September 13, 1912] 



SCIENCE 



339 



not drive it. The problem of velocity may 

 then be stated as follows : Required a motor 

 which shall be capable of driving itself and 

 accessory parts, including framework and 

 sustaining surface, against its own resistance 

 at high velocity. Undoubtedly the problem so 

 stated is too simplified, but the motor must 

 be capable of developing at least that power. 



The solution of the problem does not lie 

 in the construction of larger motors homo- 

 thetic to those now in use, for the " equiva- 

 lent resisting surface " is increased at the 

 same time that the power is augmented, and if 

 the calculated attainable speed be based on the 

 assumptions of power proportional to weight, 

 weight proportional to cube of linear dimen- 

 sions, and " equivalent resisting surface " 

 proportional to square of linear dimensions, 

 then the power must be increased 512 fold in 

 order to double the speed. In particular, if a 

 motor developing 100 horse power could drive 

 an aeroplane at a speed of 100 kilometers an 

 hour, a homothetic motor developing 800 horse 

 power would, under the conditions stated 

 above, drive its aeroplane at 126 kilometers 

 per hour. 



These assumptions are at the present time 

 well within the range of consideration, and 

 give a general idea of what to expect along 

 the line of motor development. 



The solution of the problem may, however, 

 be in quite another direction : in the construc- 

 tion of steam line body forms for the aero- 

 planes of the future. Stream line forms offer 

 a minimum resistance at high velocities, and 

 their attainment is the immediate problem of 

 the future so far as the development of high 

 speeds is concerned. The architecture of the 

 aeroplane is thus seen to be of paramount im- 

 portance, and it is in that direction that fu- 

 ture advance may be looked for. 



The Problem, of Stability. — More important 

 than the attainment of high velocity is the 

 realization of stability in flight. At the pres- 

 ent time it is to a very large extent dependent 

 on the personal skill of the aviator, and how- 

 ever great this may become, it is highly de- 

 sirable that the aeroplane should be rendered 

 automatically stable in straightaway flight at 



least, if for no other reason than to leave the 

 aviator free to attend to such other matters . 

 as may legitimately engage his attention. 



The distribution of the mass of the aero- 

 plane about its center of gravity is at once 

 felt in the sensitiveness of the response which 

 the machine accords to disturbing forces. If 

 the aeroplane be disturbed by some external 

 force so that the angle of attack becomes a in- 

 stead of i, it will oscillate about its position of 

 equilibrium under the equation; 



(6) 7f = .F^(a-.0-2AFj, 



where I is the moment of inertia about a hori- 

 zontal gravity axis perpendicular to the di- 

 rection of motion, and a- and h are constants. 

 This equation shows at once that if the sus- 

 taining plane pitches slightly, the initial 

 oscillation will be the more violent the smaller 

 the value of I and hence the closer the heavy 

 masses to the center of gravity G. A more 

 complete discussion of equation (6), how- 

 ever, shows that the motion defined by it, 

 under the initial conditions 



dies down the more rapidly the smaller the 

 value of 7, and hence the initial disadvan- 

 tage of violent oscillation is more than com- 

 pensated by the rapidity with which these os- 

 cillations disappear under damping. From 

 the standpoint of stability the best type of 

 machine would seem to be that in which the 

 heavy masses are concentrated in the neigh- 

 borhood of the center of gravity. Such a dis- 

 tribution, however, produces a machine very 

 sensitive to external disturbances and too 

 small a value of I will produce too great an 

 initial value of a, and equation (6) will no 

 longer define the motion. Theoretically, at 

 least, under equation (6) the moment of in- 

 ertia of a given machine might be made so 

 small that the damping would produce 

 a periodic motion, but practically the initial 

 displacement would then be so large for a 

 small force that the orientation would no 

 longer be in the neighborhood of the equilib- 

 rium orientation. It is necessary that some 



