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. R-h	—	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) Derived Parameters Parameter Symbol Units Source Value Main rotor stiffness {dM/dax)M ft lb/rad Calc, Chap 7 200940 Tail rotor lat. flapping К ST rad Calc, based on chap 3 -.0054 Horiz. stab, dynamic pressure ratio Ян/q — Table 8.2 0.6 Horiz. stab, slope of lift curve aH CJ rad Table 8.2 4.0 Horiz. stab, span efficiency factor 5/H — Table 8.2 .02 Horiz. stab, zero lift drag coefficient Cd°h — Table 8.2 .0064 Horiz. stab, rotor induced velocity ratio vh/v 1 — Table 8.2 1.5 Horiz. stab, fuselage induced velocity constant eF V=oH rad Figure 8.12 .024 Horiz. stab, fuselage induced velocity slope (deF/daF)H — Figure 8.15 .23 Vert. stab, rotor induced velocity ratio vv/vx — Figure 8.11 1.5 Vert. stab, fuselage induced velocity constant 05 # ll о rad Figure 8.12 .024 Vert. stab, fuselage induced velocity slope (dEF/da. p)v — – Figure 8.15 .23 Vert. stab, sidewash angle from main rotor rad Table 8.3 -.052 Vert. stab, sidewash angle from tail rotor “Пту rad Calc. .045 Fuselage lift constant (L/qaF=0)F ft2 Appendix A -1.5 Fuselage lift slope (dL,/q/daF)F ft2/rad Appendix A 75 Fuselage pitching moment constant W$Vo)f ft5 Appendix A -160 Fuselage pitching moment slope (dM/q/daF)F ft У rad Appendix A 1780 Fuselage side force slope (dS. f./i/Щр ft2/rad Appendix A -220 Fuselage rolling moment slope (JR./q/Jp)F ft3/rad Appendix A 230 Fuselage yawing moment slope (dN/q/d$- ft У rad Appendix A -820

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°.