Hiram S. Maxim

It has been my aim in preparing this little work for publication to give a description of my own experimental work, and explain the machinery and methods that have enabled me to arrive at certain conclusions regarding the problem of flight. The results of my experiments did not agree with the accepted mathematical formulÆ of that time. I do not wish this little work to be considered as a mathematical text-book; I leave that part of the problem to others, confining myself altogether to data obtained by my own actual experiments and observations. During the last few years, a considerable number of text-books have been published. These have for the most part been prepared by professional mathematicians, who have led themselves to believe that all problems connected with mundane life are susceptible of solution by the use of mathematical formulÆ, providing, of course, that the number of characters employed are numerous enough. When the Arabic alphabet used in the English language is not sufficient, they exhaust the Greek also, and it even appears that both of these have to be supplemented sometimes by the use of Chinese characters. As this latter supply is unlimited, it is evidently a move in the right direction. Quite true, many of the factors in the problems with which they have to deal are completely unknown and unknowable; still they do not hesitate to work out a complete solution without the aid of any experimental data at all. If the result of their calculations should not agree with facts, “bad luck to the facts.” Up to twenty years ago, Newton’s erroneous law as relates to atmospheric resistance was implicitly relied upon, and it was not the mathematician who detected its error, in fact, we have plenty of mathematicians to-day who can prove by formulÆ that Newton’s law is absolutely correct and unassailable. It was an experimenter that detected the fault in Newton’s law. In one of the little mathematical treatises that I have before me, I find drawings of aeroplanes set at a high and impracticable angle with dotted lines showing the manner in which the writer thinks the air is deflected on coming in contact with them. The dotted lines show that the air which strikes the lower or front side of the aeroplane, instead of following the surface and being discharged at the lower or trailing edge, takes a totally different and opposite path, moving forward and over the top or forward edge, producing a large eddy of confused currents at the rear and top side of the aeroplane. It is very evident that the air never takes the erratic path shown in these drawings; moreover, the angle of the aeroplane is much greater than one would ever think of employing on an actual flying machine. Fully two pages of closely written mathematical formulÆ follow, all based on this mistaken hypothesis. It is only too evident that mathematics of this kind can be of little use to the serious experimenter. The mathematical equation relating to the lift and drift of a well-made aeroplane is extremely simple; at any practicable angle from 1 in 20 to 1 in 5, the lifting effect will be just as much greater than the drift, as the width of the plane is greater than the elevation of the front edge above the horizontal—that is, if we set an aeroplane at an angle of 1 in 10, and employ 1 lb. pressure for pushing this aeroplane forward, the aeroplane will lift 10 lbs. If we change the angle to 1 in 16, the lift will be 16 times as great as the drift. It is quite true that as the front edge of the aeroplane is raised, its projected horizontal area is reduced—that is, if we consider the width of the aeroplane as a radius, the elevation of the front edge will reduce its projected horizontal area just in the proportion that the versed sine is increased. For instance, suppose the sine of the angle to be one-sixth of the radius, giving, of course, to the aeroplane an inclination of 1 in 6, which is the sharpest practical angle, this only reduces the projected area about 2 per cent., while the lower and more practical angles are reduced considerably less than 1 per cent. It will, therefore, be seen that this factor is so small that it may not be considered at all in practical flight.

Fig. 1.—Diagram showing the reduction of the projected horizontal area of aeroplanes due to raising the front edge above the horizontal—a, b, shows an angle of 1 in 4, which is the highest angle that will ever be used in a flying machine, and this only reduces the projected area about 2 per cent. The line c b shows an angle of 1 in 8, and this only reduces the projected area an infinitesimal amount. As the angle of inclination is increased, the projected area becomes less as the versed sine f d becomes greater.

Some of the mathematicians have demonstrated by formulÆ, unsupported by facts, that there is a considerable amount of skin friction to be considered, but as no two agree on this or any other subject, some not agreeing to-day with what they wrote a year ago, I think we might put down all of their results, add them together, and then divide by the number of mathematicians, and thus find the average coefficient of error. When we subject this question to experimental test, we find that nearly all of the mathematicians are radically wrong, Professor Langley, of course, excepted. I made an aeroplane of hard rolled brass, 20 gauge; it was 1 foot wide and dead smooth on both sides; I gave it a curvature of about ¹/₁₆ inch and filed the edges, thin and sharp. I mounted this with a great deal of care in a perfectly horizontal blast of air of 40 miles an hour. When this aeroplane was placed at any angle between 1 in 8 and 1 in 20, the lifting effect was always just in proportion to its angle. The distance that the front edge was raised above the horizontal, as compared with the width of the aeroplane, was always identical with the drift as compared with the lift. On account of the jarring effect caused by the rotation of the screws that produced the air blast, we might consider that all of the articulated joints about the weighing device were absolutely frictionless, as the jar would cause them to settle into the proper position quite irrespective of friction. I was, therefore, able to observe very carefully, the lift and the drift. As an example of how these experiments were conducted, I would say that the engine employed was provided with a very sensitive and accurate governor; the power transmission was also quite reliable. Before making these tests, the apparatus was tested as regards the drift, without any aeroplane in position, and with weights applied that would just balance any effect that the wind might have on everything except the aeroplane. The aeroplane was then put in position and the other system of weights applied until it exactly balanced, all the levers being rapped in order to eliminate the friction in their joints. The engine was then started and weights applied just sufficient to counterbalance the lifting effect of the aeroplane, and other weights applied to exactly balance the drift or the tendency to travel with the wind. In this way, I was able to ascertain, with a great degree of accuracy, the relative difference between the lift and drift. If there had been any skin friction, even to the extent of 2 per cent., it would have been detected. This brass aeroplane was tested at various angles, and always gave the same results, but of course I could not use thick brass aeroplanes on a flying machine; it was necessary for me to seek something much lighter. I therefore conducted experiments with other materials, the results of which are given. However, with a well-made wooden aeroplane 1 foot wide and with a thickness in the centre of ⁷/₁₆ inch, I obtained results almost identical with those of the very much thinner brass aeroplane, but it must not be supposed that in practice an aeroplane is completely without friction. If it is very rough, irregular in shape, and has any projections whatsoever on either the top or bottom side, there will be a good deal of friction, although it may not, strictly speaking, be skin friction; still, it will absorb the power, and the coefficient of this friction may be anything from ·05 to ·40. These experiments with the brass aeroplane demonstrated that the lifting effect was in direct proportion to the angle, and that skin friction, if it exists at all, was extremely small, but this does not agree with a certain kind of reasoning which can be made very plausible and is consequently generally accepted.

Writers of books, as a rule, have always supposed that the lifting effect of an aeroplane was not in proportion to its inclination, but in proportion to the square of the sine of the angle. In order to make this matter clear, I will explain. Suppose that an aeroplane is 20 inches wide and the front edge is raised 1 inch above the horizontal. In ordinary parlance this is, of course, called an inclination of 1 in 20, but mathematicians approach it from a different standpoint. They regard the width of the aeroplane as unity or the radius, and the 1 inch that the front edge is raised as a fraction of unity. The geometrical name of this 1 inch is the sine of the angle—that is, it is the sine of the angle at which the aeroplane is raised above the horizontal. Suppose, now, that we have another identical aeroplane and we raise the front edge 2 inches above the horizontal. It is very evident that, under these conditions, the sine of the angle will be twice as much, and that the square of the sine of the angle will be four times as great. All the early mathematicians, and some of those of the present day, imagine that the lift must be in proportion to the square of the sine of the angle. They reason it out as follows:—If an aeroplane is forced through the air at a given velocity, the aeroplane in which the sine of the angle is 2 inches will push the air down with twice as great a velocity as the one in which the sine of the angle is only 1 inch, and as the force of the wind blowing against a normal plane increases as the square of the velocity, the same law holds good in driving a normal plane through still air. From this reasoning, one is led to suppose that an aeroplane set at an angle of 1 in 10 will lift four times as much as one in which the inclination is only 1 in 20, but experiments have shown that this theory is very wide of the truth. There are dozens of ways of showing, by pure mathematics, that Newton’s law is quite correct; but in building a flying machine no theory is good that does not correspond with facts, and it is a fact, without any question, that the lifting effect of an aeroplane, instead of increasing as the square of the sine of the angle, only increases as the angle. Lord Kelvin, when he visited my place, was, I think, the first to mention this, and point out that Newton’s law was at fault. Professor Langley also pointed out the fallacy of Newton’s law, and other experimenters have found that the lifting effect does not increase as the square of the sine of the angle. In order to put this matter at rest, Lord Rayleigh, who, I think we must all admit, would not be likely to make a mistake, made some very simple experiments, in which he demonstrated that two aeroplanes, in which we may consider the sine of the angle to be ¹/₄ inch, lifted slightly more than a similar aeroplane in which the sine of the angle was only ¹/₂ inch. Of course, Lord Rayleigh did not express it in inches, but in term of the radius. His aeroplanes were, however, very small. We can rely upon it that the lifting effect of an aeroplane at any practical angle, everything else being equal, increases in direct proportion to the angle of the inclination. In this little work, I have attempted to make things as simple as possible; it has not been written for mathematicians, and I have, therefore, thought best to express myself in inches instead of in degrees. If I write, “an inclination of 1 in 20,” everyone will understand it, and only a carpenter’s 2-foot rule is required to ascertain what the angle is. Then, again, simple measurements make calculations much simpler, and the lifting effect is at once understood without any computations being necessary. If the angles are expressed in degrees and minutes, it is necessary to have a protractor or a text-book in order to find out what the inclination really is. When I made my experiments, I only had in mind the obtaining of correct data, to enable me to build a flying machine that would lift itself from the ground. At that time I was extremely busy, and during the first two years of my experimental work, I was out of England fourteen months. After having made my apparatus, I conducted my experiments rather quickly, it is true, but I intended later on to go over them systematically and deliberately, make many more experiments, write down results, and prepare some account of them for publication. However, the property where I made these experiments was sold by the company owning it, and my work was never finished, so I am depending on the scraps of data that were written down at the time. I am also publishing certain observations that I wrote down shortly after I had succeeded in lifting more than the weight of my machine. I think that the experiments which I made with an aeroplane only 8 inches wide will be found the most reliable. All the machinery was running smoothly, and the experiments were conducted with a considerable degree of care. In making any formula on the lifting effect of the aeroplane, it should be based on what was accomplished with the 8-inch plane. Only a few experiments were made to ascertain the relative value of planes of different widths. However, I think we must all admit that a wide plane is not as economical in power as a narrow one. In order to make this matter plain, suppose that we have one aeroplane placed at such an angle that it will lift 2 lbs. per square foot at a velocity of 40 miles an hour; it is very evident that the air just at the rear of this aeroplane would be moving downward at a velocity corresponding to the acceleration imparted to it by the plane. If we wish to obtain lifting effect on this air by another plane of exactly the same width, we shall have to increase its inclination in order to obtain the same lifting effect, and, still further, it will be necessary to use more power in proportion to the load lifted. If a third aeroplane is used, it must be placed at an angle that will impart additional acceleration to the air, and so on. Each plane that we add will have to be placed at a sharper angle, and the power required will be just in proportion to the average angle of all the planes. As the action of a wide aeroplane is identical with that of numerous narrow ones placed in close proximity to each other, it is very evident that a wide aeroplane cannot be as efficient in proportion to its width as a narrow one. I have thought the matter over, and I should say that the lifting effect of a flat aeroplane increases rather faster than the square root of its width. This will, at least, do for a working hypothesis. Every flying machine must have what we will call “a length of entering edge”—that is, the sum of entering edges of all the aeroplanes must bear a fixed relation to the load carried. If a machine is to have its lifting effect doubled, it is necessary to have the length of entering edge twice as long. This additional length may, of course, be obtained by superposed planes, but as we may assume that a large aeroplane will travel faster than a small one, increased velocity will compensate in some degree for the greater width of larger aeroplanes. By careful study of the experiments which I have made, I think it is quite safe to state that the lifting effect of well-made aeroplanes, if we do not take into consideration the resistance due to the framework holding them in position, increases as the square of their velocity. Double their speed and they give four times the lifting effect. The higher the speed, the smaller the angle of the plane, and the greater the lifting effect in proportion to the power employed. When we build a steamship, we know that its weight increases as the cube of any one of its dimensions—that is, if the ship is twice as long, twice as wide, and twice as deep it will carry eight times as much; but at the very best, with even higher speed, the load carried by a flying machine will only increase with the square of any one of its dimensions, or perhaps still less. No matter whether it is a ship, a locomotive, or a flying machine that we wish to build, we must first of all consider the ideal, and then approximate it as closely as possible with the material at hand. Suppose it were possible to make a perfect screw, working without friction, and that its weight should only be that of the surrounding air; if it should be 200 feet in diameter, the power of one man, properly applied, would lift him into the air. This is because the area of a circle 200 feet in diameter is so great that the weight of a man would not cause it to fall through the air at a velocity greater than the man would be able to climb up a ladder. If the diameter should be increased to 400 feet, then a man would be able to carry a passenger as heavy as himself on his flying machine, and if we should increase it still further, to 2,000 feet, the weight of a horse could be sustained in still air by the power which one man could put forth. On the other hand, if we should reduce the diameter of the screw to 20 feet, then it would certainly require the power of one horse to lift the weight of one man, and, if we made the screw small enough, it might even require the power of 100 horses to lift the same weight. It will, therefore, be seen that everything depends upon the area of the air engaged, and in designing a machine we should seek to engage as much air as possible, so long as we can keep down the weight. Suppose that a flying machine should be equipped with a screw 10 feet in diameter, with a pitch of 6 feet, and that the motor developed 40 horse-power and gave the screw 1,000 turns a minute, producing a screw thrust, we will say, of about 220 lbs. If we should increase the diameter of the screw to 20 feet, and if it had the same pitch and revolved at the same rate, it would require four times as much power and would give four times as much screw thrust, because the area of the disc increases as the square of the diameter. Suppose, now, that we should reduce the pitch of the screw to 3 feet, we should in this case engage four times as much air, and double the screw thrust without using any more power—that is, assuming that the machine is stationary and that the full power of the engine is being used for accelerating the air. The advantages of a large screw will, therefore, be obvious. I have been unable to obtain correct data regarding the experiments which have taken place with the various machines on the Continent. I have, however, seen these machines, and I should say when they are in flight, providing that the engine develops 40 horse-power, that fully 28 horse-power is lost in screw slip, and the remainder in forcing the machine through the air. These machines weigh 1,000 lbs. each, and their engines are said to be 50 horse-power. The lifting effect, therefore, per horse-power is 20 lbs. If the aeroplanes were perfect in shape and set at a proper angle, and the resistance of the framework reduced to a minimum, the same lifting effect ought to be produced with an expenditure of less than half this amount of power, providing, of course, that the screw be of proper dimensions. It is said that Professor Langley and Mr. Horatio Philipps, by eliminating the factor of friction altogether, or by not considering it in their calculations, have succeeded in lifting at the rate of 200 lbs. per horse-power. The apparatus they employed was very small. The best I ever did with my very much larger apparatus—and I only did it on one occasion—was to carry 133 lbs. per horse-power. In my large machine experiments, I was amazed at the tremendous amount of power necessary to drive the framework and the numerous wires through the air. It appeared to me, from these experiments, that the air resisted very strongly being cut up by wires. I expected to raise my machine in the air by using only 100 horse-power, and my first condenser was made so that it did actually condense water enough to supply 100 horse-power, but the framework offered such a tremendous resistance that I was compelled to strengthen all of the parts, make the machine heavier, and increase the boiler pressure and piston speed until I actually ran it up to 362 horse-power. This, however, was not the indicated horse-power. It was arrived at by multiplying the pitch of the screws, in feet, by the number of turns that they made in a minute, and by the screw thrust in pounds, and then dividing the product by the conventional unit 33,000. I have no doubt that the indicated horse-power would have been fully 400. On one occasion I ran my machine over the track with all the aeroplanes removed. I knew what steam pressure was required to run my machine with the aeroplanes in position at a speed of 40 miles an hour. With the planes removed, it still required a rather high steam pressure to obtain this velocity, but I made no note at the time of the exact difference. It was not, however, by any means so great as one would have supposed. From the foregoing, it will be seen how necessary it is to consider atmospheric resistance. Although I do not expect that anyone will ever again attempt to make a flying machine driven by a steam engine, still, I have thought best to give a short and concise description of my engine and boiler, in order that my readers may understand what sort of an apparatus I employed to obtain the data I am now, for the first time, placing before the public. A full description of everything relating to the motor power was written down at the time, and has been carefully preserved. An abridgement of this will be found in the Appendix.