strength with the minimum of weight is one of the, if not the most, difficult problems which the student has to solve.

§ 3. The theoretical reason why weight is such an all-important item in model aeroplaning, much more so than in the case of full-size machines, is that, generally speaking, such models do not fly fast enough to possess a high weight carrying capacity. If you increase the area of the supporting surface you increase also the resistance, and thereby diminish the speed, and are no better off than before. The only way to increase the weight carrying capacity of a model is to increase its speed. This point will be recurred to later on. One of Mr. T.W.K. Clarke's well-known models, surface area 1¼ sq. ft., weight 1¼ lb., is stated to have made a flight of 300 yards carrying 6 oz. of lead. This works out approximately at 21 oz. per sq. ft.

The velocity (speed) is not stated, but some earlier models by the same designer, weight 1½ lb., supporting area 1½ sq. ft., i.e., at rate of 16 oz. per sq. ft., travelled at a rate of 37 ft. per second, or 25 miles an hour.

The velocity of the former, therefore, would certainly not be less than 30 miles an hour.

§ 4. Generally speaking, however, models do not travel at anything like this velocity, or carry anything like this weight per sq. ft.

An average assumption of 13 to 15 miles an hour does nor err on the minimum side. Some very light fabric covered models have a speed of less than even 10 miles an hour. Such, of course, cannot be termed efficient models, and carry only about 3 oz. per sq. ft. Between these two types—these two extremes—somewhere lies the "Ideal Model."

The maximum of strength with the minimum of weight can be obtained only:—

1. By a knowledge of materials.

2. Of how to combine those materials in a most efficient and skilful manner.

3. By a constant use of the balance or a pair of scales, and noting (in writing) the weight and result of every trial and every experiment in the alteration and change of material used. Weigh everything.

§ 5. The reader must not be misled by what has been said, and think that a model must not weigh anything if it is to fly well. A heavy model will fly much better against the wind than a light one, provided that the former will fly. To do this it must fly fast. To do this again it must be well powered, and offer the minimum of resistance to the medium through which it moves. This means its aerofoil (supporting) surfaces must be of polished wood or metal. This point brings us to the question of Resistance, which we will now consider.

CHAPTER II.

THE QUESTION OF RESISTANCE.

§ 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