Popular Science Monthly/Volume 34/November 1888/The Problem of a Flying-Machine
By JOSEPH LE CONTE,
PROFESSOR OF GEOLOGY AND NATURAL HISTORY IN THE UNIVERSITY OF CALIFORNIA.
IN "The Popular Science Monthly" for November, 1885 (vol. xxviii, p. 1), Mr. Mather closes an excellent article on flying-machines with the following weighty remark: "These are the most important inventions of this class — i. e., self-raising, self-propelling machines. It must be confessed that the results are far from encouraging. But, there are the birds; and they completely refute the argument of those who say that it is impossible to make a flying-machine."
Now, I wish to take issue with Mr. Mather in this conclusion. I am one of those who think that a flying-machine, in the sense indicated above — i. e., self-raising, self-propelling — is impossible, in spite of the testimony of the birds. Of course, it is understood that I am speaking of true flight, like that of a bird or an insect, and not of ballooning nor any combination of ballooning with flying. This is sufficiently implied in the words "self-raising and self-propelling." I wish now to give, very briefly, a reason for my faith. I can best do so with brevity and clearness by a series of propositions which I hope will lead us, step by step, to absolute demonstration. I believe this is important, in order to check baseless expectations and limit effort to the right direction. 1. Two Kinds of Impossibles. — On the very threshold of my subject I am met by the objection that" many things far more wonderful, and, before their realization, seemingly far more impossible, than flying-machines, have, nevertheless, actually come to pass. Then why not this also? He is a bold man that declares anything impossible in this age of rapid progress and startling inventions." I answer: True enough, many wonderful and apparently impossible things have indeed come to pass; and that, too, in spite of the adverse predictions of some rash scientists. But there are two kinds of impossibles — the seeming and the real. The seeming impossibles we believe to be impossible, only because we do not yet understand the principles involved in the problem, and therefore can not conceive the conditions necessary for their successful application. Such are all the cases which most readily occur to the mind as triumphs of science — such, for example, as the locomotive, the telegraph, the telephone, etc. The real impossibles, on the contrary, we know to be such, because we see clearly through all the principles involved in the problem and the limits of their possible application. Of this kind are the problem of a perpetual-motion machine, and of a self-supporting arch of indefinite length. Now observe — that, of these two kinds of impossibles, to the unreflecting the seeming are far the more impossible and wonderful. In fact, to most people the real impossibles do not seem impossible, or wonderful, or even difficult at all. Hence, in every age and country we find men who waste their lives in vain attempts to make perpetual-motion machines. So, also, in regard to the indefinite arch. Most people do not see at once why an arch of any length should not support itself if only it be big and strong in proportion to its length.
Let me stop a moment to illustrate this by an anecdote, I remember many years ago meeting a traveling agent of a Remington bridge (a wooden suspension-bridge), who had with him for exhibition a small model which, when set up, was about twenty feet long, and had stringers about as big as my finger. This little model not only sustained itself, but, in addition, the weight of a stout looker-on — "a fat and greasy citizen" — twenty times as heavy as the bridge itself. "Now," said the plausible agent," if you increase the size and strength of the stringers in proportion as you increase the length of your bridge, it is evident that a bridge of this pattern, of any length, will not only sustain itself, but twenty times its own weight in the form of loaded wagons," Most of those who heard it accepted his reasoning as irrefutable. Of course, every engineer knows that this is not true. For, while the weight of the bridge increases as the cube of the diameter of all its parts, the strength of the stringers increases only as the square of their diameter. In increasing the size in all dimensions, therefore, the weight will quickly overtake the strength. There is a limit, therefore, beyond which it is impossible to make an arch or suspension-bridge support itself. This fact is so well recognized that it is unnecessary to dwell upon it. I have brought it forward at all only because I wish to apply the principle to other cases where it is not so well recognized.
2. Application to Walking. — Now, this principle applies not only to bridges and arches, but to all kinds of structures, and therefore, also, to locomotive-machines, whether natural or artificial. For example, there is a limit of size beyond which it is impossible to make a successful walking - machine, and beyond which, therefore, a walking animal can not exist. Beyond that limit the supporting bones would crush beneath the weight of the animal. It is in vain to say that we will make the bones and muscles thick and strong in proportion to the increasing size of the animal; for, as the animal increases in size, its weight increases as its volume or as the cube, while the strength of bones and muscles increases only as the cross-section or as the square of the diameter. Therefore, as the animal increases in size, a larger and longer portion of the whole strength is consumed in the support, and less and less is left over for motion, until, finally, the weight overtakes the utmost strength of bones to support or muscles to move. It is probable that the limit of an efficient walking-machine has actually been reached in the largest animals which have walked the earth; such, for example, as the huge dinosaurs of the Jurassic period, recently brought to light by the researches of Marsh and Cope. The whale has probably passed the limit, and therefore was compelled to change its form and take to the water, and become a swimming-machine. Or, to speak more definitely and also more truly, the whale family in times long ago, perhaps in earliest Tertiary times, before it became a true whale family, found it profitable, either for food or for safety, to take to the water; and this not only determined a change of form, but also allowed it to attain a greater size than was compatible with walking.
This principle explains many other things in nature which would otherwise be inexplicable. The marvelous vivacity and energy of insect-motion — the arrowy swiftness of flight of many kinds of flies, the prodigious leaps of fleas, the immense weights dragged by ants — are familiar to all. In text-books on natural history these are given as examples of the almost inconceivable nervous and muscular energy of insects, as compared with vertebrates. It is often said that if our nerve- and muscle-energy were as great as that of a flea, we might easily leap a quarter of a mile. In that case we would have little use for railroads or for seven-league boots, or indeed for flying-machines. Now, this is an entire misconception. There is no reason to believe that our muscular energy is any whit less than that of insects — that, taking a bundle of muscular fibers of equal cross-section, the contractile power is any less in our case than in theirs. The explanation is easily found in the principle above stated. These apparently wonderful feats of insects are simply the result of their small size. Weight decreases as well as increases as the volume, i. e., as the cube, while strength of muscle only as the cross-section, i. e., as the square of the diameter. Therefore, with decreasing size weight decreases far more rapidly than strength, and therefore the ratio of strength to size increases; and therefore, finally, less and less energy is consumed in support, and more and more is left over for motion. If any one desires to pursue this subject further, he will find it fully treated in a previous number (April, 1883) of "The Popular Science Monthly," in an article by Delbœuf on "Dwarfs and Giants."
3. Application to Natural Flying. — Now, this same principle of limit applies with greatly increased force to flying. There is a limit of size and weight of a flying animal; and on account of the prodigious energy required for aërial locomotion that limit is very low, not much more than fifty pounds, certainly much less than one hundred pounds. The largest flying-birds, such as the bustard, the turkey-cock, and the condor, rise with difficulty. They are evidently near the limit. There are, indeed, birds which are much larger, such as the ostrich, the emu, and especially the extinct Dinornis and Epiornis, but these are all flightless. They do not fly, not because their wings are aborted, but, on the contrary, their wings became aborted because they did not fly, and they did not fly because they had grown too large. Nature could not make them fliers, and therefore did not try. Or rather, it might perhaps be said, she tried her best and failed. Their wings became aborted because their size had passed the limit of possibility of flight. I imagine that the history of their evolution was briefly something as follows : They sprang originally from large birds of heavy flight; but being somewhat isolated from severe competition, on islands with abundant food, natural selection took the direction of size and strength for victory in contest, rather than swiftness of flight for escape from danger. They quickly passed the limit of size for flight, and their wings becoming useless were aborted.
4. Relation of Rising to Propulsion in Flight. — There is another principle involved in flight which must now be stated. There are two things to be considered, viz., rising and propulsion. We have already shown that the ratio of weight to strength, and therefore the difficulty of rising, increases as the size or weight. We now add that the resistance of the air to motion through it, and therefore the difficulty of propulsion of a flying animal, decreases in the same ratio. The one varies directly, the other inversely, as the size.
This is a principle of very wide application, and I stop to illustrate it by many familiar phenomena. The floating of dust and smoke, the suspension of clouds, the slow settling of fine sediments, are examples. As the particles become smaller, the resistance of the air or water to falling through it, decreasing as the surface, i. e., as the square of the diameter of the particle (d 2), while the force of motion or weight decreases as the volume, i. e., as the cube (d 3) of the diameter — evidently the force decreases much faster than the resistance, and therefore the ratio of force to resistance, or the effective force of motion, becomes less and less, until in very small particles it is a vanishing quantity. For this reason it matters not how great the specific gravity of a substance may be, if the particles are only small enough they will float indefinitely in air or in water. Particles of gold may be made so small by precipitation from solution that they will require months to settle. Krakatoa-dust (if that be the true cause of the afterglow and of Bishop's ring) remained suspended in the air for more than two years. The perennial blue of the sky and of mountain-lake water is due to suspended particles.
Now, this principle applies not only to resistance of the air to the force of gravity in falling bodies, but also to resistance of the air to the force of propulsion in flying bodies. As a flying animal becomes smaller (as in the smaller birds and in insects), a larger and larger proportion of the whole flight-energy is consumed in propulsion, and a less and less proportion is necessary for rising. On the other hand, as a bird becomes larger, a progressively larger portion of the whole flight-energy is necessary for rising, and less and less is necessary for propulsion, until finally at the limit the whole is necessary for rising. Beyond this, of course, flight is impossible. This explains why large birds like the condor rise with difficulty; but once up they sail with ease and grace, while small birds and insects rise with ease, but require rapid and incessant fluttering in progressing.
5. Application to a Flying-Machine. — Many readers who have followed me thus far with entire assent will probably object right here that, while all this may be true of flying animals, it may not be true at least to the same extent — i. e., the limit may not be so low — in flying-machines. There are forces, they will say, such as steam, electricity, explosions, etc., which are far more powerful than muscular contraction. Especially is electricity looked to in a vague way to do for us many wonderful things, this of flying among the number. Now, this is again a great mistake. Nerve-energy acting through muscular contraction, and supplied by the combustion of foods, such as oils, fats, starch, sugar and fibrin, together form the most perfect and efficient engine that we know anything of ; i, e., will do more work with the same weight of machinery and fuel.
There was much loose talk a few years ago about condensing and storing electricity in immense quantity, in small space, by the use of Faure's battery. Millions of foot-pounds, it was said, may be thus condensed and stored in a small box and carried about. To the unreflecting, millions of foot-pounds seems a very large quantity. Extravagant expectations were thus raised in the popular mind. I remember at that time talking with a very intelligent gentleman on this very subject of flying-machines; and he, in rebuttal of my argument, suggested the use of stored electricity. "Why," said I, "there is more energy stored in a piece of coal that may be put in the vest-pocket than can be stored in a Faure's battery weighing three hundred pounds!" Faure's battery is doubtless a good thing, but chiefly, like a fly-wheel, not for increasing the amount but regulating the flow of force. He then suggested the enormous force of explosives, such as the nitro-compounds. The feeding of these to the engine might, he rightly thought, be so regulated as to supply a continuous force. But here also lurks a fallacy, the result again of a misconception. The force of such compounds is characterized by great intensity rather than great quantity. The whole force is compressed into an almost infinitely small space of time, and therefore very intense. But stretch it out as a continuous force and it becomes no greater, probably less, than that of an equal weight of burning coal. There is probably no greater available energy in the world than that produced by the burning of carbon and hydrogen. It is this form of energy that we use in steam-engines; this we find most powerful and economical in making electricity; this, also, is what is used in the animal machine. The only question that remains, then, is the relative economy of its use. Now, I think it will be admitted on all hands that no known engine compares in this respect with the animal body. It is acknowledged by mechanical engineers that the animal machine, burning hydrocarbonaceous food, and acting through nerve and muscle, more nearly approaches the theoretical limit of possible work than any, even the best, steam-engines. More accurately, the animal body is about twice as effective as the best Cornish engine. The reason of this wonderful effectiveness of the animal machine is obvious. See how this machine has been gradually perfected throughout infinite ages, especially in birds. During the whole geological history of the earth this machine has been steadily improving in structure of skeleton, energy of muscle, and rapidity of combustion of fuel, by struggle for life and survival of only the swiftest, the most energetic, and the hottest-blooded, until an almost incredible intensity is reached in birds. Moreover, in them everything is sacrificed to the supreme necessity of flight. Viscera, skeleton, legs, head, all are made as small and light as possible to make room for the great pectoral muscles working the wings. Add to this the exquisite structure of the wings and feathers, adapting them for the greatest effectiveness; and we must admit that a bird is an incomparable model of a flying-machine. No machine that we may hope to devise, for the same weight of machine, fuel, and directing brain, is half so effective. And yet, this machine thus perfected through infinite ages by a ruthless process of natural selection, reaches its limit of weight at about fifty pounds! I said, "weight of machine, fuel, and directing brain." Here is another prodigious advantage of the natural over the artificial machine. The flying animal is its own engineer, the flying-machine must carry its engineer. The directing engineer in the former (the brain) is perhaps an ounce, in the latter it is one hundred and fifty pounds. The limit of the flying animal is fifty pounds. The smallest possible weight of a flying-machine, with its necessary fuel and engineer, even without freight or passengers, could not be less than three or four hundred pounds.
Now, to complete the argument, put these three indisputable facts together: 1. There is a low limit of weight, certainly not much beyond fifty pounds, beyond which it is impossible for an animal to fly. Nature has reached this limit, and with her utmost effort has failed to pass it. 2. The animal machine is far more effective than any we may hope to make; therefore the limit of the weight of a successful flying-machine can not be more than fifty pounds. 3. The weight of any machine constructed for flying, including fuel and engineer, can not be less than three or four hundred pounds. Is it not demonstrated that a true flying-machine, self-raising, self-sustaining, self-propelling , is physically impossible?
6. Application to a Swimming-Machine. — But is there not a way of escape from the toils of this inexorable logic? We have said the limit of the weight of a flying animal is about fifty pounds. The limit for a walking animal is much higher, probably several tons. For a swimming animal there is no limit of weight and size, because the water sustains the weight, and therefore the whole energy may be used in propulsion alone. Now some may think they see in this a solution of the problem. They will say, "Why not sustain the machine by gas, so that the whole energy may be expended in propulsion alone?" I answer, that in proportion as the balloon principle is added to the flying principle, in the same proportion is size increased without corresponding increase in power; and therefore in the same proportion is increased the resistance of the air to propulsion, and, what is worse, in the same proportion is our machine at the mercy of winds. But it will be objected: "See the fishes, how they swim! They are not at the mercy of currents. They float suspended in the water — they dart forward against currents — they ascend cascades and leap waterfalls; in a word, they are largely independent of water-currents. Now suppose we make a machine exactly the shape of a fish, tail and all; then, by the addition of gas, make it the same specific gravity as the air; then, by machinery, make it wiggle its tail in the manner of a fish. Where is the difference? Why may we not make an aërial swimming-machine, if not a true flying-machine?" Doubtless it is in this direction that we must seek the partial solution of the problem, not indeed of flying, but of aërial navigation. Yet the answer to the extravagant expectations expressed above is plain. The fish — its bones, muscles, viscera, brain — the materials out of which are made machine, fuel, and engineer, are of the same specific gravity as the medium (water) in which it swims. Now, whenever we can find materials out of which to make our machine, fuel, and engineer, which shall have the same specific gravity as the air, then, indeed, we may make a successful swimming-machine which shall be independent of winds. But so long as our materials are six or seven hundred times (wood), or five or six thousand times (iron), as heavy as air, we shall not succeed, because of the enormous dead space filled with gas that we are compelled to use, which adds to the resistance of the air and the power of the winds, without adding anything to the power of propulsion.
Therefore, we repeat, a pure flying-machine is impossible. All that we can expect — all that true scientists do expect — is, by skillful combination of the balloon principle with the true flying principle, to make aërial navigation possible in moderately favorable weather — in other words, to make a locomotive balloon; or, if we choose so to call it, an aërial swimming-machine. That something really useful of this kind will eventually be made, there can be no reasonable doubt.
- Marey has lately ("Nature," vol. xxxvii, p. 369, 1888) shown that there is still another reason for the greater ease of flight after the bird is well on its way. In starting, the wing, except at the very beginning of the stroke, pushes against air which is already in motion in the same direction as the wing itself; but in swift flight the whole stroke is against dead air, for the air beneath the wing is continually renewed by the motion of the bird.