284 



SCIENCE 



[N. S. Vol. XXIX. No. 738 



center of mass. To illustrate, a good ex- 

 ample of dynamic balance is found in a 

 submarine torpedo, or a fish. 



Stability.— The foregoing adjustments 

 still allow the center of mass to be placed 

 below the center of buoyancy. This is a 

 provision that is important in aeronautics 

 as well as in marine architecture ; indeed, it 

 is the only practical provision for keeping 

 an even keel and preventing heeling when 

 the ship is at rest, or simply drifting with 

 the wind. If the center of gravity be well 

 below the center of buoyancy, the vessel is 

 proportionately stable, but, of course, the 

 stability is pendular, and may admit of 

 considerable roUing and pitching due to 

 shifting loads, sudden gusts of wind, etc., 

 unless special devices be used to dampen 

 or prevent these effects. 



Natural Period and Oscillations. — It may 

 happen also that the equilibrium of the 

 ship is disturbed by periodic forces whose 

 periods are simply related to the natural 

 period of the ship itself. In this case the 

 oscillations will be cumulative and may 

 become very large. Such effects are well 

 known to marine engineers, and may be 

 treated as in ordinary ship design. 



n. AVIATION 



This division comprises all those forms 

 of heavier-than-air flying-machines which 

 depend for their support upon the dynamic 

 reaction of the atmosphere. There are sev- 

 eral subdivisions of this class dependent 

 upon the particular principle of operation. 

 Among these may be mentioned the aero- 

 plane, orthopter, helicopter, etc. The only 

 one of these that has been sufficiently devel- 

 oped at present to carry a man in practical 

 flight is the aeroplane. There have been a 

 large number of types of aeroplanes tested 

 with more or less success and of these the 

 following are selected for illustration. 



The design of an aeroplane may be con- 

 sidered under the heads of support, resist- 



ance and propulsion, stability and control. 

 Support.— In this class of flying-ma- 

 chines, since the buoyancy is practically 

 insignificant, support must be obtained 

 from the dynamic reaction of the atmos- 

 phere itself. In its simplest form, an 

 aeroplane may be considered as a single 

 plane surface moving through the air. 

 The law of pressure on such a surface has 

 been determined and may be expressed as 

 follows : 



P = 2k<TAV' sin a, 



in which P is the normal pressure upon the 

 plane, fc is a constant of figure, <t the density 

 of the air, A is the area of the plane, V the 

 relative velocity of translation of the plane 

 through the air, and a the angle of flight. 



This is the form taken by Duchemin's 

 formula for small angles of flight such as 

 are usually employed in practise. The 

 equation shows that the upward pressure 

 on the plane varies directly with the area 

 of the plane, with the sine of the angle of 

 flight, with the density of the air, and also 

 with the square of the velocity of trans- 

 lation. 



It is evident that the total upward pres- 

 sure developed must be at least equal to the 

 weight of the plane and its load, in order 

 to support the system. If P is greater than 

 the weight the machine will ascend, if less, 

 it will descend. 



The constant k depends only upon the 

 shape and aspect of the plane, and should 

 be determined by experiment. For ex- 

 ample, with a plane 1 foot square ](cr = 

 0.00167, as determined by Langley, when 

 P is expressed in pounds per square foot, 

 and V in feet per second. 



The first equation may be written 



AV' — P/2k(7 sin a. 



If P and a are kept constant then the 

 equation has the form 



Ar- = constant. 



