98. The airplane. The simplest way to illustrate the problem of flying is with a boy's kite. Suppose AB (Fig. 81 (1)) is a kite flying in a wind and held by a string; let us suppose also that the kite has no weight, and flies steadily in such a position that its surface makes the angle with the wind denoted by i. Now it is well known that the effect of the wind is twofold. It tends to raise the kite and to drive it back. These effects may be represented by the vertical line marked lift and the horizontal line marked drag. But since the string prevents the wind from doing what it tends to do, the tension in the string must just balance these two forces lift and drag. We explain this action by saying that the force in the string must

FIG. 81. Forces acting upon a kite and an airplane

be equal to the resultant of lift and drag, opposite in direction and applied at the same point. This resultant is always nearly perpendicular to AB. The friction of the air on AB is what prevents it from being absolutely perpendicular.

If instead of using one force in a string we use two independent forces, one downward to offset lift and the other forward to offset drag, we shall obtain the same result. In the airplane (Fig. 81 (2)) this is just what we do. The downward force is the weight of the airplane, which in the state of steady motion is just equal and opposite to the lift force, and the forward force is due to the propeller turned by the motor and is equal and opposite to the drag. In brief, an airplane is supported because the force of the propeller drags it forward and thus causes a relative wind to strike the wing in such a way as to develop a lift force equal to the weight of the plane.

99. Gliding flight. When the engine stops, the airplane glides to the ground under the action of gravity. Fig. 82 shows the forces acting in such gliding flight in still air when there is no power. The surface is moving downward and forward at some angle i and along the path op. The relative wind po, which in still air is opposite in direction to the path, produces on the wing an effect that may be represented by some resultant force oa which, as explained in § 98, is nearly perpendicular to the surface of the plane. If we resolve this force oa into vertical and horizontal components, we get ob and oc; the first, ob, balances the weight, and the second, oc, is the air pressure that now forces the machine forward.

100. The principle of the curved ball. There is a further principle involved in flight, which is the same as that underlying the curved ball or Flettner's new rotor ship. Let A (Fig. 83 (1)) be

a ball that is forced to rotate from right over to left as shown. Let RR (Fig. 83 (2)) be huge cylinders caused to rotate rapidly by machinery while a strong wind is blowing past them. Because of the forward motion of the ball in the one case and the wind on the rotors in the other, the air passes the revolving bodies in the direction shown by the dotted straight arrows. In the lower side of the diagram the air currents which are set up by the drag of the rotating bodies upon the air about them (see dotted circles) obviously oppose the currents indicated by the straight dotted arrows, and thus cause an increase of air pressure on the lower side (see +). On the top side the two sets of currents are in the same direction and cause reduction in air pressure (see —), so that the spinning bodies are pushed by this difference in pressure in the direction of the vertical arrows and at right angles to the direction of motion of the ball, or the direction of the relative wind.

While an airplane wing is not a rotating body, the shape which is given it is such that its forward motion tends to cause the air to circulate around it from right over to left and thus to create, just as in Fig. 83, (1) and (2), an excess of atmospheric pressure on the lower side. This may actually be sufficient to keep the plane

200-horse-power, 9-cylinder, air-cooled engine; extensively used for commercial purposes: passenger carrying, photography, mapping, cotton-boll-weevil dusting, and forest-fire patrol. The plane shown on the previous page is equipped with this engine. (Courtesy of the Wright Aeronautical Corporation)

flying horizontally even when its lower face is tipped slightly down, as in Fig. 82. Perhaps an even simpler way of explaining this difference in pressure is with the aid of Bernouilli's principle (Fig. 83). On account of the shape of the wing the air speed past the wing is higher on the top side than at the bottom; hence the air pressure against the wing is less at the top than at the bottom.

(1)

Motion of ball

R

(2)

Wind

FIG. 83. The curved ball and the rotor ship illustrate Bernouilli's principle, which states that, in general, where the air velocity tangential to a surface is low the air pressure is high, and vice versa

SUMMARY. In a vacuum falling bodies descend at the same rate, irrespective of their weight or size.

The total distance traversed by a falling body in any number of seconds is the distance traversed the first second times the square of the number of seconds, or S = Dt 2.

Velocity is the instantaneous rate of motion. It is numerically equal to the distance through which the body will move per second provided that, at the instant considered, its rate of motion becomes uniform. Acceleration is rate of change of velocity.

Uniformly accelerated motion is motion in which velocity is gained or lost at a constant rate. The acceleration is numerically equal to twice the distance traversed during the first second, or a = 2 D. The velocity gained or lost equals the acceleration times the time, or v = at.