# 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)

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°.