The direction of the resultant force due to pressure

It is often incorrectly thought, that the resultant force due to the pressure acts more or less at right angles to the plane of the wing. However, referring to Fig. 1.16, it may be seen that in addition to a perpendicular or normal force component N, produced by the difference in pressure between upper and lower surfaces, there is also a tangential component T, produced as a consequence of the low pressure acting on the leading edge. This ties in with theory which indicates that in the absence of three-dimensional effects, and as long as the flow follows the contours of the aerofoil, the lift force should be at right angles to the direction of the main air stream, and not at right angles to the plane of the wing.

Even when the wing is virtually a flat plate with a small leading edge area, as in Fig. 1.16, the very low pressure acting on it results in a significant forward force. If the plate is very thin, then the air simply fails to follow the contours of the surface at anything other than very small angles of attack, and the amount of lift generated is relatively small. In this case the resultant force is more or less at right angles to the plate.

The resultant aerodynamic force is never quite at right angles to the free – stream direction in practice, as there is always a rearward drag component due to friction caused by the influence of the viscosity of the air.

Force due to difference in pressures

between upper and lower surfaces

Force due to difference in pressure between leading and trailing faces

Fig. 1.16 The direction of the resultant force due to pressure

As long as the flow follows the contours of the section, there is a small tangential component of force resulting from the low pressure on the leading edge

Lift coefficient

The amount of lift produced by a wing depends on its plan area, the density of the air, the flight speed, and a factor that we call the lift coefficient (CL). The relationship can be expressed by

Lift = 2pV 2SCl

where S represents the wing plan area, p is the density, and V is the speed. You will see that the dynamic pressure (-pV2) occurs in this expression, and that, as mentioned earlier, the lift force is directly related to it.

The lift coefficient CL may be thought of as being a measure of the lifting effectiveness of the wing, and depends mainly on the wing geometry; that is, on the section shape, planform and angle of attack. CL also depends on the compressibility and the viscosity of the air, but for the time being, it will be convenient to ignore these latter influences.

The lift coefficient depends mainly on the shape of the wing, and is only relatively weakly dependent on its size. This is extremely convenient, because we can measure CL quite easily using a model in a wind tunnel, and with the aid of the above expression, we can calculate the amount of lift that would be produced by any size of wing at any required combination of speed and air density.

A further advantage is that for the whole range of flying conditions, the variation of lift with angle of attack can be calculated by using a single graph of CL plotted against angle of attack.

Unfortunately, when accurate predictions are required, the influences of viscosity and compressibility mentioned above, have to be allowed for, and the procedure can become much more complicated.

Another useful feature of CL, is that it is a dimensionless quantity (like a ratio), which means that it has the same numerical value, regardless of what system of units is used (e. g. Imperial or SI).