Approximate Method
The foregoing method is rigorous in accounting for the contributions of every aircraft component to the equations of equilibrium. A study of the numerical values in the example shows, however, that only a few terms dominate; the others have little effect on the final solutions. This observation leads to an approximate method involving solving the moment equation using only initial trim values to give the approximate value of the longitudinal flapping:
TABLE 8.5
Elements of the Longitudinal Equilibrium Equations for the Example Helicopter at 115 Knots
Unknown 
Symbol 
Units 
Condition 
Symbol 
Units 
Value 
Rotor thrust 
Tm 
lb 
Gross weight 
G. W. 
lb 
20,000 
Longitudinal flapping 
ai SM 
rad 
Climb angle 
Ус 
rad 
0 
Fuselage attitude 
© 
rad 
Dynamic pressure 
Я 
lb/ft2 
45 
Unknowns 
Flight Conditions 
Physical Dimensions (See Appendix A)
Initial Trim Forces (From Chap 3)
Dimension
Main rotor disc area Main rotor shaft incidence Main rotor long, offset Main rotor vert, offset Tail rotor long, offset Tail rotor vert, offset Horiz. stab, area Horiz. stab, aspect ratio Horiz. stab, incidence Horiz. stab, angle of zero lift Horiz. stab. long, offset Horiz. stab. vert, offset Vert. stab. long, offset Vert. stab. vert, offset Fuselage long, offset Fuselage vert, offset
Symbol 
Units 
Value 
sq ft 
2827 

?M 
rad 
0 
ft 
.5 

к>м 
ft 
7.5 
h 
ft 
37 
hr 
ft 
6 
A„ 
sq ft 
18 
A. Rh 
— 
4.5 
>H 
rad 
.052 
aLOH 
rad 
0 
ІН 
ft 
33 
hH 
ft 
1.5 
ly 
ft 
35 
hv 
ft 
3 
h 
ft 
.5 
bF 
ft 
.5 
TABLE 8.5 (continued)

The numerical values called for in this equation were all given in Table 8.5. The result is:
ax = .019 rad = — 1.Г
This is exactly the same as the —1.1° calculated by the more rigorous method. The pitch attitude, 0, can also be approximated since:
/ Д» ^ =0 + Ar + Af + Dy + ДЛ
aTpp = 0 + <*■+/* = – —————– =—– z——–
V G. W. – L„ — Lf )
For the example calculation:
%ax = —.038 rad = —2.2*
and thus
© = 2.2 + 1.1 =1.1° which compares to the more exact value of —0.9°.
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