Aerofoil section geometry

A symmetrical aerofoil profile is shown in Fig. 5.3(a) and below it the same section modified, by the

introduction of camber. The aerofoil definitions are based upon the American NASA (National Aeronautical and Space Administration) series of sections. It should be noted that the thickness distribution along the chord of the section, the position and amount of camber and the radius of the leading edge circle determine the curvature and slope of the upper and lower surfaces at any point.

Fig. 5.3 Basic aerofoil geometry.

The pressure over an aerofoil surface is made up of three components, the last two of which have been combined here. The resultant pressure is approximated to the algebraic sum of:

(a) The pressure arising from the displacement of the air around the basic symmetrical section at zero angle of attack — clearly a function of the thickness distribution along the chord.

(b) The pressure distribution over a thin plate having the same camber distribution and generating the same lift as the aerofoil in question.

Many factors are taken into account when choosing the aerofoil sections for wings and tails, simply because no one section possesses all of the needed qualities. A fully cantilever monoplane wing requires a thicker section than an externally braced wing, such as a biplane might use. The final choice depends upon the relative importance of the aerodynamic, structural and stowage properties of wings.

To aid the designer in his choice various useful families of related sections have been designed in different countries at different times. The best known is the NASA series of America. There is no precise equivalent in the UK, although a historical series of RAF (Royal Aircraft Factory, later the Royal Aircraft Establishment) sections was used during and after World War I.

Let us now consider the way in which section geometry determines aerodynamic properties. 5.2.2 Circulation and vortices

Imagine a mass of air particles being met by an aerofoil section moving with velocity V (the argument is much the same if the air is moving instead towards a stationary aerofoil, as in a wind-tunnel). Two particles, A and B, are deflected above and below the section which, because of the camber and angle of attack, presents upper and lower surfaces of different lengths and curvatures to the air it meets (Fig. 5.4(a)).

Fig. 5.4 The generation of circulation by an aerofoil in its passage through a mass of air.

The major effect of the aerofoil surfaces is to give both A and B a forward impulse, at the same time separating them: A upwards, B downwards. In doing so the particles are crowded into the mass of air ahead of the leading edge and the local pressure is increased. Each particle is able to slip, with friction, over their respective surfaces. After a small interval of time, when each is adjacent to station 1 (upper and lower), the impulse given by the surfaces has decreased, because of the reduced slope of each, although the impulse given to A is larger than to B, because the slope of the upper surface is steeper than the lower.

As the aerofoil passes, the slope of the surfaces decreases, and the high pressure of the particles crowded ahead of the aerofoil is able to thrust A and B rearwards, over the crest at the point of maximum thickness of each surface. The surfaces are shaped like the tube with curving walls in Fig. 5.2(b), and as the particles move rearwards the static pressure falls. Beyond the crest, however, the air displaced by the retreating aerofoil comes crowding back, forwards, inwards, to fill the rarefied regions left by its passage. A and B are therefore retarded in their rearward motion and squeezed (as it were) by increasing pressure forwards and inwards again, until — agitated and displaced downwards (relative to their original positions) — they are left in the wake behind the retreating section.

If one could draw the locus of each particle at successive intervals, corresponding with stations 1—10 across each surface, it would be seen that A and B had been forced to circulate around paths looking rather like those in Fig. 5.4(b). The circuits of each would be in opposition, but the algebraic sum of the two motions would be dominated by the more vigorous motion of A (because of A’s greater displacement in the time), leaving a resultant clockwise motion with average velocity of rotation AVAB, as shown in Fig. 5.4(c). Further, both have been pushed downwards, as downwash.

An aerofoil surface can be replaced, theoretically, by a chordwise sheet of bound vortices stretching from tip to tip — for the circulation shown in Fig. 5.4(c) could well apply at any average station across the chord. In fact ΔVAB varies from station to station as the particles are initially accelerated, and then decelerated

again behind the crests of the upper and lower surfaces. We are not concerned with the mathematics of such a vortex system. Suffice it to say that by postulating such a system, and then adding vectorially the relative

velocities around each vortex to the undisturbed relative airflow, V, we may obtain a reasonable approximation to the relative airflow around the aerofoil, this is shown in Fig. 5.5.

Fig. 5.5 The relative airflow pattern around an aerofoil due to circulation around an induced vortex system. The vector sum across the chord of an aerofoil of biconvex section, such as we have used for

illustration, shows an increase in relative velocity of the airstream over the crests of the surfaces. However, the relative velocity is higher over the upper surface than over the lower. If we now apply Eqn (5-1), using the relative velocity at any point, we may calculate the pressure distribution across the chord. The spanwise pressure distribution is as shown in Fig. 5.6(a). Clearly, if the pressure is lower across the upper surface than across the lower surface, there is a net lift across the chord of every spanwise station. The spanwise lift distribution varies with different planforms and body arrangements, and this will be discussed shortly.

Fig. 5.6 Aerodynamic load distribution on a subsonic rectangular aerofoil.

In theory a vortex can neither begin nor end in a fluid, it must form either a closed loop or end at a surface. The sheets of bound vortices do not end at the tips of an aerofoil but are shed across the span, to wrap themselves into the large trailing vortices already mentioned, lying in the wake of each tip. In fact the vortices eventually die away due to friction and turbulence behind the aircraft, forming a horseshoe vortex system when taken as a whole.