Aeroplane Construction and Operation

by John B. Rathbun

A peculiar feature of the aerofoil lies in the fact that lift is still obtained with a zero angle of incidence, and even with a negative angle. With the aerofoil shown in Fig. 2 there will be a considerable lift when the flat bottom is parallel with the direction of travel, and some lift will still be obtained with the front edge dipped down (Negative Angle). The curved upper surface causes the air stream to rise toward the front edge, as at E, hence the wing can be dipped down considerably in regard to the line of motion X-X, without going below the actual air stream.

Action in Producing Lift. At comparatively high angles of incidence, where there is turbulent flow, the lift and drag are due principally to the difference in pressure between the upper and lower surfaces as in the case of the flat plate.

There is a positive pressure below as in the front of a flat inclined plane, and a vacuous region above the upper surface. The drag with the plane below the burble point, and above the "Lower Critical Angle," is due both to skin friction and turbulence—principally to the latter. Below the first critical angle (6°), the skin friction effect increases, owing to the closeness with which the air stream hangs to the upper surface.

Since there is but little turbulence at the small angles below 6°, the theory of the lift at this point is difficult to explain. The best explanation of lift at small angles is given by Kutta's Vortex Hypothesis. This theory is based on the fact that a wing with a practically streamline flow produces a series of whirling vortices (Whirlpools) in the wake of the wings, and that the forward movement of the plane produces the energy that is stored in the vortices. The relation between these vortices is such, that when their motion is destroyed, they give up their energy and produce a lifting reaction by their downward momentum. The upward reaction on the wing is thus equal and opposite to the downward momentum of the air vortices.

Drag Components. At large angles of incidence where turbulence exists, the lift and also the drag are nearly proportional to the velocity squared (V²). Where little turbulence exists, and where the air stream hugs the surface closely, the drag is due largely to skin friction, and consequently this part of the drag varies according to Zahm's law of friction (V²). For this reason it is difficult to estimate the difference in drag produced by differences in velocity, since the two drag components vary at different rates, and there is no fixed proportion between them. Since the frictional drag does not increase in proportion to the area, but as A⁰.⁹⁸, difficulty is also experienced in estimating the drag of a full size wing from data furnished by model tests.

Incidence and Lift. Up to the burble point the lift increases with an increase in the angle; but not at a uniform rate for any one aerofoil, nor at the same rate for different aerofoils. The drag also increases with the angle, but more rapidly than the lift after an incidence of about 4° is passed, hence the lift-drag ratio is less at angles greater than 4°. Decreasing the angle below 4° also decreases the lift-drag, but not so rapidly as with the larger angles. At the angle of "No Lift" the drag is principally due to skin friction.

Fig. 3 shows a typical lift and incidence chart that gives the relation between the angle of incidence Ɵ and the lift coefficient. This curve varies greatly for different forms of aerofoils both in shape and numerical value, and it is only given to show the general form of such a graph. The curve lying to the left, and above the curve for the "Flat plate," is the curve for the particular aerofoil shown above the chart. The "Lift-Coefficients" at the left hand vertical edge correspond to the coefficient Ky, although these must be multiplied by a factor to convert them into values of Ky. As shown, they are in terms of the Absolute units used by the National Physical Laboratory and to convert them into the Ky unit they must be multiplied by 0.0051V² where V is in miles per hour, or 0.00236v² where v = feet per second. The incidence angle is in degrees.

Fig. 3. Chart Showing Relation Between Incidence And Lift.

It will be noted that the lift of the aerofoil is greater than that of the plate at every angle as with nearly every practical aerofoil. The aerofoil has a lift coefficient of 0.0025 at the negative angle of -3°, while the lift of the flat plate of course becomes zero at 0°. As the incidence of the aerofoil increases the lift coefficient also increases, until it reaches a maximum at the burble point (Stalling angle) of about 11.5°. An increase of angle from this point causes the lift coefficient to drop rapidly until it reaches a minimum lift coefficient of 0.46 at 17°. The flat plate as shown, reaches a maximum at the same angle, but the lift of the plate does not drop off as rapidly. The maximum coefficient of the aerofoil is 0.58 and of the plate 0.41. The rapid drop in pressure, due to the air stream breaking away at the burble point, is clearly shown by the sharp peak in the aerofoil curve. The sharpness of the drop varies among different aerofoils, the peaks in some forms being very flat and uniform for quite a distance in a horizontal direction, while others are even sharper than that shown. Everything else being equal, an aerofoil with a flat peak is the more desirable as the lift does not drop off so rapidly in cases where the aviator exceeds the critical angle, and hence the tendency to stall the machine is not as great. This form of chart is probably the simplest form to read. It contains only one quantity, the lift-coefficient, and it shows the small variations more clearly than other types of graphs in which the values of Kx, lift-drag, and the resultant force are all given on a single sheet.