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°.

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