Aeroplane Construction and Operation

by John B. Rathbun

Forces Acting on Aerofoil. Fig. 7 is a section through an aerofoil of a usual type, with a concave under-surface In an aerofoil of this character all measurements are made from the chordal line X-X which is a straight line drawn across (and touching) the entering and trailing edges of the aerofoil. The angle made by X-X with the horizontal is the angle of incidence (i). The width of the section, measured from tip to tip of the entering and trailing edges, is called the "Chord." In this figure the entering edge is at the left. The direction of lift is "Up" or as in the case of any aerofoil, acts away from the convex side.

In the position shown, with horizontal motion toward the left, the lift force is indicated by L, and the horizontal drag force by D, the direction of their action being indicated by the arrow heads. The force that is the resultant of the lift and drag, lies between them, and is shown by R. The point at which the line of the resultant force intersects the chordal line X-X is called the "Center of Pressure" (C. P.) The resultant is not always at right angles to the chordal line as shown, but may lie to either side of this right angle line according to the angle of incidence (i). A force equal to and in the same direction as R, will hold the forces L and D in equilibrium if applied at the center of pressure (C. P.) Owing to the difference in the relative values of L and D at various angles of incidence, the angle made by R with the chordal line must vary. The lift and drag are always at right angles to one another. The resultant can be found by drawing both the lines L and D through the C. P., and at right angles to one another, and then closing up the parallelogram by drawing lines parallel to L and D from the extreme ends of the latter. The resultant force in direction and extent will be the diagonal R drawn across the corners of the parallelogram.

Fig. 7. Forces Acting on an Aerofoil, Lift, Drag, and Resultant. Relative Wind Is from Left to Right.

The forces acting on the upper and lower surfaces are different, both in direction and magnitude, owing to the fact that the upper and lower surfaces do not contribute equally to the support of the aerofoil. The upper surface contributes from 60 to 80 per cent of the total lift. A change in the outline of the upper curved surface vitally affects both the lift and lift-drag, but a change in the lower surface affects the performance to an almost negligible amount.

In the case of thin circular arched plates the curvature has a much more pronounced effect. When the curvature of a thin plate is increased, both the upper and lower surfaces are increased in curvature, and this undoubtedly is the cause of the great increase in the lift of the sheet metal aerofoils tested by Eiffel.

The drag component of the front upper surface is "Negative," that is, acts with the horizontal force instead of against it. The lower surface drag component is of course opposed to the horizontal propelling force by enough to wholly overcome the assisting negative drag force of the front upper surface. The resultants vary from point to point along the section of the aerofoil both in extent and direction. A resultant true for the entering edge would be entirely different at a point near the trailing edge.

Distribution of Pressure. To fully understand the relative pressures and forces acting on different parts of the aerofoil we must refer to the experimental results obtained by the Eiffel and the N. P. L. laboratories. In these tests small holes were drilled over the aerofoil surface at given intervals, each hole in turn being connected to a manometer or pressure gauge, and the pressure at that point recorded. While the reading was being taken, the wind was passed over the surface so that the pressures corresponded to actual working conditions. It was found that the pressure not only varied in moving from the entering to trailing edge, but that it also varied from the center to the tips in moving along the length of the plane. The rate of variation differed among different aerofoils, and with the same aerofoil at different angles of incidence.

On the upper surface, the suction or vacuum was generally very high in the immediate vicinity of the entering edge. From this point it decreased until sometimes the pressure was actually reversed near the trailing edge and at the latter point there was actually a downward pressure acting against the lift. The positive pressure on the under surface reached a maximum more nearly at the center, and in many cases there was a vacuum near the entering edge or at the trailing edge. With nearly all aerofoils, an increase in the curvature resulted in a decided increase in the vacuum on the upper surface, particularly with thin aerofoils curved to a circular arc.