842 – 1912) supplied the answer. He studied the flow conditions that govern the transition from laminar flow to turbulent flow and developed the theory that enables engineers to convert small-scale results to fullsize cars.
RELATION BETWEEN POWER AND SPEED
The above drag equation also holds if the air is stationary and the body is moving, and in this case V becomes the speed of the body. Also, since power is equal to force times speed, the force F can be changed to power by multiplying each side by V, so that V2 becomes V3. If the answer is then divided by 1 000, it will be in kilowatt, so that:
kW = (0,5pCdAV3)/1000 This gives the power needed to attain the speed V.
Unfortunately, this formula can seldom be used to calculate a car’s maximum speed because both the drag factor and the frontal area are often unknown. Even if these numbers were known, the gearing chosen often results in a maximum speed that does not correspond to the maximum power output.
Next issue: Combating drag: Part 2 – Formula One aerodynamics