[After the foregoing pages were all in type, the index printed and ready to go to the binder, a paper was received from Herr Lilienthal describing his 1893 experiments, which so fully sustains the views set forth in this book, and holds out such promise of success in the near future, that it has been decided, at some inconvenience, to include a translation of this paper in an extra appendix.]
I PRESENT herewith an account of my personal experience in soaring flight during the past year, this being the third annual report published by me in this journal. I have now reached the close of a series of experiments during which I had set myself a definite task. This was to construct an apparatus with curved carrying surfaces which should enable me to sail through the air, starting from high points and gliding as far as possible--that is to say, at the least obtainable inclination; and to do this with stability and safety even in winds of medium strength.
I may be permitted, in giving this account of experiments in which artificial arched wings were used, perhaps for the first time, in a certain form of flight, to refer again to the introduction of this important element in the technics of flight.
Four years ago I completed a series of experiments on the carrying capacity of arched wings, which I had carried on with my brother for many years, and I published the results in my book, "The Flight of Birds as the Basis of the Art of Flying." In this work a new theory of flying, fairly explaining all the phenomena of bird-flight, was for the first time completely made known. The novel data involved in our calculations, and the remarkable results arrived at in our experiments, were my motives for not coming sooner before the public, until by numerous and repeated trials every chance of error appeared to be eliminated.
Now I have been accused in No. 6 of last year's issues of this journal1 with having gone wrong in keeping back these discoveries so long. I am told that I should have come before the public with them immediately after my first discovery of the new laws of air resistance more than 20 years ago. That while I was censuring the balloon for a delay of many decades I was myself postponing the solution of the question of aerial navigation for two decades more by my silence.
Flattering as it is for me to see so great an influence on the solution of the problem of flying attributed to the new discoveries presented by me, yet I will not forbear to point out that by these researches the theory of flight was merely put upon a somewhat sounder basis, but that for the full solution of the problem other very important questions will have to be settled.
The mere discovery that with arched wings supporting forces are evolved which permit soaring to be performed with little effort is far from being the final invention of flying. The successful practical utilization of this important phenomenon in air resistance is going to demand a considerable amount of ingenuity. To get the upper hand over the wind with flying machines and to bring about a beneficial utilization of those favorable supporting forces--for such a task many a technical man will have a chance to throw his talent into the scale; for the field of work lying before us is no small one.
The great delay in publishing discoveries of myself and brother on aviation was only the natural result of the circumstances under which they were made. Even when we were devoting every hour of our leisure to the question of aviation, and were already on the track of the laws which were to evolve this problem, people in Germany still considered every man who occupied himself with this unprofitable art as little better than a lunatic. This was sufficient cause for our not attracting unnecessary attention to such studies. The principal professor of mathematics at the Berlin Gewerbe Academie in the sixties heard from one of my fellow-students--they had given me even then an appropriate nickname--that I was occupied with investigations in aeronautics. The Professor sent word to me that there was no harm in my amusing myself with such calculations, but that I "should, for Heaven's sake, not spend any money for such things." The professor, it is true, did not know that this last advice was (for cause) quite unnecessary.
At that time a special learned commission appointed by the State had just officially declared, once for all, that man would never be able to fly; by which declaration naturally public opinion, in favor of experiments on this problem, was not exactly stimulated. Even later on the interest in aviation was much less than it is to-day. German societies for the advancement of aerial navigation were not yet in existence; and when they were formed the balloon, which I have always considered an obstacle in the development of free flight, monopolized their entire attention. For this reason I did not at that time think it advisable to join any one of the societies. When, however, I had done so, and aviation had other representatives in the society, I soon took advantage of the opportunity by communicating our experimental results in a series of lectures, which were followed shortly by the publication of my book.
To-day, with clear and comprehensive diagrams before us, the explanation of the flight of birds seems very simple and natural, while formerly every crow that flew by assigned us the puzzle of its slowly moving wings to solve. To-day, too, it is easy, in investigations on air resistance, to take surfaces curved like the wings of a bird instead of flat plates, and to develop in succession those wonderful effects, the first discovery of which was, after all, not quite so simple and self-evident as some may be inclined to assume now. The thoughtful reader will readily understand that it took much time and study to arrive at the conclusion that the slight curvature of the wing was the real secret of flying. This was a conclusion which we reached purely as a logical deduction from the flight of birds, and which some noted investigators are not willing to admit even at this late day. Besides this, being young men entirely without resources, we were compelled to procure the means for carrying on our experiments by the most petty economies, and at times to suspend entirely our work in aeronautics by reason of the struggle for existence. We should not at that time in any event have been able to publish our results in proper form. Even at the last I had the very greatest difficulty in finding a publisher for my book.
Although, then, the delay in publishing my work was simply the result of circumstances, the position assumed toward it, in the sequel, by certain investigators, proved to me that my satisfaction in my work would have been much diminished if it had been published before the entire data were on hand in a complete form.
I must confess, however, that to us who abandoned flat wings fully two decades ago, it seemed almost inconceivable that experimenters should cling so tenaciously to the aeroplane and to hopeless calculations on the resistances of plane surfaces. as practically all of them did during this whole period. Even to the present hour the majority of aviators expend much painful effort in attempting the hopeless task of trying to fly with flat wings.
Our expectation that the publication of our experiments, showing the problem of flight in an entirely new light, would be followed by practical tests as to the correctness of the new laws indicated by us was not at once realized. Our results stood alone and unsupported until very lately, and have but recently been corroborated by the work of Wellner and Phillips. Even now the flat wing does not show any signs of disappearing from the field very soon.
When it became known that the French Government2 had granted funds for experiments on air resistance, I sought to induce the president of the commission in charge of them to include curved surfaces as well as flat plates within the field of his experiments. At the same time I sent him a copy of my work, and by means of my diagrams pointed out to him the favorable results in air resistance obtained with curved wings.
M. Hureau de Villeneuve thanked me for the book, pronounced it to be very interesting, but declined to grant my request as to the consideration of hollow surfaces in his researches.
His reasons for this course literally translated were the following:
"I consider wings, pre-eminently, as moving organs for propelling at great speed, and when this speed has been reached the force necessary for supporting may be neglected. I have shown this by constructing mechanical birds with flat wings which fly very fast and keep themselves up very well when flying in the air. I try to make the wings true planes as far as I can, for the flatter they are the greater is the speed attained."
After this expression of opinion, there is, I think, for the present little prospects that experiments to be made in aeronautics with the aid of the French Government will be of any considerable benefit to the technics of flight. It is also to be greatly regretted that the extended experiments of Professor Langley carried out with so much care and expense, were limited to the resistance of plane surfaces, as for such surfaces data have long been on record sufficient for computing all cases occurring in practice.
German and Austrian aviators, it is true, since the publication of my book have largely put aside flat wing and sail surfaces and introduced arched wings. However this was done mainly on paper, in projects, and in aeronautical papers and discussions. I therefore felt impelled all the more to carry out myself my theory in practice, and to utilize the results of my preliminary small scale experiments. Through my long familiarity with air and wind I had come to the conclusion that a particular class of difficulties was next to be overcome. In trials with movable wings, in the building of steam air ships in experiments with mechanical birds of all kinds, I had found out how hard it is to maintain a stable equilibrium in the air and to counteract the "whims" of the wind.
For this reason I gave up for the time being motor mechanisms altogether, and limited myself to the simplest form of flight--namely, gliding downward in an inclined direction. The object of this was to ascertain practically whether stable sailing and equilibrium through the air was possible; whether by practice we could learn to overcome the wind, that archenemy of all wing builders, and, above all, whether with large "human" wings the favorable carrying capacities of arched wings would be maintained, which our experiments in small wings (not over 1/2 sq. m. in area) had shown.
It was further my purpose to extend my former experience in practical wing construction, and to build safer and lighter sailing apparatus which should permit soaring safely at considerable heights. As a final result we would also ascertain at what angles of inclination sailing flight can be maintained with and without the wind and what conclusions can be drawn from this as to the "work" or power required for flying in general.
In addition to the details given in my communications of 1891 and 1892 I will mention briefly that this spring I erected a special flying station on the "Mai" hill, near Steglitz. The owner of the property, Mr. Seldis, allowed me in the kindest way to arrange a little earthmound at this spot for experiments in soaring. By building a shed in the shape of a tower, from the roof of which I sailed, I obtained a "jumping off" place 10 m. (33 ft.) high. The shed serves also for storing my apparatus. The earth slope around the shed falls off toward the southwest, the west, and the northwest. The roof is covered with sod to give a firm footing in taking a run, and slopes in the above-mentioned directions. In the assumption that I had thus provided sufficiently for the frequent changes in the direction of the wind I was entirely mistaken. During the first half of this summer the wind varied almost entirely between the east and the north, and my flying tower remained unused for nearly three months. The wind, be it understood once for all, cannot be depended upon. A hill well suited for trials in sailing flight should consist of a cone sloping on all sides, so that the start may be made against the wind in any direction.
The two figures (figs. 1 and 2) show the "jumping-off" place from this tower, from in front as well as from the side. The second figure shows also the attachment of the apparatus to the body, already described in the past, which consists in simply grasping it with both hands.
FIG. 1.--LILIENTHAL'S "JUMPING-OFF" PLACE.
A novelty that I introduced this year in my apparatus is the possibility of folding it up. The wings are formed of ribs arranged radially and can be closed up, somewhat like the wings of a bat. In this way it became more portable and can be stored anywhere.
FIG. 2.--LILIENTHAL'S "JUMPING-OFF" PLACE.
I have gradually given up the great "spread" of my former apparatus. The unequal strength and direction of the wind under the right or the left wing, frequently produce a considerable displacement of the center of action of the air pressure, which becomes worse the greater the "spread" of the wings. This spread I now never make greater than 7 m. (23 ft.), and I am thus always able to restore equilibrium by a simple change in my center of gravity.
The breadth of the wings has also its limits. It must be possible, in an instant, to transfer the center of gravity so far from front to back as the point of action of the supporting air resistance can move. The furthest backward limit of this motion is the center of gravity of the wing surface. When you fall vertically with this apparatus in calm air it acts entirely as a parachute. The air strikes vertically from below and presses uniformly on all parts of the surface. It is possible to get into this position in flying if the aviator uses up, in gliding upward, all the vis-viva acquired in flying forward and downward whence the velocity will decrease very rapidly on the upward turn. I have often been obliged thus to pass over some obstacles--a tree, a crowd-of people, or the photographer who was getting a view of me from the front. It is easy to rise in this way, but the apparatus comes to a stand at the summit, and if it cannot be properly and promptly slanted down behind, it will be tilted toward the front in falling, and the front edge will be broken when it touches the ground.
The center of the supporting air pressure reaches its limit toward the front, when the machine is struck by a stronger wind gust in flying. It is then necessary for the aviator to throw himself as far forward as possible and also to stretch his legs forward, otherwise velocity is lost, and the machine will be driven back by the wind. The figure (No. 3) shows such a critical position. I had started in a wind estimated by me at from 6 to 7 m. velocity per second (13 to 16 miles per hour), and while I was in motion the velocity of the air rose to probably about 10 m. (22 miles), for I was suddenly raised with so much force that I became suspended in the air at a higher level than my point of starting. Then I remained fixed at this point for several seconds until the wind decreased, when I again sailed forward and moved downward slowly. In order to be able to conveniently equalize this fore-and-aft motion of air pressure, by a change in the center of gravity, it is advisable to make the breadth of wing not greater than 2 1/2 m. (8.2 ft.). From these conditions we arrived at a pretty definite relation in the shape and the size of the wings. With a spread of 7 m. (23 ft.) and a breadth of 2 1/2 m. (8.2 ft.) we get, allowing for the rounding of the ends, an area of 1.4 sq. m. (1512 sq. ft ), which is sufficient to carry the mean weight of a man. Such wings weigh about 20 kilograms (44 lbs.). My own weight is 80 kilograms (176 lbs.), giving a total weight of exactly 100 kilograms (220 lbs.).
FIG. 3.--LILIENTHAL'S FLIGHT.
I have now moved my main practice ground to the Rhinow Hills, which I referred to in my last year's communication. The topography is here as if made especially for experiments in flying. Out of the surrounding flat fields a range of hills, covered only with grass and heather, rises to a height of 60 m. (200 ft.) with inclined slopes on all sides. The inclinations of the slopes vary from 10° to 20°, so that one can select a place for sailing along in any direction. When, this year, I unfolded my flying outfit for the first time on these slopes, a somewhat anxious feeling came over me, when I said to myself, "From up here you are now to sail down into the land spread out deep before you." But the first few careful leaps soon gave me back a feeling of security, as the soaring flight began here far more gently than from my flying tower. The wind did not "rear up" here as it did in front of the tower, where I always felt a sudden upward blast from the wind in passing the edge, which often threatened to be dangerous.
You run down hill against the wind with lowered wings at the proper moment you raise the carrying surface up a little, so that it is approximately level; and then, springing forward, you try, by a proper position of the center of gravity of the apparatus, to give it such an inclination that it will glide along rapidly and drop as little as possible. Beginners will do well to select for this a gentle slope, over which they may glide along a low elevation. The first rule is to keep your legs well extended toward the front, and in landing to throw the upper part of the body backward, so that the front edge raises itself and thus checks the motion, as may be seen whenever a crow alights. The starting and landing must be done exactly square against the wind. The fixed vertical rudder will keep the apparatus exactly in the wind when in a state of rest. The horizontal rudder keeps the apparatus from tipping over forward, a thing that arched surfaces are inclined to do. In landing, however, the horizontal rudder must not hinder a rapid tipping up of the machine; hence it must turn freely on its forward edge when the air presses upward, and its motion must be limited at the bottom only.
The following mistake is to be particularly avoided. The experimenter is soaring in the air and feels himself suddenly raised by the wind, but unequally, as is usually the case--for instance, the left wing more than the right. The inclined position forces him toward the right. The beginner involuntarily stretches his legs to the right, because he foresees that he will strike the earth on the right hand. The result is that the right wing, which is already lower, is loaded still more, and flight tends more and more downward and to the right, until the tips of the right wing strike the earth and are broken. For life and limb there is less danger, as the apparatus forms an efficient guard in every direction, which checks the force of the blow. The correct thing to do is always to extend one's legs toward the wing* that is rising, and thus to press it down again. In the beginning this requires some force of will, but this useful movement soon becomes an unconscious one, after we see how surely the wings can be guided this way and be protected from damage.
Beginners are also easily tempted to utilize the momentum which the easy downward glide gives them for a bold upward flight. They are likely to forget, however, that at the summit of the rising curve their apparatus becomes a mere parachute. They do not lean back far enough and incur damages requiring considerable repairs to the machine. It is better to postpone such tricks until the regulating of the center of gravity has become a second nature, like balancing on the bicycle, and rather to lay most stress on gliding ahead at an inclination which shall be uniform and as slight as possible, and particularly to endeavor to make an elegant landing. Of course we do not have time enough when in the air to consider carefully whether the position of the wings at any particular time is the correct one. This is entirely a matter of practice and experience. After a few trials one begins to have a feeling of mastery over the situation. A consciousness of safety crowds out the first feeling of anxiety. Finally we become perfectly at ease, even when soaring high in the air, while the indescribably beautiful and gentle gliding over the long sunny slope rekindles our ardor anew at every trial. It does not take very long before it is quite a matter of indifference whether we are gliding along 2 m. or 20 m. (6 ft. or 65 ft.) above the ground; we feel how safely the air is carrying us, even though we see diminutive men looking up at us with astonishment. Soon we pass over ravines as high as houses, and sail for several hundred meters through the air without any danger, parrying the force of the wind at every movement.
After we have reached a feeling of safety in direct flight against the wind, we involuntarily try, first a very little and then more and more, to direct the course of our flight to the right and to the left. A slight change in the center of gravity to one side produces at once a small inclination of the carrying surface, so that the supporting air pressure also moves to this side and changes the direction of flight. There is nothing simpler than steering flying machines. It is important not to forget in this connection that the landing must always be made dead against the wind.
On the occasion shown by fig. 4, which represents a very long and high flight, I had carried the deviation from straight flight so far that at times I was flying almost in an opposite direction. Coming from the hill at the right hand, I had almost turned my back to the plain at the moment the picture was taken.
FIG. 4.--LILIENTHAL'S FLIGHT.
For the present it does not appear to me to be advisable to endeavor to bring the body into a horizontal position. because the legs must always be ready for action in running, jumping, steering and landing. Later on it will, perhaps, be possible to make this change, after some other important improvements have been made in the apparatus. Of course this would be very important for producing easier passage through the air and the consequent saving of energy in flying.
In the annexed figure (5) several lines of flight are illustrated. The dotted line d e shows the path traversed in a calm. At the top of the hill, at the point a, a running start is taken with as high speed as possible and with wings lowered. The steeper the hill the better. Then at b you raise your wings a very little in front and try to glide along as close to the ground as possible, with your legs extended to the front. The diagram at C shows how the air resistance L has at the same time a supporting and propelling force or component. Soon our velocity has increased so much that at d we can change to a flatter inclination. Thus at an angle of 9° to 10° we approach the valley and do not raise our wings in front till the very end at e, when we apply a strong force by throwing the upper part of our body back. Then the pressure of the air, acting suddenly at the front, checks the motion, and we drop on to our feet quite gently, just as if we had jumped, without wings, from the height of a chair.
FIG. 5.--LILIENTHAL'S FLIGHT.
When there is any wind the motion is still more gentle. Flight against the wind, in reference to the earth, is in all cases slower, as, of course, the relative motion of the air and the apparatus governs the speed. The relative velocity attained is felt by the strength of the breeze striking the face while flying. A convenient device would be a little indicator pressure gauge in the front of the apparatus, on which we could constantly read the relative speed of the air. This would not involve any appreciable increase in the resistance.
Although the wind compels us to resort to various extraordinary manoeuvres it also furnishes us an opportunity for testing the real value and scope of sailing flight. By our calculations, based on experiments with arched surfaces on a small scale during windy weather, extended and prolonged sailing flight can be explained without further trouble. With wings of a proper form and position, the wind needs only to reach the necessary strength in order to keep the experimenter from falling. Even with light winds of 4-5 m velocity per second (9 to 11 miles per hour), we can with some little practice glide along at the slight angle of 6° to 8°, as is shown in the line b f.
The greatest velocity of the wind at which I dared to start was about 7-8 m. per second (15 to 18 miles per hour). In these flights I often had a very interesting though not dangerous struggle with the wind, in which I sometimes came to a state of absolute rest, and was suspended in the air at one point for several seconds, almost exactly as the falcons of the Rhinow Mountains are. Sometimes I was suddenly lifted from such a position of rest many meters in a vertical direction, so that I became alarmed lest the wind should carry me off altogether. As, however, I never ventured out except when such gusts were exceptional, I was always able to continue my flight and to land safely. The line b g shows a wavy course, brought about by gusts, during which I rose to the height of my point of starting.
I want to emphasize particularly that the results obtained in actual sailing agree well with my small-scale experiments on the supporting power of arched surfaces. During a calm it is quite feasible, with proper practice in placing the wings, to sail downward at an angle of 9°. Observation shows that the wings are then approximately level. According to my diagrams on Plate VII3 the supporting force of the air would then be 80 per cent. of the resistance of the surfaces normally acted upon. In a calm the velocity of flight as measured was about 9 m. per second, with a surface of 14 sq. m.; the uplifting force would be = 0.8 X 0.13 X 14 X 92 = 118 kilograms, while 100 kilograms would suffice.
According to the diagram on Plate VI if a curved surface is struck at an angle of 9°, its pressure will act toward the front at an angle of 3° with the normal to the chord of the surface. The propelling effect of the air pressure will therefore be:
100 X sin. 3° = 5 kilograms.
This force is used up in propelling through the air the cross sections of the body and of the framework at a velocity of 9 m. per second. This would correspond to a projected area F to be deduced from the equation:
5 kgm. = 0.13 X F X 92
which gives F = 0.5 sq. m., a result agreeing well with the actual fact.
In a medium wind a practiced "sailer" can pass over considerable space at an angle of 6°, as I have proved from experience; the velocity of motion in this case is about 5 m. per second. It is a fair assumption that the wind as it strikes the mountains has a greater ascending trend, but I succeeded in maintaining the same angle of descent on somewhat narrow hill-sides, where the wind could escape easily to either side, and also at a considerable distance away from the mountains. For this reason I think it likely that the same results could be obtained upon extended flights.
There can be no doubt, in my opinion, that by perfecting our present apparatus, and by acquiring greater skill in using it, we shall achieve still more favorable results with it, and finally succeed in taking long sails even in rather strong winds. Even without considering the chances of such continued sailing without effort, the results already obtained provide us with data as to the energy to be expended if horizontal flight is to be prolonged by mechanical means.
The wind seldom has a velocity exceeding 4-5 m. per second. Sailing against the wind there will be a drop per second of:
5 sin. 6° = 0.5 m. = 1.64 ft.
If we disregard minor details the "work" of my apparatus will, therefore, be: 100 X 0.5 = 50 kilogrammeters per second, or 2/3 H.P. This is for the purely ideal case, when the wings move downward uniformly in the line of flight, and are raised without appreciable loss of time; but the weight of the motor, and the decrease in carrying force during the upward stroke of the wings will, of course, increase the total work necessary. I have already completed a steam-engine which I intend to use for moving wings in some experiments to be made in the near future. It develops 2 H.P., will work half an hour, and weighs 20 kilograms (44 lbs.), including all its accessories. In this way the "work" required will be increased to 60 kilogrammeters per second. When the separate surfaces at the tip of the wings, corresponding to the primary feathers, move up and down, 1st, the surfaces will move at a more favorable angle of incidence, and, 2d, a further increase in lifting power is produced by the beating action of the wings, both of which facts decrease the necessary expenditure of power. It thus appears possible that we may succeed in maintaining horizontal flight with the above-mentioned motor, though the upright position of the body is unfavorable to flying.
Of course it will be a matter of practice to learn how to guide such a flying machine, with beating wings, as surely as a simple sailing apparatus. For this reason I shall first use my new machine with rigid wings as a simple sailing apparatus. Later on, when I have again acquired perfect confidence, I shall allow the tips of the wings to make very small beats, and shall increase these very gradually to their full stroke.
In this way, passing by small gradations from sailing flight to rowing flight with wings, the length and duration of flight may be considerably increased, so that we may venture at last to fly with the wind for a time and then try flying in circles.
In my trials with such large carrying surfaces in flying I have found that the concavity of the wings should be less than results from my experiments in small models. While with small surfaces, of less area than 1 sq. m., a depth of one-twelfth of the breadth of the wing gave the best results, on the large wings of 14 sq. m., a depth of one-eighteenth to one twentieth of the breadth proved to be the best. I have made frequent changes in the profile of the wings to make certain of this fact. My apparatus was specially arranged to permit this.
Of late much stress has been laid on the parabolic cross-section of the bird's wings. It is evident that the "projectile curve" would be the natural form for diverting the air current under the wing. Apparently the various profiles actually represented have been drawn rather arbitrarily. If we compare the circle with the half vertex of the parabola, which is the part generally shown, the difference is found to be so slight as to be hardly worth considering. On the other hand, in the sketches so presented by others, the front of the arch shows decidedly more curvature than the back; this was probably done to explain the greater inclination of the air pressure in front. Of course, it is quite feasible to give up the ordinary parabola of the second degree, and use instead a parabola of a higher order, which rises at first more steeply and runs out more gradually. During three years of practical experiments I have repeatedly tried such profiles in sailing, but I can only advise strongly against making the surface too steep in front, as there is a risk of getting a dangerous upward pressure. My advice is to stick to the ordinary parabola even when it almost coincides with a circle.
In closing, I would express the wish that the publication of my results may incite others to take up the problem of flight practically. I represent merely but one certain line of thought, which has led me so strongly to the imitation of the flying birds, that I have even been accused of "aping" them. Such accusations cannot, however, divert me from the path I have chosen. I do not imitate the flight of the birds because it happens to be convenient to copy, but because it combines logical correctness with so many practical advantages which no other principle of flying could furnish me.
The only method which, in my opinion, might to a certain degree offer the advantages of moving wings is that of rotating air propellers, which lift and propel at the same time. I have already expressed my opinion in the past that possibly good results may be obtained with such devices if skilfully worked out. Actual trial alone can decide this question, as we must let the air and the wind have their say in the matter. For this reason it would be desirable to have some such ideas carried out in practice, so that there will be an end to fruitless discussions.
1 Translated from Zeitschrift
fur Luftschiffahrt and Physic de Atmosphare for November, 1893.
2 He means the French Society for the Advancement of Science.--ED.
3 Lilienthal: "Der Vogelflug als Grundlage der Fliegekunst."
*Webmaster's note: The text as typeset read "The correct thing to do is always to extend one's legs toward the wind that is rising, and thus to press it down again." To me, it seems that the intended word was "wing", so I made the substitution.
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