not merely that the velocity will tend to increase in a certain ratio with the length, but that it must do so as an essential and primary condition of the birdãs remaining aloft. It is accordingly of great practical importance in aeronautics, for it shews how a provision of increasing speed must accompany every enlargement of our aeroplanes. If a given machine weighing, say, 500 lbs. be stable at 40 miles an hour, then one geometrically similar which weighs, say, a couple of tons must have its speed determined as follows:
Therefore
But
Therefore
That is to say, the larger machine must be capable of a speed equal to 1ôñ414ã₤ûã₤40, or about 56ô§ miles per hour.
It is highly probable, as Lanchester18 remarks, that Lilienthal met his untimely death not so much from any intrinsic fault in the design or construction of his machine, but simply because his engine fell somewhat short of the power required to give the speed which was necessary for stability. An arrow is a very imperfectly designed aeroplane, but nevertheless it is evidently capable, to a certain extent and at a high velocity, of acquiring ãstabilityã and hence of actual ãflightã: the duration and consequent range of its trajectory, as compared with a bullet of similar initial velocity, being correspondingly benefited. When we return to our birds, and again compare the ostrich with the sparrow, we know little or nothing about the speed in flight of the latter, but that of the swift is estimated19 to vary from a minimum of 20 to 50 feet or more per second,ãsay from 14 to 35 miles per hour. Let us take the same lower limit as not far from the minimal velocity of the sparrowãs flight also; and it {27} would follow that the ostrich, of 25 times the sparrowãs linear dimensions, would be compelled to fly (if it flew at all) with a minimum velocity of 5ã₤ûã₤14, or 70 miles an hour.
The same principle of necessary speed, or