CHAPTER VI.

THE CENTER OF PRESSURE ON FLAT AND CURVED PLANES

IN unsteady winds the center of pressure on an aeroplane moves about greatly, and tends, by its variation in position, to upset the equilibrium, so that the efforts of many experimenters, noticeably Alexander Graham Bell, have been directed to the construction of an aeroplane in which the movement of the center of pressure is made very small. On a small tetrahedral cell the movement is very light, and probably one of the greatest advantages in the Bell "compound tetrahedral" structure is that the resultant center of pressure shifts to no greater extent than for one cell itself. This tends to give an unusual stability to the entire structure.

Newton implicitly assumed that when a rectangular plate was moved through the air at an angle of inclination to the line of motion, the center of pressure and the center of the surface were always coincident. It has long been recognized, however, that this is not the case, and that the position of the center of pressure varies with the incident angle.

Joessel, in 1869, was the first to experimentally determine the variation of position of the center of pressure at different angles.1 His experiments were conducted on square flat planes and he deduced as a result of his experiments the formula:

where C is the distance of the center of pressure from the front edge of the plane, a is the angle of incidence, L is the width from front to back of the plane, and d is the distance of the center of pressure from the center of surface. These formulæ indicate that the center of pressure varies from 0.5 to 0.2 of the distance from the front to the center of the plane.

In 1875 Kummer also conducted experiments on the position

of the center of pressure. The method of experiment adopted by him consisted essentially in finding the angle of inclination of the plane, corresponding to a series of fixed distances of the center of pressure from the center of figure.

The experiments conducted by Langley with the "counterpoised eccentric plane" were also of this character. Both of these sets of experiments were on flat square planes, and their general results given in the table on this page show how closely they agree.

Neither of these experimenters obtained values for very low angles.

M. Rateau, in the aerodynamic experiments recently conducted by him, investigated the variation of position of the center of pressure on flat planes. His results are shown graphically in Curve 7, and indicate that at 0 deg. and near 39 deg. there are regions of great instability. The results of Langley and Kummer are also plotted on this curve for comparison.

The movement of the center of pressure on curved surfaces is quite different from that on flat surfaces.

In deeply arched surfaces the center of pressure moves steadily forward from the center of surface as the inclination is turned down from 90 deg. until a certain point is reached, varying with the depth of curvature. After this point is passed a curious phenomenon takes place: the center of pressure instead of continuing to move forward with decrease of angle, turns rather abruptly and moves rapidly to the rear. According to Mr. Wilbur Wright, this action is due largely to the pressure of the wind acting also on the upper side of the arched surface at low angles. The action, however, is unmistakable, and has often been observed in practice.

The experiments of M. Rateau, already alluded to, also included an investigation of the movement of the center of pressure on an arched surface, the results of which are shown graphically in Curve 8. The reversal in movement is very apparent in the neighborhood of 15 deg. and shows strikingly how different the conditions of pressure on a curved surface at low angles are from those on flat surfaces. A region of instability at 30 deg., however, seems also to be present in this curved surface.

The 1910 Eiffel experiments on the curved surface, 900 millimeters 150 millimeters, already referred to, included a determination of the movement of the center of pressure. The results are given in graph No. 1, on curve sheet No. 9. A reversal at about 15 deg. is here observed, but the backward movement is not as pronounced as in the Rateau determination.

On curve sheet No. 9 are also given the results of the experiments of Prof. Prandtl, on planes of different curvature. These show that as the depth of curvature is decreased the reversal point moves farther forward, and in addition, the reversal takes place at a lower angle and more suddenly. The backward movement, however, is greatest for the deepest curved surface (1/10). The results lead to the conclusion that because of the greater suddenness of reversal, very slightly curved surfaces are more dangerous than highly arched ones, but it must be borne in mind. that the truly dangerous condition of movement of the center of pressure would be represented on the curve sheet by the most