c. Figure 21 shows case No. 3. Figures showing the other cases would be quite similar. Referring to figure 21, the following forces, lever arms, and moments, all general to cases Nos. 1 to 6, inclusive, are noted: 

(1) Forces: 

(a) L$_{9 }$ = Lifting force of gas. 

(b) W = Total weight. 

(c) Fe=Resultant air force on hull. 

(d) Le= Vertical component of dynamic force on hull. 

(e) Re=H orizontal component of dynamic force on hull. 

(/ ) F a=Resultant force on tail surfaces. 

(g) L$_{8}$ = Li£t of tail surfaces. 

(h.) R a=Drag of tail surfaces. 

( i) T =Thrust of propellers. 

(j) t = Horizontal component of propeller thrust. 

(k) Lt=Vertical component of propeller thrust. 

(2) Lever mms about G.-Lever arm of- 

(a) W =k sin (a–8). 

(b) L$_{9}$= o. 

(c) T = (c+h). 

(d) F$_{8}$ =a (assuming F, perpendicular to the surfaces). 

(e) L$_{8}$ =a cos (a –8). 

{f) Rs=a sin (a– 8). 

(g) Fe varies with the position of P, which in turn depends on the angle 8. 

(h) L e=b COS (a–8). 

(3) Moments about G.-Moment of- 

(a) Weight. Defined as static righting moment. It is present irrespective of speed and at all times equals W h sin (a– 8). 

(b) P ropeller thrust, T ( c +h). 

(c) F 6 • D ue to increased pressure below the hull, Fe tends to rotate entire airship in a positive direction about M. This is assisted by reduced pressure beneath the tail (see fig. 17). The force below nose and tail are opposite in direction. T heir difference, since the nose force is slightly the greater, is called dynamic lift of hull. However, both forces cause rotation in the same direction, and their moment is referred to as dynamic upsetting moment, Me. I t will be evaluated later. 

NOTE.-Tbe force beneath the tail has been omitted from the figure in order to avoid confusion in the drawing, the entire upsetting moment being treated as though it were caused by the increased pressure under the nose. 

