Читать книгу The Theory and Practice of Model Aeroplaning - V. E. Johnson - Страница 8

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§ 1. It is, or should be, the function of an aeroplane—model or otherwise—to pass through the medium in which it travels in such a manner as to leave that medium in as motionless a state as possible, since all motion of the surrounding air represents so much power wasted.

Every part of the machine should be so constructed as to move through the air with the minimum of disturbance and resistance.

§ 2. The resistance, considered as a percentage of the load itself, that has to be overcome in moving a load from one place to another, is, according to Mr. F.W. Lanchester, 12½ per cent. in the case of a flying machine, and 0·1 per cent. in the case of a cargo boat, and of a solid tyre motor car 3 per cent., a locomotive 1 per cent. Four times at least the resistance in the case of aerial locomotion has to be overcome to that obtained from ordinary locomotion on land. The above refer, of course, to full-sized machines; for a model the resistance is probably nearer 14 or 15 per cent.

§ 3. This resistance is made up of—

 1. Aerodynamic resistance.

 2. Head resistance.

 3. Skin-friction (surface resistance).

The first results from the necessity of air supporting the model during flight.

The second is the resistance offered by the framework, wires, edges of aerofoils, etc.

The third, skin-friction or surface resistance, is very small at low velocities, but increases as the square of the velocity. To reduce the resistance which it sets up, all surfaces used should be as smooth as possible. To reduce the second, contours of ichthyoid, or fish-like, form should be used, so that the resultant stream-line flow of the medium shall keep in touch with the surface of the body.

§ 4. As long ago as 1894 a series of experiments were made by the writer[6] to solve the following problem: given a certain length and breadth, to find the shape which will offer the least resistance. The experiments were made with a whirling table 40 ft. in diameter, which could be rotated so that the extremity of the arm rotated up to a speed of 45 miles an hour. The method of experimenting was as follows: The bodies (diam. 4 in.) were balanced against one another at the extremity of the arm, being so balanced that their motions forward and backward were parallel. Provision was made for accurately balancing the parallel scales on which the bodies were suspended without altering the resistance offered by the apparatus to the air. Two experiments at least (to avoid error) were made in each case, the bodies being reversed in the second experiment, the top one being put at the bottom, and vice versa. The conclusions arrived at were:—

For minimum (head) resistance a body should have—

1. Its greatest diameter two-fifths of its entire length from its head.

2. Its breadth and its depth in the proportion of four to three.

3. Its length at least from five to nine times its greatest breadth (nine being better than five).

4. A very tapering form of stern, the actual stern only being of just sufficient size to allow of the propeller shaft passing through. In the case of twin propellers some slight modification of the stern would be necessary.

5. Every portion of the body in contact with the fluid to be made as smooth as possible.

6. A body of such shape gives at most only one-twentieth the resistance offered by a flat disk of similar maximum sectional area.

Results since fully confirmed.

Fig. 1.—Shape of Least Resistance.

The design in Fig. 2 is interesting, not only because of its probable origin, but because of the shape of the body and arrangement of the propellers; no rudder is shown, and the long steel vertical mast extending both upwards and downwards through the centre would render it suitable only for landing on water.

§ 5. In the case of a rubber-driven model, there is no containing body part, so to speak, a long thin stick, or tubular construction if preferred, being all that is necessary.

The long skein of elastic, vibrating as well as untwisting as it travels with the machine through the air, offers some appreciable resistance, and several experimenters have enclosed it in a light tube made of very thin veneer wood rolled and glued, or paper even may be used; such tubes can be made very light, and possess considerable rigidity, especially longitudinally. If the model be a biplane, then all the upright struts between the two aerofoils should be given a shape, a vertical section of which is shown in Fig. 3.

§ 6. In considering this question of resistance, the substance of which the aerofoil surface is made plays a very important part, as well as whether that surface be plane or curved. For some reason not altogether easy to determine, fabric-covered planes offer considerably more resistance than wooden or metal ones. That they should offer more resistance is what common sense would lead one to expect, but hardly to the extent met with in actual practice.

Fig. 2.—Design for an Aeroplane Model (Power Driven). This design is attributed to Professor Langley.

Built up fabric-covered aeroplanes[7] gain in lightness, but lose in resistance. In the case of curved surfaces this difference is considerably more; one reason, undoubtedly, is that in a built up model surface there is nearly always a tendency to make this curvature excessive, and much more than it should be. Having called attention to this under the head of resistance, we will leave it now to recur to it later when considering the aerofoil proper.

Fig. 3.—Horizontal Section of Vertical Strut (enlarged.)

§ 7. Allusion has been made in this chapter to skin friction, but no value given for its coefficient.[8] Lanchester's value for planes from ½ to l½ sq. ft. in area, moving about 20 to 30 ft. per second, is

0·009 to 0·015.

Professor Zahm (Washington) gives 0·0026 lb. per sq. ft. at 25 ft. per second, and at 37 ft. per second, 0·005, and the formula

f = 0·00000778l ^·93v^1·85

f being the average friction in lb. per sq. in., l the length in feet, and v the velocity in ft. per second. He also experimented with various kinds of surfaces, some rough, some smooth, etc.

His conclusion is:—"All even surfaces have approximately the same coefficient of skin friction. Uneven surfaces have a greater coefficient." All formulæ on skin friction must at present be accepted with reserve.

§ 8. The following three experiments, however, clearly prove its existence, and that it has considerable effect:—

1. A light, hollow celluloid ball, supported on a stream of air projected upwards from a jet, rotates in one direction or the other as the jet is inclined to the left or to the right. (F.W. Lanchester.)

2. When a golf ball (which is rough) is hit so as to have considerable underspin, its range is increased from 135 to 180 yards, due entirely to the greater frictional resistance to the air on that side on which the whirl and the progressive motion combine. (Prof. Tait.)

3. By means of a (weak) bow a golf ball can be made to move point blank to a mark 30 yards off, provided the string be so adjusted as to give a good underspin; adjust the string to the centre of the ball, instead of catching it below, and the drop will be about 8 ft. (Prof. Tait.)