262 Reporter's Statement of the Case When the aeroplane is placed in a diving attitude, the air forces then act upon the front surfaces of the blades, causing the propeller to drive the engine in a similar manner to that of an engine of an automobile being driven by the wheels when the automobile goes down a hill. During diving there is a negative thrust with a consequent tendency of the air forces to bend the blades backward. There is no satisfactory estimate known to those skilled in the art of propeller design as to what the tip deflection of a blade would be in order to impair the aerodynamic efficiency, but it is generally agreed that the aerodynamic efficiency of a propeller is not measurably impaired by the bending of the blade at the tip amounting to 4% of the diameter of the propeller. 10. In addition to the tendency of the air forces to bend the blades out of the plane of rotation, there is also a tendency of the blade to bend in its plane of rotation. This may be expressed as a tendency of the blade tip to lag behind the position which it would otherwise assume in its rotational plane if the blade had no pitch and thus were doing no work upon the air. 11. Each particle of a rotating propeller is urged radially outward from the axis of rotation by the action of centrifugal force. Each cross section is, therefore, subjected to a tensile load equal to the pull of centrifugal force on that portion of the blade lying between the tip and the section in question. Furthermore, since the direction of action of centrifugal force on each portion of the blade is radial, i. e., perpendicular to the axis of rotation, if the center of gravity of the portion of the blade between any cross section and the tip does not lie in the same radial line as the center of gravity of that cross section, then, in addition to the tensile load, centrifugal force will impose a bending moment on the section. The direction of action of this bending moment is such as to urge the rotating blade toward a position in which the axis of the blade, i. e., the line joining the centers of gravity Reporter's Statement of the Case 95 C. Cls. of the various cross sections, would lie in a straight radial line perpendicular to the axis of rotation. The plane generated by such a radial line as it rotates is referred to as the plane of rotation. Another way of stating the action of centrifugal force in producing bending moments in a propeller is that if the axis of a rotating blade is not already located in the plane of rotation, centrifugal force tends to move it there. In metal propellers such as are herein involved, the pull due to centrifugal force on a blade near the hub is approximately twenty-five tons. 12. The effects of the air load and centrifugal force as described in findings 9 and 11 are graphically represented in exaggerated form in the drawing reproduced in this finding. In this drawing, which shows a radial propeller of the tractor type driven by an internal-combustion engine, the position of the propeller blades when at rest is indicated at 1. If the propeller is contemplated as revolving in normal operation but without the effect of centrifugal force (a consideration possible in theory only), the tips of the propeller will be deflected by the air load and consequent thrust into a position designated by the reference character 2. It is possible to calculate the air load as applied to the rear face of the propeller and to calculate the amount of tip deflection of the same under this theoretical condition, as well as the bending stresses imparted to the blade by such deflection. These bending stresses may be mathematically contemplated as a tensile stress in the rear portions of the blade and a compression stress in the front portions of the blade. With the propeller in actual flight operation, centrifugal force tends to restore the blades to a radial position and therefore to resist the flexure or bending due to the air load alone. The propeller will therefore assume position 3 intermediate the no-load position 1 and the flexed position 2 due to air load alone. In position 3 the degree of flexure will be less, and hence the tensile stresses due to air load alone will be less. The 13. The centrifugal force is a fairly constant quantity per revolution at any given engine power and propeller speed. The air load on the propeller blades is fluctuating in character. One cause of such fluctuation is due to interference between the blade and certain portions of the aeroplane behind the blade, such as a wing or landing gear 449973-42-CC-vol. 95- -19 262 Reporter's Statement of the Case total tensile stress however will be the tensile stress due to centrifugal force added to the tensile stress due to air load with the degree of flexure indicated in intermediate position 3. Reporter's Statement of the Case 95 C. Cls. strut which causes changes in the air load as the blade passes that portion of the aeroplane. It is possible to calculate the approximate air load at various positions along a propeller blade and then to mount the propeller in a horizontal position and apply the calculated load by means of weights at calculated points on the propeller blade. By means of such procedure termed a static test, it is possible to directly measure the tip deflection of a propeller blade due to the air load, and as indicated by position 2 in the drawing reproduced in finding 12. A second form of test known as the whirl test involves the mounting of a propeller either on the shaft of an internalcombustion engine or an electric motor, rotating the same under various speeds and power conditions, and observing or measuring the tip deflection by means of an optical system. Such a test gives the resultant deflection as indicated in position 3 of the above-mentioned drawing and which is due to the combined action of air load and centrifugal force. 14. As a propeller blade rotates, the air load acting on the inclined surfaces of the blade tends in general to increase the pitch angle of the blade, or expressed in another way, the blade tends to bite deeper into the air. Such action is shown in the following sketch, "Effect of Torsion Stresses," in which the normal position of a propeller blade is shown in cross section at 1, its direction of rotation being indicated by the vertical arrow. The air load tends to twist the blade about its axis toward a position indicated by the dotted lines at 2. Such tendency or the degree of torsional stress thus set up at any given cross section is dependent upon a number of factors, such as the pitch angle of the blade, its thickness, its taper, its center of pressure, and its ratio of width to thickness at various sections, and its lineal speed relative to the air at that section. 15. Centrifugal force tends to bring all of the particles of the blade into the same plane and thus tends to decrease the pitch angle of the blade. As shown in the sketch, the tendency of centrifugal force is to twist the blade into the position shown in the dotted line section 3. 262 Reporter's Statement of the Case 16. The combined effect of air load and centrifugal force on the torsional stresses set up in the blade is the algebraic sum of these at any given point or cross section. The torsional stresses due to centrifugal force near the hub of the propeller are ten or twelve times that of the torsion due to air load, and the resultant tendency is to reduce the pitch. Near the tip or outer portions of the blade, however, where the sections of the blade are relatively thin and light, the torsion due to air load is greater than the opposite torsional effect due to centrifugal force. There is in general therefore, and under the action of these combined stresses, a tendency for the blade to increase its pitch near the tip and to decrease its pitch in the central part and for certain sections near the hub. 17. If the tips of the propeller are very thin, the tendency of the blade at the tip portion to increase in pitch angle actually causes a deflection of the same. This increases the |