NO. 3 LANCI.KY MEMOIR ON MECHANICAL FLIGHT 47 



The center of pressure on each wing with a horizontal motion of 2000 feet 

 per minute, is two-fifths of the distance from front to rear. Where there are 

 two pair of wings of equal size, one following the oilier, and placed at such a 

 distance apart and witli such a relation to the propellers as here used, the fol- 

 lowing wing is assumed to have two-thirds of the efficiency of the leader per unit 

 of surface. If it is half the size of the leader, the efficiency is assumed to be one- 

 half per unit of surface. If it is half as large again as the leader, its efficiency 

 is assumed to be eight-tenths per unit of surface. For intermediate sizes of fol- 

 lowing wing, intermediate values of the efficiency may be assumed. 



These rules are purely empirical and only approximate. As approxima- 

 tions, they are useful in giving a preliminary balance, but the exact position of 

 the center of pressure is rarely determinable in either the horizontal or vertical 

 plane, except by experiment in actual flight. The position of the center of grav- 

 ity is found with all needed precision by suspending the aerodrome by a plumb- 

 line in two positions, and noting the point of intersection of the traces of the 

 line, and this method is so superior to that by calculation, that it will probably 

 continue in use even for much larger constructions than the present. 



The principal factor in the adjustment is the position of the wings with ref- 

 erence to the center of gravity, but the aerodrome is moved forward by the thrust 

 of its propellers, and we must next recall the fact of experiment that as it is for 

 constructional reasons difficult to bring the thrust line in the plane of the cen- 

 ter of pressure of the wings, it is in practice sufficiently below them to tend to tip 

 the front of the aerodrome upward, so that it may be that equilibrium will be 

 attained only when C'P, is not over CG X . 



In the discussion' of the equilibrium, then, we must consider also the effect 

 of thrust, and usually assume that this thrust-line is at some appreciable distance 

 below the center of pressure. 



We may conveniently consider two cases: 



1. That the center of pressure is not directly over the center of gravity ; that 

 is, CG t - CPi = a, and estimate what the value of a should be in order that, dur- 

 ing horizontal flight, the aerodrome itself shall be horizontal ; or, 



'According to Wellner (" Zeitsehrift fur Luftsehiffahrt," Beilage, 1S9:1), in a curved surface 

 with 1/12 rise, if the angle of inclination of the chord of the surface be a, and the angle between 

 the direction of resultant air pressure and the normal to the direction of motion be ji, then/?<x and 

 the soaring speed is 



V= /I 1 



\ K x F(o)X cos/? 

 while the efficiency is 



W _ We ight _ 

 E ~ Resistance ~ 

 The following values were derived from experiments in the wind: 



<x=— 3° 0° +3° 6° 9° 12" 



F(a)= 0.20 0.8d 0.75 0.90 1.00 1.05 



Tan ; )= 0.01 0.02 0.03 0.04 0.10 0.17 



so that according to him. a curved surface shows finite soaring speeds when the angle of inclination 

 is 0° or even slightly negative. 



