Later experiments conducted under my direction by Mr. E. C. Huffaker, some of which will appear in Part III, indicate that upon the curved surfaces I employed, the center of pressure moves forward with an increase in the (small) angle of elevation, and backward with a decrease, so that it may lie even behind the center of the surface. Since for some surfaces the center of pressure moves backward, and for others forward, it would seem that there might be some other surface for which it will be fixed. Such a surface in fact appears to exist in the wing of the soaring bird. These experiments have been chiefly with rigid surfaces, and though some have been made with elastic rear surfaces, these have not been carried far enough to give positive results.
The curved wings used on the aerodromes in late years have a rise of one in twelve, or in some cases of one in eighteen,[24] and for these latter the following empirical local rule has been adopted: [p047]
The center of pressure on each wing with a horizontal motion of 2000 feet per minute, is two-fifths of the distance from front to rear. Where there are two pairs of wings of equal size, one following the other, and placed at such a distance apart and with such a relation to the propellers as here used, the following wing is assumed to have two-thirds of the efficiency of the leader per unit of surface. If it is half the size of the leader, the efficiency is assumed to be one-half per unit of surface. If it is half as large again as the leader, its efficiency is assumed to be eight-tenths per unit of surface. For intermediate sizes of following wing, intermediate values of the efficiency may be assumed.
These rules are purely empirical and only approximate. As approximations, they are useful in giving a preliminary balance, but the exact position of the center of pressure is rarely determinable in either the horizontal or vertical plane, except by experiment in actual flight. The position of the center of gravity is found with all needed precision by suspending the aerodrome by a plumb-line in two positions, and noting the point of intersection of the traces of the line, and this method is so superior to that by calculation, that it will probably continue in use even for much larger constructions than the present.
The principal factor in the adjustment is the position of the wings with reference to the center of gravity, but the aerodrome is moved forward by the thrust of its propellers, and we must next recall the fact of experiment that as it is for constructional reasons difficult to bring the thrust line in the plane of the center of pressure of the wings, it is in practice sufficiently below them to tend to tip the front of the aerodrome upward, so that it may be that equilibrium will be attained only when CP1 is not over CG1.
In the discussion of the equilibrium, then, we must consider also the effect of thrust, and usually assume that this thrust-line is at some appreciable distance below the center of pressure.
We may conveniently consider two cases:
1. That the center of pressure is not directly over the center of gravity; that is, CG1−CP1 = a, and estimate what the value of a should be in order that, during horizontal flight, the aerodrome itself shall be horizontal; or, [p048]
2. Consider that the center of pressure is directly over the center of gravity (CP1−CG1 = 0), and in this case inquire what angle the aerodrome itself may take during horizontal flight.
First case. The diagram (Fig. 4) represents the resultants of the separate system of forces acting on the aerodrome, and these resultants will lie in a vertical medial plane from the symmetry of their disposition.