Aerodynamics is all the rage. Many a motor manufacturer in search of fuel economy is now discovering this science, which is also an art.

As was the case for the "traction avant" - or front wheel drive car, this is one of the fields in which Citroën has been disporting for many years. Followed today by many others.

During the year 1979, the German magazine "Stern" wind tunnel tested ten cars - and noted the GS's aerodynamic superiority.

A year later, the newspaper "Die Welt" remarked that the lines of the "cars of the future" currently elaborated by stylists have in fact been in existence since 1974: they are those of the Citroën CX , the car with the apt name (the Cx of a car is its coefficient of penetration through the air). Other observers noted that such and such so-called experimental models, French or foreign, intended for the years 1982-85, are still far from reaching the Cx of the standard production Citroën GSA X3. A German Consumer Association wrote to Citroën precisely to cast doubts on the real value of this model's CX. The marque thereupon provided all the proofs:

The Cx of the GSA X3, as measured at the Aerotechnical Institute at Saint-Cyr l'Ecole, with two occupants (310 lbs) and 130 lbs of luggage aboard, with the engine running to maintain a normal road clea-rance, is in fact 0.318. The Consumer Association took cognisance of this and naïvely admitted: "The specialists who advised us were of the opinion that such a sensational value was practically unattainable". Yet it is the best Cx in the world for a standard production car. Thanks for recognising the fact!

All over the World, the Cx battle rages, with penetration coefficients as its weapons. Hardly have they been discovered when attempts are already under way to manipulate them. It is now useful to take stock: what is aerodynamics to-day?

1 The science of the wind 

Aerodynamics is an experimental science whose aim is the study of the relative motions of a solid body with regard to the surrounding air. Its application to the design of a car body constitutes one of the chief lines of the quest for energy economy in motor vehicles.

In order to move over the ground, a body must overcome two forces:

• resistance to tyre tread motion, which is dependent on the state of the surfaces in contact and proportional to the vehicle's mass. The slower the vehicle moves, the greater its effect.
  

• resistance to forward motion, which depends on the shape of the body and on its frontal area. The higher the speed, the greater its effect.
  
  

All this leads one to see in motor-car aerodynamic research a means of reconciling economy and comfort while respecting the imperatives of safety.

In the XVIth century, the first, measurements of air resistance were carried out on freely falling bodies, and it was only at the end of the XIXth century that a new method appeared: submitting the body to be studied to an artificial air stream. It is on this principle that wind tunnels work. 

The initial means of ventilating wind tunnels was compressed air, then the fan, first used as a blower, and later (as is now the case) for suction. In 1909, the well- known engineer Eiffel added two essential devices: an intake and a diffuser. This type of wind-chamber is the prototype of all present day tunnels.

In applications of motor car aerodynamics, the cross section of the experimental chamber is of the order of 15 to 20 m2 (160 to 215 sq. ft.), i.e. 10 to 20 times the vehicle's cross-section. In the main stream, wind speed reaches 100 mph with a stability of  ±1% in experimental time and space.

This homogeneity is fundamental, as is a low ground-limit layer (dead fluid zone).

Automotive aerodynamics also relies on reduced scale wind tunnels for use with models, the scale usually being 1/5. These preliminary shape-research trials, quicker and less costly than full-scale ones, eliminate gross errors on the first prototypes.

Wind-tunnels are fitted with relatively complex dynamometric devices allowing measurement of all aerodynamic forces. The car-dynamometer system forms a unit which can be turned through a certain angle relative to the wind, thus allowing the simulation of side wind.

It should however be borne in mind that there is no universal standard for these measurements. Each wind tunnel itself constitutes the standard for the experimental research done there. From one wind tunnel to another, there may be dynamometric or blown-wind dispersions provoking slight distortions between the results found with one or another tunnel.  For this reason, it is always well to know where and in what circumstances the measurements put forward were made.

It is, in particular, important to know whether the results stated were obtained with a full-scale car, rather than with a 1/5 scale model (whose aerodynamic results are generally about 20% better), but also whether the car was a real one, and loaded.

All coefficients Cx Cy Cz Cl Cm Cn are read in the wind tunnel for various angles of side-slip ß (angle between the axis of the vehicle on test and the axis of the wind tunnel).

Running at 80.8 mph with a 25 mph side wind is simulated in a wind tunnel by an 84.5 mph wind and an angle of 17 degrees between the model and the wind.

Vo = 84.5 mph (136 km/h)

Vl = 25 mph (40 km/h)

Vv = 80.8 mph (130 km/h)

ß = 17 degrees

Knowing the distribution of weights and lifts on the front and rear axles, it becomes possible to calculate the weight taken off the wheels at all vehicle speeds with different side winds.

For instance, for a standard vehicle with a total weight of 2 640 lbs (1760 lbs forward, 880 lbs rear), the weight taken off  the front axles may be 1 000 N (216 lbs) at 93.6 mph with a 50 mpg side wind, whereas a racing car may have a weight lift equivalent to the axle load.

Using forces and moments, it becomes easy, by simple computation, to define the position of the centre of lateral thrust in relation to the centre of gravity. Together with lift, this is one of the criteria of road stability.

2 Visualisation of air fillets 

Visualisation of air-flow is indispensable to the comprehension and analysis of the results founded. Two methods are in current use:

• Visualisation of air fillets with strands of wool stuck to the vehicle  
  

• Visualisation by means of smoke produced by one or more movable jets.  
  

The study of air-flow patterns makes it possible, among other things, to look for means of compensating any aerodynamic effects which might oppose the operation of certain components of the car. Nothing is ever simple! Thus the (highly desirable) improvement of a vehicle's coefficient of drag may prove detrimental to the cooling of the braking system (highly regrettable).

This is why, during wind tunnel tests, the temperature of various braking-system parts is monitored. The visualisation of air fillets then makes it possible to design practical means of air supply to ensure the indispensable cooling of disc brakes.

Example: the aerodynamic study of the Citroën CX led to the setting up of an elaborate braking system: ventilated front brakes, sheet-steel deflectors forcing the air towards the braking system on the pivot, air guides fixed on the under-part of the front of the body.

3 Pressure measurements  

These measurements help to provide a partial solution to the problems of engine cooling and passenger cabin air-conditioning.

Pressures are expressed as a non-dimensional coefficient independent of speed:

Cp = P-Po
1/2 V2

Bernouilli's equation : 1/2 pV2 + P = Constant along an air fillet is valid as a first approximation for the front of the vehicle. It proves that high-pressure areas have low air speed. Conversely, where the air fillets cling to the body, there is a depression. (The drawing will help you to understand this relation between air speeds and pressures at any point). 

Pressure measurements make it possible to trace isobars (lines perpendicular to the air fillets visualising the lines along which pressure remains equal at a given value) on the vehicle's form.

The choice of the position of the air inlet for passenger-cabin air-conditioning will lie in the pressure zone at the foot of the windscreen.

4 An air of economy

The power that the engine must develop in order to overcome different forms of resistance (apart from accelerations and gravity) is represented by the formula:

W wheels  = N. Wm = 1/2QCxSV3 +f. M.V.

where:

• W wheels = power on driving wheels
  

• N = transmission efficiency
  

• Wm = power on engine output shaft
  

• Q = air density
  

• S = frontal area of car
  

• Cx = coefficient of drag
  

• f = frictional coefficient
  

• M = vehicle mass
  

• V = vehicle speed
  

• 1/2 CxSV3 = aerodynamic resistance
  

• f.M.V. = running resistance
  

The two following graphs represent respectively the formulae above, applied to a current standard production car, and the car's consumption in litres per 100 km according to speed. We can note the importance of streamlining for speeds approaching and over 90 km/h /56 mph), and the similarity between resistance and consumption curves, demonstrating the important role played by aerodynamics in fuel saving.

To travel at 120 kph (75 mph)

• the B2 of 1921 with a CxS of 1,437 required 75 bhp

• the Traction of 1934 with a CxS of 1,230 required 56 bhp

• the DS of 1956 with a CxS of 0,817 required 48 bhp

• while the GSA X3 of 1980 required only 31 bhp thanks to its very low CxS of 0,575.

In this respect, let us point out the misconception of which stylists, manufacturers, journalists and public alike are guilty about items such as spoilers and aerofoils, considered by one and all as optional extras for a sports car, whereas in fact, when, properly designed, they are first and foremost energy economisers which could easily and cheaply by provided for in standard production models.

Knowing that the shape of the body weighs heavily in the decision to buy a car, it is the stylists, at Citroën's, who combine the results of body studies with respect of the various restrictions they must comply with:

1. volume restrictions regarding overall dimensions, inside spaciousness, the engine, location of the tank, the spare wheels and the boot.
   

2. accessibility restrictions for the number of doors and visibility restrictions for the windows.
   

3. standards for shock absorbers, head-lamps, rear lights, traffic indicators, number plates etc...
   

4. restrictions connected with production, such as stamping and assembly problems with sheet metal whose nature imposes the shapes being cut up in various elements.
   

The aerodynamicist, for his part, has to check the results found with the first few shapes made up, and to suggest possible improvements to the stylist. The entire effectiveness of their collaboration takes form in their definition of an ambitious aerodynamic performance project and in their aptitude to achieve it in a seductive form.

Diagram of the wind tunnel at the St-Cyr Aerotechnical Institute, used by all French motor-car manufacturers:

1. stabilisation chamber 

2. injet  
   

4. test tunnel  
   

5. roller bench  
   

6. aero-dynamometer  
   

7. central diffuser  
   

8. lateral diffusers  
   

9. motor fan unit 
   

10. refrigeration exchanger

Axes of measurement for the forces and moments applied to a Citroën CX

• Trainée = Drag Roulis = Roll

• Dérive = Drift Tangage = Pitch

• Portance = Lift Lacet = Yaw

It can be seen that the resistance to a vehicle's motion of Drag Fx varies with air density and speed, but also with its CxS (coefficient of drag multiplied by frontal vehicle area), and not merely with its more usually quoted CX alone.

Example: with a Cx definitely less good than that of the CX (0.39 against 0.36) but a smaller frontal area (1.70 m2 = 18.3 sq. ft against 1.92m2 = 20.7 sq. ft) the aerodynamic coefficient of the LNA is better (0.66, as against 0.71 for the CX). 

It should be noted that, in aerodynamics, the coefficients are non-dimensional and that Cy and Cz have no absolute physical significance; the frontal area S is retained for a force Fy acting on the lateral surface of the vehicle (profile)

BALANCE OF FORCES AND AIR FILLETS  

Aerodynamic research as regards motor cars is done experimentally by measuring forces and pressures and by visualising the air stream with fillets. 

1. Measurement of forces 

A car in a wind is subjected to 3 forces (drag, drift and lift) and 3 moments (force multiplied by leverage) which are roll, pitch and yaw, related to the trihedral XYZ.

The diagram shows the axes of measurement of the forces and moments (force x leverage) applied to a vehicle (Citroën CX) when it is running. Force X is known as Drag, and its moment as Roll. Force Y is Drift and its moment Pitch. Force Z is Lift (broken down into forward Lift and rear Lift), and its moment is Yaw.

Where energy saving is concerned, drag, also known as resistance to the vehicle's motion, is alone involved. The aim is to reduce it as much as possible.

All the other components play a role in the vehicle's stability and more especially in its sensitiveness to gusty side winds.

Forces and moments depend on the square of the wind's velocity (i.e., in current practice, of vehicle speed) according to the following formulae:

where:

• P = air density
  

• V = wind velocity in tunnel
  

• S = frontal area of vehicle
  

• E = wheelbase
  

• Cx = coefficient of drag 
  

• Cy = coefficient of drift 
  

• Cz = coefficient of lift
  

• Cl = coefficient of roll
  

• Cm = coefficient of pitch 
  

• Cn = coefficient of yaw

Figurative distribution of areas and force of  pressures (+) and of depression (-) exerted by the air along the longitudinal axis of a Citroën GSA

• Refroidissement moteur = engine cooling
  

• Entrée d'air de climatisation = cabin air intake
  

• Evacuation de l'air habitacle = expulsion of cabin air

When a car's CxS is improved by 10 %, consumption at 120 km/h (74.6 mph) goes down by 7 %, at 90 km/h (56 mph) by 5 %, in town traffic by 1 %.

The characteristics of motor cars' resistance to motion can be improved by entirely redesigning their bodywork.

The bodies of current 4-door saloons have Cxs coefficients lying between 0.575m2 (6.19 sq.ft) for the best and 0.900 m2 (9.69 sq.ft) for the least good, or CxS of between 0.32 and 0.48.

The improvement of known aerodynamic forms can also be achieved by fitting corrective adjuncts.