THE FLYING-MACHINE PROBLEM.
Editor Popular Science Monthly:
SIR: To the greater part of Prof. Le Conte's article, "The Problem of a Flying-Machine," in the November number of "The Popular Science Monthly," I give hearty assent, and yet I can not admit that his premises warrant his very discouraging conclusions. lie shows clearly that as the animal, flying or walking, increases in size, the ratio between power and weight grows smaller, until finally the limit of muscular strength is reached; or the "weight over-takes the utmost strength of bones to support or muscles to move." He shows that, among mammals, this limit was probably reached in the gigantic dinosaurs; and that the largest flying-birds, such as the turkey-cock and condor, are "evidently near the limit," and that the ostrich and emu have passed it, and hence arc unable to fly.
He then speaks of the wonderful efficiency of the animal machine as a means for turning heat into work. "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. . . . 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. . . . The smallest possible weight of a flying-machine with necessary fuel and engineer even without freight or passengers, could not be less than three or four hundred pounds"; and hence Prof. Le Conte concludes that "since the animal machine is far more effective than any we may hope to make, therefore the limit of weight of a successful flying-machine can not be more than fifty pounds," and that a "true flying-machine, self-raising, self-sustaining, self-propelling, is physically impossible."
Can this be so? Is the animal machine more effective than any we can hope to make? Will it necessarily "do more work with the same weight of machinery and fuel"? Does the limit of weight in a flying animal mark the limit for a flying-machine? At the risk of not being considered "a true scientist" I must decidedly dissent from these views; I can not look upon machine-flight as a real impossibility, similar to the production of perpetual motion or of a self-supporting arch of indefinite length.
Before making a comparison between the power of birds and motors, we must get some idea of the power exerted by the former. How much work must a bird of given weight actually do in order to raise himself from the ground and fly? It is well known that, once in the air, the power required is very much less than that necessary for rising. How much less is uncertain, but in a brisk wind an eagle, or condor, or albatross will circle around for hours, hardly ever flapping his wings, and seemingly the only work is that due to muscular effort in keeping the wings outstretched. The work done in getting up is, then, the greatest the bird or machine would be called upon to do. This work will evidently depend upon the ratio of the wing-surface to the weight; with wings only a square foot in area, the most powerful condor could not fly; and the greater the wing-surface, provided the muscles are strong enough to manage it, the less the power required.
This ratio has been measured on many birds. The vulture, for example, can spread 0·82 of a square foot for each pound of weight, and, assuming the entire weight to be thirty pounds, the total wing-surface would be 24·6 square feet.
We now have a ready means for calculating approximately the maximum power such a bird must be able to exert. In order to rise vertically, he must force the air down-ward until the reaction is equal to his weight. Calling v the velocity of the air in feet per second, R the reaction in pounds, w the weight of a cubic foot of air, A the area of wing-surface in square feet, and g the acceleration due to gravity, we may make use of the well-known formula for reaction:
or from which substituting values, we find the necessary velocity to be about twenty-three feet per second. The work done in giving the air this velocity would equal , or three hundred and forty-five foot-pounds per second, equivalent to about six tenths of a horse-power. It is here assumed that the air is driven downward in parallel streams; but a bird's wing would naturally send off a part in other directions, and consequently the power necessary would be somewhat greater. Allowing twenty-five per cent for this and other losses, we see that a vulture weighing thirty pounds would not need to exert more than three quarters of a horse-power, and this only for a few moments while rising.
Suppose, now, our flying-machine to weigh six hundred pounds, or twenty times
