## 142 Aerodynamic drag

14.2.1 Pressure (form) drag (Figs 14.12(a-e) and 14.13)

When viscous air flows over and past a solid form, vortices are created at the rear causing the flow

Vortices

Direction of air flow

Vortices

(a) Flat plate

(b) Circular section

(c) Circular/lobe section

(b) Circular section

(c) Circular/lobe section

(d) Aerofoil section

Fig. 14.12 (a-e) Air flow over various shaped sections a/3

(d) Aerofoil section

Fig. 14.12 (a-e) Air flow over various shaped sections to deviate from the smooth streamline flow, see Fig. 14.12(a). Under these conditions the air flow pressure in front of the solid object will be higher than atmospheric pressure while the pressure behind will be lower than that of the atmosphere, consequently the solid body will be dragged (sucked) in

the direction of air movement. Note that this effect is created in addition to the skin friction drag. An extreme example of pressure drag (sometimes known as form drag) can be seen in Fig. 14.13 where a flat plate placed at right angles to the air movement will experience a drag force in the direction of flow represented by the pulley weight which opposes the movement of the plate.

Pressure drag can be reduced by streamlining any solid form exposed to the air flow, for instance a round tube (Fig. 14.12(b)) encourages the air to flow smoothly around the front half and part of the rear before flow separation occurs thereby reducing the resistance by about half that of the flat plate. The resistance of a tube can be further reduced to about 15% of the flat plate by extending the rear of the circulating tube in the form of a curved tapering lobe, see Fig. 14.12(c). Even bigger reductions in resistance can be achieved by proportioning the tube section (see Fig. 14.12(d)) with a fineness ratio a/b of between 2 and 4 with the maximum thickness b set about one-third back from the nose, see Fig. 14.12(e). This gives a flow resistance of roughly one-tenth of a round tube or 5% of a flat plate.

14.2.2 Air resistance opposing the motion of a vehicle (Fig. 14.13)

The formula for calculating the opposing resistance of a body passing though air can be derived as follows:

Let us assume that a flat plate body (Fig. 14.13) is held against a flow of air and that the air particles are inelastic and simply drop away from the perpendicular plate surface. The density of air is the mass per unit volume and a cubic metre of air at sea level has an approximate mass of 1.225 kg, therefore the density of air is 1.225 kg/m3.

Then let

Density of air flow = p kg/m3

Frontal area of plate = A m2

Velocity of air striking surface = v m/s

Volume of air striking plate per second = Q = vA m3

Momentum of this air (mv) = pvA x v therefore momentum lost by air per second = p Av2

From Newton's second law the rate at which the movement of air is changed will give the force exerted on the plate.

Roller

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Air flow

77777s777? 7ST?? vs Vortices

Air flow

Fig. 14.13 Pressure drag apparatus

Hence force on plate = p Av2 Newton's

However, the experimental air thrust against a flat plate is roughly 0.6 of the calculated pAv2 force. This considerable 40% error is basically due to the assumption that the air striking the plate is brought to rest and falls away, where in fact most of the air escapes round the edges of the plate and the flow then becomes turbulent. In fact the theoretical air flow force does not agree with the actual experimental force (F) impinging on the plate, but it has been found to be proportional to p Av2

hence

F a Av2

therefore air resistance F = CD Av2 where CD is the coefficient of proportionality.

The constant CD is known as the coefficient of drag, it has no unity and its value will depend upon the shape of the body exposed to the airstream.

This is the turbulent volume of air produced at the rear end of a forward moving car and which tends to move with it, see Fig. 14.14. The wake has a cross-sectional area equal approximately to that of the rear vertical boot panel plus the rearward projected area formed between the level at which the air flow separates from the downward sloping rear window panel and the top edge of the boot.

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