420 Prof. M. F. FitzGerald. 



"On Flapping Flight of Aeroplanes." By MAURICE F. FITZ- 

 GERALD, Professor of Engineering, Queen's College, Belfast. 

 Communicated by Professor G. F. FITZGERALD, F.T.C.D., 

 F.RS. Eeceived February lo, Bead March 2, 1899. 



It has been long known, principally through experiments on soaring, 

 that a large, if not by far the largest, part of the supporting force obtained 

 by birds in regular flight, is probably furnished by upward air pressure 

 on their wings, regarded as planes moving horizontally, with their 

 surfaces slightly inclined to the direction of motion. 



Langley's " Experiments on Aero-dynamics" furnish some numerical 

 data for estimating the power required to sustain an aeroplane of 

 given weight, propelled horizontally by a known force, and he applies 

 these to the determination of the problem whether this could be 

 effected by screw propellers, analogous to those of a ship, actuated by 

 machinery of existing type. 



The older mathematical investigation by Navier of the problem of 

 flapping flight, seems to be quite discredited, and, indeed, the results 

 brought out always laboured under the physiological difficulty of 

 demanding an amount of horse power per pound of muscle in birds 

 which surpassed, to an almost incredible extent, that available from the 

 better known muscular tissues of other animals. One horse power is 

 550 ft.-lbs. per second ; a horse can ordinarily exert about two-thirds 

 of this, and if we take him to weigh about 10 cwt., we get about a 

 third of a ft.-lb. per second per pound of horse. A man can work at 

 the rate of about 50 ft.-lbs. per second ; this, again, is about a third of 

 a ft.-lb. per second per pound of man ; and so on with other animals. 

 But, for the flight of birds, it was made out that from about 30 to 

 1300 ft.-lbs. per second per pound of bird were necessary, which, even 

 after all allowance for higher temperature of their bodies, and large 

 relative mass of wing muscles, compared with those of the limb? of 

 horses, men, &c., seemed highly improbable. 



In the following paper an attempt is made to indicate how both 

 progressive and hovering flight may be effected by aeroplanes, attached 

 to a heavy mass, and flapped after the manner of wings, under con- 

 ditions sufficiently nearly approaching those of Langley's experiments 

 to justify the inference, from his figures, of numerical results, not 

 indeed presumably exact, but sufficiently indicating the order of magni- 

 tude of the quantities involved. The figures given may be taken, 

 commercially speaking, as near enough to the truth to enable us to 

 judge whether we are dealing with pounds or with pence, though not 

 exact enough to adjust the change out of half -a-cr own in paying for 

 our power. 



Let, then, a heavy mass be supposed to be flying through the air 



