Art. XIV.—Experiments on the Lifting Power of Inclined Planes in Aerial Transit.
[Read before the Otago Institute, 9th October, 1877.]
One of the great difficulties in aeronautics is the steering the apparatus if a balloon be employed, and even if any other method of aerial transit be attempted the additional difficulty presents itself of rendering the apparatus stable in high winds.
To steer a balloon does indeed appear a hopeless task; but to the question, is it possible that an aerial machine could be devised which would retain its position of equilibrium in the fitful and uncertain currents of the atmosphere, while at the same time it could be propelled at an angle more or less against the wind, so that by tacking it could, like a ship, navigate against the wind, it will be my endeavour in this and two following papers, from observation, experiment, and demonstration to answer in the affirmative.
The whole animal kingdom, from mammals, birds, fishes, lizards, and insects furnishes us with creatures more or less endowed with powers of flight; but it is more especially to the sailing flight of sea-birds that our attention will be at present directed. What must attract notice is their
prolonged power of buoyancy under certain circumstances with scarcely any flapping of the wings. On watching carefully this kind of flight it can be seen that the wings are kept nearly horizontal but with the anterior margin very slightly elevated above the posterior and thin edge of the wing. The angle thus formed by the wing with the line of motion is very small, indeed if it were not small it is easily proved that the onward motion of the bird would be quickly arrested from the quantity of air which would require to be displaced. It does indeed appear wonderful that a bird weighing perhaps ten pounds can be supported in this manner so long a time when it has once obtained a certain velocity. In every-day life, however, we have many instances of the lateral pressure of the air on planes in a direction transverse to the motion; we have only to walk slowly with a piece of paper held at an oblique angle to the line of progression, or to open an outer door of a building an inch or two if the door opens outwards when the wind is blowing obliquely in, when it will be at once noticed, and if a gale of wind is blowing it will be found impossible by main force to prevent the door flying open in a surprising manner if it is once opened a few degrees.
If solids are made to impinge on planes, then the angle of reflection is equal to the angle of incidence. If, however, a current of air impinges on a plane, then the elasticity of the air comes into play with very curious results. The following experiments, which I now repeat, were made with a view of ascertaining the action of the air on inclined planes at different angles:—
Experiment, No. 1.—If a book one or more inches thick is placed flat on a table, and any small light body is also placed on it, about as far beyond the book as the book is thick, it will be found impossible to so blow across the book as to send the light body away, for instead of moving from you it flies towards you.
Experiment, No. 2.—If a current of air is blown obliquely onto a table covered with sawdust, we shall observe that the whole of the sawdust affected by the wind is not blown in the direction of the current, but that a considerable portion is actually blown along the plane towards the primitive current.
Experiment, No. 3.—If a current of air blown through a tube impinges at any given oblique angle upon a point in a horizontal plane, the incident current I P (figure 1) is not reflected at an equal angle to the plane from the point P along the line P Q, as might be supposed; for, if a lighted taper be held at Q, the flame is actually drawn downwards, and if the taper be moved over a large range of angular vertical measurement the flame is still drawn towards the plane.
These apparent paradoxes may be partly explained when we consider the perfect elasticity of the air; for when it strikes the point P it then, after compression, by virtue of its elasticity, diverges from P at all angles along the plane; so readily does it escape laterally that it appears to draw a large volume of formerly quiescent air down too.
Experiment, No. 4.—Reversing experiment No. 3, “action and reaction being equal and contrary,” it follows that when a plane A P B (figure 2) oblique to the horizon is carried with its upward and anterior edge in a horizontal direction, the tendency of the incident current I P is not to be reflected along the line P Q, but the air is retained closer to the surface of the plane, which fact must very materially increase the lateral pressure, and therefore greatly assist in buoying up the plane.
Experiment, No. 5.—In order to ascertain the lifting pressure exerted by the inertia and elasticity of the air on a plane set at various angles and travelling with a given velocity, the apparatus here exhibited was devised; it consists of a thin sheet of metal a foot square, so connected with a spring balance that it can be set to any given angle. Action and reaction being equal and contrary, it is clear that if this instrument be set in a current of air the same effects are obtained as if the plane were moved at the same velocity through still air. The instrument was placed in a strong wind, and when the plane was first placed at a right angle to the current, with the spring so arranged as to show the horizontal pressure, it registered an average pressure of 2.7 Ibs. on the square foot, indicating a velocity of the air of 23 miles per hour. The instrument was then so arranged as to measure the vertical pressure when the plane was set at various angles to the horizon. The following table gives a summary of the average results of a number of experiments therewith:—
|Angle to Horizon.||Lifting Pressure in Lbs.|
By this we see that the lifting pressure of a plane one foot square travelling through still air is more than half as great at an angle of 5° as it is at 40°, while we know that the resistance to its forward or horizontal motion is almost removed, for considerably less air has to be displaced. In fact, the inertia of the air is utilized with small angles, for considerably greater velocity can be imparted to the plane with the same expenditure of force.
From the foregoing experiments it appears that the law of “resolution of forces” as applied to solids is inapplicable in the case of gases. More-
over, the nature of the surface of the plane, and also the nature of the impinging body, materially influence the results.
These experiments assist in explaining the prolonged sailing flight of birds, for, when the wings are retained so as to form a very small angle to the horizontal line, there will still be a very considerable upward pressure to sustain the bird in its progress through the air; they also show that if, as has been asserted, birds prolong their flight by gradually increasing the angle of their wing planes, then that alteration need be and indeed can be only within very narrow limits; for a bird sailing in still air with its wing planes at an angle of 5° and travelling with a velocity of 23 miles per hour receives a support of 1.13 lbs per square foot of wing area, while if it alters its planes to 20° it only receives about half as much more support, even if we suppose its velocity unaltered; four times the angle of inclination to the horizon only giving one half more support. Now the resistance horizontally which the wing encounters at 20° is about 16 times as great as what it encounters at 5°, which would quickly arrest its progress, somewhat similarly to what may be observed when pigeons are alighting, for when near the ground they suddenly raise the anterior portions of their wings, their horizontal motion is stopped, a very slight rise is also noticed, and they alight without injury.
It appears, therefore, that it is only within small angular ranges that the alteration of wing plane prolongs the power of flight.
The wing of a bird is so constructed that it can be retained with sufficient rigidity at these minute angles.