Lift is that component of total aerodynamic reaction which is perpendicular to the flight path of the aircraft.
It can be demonstrated experimentally that the total aerodynamic reaction, and therefore the lift acting on a wing moving through air, is dependent upon at least the following variables:
- Free stream velocity (V²).
- Air density (ρ).
- Wing area (S).
- Wing shape in section and in planform.
- Angle of attack (α).
- Condition of the surface.
- Viscosity of the air (µ).
- The speed of sound “a”, i.e. the speed of propagation of small pressure waves.
It is known that lift increases when the angle of attack of a given aerofoil section increases, and that the increase in lift was achieved mechanically by greater acceleration of the airflow over the section, with an appropriate decrease in pressure. The general and simplified equation for aerodynamic force is ½ ρ V² S X a coefficient, and the coefficient indicates the change in force which occurs when the angle of attack is altered.
The equation for lift is CL½ρV²S, and CL for a given aerofoil section and planform allows for angle of attack and all the unknown quantities which are not represented in the force formula.
Factors Affecting CL
The coefficient of lift is dependent upon the following factors:
- Angle of attack.
- Shape of the wing section and planform.
- Condition of the wing surface.
- Reynolds Number.
- Speed of sound (Mach number).
Angle of Attack. A typical lift curve is shown in Fig below for a wing of 13% thickness/chord (t/c) ratio and 2% camber (the zero lift angle of attack (αL0), is negative, its magnitude is often roughly equal, in degrees to the percentage camber, e.g. an aerofoil with 2% camber will have αL0 ≈ -2º (For a symmetrical aerofoil, αL0 = 0). The greater part of the curve is linear and the airflow follows the design contour of the aerofoil almost to the trailing edge before separation. At higher angles of attack the curve begins to lean over slightly, indicating a loss of lifting effectiveness. From the point of maximum thickness to the trailing edge of the aerofoil, the flow outside the boundary layer is decelerating, accompanied by a pressure rise (Bernoulli’s theorem). This adverse pressure gradient thickens the existing boundary layer. In the boundary layer, the airflow’s kinetic energy has been reduced by friction, the energy loss appearing as heat. The weakened flow, encountering the thickened layer, slows still further. With increasing angle of attack, the boundary layer separation point (explained in the chapter on drag) moves rapidly forward, the detached flow causing a substantial reduction of CL. The aerofoil may be considered to have changed from a streamlined body to a bluff one, with the separation point moving rapidly forwards from the region of the trailing edge. The desirable progressive stall of an actual wing is achieved by washout at the tips or change of aerofoil section along the span, or a combination of both.
Effect of Shape. Changes in the shape of a wing may be considered under the following headings:
- Leading Edge Radius. The shape of the leading edge, and the condition of its surface largely determines the stalling characteristics of a wing. In general, a blunt leading edge with a large radius will result in a well-rounded peak of the CL curve. A small radius, on the other hand, invariably produces an abrupt stall (Fig below) but this may be modified considerably by surface roughness which is discussed later.
- Camber. The effect of camber is illustrated in Fig below. Line (a) represents the curve for a symmetrical section. Lines (b) and (c) are for sections of increasing camber. A symmetrical aerofoil at zero angle of attack will have the same pressure distribution on its upper and lower surfaces, therefore it will not produce lift. As the angle of attack is increased, the stagnation point moves from the chord line to a point below, moving slightly further backwards with increase in angle of attack. This effectively lengthens the path of the flow over the top surface and reduces it on the lower, thus changing the symmetrical section to an apparent cambered one as in. A positively cambered wing will produce lift at zero angle of attack because the airflow attains a higher velocity over the upper surface creating a pressure differential and lift. This gives it a lead over the symmetrical section at all normal angles of attack but pays the penalty of an earlier stalling angle as shown by the CL versus α curve which shifts up and left as the camber is increased The angle of attack at which the CL is zero is known as the zero-lift angle of attack (αL0) and a typical value is -3° for a cambered section.
- Aspect Ratio. Fig below shows the downward component of airflow at the rear of the wing, caused by trailing edge vortices and known as induced downwash (ω). The induced downwash causes the flow over the wing to be inclined slightly downwards from the direction of the undisturbed stream (V) by the angle α1. This reduces the effective angle of attack, which determines the airflow and the lift and drag forces acting on the wing. The effect on the CL by change of aspect ratio (AR) will depend on how the effective angle of attack is influenced by change in AR. A wing of infinite span has no induced downwash. Nearer one gets to that ideal, i.e. high AR, the less effect the vortices will have on the relative airflow along the semispan and therefore the least deviation from the shape of the CL curve of the wing with infinite AR. It can be seen from Fig below that at any α, apart from the αL0, the increase in CL with changes in α of the finite wing is lesser than the infinite wing, the lag increasing with reducing AR due to increasing α1. Theoretically the CL peak values should not be affected, but experimental results show a slight reduction of CL max as the aspect ratio is lowered.
- Sweepback. If an aircraft’s wings are swept and the wing area remains the same, then by definition the aspect ratio (span2/area) must be less than the AR of the equivalent straight wing. The shape of the CL vs. angle of attack curve for a swept wing, compared to a straight wing, is similar to the comparison between a low and a high aspect ratio wing. However, this does not explain the marked reduction in CL max at sweep angles in excess of 40-45°, which is mainly due to earlier flow separation from the upper surface. An alternative explanation is to resolve the airflow over a swept wing into two components. The component parallel to the leading edge produces no lift. Only the component normal to the leading edge is considered to be producing lift. As this component is always less than the free stream flow at all angles of sweep, a swept wing will always produce less lift than a straight wing.
- Effect of Surface Condition. Surface roughness, especially near the leading edge, has a considerable effect on the characteristics of wing sections. The maximum lift coefficient, in particular, is sensitive to the leading edge roughness. Fig below illustrates the effect of a roughened leading edge compared to a smooth surface. In general, the maximum lift coefficient decreases progressively with increasing roughness of the leading edge. Roughness of the surface further downstream than about 20% chord from the leading edge has little effect on CL max or the lift-curve slope.
- Effect of Reynolds Number. The formula for Reynolds Number is:
RN = ρ V L/ µ
that is (density) x (velocity) x (mean chord length), divided by viscosity. If we consider an aircraft operating at a given altitude, L is constant, ρ is constant, and at a given temperature the viscosity is constant. Therefore the only variable is V. For all practical purposes the graph in Fig below shows the effect on CL of increasing velocity on a general purpose aerofoil section. It should be remembered than an increase in Reynolds Number, for any reason, will produce the same effect. Fig below shows that with increasing velocity both the maximum value of CL and the stalling angle of attack is increased. An increase in the velocity of the airflow over a wing will produce earlier transition and an increase in the kinetic energy of the turbulent boundary layer due to mixing, the result is delayed separation. An increase in density or a reduction in viscosity will have the same effect on stall.