What Holds It Up?
Octave Chanute (died 1910)
To the researches of Chanute and Langley must be ascribed much of American progress in aviation.
When a flat surface like the side of a house is exposed to the breeze, the velocity of the wind exerts a force or pressure directly against the surface. This principle is taken into account in the design of buildings, bridges, and other structures. The pressure exerted per square foot of surface is equal (approximately) to the square of the wind velocity in miles per hour, divided by 300. Thus, if the wind velocity is thirty miles, the pressure against a house wall on which it acts directly is 30 × 30 ÷ 300 = 3 pounds per square foot: if the wind velocity is sixty miles, the pressure is 60 × 60 ÷ 300 = 12 pounds: if the velocity is ninety miles, the pressure is 90 × 90 ÷ 300 = 27 pounds, and so on.
Pressure of the Wind
If the wind blows obliquely toward the surface, instead of directly, the pressure at any given velocity is reduced, but may still be considerable. Thus, in the sketch, let ab represent a wall, toward which we are looking downward, and let the arrow V represent the direction of the wind. The air particles will follow some such paths as those indicated, being deflected so as to finally escape around the ends of the wall. The result is that a pressure is produced which may be considered to act along the dotted line P, perpendicular to the wall. This is the invariable law: that no matter how oblique the surface may be, with reference to the direction of the wind, there is always a pressure produced against the surface by the wind, and this pressure always acts in a direction perpendicular to the surface. The amount of pressure will depend upon the wind velocity and the obliquity or inclination of the surface (ab) with the wind (V).
Now let us consider a kite—the “immediate ancestor” of the aeroplane. The surface ab is that of the kite itself, held by its string cd. We are standing at one side and looking at the edge of the kite. The wind is moving horizontally against the face of the kite, and produces a pressure P directly against the latter. The pressure tends both to move it toward the left and to lift it. If the tendency to move toward the left be overcome by the string, then the tendency toward lifting may be offset—and in practice is offset—by the weight of the kite and tail.
Forces Acting on a Kite
We may represent the two tendencies to movement produced by the force P, by drawing additional dotted lines, one horizontally to the left (R) and the other vertically (L); and it is known that if we let the length of the line P represent to some convenient scale the amount of direct pressure, then the lengths of R and L will also represent to the same scale the amounts of horizontal and vertical force due to the pressure. If the weight of kite and tail exceeds the vertical force L, the kite will descend: if these weights are less than that force, the kite will ascend. If they are precisely equal to it, the kite will neither ascend nor descend. The ratio of L to R is determined by the slope of P; and this is fixed by the slope of ab; so that we have the most important conclusion: not only does the amount of direct pressure (P) depend upon the obliquity of the surface with the breeze (as has already been shown), but the relation of vertical force (which sustains the kite) to horizontal force also depends on the same obliquity. For example, if the kite were flying almost directly above the boy who held the string, so that ab became almost horizontal, P would be nearly vertical and L would be much greater than R. On the other hand, if ab were nearly vertical, the kite flying at low elevation, the string and the direct pressure would be nearly horizontal and L would be much less than R. The force L which lifts the kite seems to increase while R decreases, as the kite ascends: but L may not actually increase, because it depends upon the amount of direct pressure, P, as well as upon the direction of this pressure; and the amount of direct pressure steadily decreases during ascent, on account of the increasing obliquity of ab with V. All of this is of course dependent on the assumption that the kite always has the same inclination to the string, and the described resolution of the forces, although answering for illustrative purposes, is technically incorrect.
It seems to be the wind velocity, then, which holds up the kite: but in reality the string is just as necessary as the wind. If there is no string, and the wind blows the kite with it, the kite comes down, because the pressure is wholly due to a relative velocity as between kite and wind. The wind exerts a pressure against the rear of a railway train, if it happens to be blowing in that direction, and if we stood on the rear platform of a stationary train we should feel that pressure: but if the train is started up and caused to move at the same speed as the wind there would be no pressure whatever.
One of the very first heavier-than-air flights ever recorded is said to have been made by a Japanese who dropped bombs from an immense man-carrying kite during the Satsuma rebellion of 1869. The kite as a flying machine has, however, two drawbacks: it needs the wind—it cannot fly in a calm—and it stands still. One early effort to improve on this situation was made in 1856, when a man was towed in a sort of kite which was hauled by a vehicle moving on the ground. In February of the present year, Lieut. John Rodgers, U.S.N., was lifted 400 feet from the deck of the cruiser Pennsylvania by a train of eleven large kites, the vessel steaming at twelve knots against an eight-knot breeze. The aviator made observations and took photographs for about fifteen minutes, while suspended from a tail cable about 100 feet astern. In the absence of a sufficient natural breeze, an artificial wind was thus produced by the motion imparted to the kite; and the device permitted of reaching some destination. The next step was obviously to get rid of the tractive vehicle and tow rope by carrying propelling machinery on the kite. This had been accomplished by Langley in 1896, who flew a thirty-pound model nearly a mile, using a steam engine for power. The gasoline engine, first employed by Santos-Dumont (in a dirigible balloon) in 1901, has made possible the present day aeroplane.
Sustaining Force in the Aeroplane
What “keeps it up”, in the case of this device, is likewise its velocity. Looking from the side, ab is the sail of the aeroplane, which is moving toward the right at such speed as to produce the equivalent of an air velocity V to the left. This velocity causes the direct pressure P, equivalent to a lifting force L and a retarding force R. The latter is the force which must be overcome by the motor: the former must suffice to overcome the whole weight of the apparatus. Travel in an aeroplane is like skating rapidly over very thin ice: the air literally “doesn’t have time to get away from underneath.”
Direct, Lifting, and Resisting Forces
If the pressure is 10 lbs. when the wind blows directly toward the surface (at an angle of 90 degrees), then the forces for other angles of direction are as shown on the diagram. The amounts of all forces depend upon the wind velocity: that assumed in drawing the diagram was about 55 miles per hour. But the relations of the forces are the same for the various angles, no matter what the velocity.
If we designate the angle made by the wings (ab) with the horizontal (V) as B, then P increases as B increases, while (as has been stated) the ratio of L to R decreases. When the angle B is a right angle, the wings being in the position a´b´, P has its maximum value for direct wind—1/300 of the square of the velocity, in pounds per square foot; but L is zero and R is equal to P. The plane would have no lifting power. When the angle B becomes zero, position a´´b´´, wings being horizontal, P becomes zero and (so far as we can now judge) the plane has neither lifting power nor retarding force. At some intermediate position, like ab, there will be appreciable lifting and retarding forces. The chart shows the approximate lifting force, in pounds per square foot, for various angles. This force becomes a maximum at an angle of 45° (half a right angle). We are not yet prepared to consider why in all actual aeroplanes the angle of inclination is much less than this. The reason will be shown presently. At this stage of the discussion we may note that the lifting power per square foot of sail area varies with
the square of the velocity, and
the angle of inclination.
The total lifting power of the whole plane will also vary with its area. As we do not wish this whole lifting power to be consumed in overcoming the dead weight of the machine itself, we must keep the parts light, and in particular must use for the wings a fabric of light weight per unit of surface. These fabrics are frequently the same as those used for the envelopes of balloons.
Since the total supporting power varies both with the sail area and with the velocity, we may attain a given capacity either by employing large sails or by using high speed. The size of sails for a given machine varies inversely as the square of the speed. The original Wright machine had 500 square feet of wings and a speed of forty miles per hour. At eighty miles per hour the necessary sail area for this machine would be only 125 square feet; and at 160 miles per hour it would be only 31-1/4 square feet: while if we attempted to run the machine at ten miles per hour we should need a sail area of 8000 square feet. This explains why the aeroplane cannot go slowly.
It would seem as if when two or more superposed sails were used, as in biplanes, the full effect of the air would not be realized, one sail becalming the other. Experiments have shown this to be the case; but there is no great reduction in lifting power unless the distance apart is considerably less than the width of the planes.
In all present aeroplanes the sails are concaved on the under side. This serves to keep the air from escaping from underneath as rapidly as it otherwise would, and increases the lifting power from one-fourth to one-half over that given by our 1/300 rule: the divisor becoming roughly about 230 instead of 300.
Shapes of Planes
Why are the wings placed crosswise of the machine, when the other arrangement—the greatest dimension in the line of flight—would seem to be stronger? This is also done in order to “keep the air from escaping from underneath.” The sketch shows how much less easily the air will get away from below a wing of the bird-like spread-out form than from one relatively long and narrow but of the same area.
A sustaining force of two pounds per square foot of area has been common in ordinary aeroplanes and is perhaps comparable with the results of bird studies: but this figure is steadily increasing as velocities increase.