A LOS PEATONES

The differential pressure and aerodynamic load distributions in Fig. 5.6 show the origin of lift but not drag. The static pressure acts at right angles to every point on the ‘wetted’ surface area of an aeroplane. It is convenient to resolve the force due to pressure acting over unit area into components that are normal and tangential to the flight path, as shown in Fig. 5.7(a).

Fig. 5.7 The aerodynamic components of static pressure and skin friction.

The frictional forces must also be taken into account, as shown in (b). The sum of the normal pressure components is the lift generated aerodynamically. The pressure drag components, when summed over the whole airframe, give the total pressure drag, D_press; while the sum of the frictional components gives the skin friction drag, D_fric. Hence, the total drag of an aeroplane is given by

D = Dpress + Dfric (5-3)

The estimation of drag is a complex problem. The pressure components in particular are affected by a large number of factors that cannot be controlled by the designer as finely as he would wish.

Circulation and downwash

We have seen that circulation is the motion around curved paths of the particles of air affected by the passage of an aerofoil surface. In fact circulation is generated by any body moving through the air at subsonic speeds: the art is to make circulation work by generating lift. Ways of increasing the local circulation of an aerofoil involve local increases of camber. Wing flaps, and all flap-like control surfaces are camber-changing devices and as such are employed to alter local lift distributions. Similarly, one often sees cambered leading-edge extensions over parts of the span of some wings and these are employed to smooth out local airflows and maintain efficient circulations.

Now, the downwash momentum imparted to the air is also a measure of the lift of an aerofoil, and it follows that there is a direct connection between the strength of circulation (i.e. the product of the air velocity around a curved path and the length of the path) and the downwash velocity. To generate a given lift at a given airspeed an aerofoil of long span has to impart a smaller downwash to the air it meets than an aerofoil of shorter span. The reason for this is that the mass of air affected in unit time is proportional to the product of the distance flown and the span: double the span and twice as much air is affected. As momentum is the product of mass and velocity, doubling the span halves the required downwash velocity to produce a constant rate of change of momentum: the force known as lift. It follows, therefore, that a long span aerofoil generates less circulation per unit span than a shorter aerofoil generating the same lift. In fact we may summarize by saying: (a) Downwash velocity varies directly with strength of circulation.

By imparting a circulation to the air an aerofoil experiences an equal and opposite reaction from the air. The reaction, in effect a torque, is called the pitching moment, which is denoted M and is nose down when the lift acts in the normal sense. The greater or lesser the lift, the greater or lesser the pitching moment.

The pressure and frictional forces acting on a lifting aerofoil section produce a resultant force which may be resolved into lift and drag components. Although the force and moment relationship depends upon the angle of attack of the aerofoil surface, it also depends upon the size of the surface, the airspeed and altitude. It is convenient, therefore, to state the lift, drag and moment characteristics of a section in terms of

dimensionless coefficients that are independent of size and of ambient conditions. Actual forces and moments can then be calculated for surfaces of different sizes and for different flight conditions by applying the

appropriate factors.

Dimensionless force and moment coefficients

If the average differential pressure across a strip section of an aerofoil Δy wide is p and the area of the strip of chord, c, is (c.Δy) then the lift of the section is

( )

l= Δ (5-4)

To eliminate the ambient factors ρ and V we may transpose Eqn (5-4) for p and divide by the dynamic pressure, obtained from Eqn (1-5) which is expressed in terms of

2 V 5 . 0 q= ρ

The ratio of p q is the lift coefficient of the section. c_l, where

( )

The section drag and moment coefficients are derived in the same way, such that:

( )

and, introducing the chord c a second time, to make the moment dimensionless: y qc m c 2 m Δ = (5-7)

If the total wing area of the aeroplane is denoted S, then the total lift, drag and pitching moments are given by S V 5 . 0 C L= _L ρ 2 (5-8) S V 5 . 0 C D= _D ρ 2 (5-8a) Sc V 5 . 0 C M= _M ρ 2 (5-8b) Aerodynamic centre, ac

The pitching moment of an aerofoil varies with lift and, if an aeroplane is to be stable, i.e. if it is to return automatically to a required attitude after a transient disturbance, stabilizing surfaces must be used that are not uneconomically large and heavy. Fortunately there is a point between the leading and trailing edge of an aerofoil about which the pitching moment coefficient is constant with attitude (angle of attack). This point is called the aerodynamic centre of the aerofoil. The aerodynamic centre, or ac, lies roughly one-quarter of the way back from the leading edge, near the 025c, or 1/4c, point. The aerodynamic centre is important, because the centre of gravity is arranged to lie near it. Lift, drag and pitching moment are usually related to the

Fig. 5.8 Aerodynamic characteristics of an aerofoil section. Note that the whole aircraft: bodies, wings,

stabilizer and other surfaces, alters the overall aerodynamic centre, neutral point, and values of c_l, c_d, and c_m, as shown in Eqns (5-5) to (5-10).

Fig. 5.8 (c) and (d) Origin of aerodynamic centre, ac, due to movement of centre of pressure, CP, in subsonic (subcritical) flight. Compare with Fig. 8.5 when compressibility is present.

The addition of a fuselage (and nacelles) has the effect of moving forward the ac of the aeroplane by 2 or 3% of the mean chord.

The aerodynamic centre is the neutral point of wing(s) plus stabilizer such that ac = NP (5-9)

A way of finding the ac by means of a lamina cutout of card is shown later in Fig. 5.11(c). 5.2.4 The boundary layer, separation and loss of lift

In Fig. 5.8(b) the CL curve is humped and the lift decreases beyond the hump with increasing angle of attack.

When the loss of lift is sharp the aeroplane is said to have a clearly defined stall. One wing may stall before the other, in which case a wing-drop occurs. Stalling usually occurs with combinations of large angle of attack and low airspeed, although an accelerated stall can be caused when maneuvering with large normal

acceleration and angle of attack. The loss of lift is caused by a decrease in local circulation.

The decrease in circulation causing the stall is brought about by the changing behavior of the boundary layer: a mass of air which, in lying close to the skin of the aerofoil, is dominated by the viscous forces that

cause skin friction. Outside the boundary layer the forces arise more from displacement than from viscosity. (picture)

Plate 5-1 Behavior of wool tufts on a wing with local boundary layer separations.

In Fig. 5.9 are shown five types of stall, each of which depends upon aerofoil section geometry.

Fig. 5.9 Types of aerofoil section stall.

The picture of the streamlined flow in Fig. 5.5(b) below the stalling angle is necessarily idealized to illustrate the idea of laminar flow, in which the air is assumed to move in smooth sheets relative to the aerofoil. As we saw earlier, however, the air particles are really moving in directed paths, impelled by an aerofoil moving relative to them. The two views are complementary: the essential point linking them is that the motion is directed and the pressure changes are controlled.

Beyond the stalling angle of attack the particles move in a highly disturbed random manner, in apparently unconnected swirls, eddies and vortices. Because the motions are no longer directed and the relative velocity is decreased, the pressure increases. The stall follows the attainment of peak suction over the upper surface of the aerofoil and one may imagine the suction to have been so intense that the air, in returning around the last part of the circuit in Fig. 5.4(b), is drawn far forward in the wake of the aerofoil by the intense pressure gradient. Therefore, instead of the air being left in the vicinity of its undisturbed position when the aerofoil has passed, it is now swept forward with an additional momentum, that represents additional power taken from the aeroplane. The boundary layer is said to have separated from the aerofoil surface when the stall occurs. Separations are accompanied by drag rise and sharp drops in the lift/drag ratio. Airframe buffeting is the result of flow separation.

Near the trailing edge of the aerofoil there can be a reversal of the relative airflow, as air creeps round the trailing edge from the lower to the upper surface. The sense of the motion is opposed to the sense of the lifting circulation and as such may be thought of as reducing the net circulation and lift (Fig. 5.10); this is shown in a wind-tunnel by the behavior of wool tufts on the upper surface of a wing with local separations.

Fig. 5.10 Trailing-edge conditions are most important at subsonic speeds. A rounded trailing edge (a)

encourages loss of circulation and oscillatory behavior in the flow which can, in turn, cause a control surface to flutter. Sharp edges are best because they cannot be negotiated by the airflow, which is encouraged no separate in a controlled manner; that shown in (c) makes a flying control surface feel heavier to the hand of the pilot.