CHAPTER III.

THE LOW CENTRE OF GRAVITY.

The first thing that occurs to the investigator on the subject of stability is that nature offers us a sure means of keeping our machines upright by adopting the simple method of placing all the heavier parts at the bottom. In all other constructions we have adopted this plan with perfect success. In boats, yachts, cars, balloons, everything man uses in fact, the simplest, best and most obvious method of keeping a thing upright is to utilize the force of gravity, place the lighter or supporting parts above and the weight below, and the thing is done.

This simple method of obtaining stability did not escape the aeroplane designers, and we have had several machines which embodied this principle, more or less. Unfortunately, however, they all proved failures. A machine would be designed, and, with the weight high, would fly well, though it was unstable. Put the weight low and you got rid of the instability, and at the same time the machine became unmanageable. It looked as if flying and instability were interchangeable terms. So, as it was a machine that would fly the designers were after, the weight was kept up and the stability was left to the pilot. The machines were made “sensitive” as it is called, that is to say, sensitive to a touch of the rudder or the balancers. They are also, it is true, equally sensitive to a gust of wind or a slight shifting of weight or pressure, and this has caused the smashing of a good many machines and some pilots; but after all this is the fortune of war, and no one is compelled to go up in an aeroplane.

The curious thing about it is that it does not seem to have occurred to our designers that if their pet design would not fly with the weight low, perhaps it might be possible to alter the design instead of altering the position of the centre of gravity, and so obtain what we are all looking for, a naturally stable machine that is yet sensitive to control.

There are two chief difficulties in the way of the low centre of gravity machine. One is that the heaviest portion of the machine being some distance below its support, it is apt to give rise to a pendulum or swaying motion. The other is that of tilting, or banking up, in turning a corner. These are really two developments of the same difficulty, i.e. pendulum motion.

If we take a strip of stiff paper to represent a plane and put a small weight in the centre of the plane, the model on being glided to earth does not tend to sway (Fig. 1). If we put our weight on a tiny piece of wire an inch or so below the plane (Fig. 2) and set the model free, it will probably acquire a swinging motion as it descends. That is the whole trouble. The trouble is real enough, but the fallacy is in supposing it to be all the fault of the low centre of gravity. All ships that were ever designed have a low centre of gravity, yet some roll dreadfully and others do not, which, in itself, should be proof sufficient that it is the design of the machine and not the position of the ballast that is at fault.

Let us now try some experiments. It will be noticed that in the machines which have employed the low centre of gravity the span of the wings has usually been 30 feet or more, and the centre of gravity about 6 feet below the centre. Here is a paper model of the present aeroplane (Fig. 1). Here is the same machine with a low centre of gravity (Fig. 2). Now bend the paper upwards as in Fig. 3 and you get rid of the swaying. Also, of course, you get rid of the supporting surface. But there is probably some point of greatest efficiency where you may compromise. If you take model 2 and bend it slightly (Fig. 4) it will sway, but not much, not so much as Fig. 2. Now with a pair of scissors clip the wings a bit at a time, and you will find that as the span gets shorter the swaying decreases, and that when you have the three points formed by the ends of the two wings and the weight equidistant from the centre where they meet, the plane is stable (Fig. 5). The reason is that it is not the pendulum with the weight at the bottom that swings so much, but the long wings that see-saw. By shortening the wings you have reduced the length of the see-saw, which is the same as reducing the length of the pendulum, and consequently, by pendulum law, the oscillations must be much quicker and shorter and will at once damp out. It is curious that this point seems to have escaped the designers. It is well known that all pendulum motion tends to damp out, and the shorter the pendulum the quicker it comes to rest. Hitherto the idea has been to shorten it vertically, but the same effect exactly is obtained by shortening it horizontally, and the low centre of gravity remains to give stability. It was stated by some sapient objector to the low centre of gravity, that the pendulum motion once set up, increased till it turned the machine over. A pendulum which increased its swing at every stroke would be something new in the scientific world.

Another development of the pendulum difficulty is the probable fore and aft sway, but this may be overcome by increasing the supporting surface of the tail. Many machines do not lift with the tail at all, and those that do employ lifting tails, have them with very small surface. Consequently, the centre of gravity comes nearly under the centre of the main plane, and the whole machine, turning on its centre of gravity in all directions as on a pivot, is liable to swing fore and aft. If the supporting surface of the tail be increased and the centre of gravity carried further aft, this pendulum motion is also rendered impossible, and the machine is stable both ways.

A few illustrations may serve to make the advantages of the low centre of gravity more clear, and to avoid complications we will suppose the planes to be still and in still air. Let Fig. 6 represent an ordinary flat plane having its centre of gravity coincident with its centre of pressure, the centre of pressure of each half or wing being at A A. The plane is in equilibrium. Now allow it to tilt (Fig. 7), and it will be seen that it is still in equilibrium, since the weight is in the centre and the wing tips equidistant from it. Let it tilt still more till it is vertical (Fig. 8), and the balance is still the same. It is evident, therefore, that such a plane would travel equally well in any of the positions shown, and that it can only be kept in position (Fig. 6) by the skilful manipulation of the pilot.

In the same way, the machine having no lifting tail is longitudinally unstable, for, being balanced on its centre of pressure which would be coincident with its centre of gravity and probably about 2 feet from the trailing edge of the plane--it may assume any position (Figs. 9, 10, 11 and 12), and still be in equilibrium, when it is evident that the proper position (Fig. 9) is only maintained by the constant control of the tail elevator.

Now take the case of a machine having a low centre of gravity. Its natural position is shown at Fig. 13, and it is at once evident that any other position such as Figs. 14 and 15 could not be maintained for a moment, since the weight being at an angle, must inevitably drag the machine back to its natural position (Fig. 13). In the same way with regard to longitudinal balance, a machine with two lifting surfaces such as Fig. 13, is in its natural position with the centre of gravity perpendicularly under the centre of pressure, any other position, such as Fig. 17, A, is impossible, as the gravity pull must drag the machine along the dotted line till it resumes its proper and natural position (B).

The next difficulty is in the banking or tilting caused by the turning of the machine in going round a curve. In a very interesting discussion carried on in the “Aero,” it was stated that a low centre of gravity machine could not bank up, as the pull of gravity acting on the low weight would prevent it. It was also stated by another writer that the machine would bank up too much and slide down sideways, because the greatest weight having the greatest momentum would swing out too much. There is evidently some confusion here. Let us consider the question.

In turning there are three forces to take into consideration:

(1) The centrifugal force, which tends to make the machine fly off at a tangent to the curve at which it is turning.

(2) The action of gravitation.

(3) The extra lift given by the wing on the outside of the curve, owing to the fact that it travels faster through the air.

The centrifugal force acts strictly in proportion to the mass it acts on, but, at the same time it must be remembered that the greater force acting on the greater mass has the greater mass to move. That is to say, that if the top part of the machine was very light and the bottom part very heavy, the force acting on the light part would be sufficient to send that part swinging out when rounding a curve, and the greater force acting on the greater mass at the bottom would be sufficient to send that out to exactly the same degree. Consequently, if only centrifugal force is considered, the whole machine would swing out without any tilting at all, retaining its upright position. But here we must take another factor into consideration, the resistance of the air. This resistance would be greater on the greater surface of the light top part than on the heavy bottom part, and consequently the bottom part would, automatically, swing out most, giving the banking effect. This would be increased by the extra lift given to the outer wing by reason of its greater speed. If we then take the force of gravitation into the problem we shall see that we have two factors--unequal speed and unequal air resistance--tending to bank up the machine, and one force--gravity--tending to pull it straight again. At a certain angle due to the amount of force exerted by each of these, the two opposing factors would balance, and the machine would be in equilibrium.

It would appear that most of the difficulties connected with the low centre of gravity machine are the result of hazy thinking and slip-shod reasoning, and that they do not exist in fact. And let it be remembered that the low centre of gravity machine with short span has not yet been tried except by the writer, who has succeeded in making a paper model on this plan turn in its own length without in any way losing its stability, swaying, banking too much, turning over, sliding sideways, or doing any of the frightful things which some people declare it must do. What it does do is to recover its balance though started from the most impossible positions and always land on its feet.