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THE SOLUTION OF THE MYSTERY OF
The Science of Aerial Locomotion has at length become a subject which is no longer considered outside the realms of prac mechanics. The world has now seen machines heavier than air rise into the air and travel through the air, supported by the air, apparently as the birds. How or why this is possible the world scarcely asks; and yet it is nevertheless a very interesting fact, and one well worthy of study.
The writer began to study bird flight early in the year 1883, some twenty-eight years ago; and has always maintained that man would one day conquer the air with machines heavier than the air.
It must not be forgotten that mechanical locomotion on land has only been achieved within the last hundred years, while mechanical locomotion in water came still later; and yet since the world began we have had natural locomotion, not only on land and in water, but also in the air.
With the steam engine already in existence, we bungled upon mechanical locomotion on land without it being necessary for us to study the natural principles underlying the act of progression; and there are few people even nowadays who can (if you ask them off-band) define the theory of progression on land.
We bungled into mechanical locomotion in water without stopping to think how progression is attained; we know it is attained, and that suffices for the greater number. We have now bungled upon mechanical locomotion in the air, with machines heavier than air, without any apparent knowledge of why the air supports us; we know that if we do certain things the air will support us, and many are satisfied to let it go at that.
The object of this paper is to explain in simple language (as far as the writer's knowledge goes) the main principles of natural progression on land, in water, and more especially in air; and to expound certain rules which must necessarily be followed when we attempt to achieve Nature's results by mechanical devices. We already comply with the natural rules as regards locomotion on land and in water, as will be explained below; but it would seem that we do not as yet correctly comply with the rules necessary for satisfactory progression in air, although undoubtedly a great measure of success has already been attained with the aeroplane. THE GENERAL LAW OF MECHANICAL versus NATURAL PROGRESSION
Action in nature is invariably intermittent or reciprocal; there is no rotary motion employed by flesh, fish, or fowl.
When we desire to imitate by mechanical means the method of progression of animals on land, we employ a rotary substitute (the wheel or rotary leg) for the reciprocal action of the natural legs. When we desire to imitate by mechanical means the method of progression of fish in water, we employ a rotary substitute (the propeller or rotary tail) for the intermittent action of the tail of a fish.
It is only reasonable, therefore, to infer that, if we desire to imitate by mechanical means the method of progression of birds in the air, we must employ rotary substitutes (rotary wings) for the flapping wings of the bird.
To do this, however, it is necessary to ascertain what is the action, and what is the result of the action, of the flapping of the bird's wings; and then comes the mechanic and the inventor 'to discover and determine how the result obtained by the fapping wings can be reproduced by means of mechanical rotary substitutes.
On land it is comparatively easy to cause a wheel to rotate by mechanical force and thus progress, even without any knowledge of the principle of progression; and still easier in water to design a rotary paddle or screw to propel, and thus by action and reaction obtain progression.
The principles of progression on land and water have, so to speak, been lost in the knowledge of certain methods by which that progression can in practice be obtained. Man, however, has not been in the habit of using the air as the birds use it, and if he wishes to do by mechanical methods what the birds do naturally he must learn the main principles of progression in air, and not straightaway form the conclusion that he has obtained real flight, simply because with the aeroplane he finds the air up to a certain point amenable to the same conditions as water. One can calculate the speed to be obtained by a vessel in water by action and reaction, one can also by a similar method calculate the speed of a' motor-plane in the air; but where does action and reaction come in in the case of the albatross, with apparently immovable wings, gliding for days and nights supported by the air, a fluid which we cannot even see? We must learn the laws of the air, and not expect complete success if we only deal with the air as if it were
water; we must ascertain the method birds use in dealing with the air, and then devise a rotary substitute for the flapping action of the wings of the bird ; we must also design the structure so that it shall be capable of passive flight, by dealing with the air as it is dealt with by the albatross when soaring. It must not be imagined that the writer wishes in any way to belittle the aeroplane; on the contrary, the aeroplane has done a noble work it has demonstrated to mankind the fact that man by mechanical means can traverse the air with machines heavier than air-but the aeroplane is only the beginning of aerial locomotion.
In spite of the fact that the aeroplane is not designed to act in accordance with the laws of bird flight, still were those laws thoroughly understood by the engineers who have designed these machines they would be capable of producing vast improvements, even if they were still to persist in adhering to the main principles upon which these machines now act, viz. propulsion by means of screw propellers, as mechanical vessels are propelled in water.
For true mechanical progression in air in accordance with the natural laws which govern bird flight we must have a rotary substitute to take the place of and do the same work as the flapping wings of the bird.
THE PRINCIPLE OF PROGRESSION ON LAND
Few people trouble to think out for themselves the reason why they stand, walk, or run, much less do they endeavour to study why a wheel-barrow, a bicycle, a motor-car, or a railway train is capable of being made to progress on land. It is done, that is all the world cares; as a matter of fact, the principle of progression on land is identical with that of progression in air, and both are quite different from that of progression in water.
The act of standing is the result of two forces in direct opposition to each other : one being the absolutely vertical downward pull of gravity due to the weight of the body, the other being an equal vertical upward thrust exerted by the legs, the result producing equilibrium. If the legs are not able to give an upward thrust equal to the weight of the body, the body will collapse towards the ground. For progression, the muscular action is used, not to thrust the body in the direction of motion, but so to alter the direction of the upward thrust of the legs that an angle is formed by the two opposing forces : the resultant force thus created produces progression. If the two opposing forces are equal, the resultant motion given is in a direction exactly one half the angle formed by the directions of the two opposing forces. We know that the downward pull of gravity is always vertical : consequently the resultant motion given by two equal opposing forces (one of which is gravity and the other is acting upwards in advance of the
vertical) must be in a direction below the horizontal. In walking or running, then, it is necessary, in order to obtain a horizontal resultant, that the upward force exerted shall be in excess of the downward pull of gravity.
The muscles are also used to give that extra upward force, and in progressing upstairs or uphill, or when jumping, that force has to be considerably increased : but in no case are the muscles used to exert a force in direct opposition to the direction of the motion of the body, as is the case when propelling in water.
The amount of upward force to be exerted can easily be calculated, and is the same for progression on land as in the air. A table of these calculations will be given under the head of Progression in Air. It must be noted that, to secure efficient progression on land, a practically immovable point, from which to alter the angle of the upward force, is desirable. If the feet are on ice, the motor-car wheel in sand or mud, or the locomotive wheels on greased rails, the efficiency of the resultant force giving forward motion is reduced by the amount of slip. As a rule on land the amount of slip is practically nil. This (although it may seem absurd to many readers) is equally true in the air : the amount of slip in the line of motion is practically nil.
THE PRINCIPLE OF PROGRESSION IN WATER
Progression in water is a totally different matter from progression on land or in air ; a vessel does not rest on the surface of the water as animals and vehicles rest on land, nor is it supported by the water as a bird is supported by the air. A duck, a fish, an animal, or properly constructed vessel sinks in the water until it displaces a body of water equal to its weight (fish totally immersed rise or descend by the action of their fins). In this state of flotation, whether partially or totally immersed, progression is obtained by propulsion-i.e. an attempt is made to push the water in a direction opposite to that in which it is desired to progress. The motion is due to the force exerted by the thrust of the propeller being greater than the resistance of the water to the vessel propelled. The speed increases with the accumulated momentum ; but it is limited to the point where the propeller can no longer exert the greater thrust. For mechanical progression a rotary motion is employed to create the thrust which in nature is accomplished by an intermittent effort. The case is very similar in the air as far as the propelling of aeroplanes in the direction of motion is concerned; but whereas in water the body or vessel is capable of floating when at rest, the aeroplane cannot in that sense be said to float in the air-it must be travelling through the air to obtain the support of the air.
PROGRESSION IN AIR.
How does a bird fly? It will generally be admitted that a bird does not propel itself through the air with its tail as a fish does in the water. As a matter of fact, the principle of progression by air is very simple : it is the same as that of natural progression on land. The force giving the forward motion is the resultant of two forces, one being the constant and absolutely vertical pull of gravity due to the weight of the animal, bird, or machine, the other being the upward thrust in advance of the vertical to obtain forward motion, and in rear of the vertical when it is desired to retard that forward motion. This upward thrust is exerted by the animal with its legs, by the birds with their wings, and by machinery with rotary wings, aided, in the case of the Aying-machine, by the stationary or fixed wings corresponding to the bird's outspread wings in soaring flight. It is really an imitation of these fixed or outspread wings, propelled through the air upon the principle of propulsion in water, which constitutes the aeroplane or motor-plane of to-day.
The real flying-machine, although it must necessarily for safety have these fixed or soaring wings, should progress in the air on the principles of bird flight, its rotary wings doing the same work as the flapping wings of the bird : it should not use a rotary propeller to do the same work as the tail of a fish in the water. What, then, is the work done by the flapping wings of the bird ? Simply to exert an upward thrust in opposition to the downward vertical pull of gravity at an angle in advance of the vertical to produce forward motion, and in rear of the vertical if it is desired to retard that forward motion.
The whole principle is easily reduced to a mathematical calculation as follows: In the diagram on the next page let the line A A A represent the
A ground, the point B the centre of gravity of a bird or machine. The point B may be on the ground, a foot off the ground, or a mile off the ground; it is placed in the diagram away from the ground simply for the purpose of illustration. Let the weight of the bird or machine, at the point B, equal 1000 units (oz., lb., or cwt.). There is then a constant and absolutely vertical downward pull of gravity equal to 1000 units acting on point B in the direction of BA. If, then, a force equal to 1000 units is exerted on point b in an absolutely vertical upward direction B c, the bird or machine, B, will remain where it is. If, however, this upward force is in a direction other than vertical, say B D, an angle is formed by the two equal forces and thereby a resultant force is created which must necessarily act along the line B E bisecting the angle formed by the two equal forces B A and B D. Presuming, then, the force exerted on