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(f = 0.01) requires a change of cyclic pitch of –2.3° in hovering flight, and since the
H-force term is always small, this change of cyclic pitch is roughly constant over
the entire speed range, as can be seen in Fig. 4.5.
With a flapping hinge offset of 31.5 cm (e = 0.04), the cyclic pitch change for the
same c.g. shift is much smaller since the control moment, as we have seen earlier, is
more than doubled by the addition of the offset hinge moment so that a given external
moment requires a correspondingly smaller amount of cyclic pitch movement to
maintain trim, resulting in a lessened fuselage attitude, Fig. 4.6. Expressed in another
way, and as clearly illustrated in Fig. 4.5, the existence of a hub couple, such as
would be obtained from offset hinges or hingeless blades, allows a much larger c.g.
travel for a given cyclic pitch range. The amount of cyclic pitch available is usually
limited by the rotor tilt allowed by the helicopter geometry, and early helicopters,
which had little or no flapping hinge offset, had only a small c.g. travel. For this
reason the fuselages of these helicopters tended to be rather wide, since the load
carried had to be confined within limited longitudinal dimensions. The larger c.g.
range of more recent helicopters with comparatively large hinge offsets, or with
hingeless blades, allows a more slender fuselage design.
Since wind-tunnel measurements of rotor forces and flapping motion generally
show good agreement with theoretical values, any discrepancy between measured
and theoretical values of the longitudinal cyclic pitch to trim is usually attributed to
incorrect estimates of the fuselage pitching moment, since this is the only moment
contribution which is likely to be seriously in error. An example of theoretical and
flight test values of the longitudinal cyclic pitch angle to trim for the Sikorsky S–51
is shown in Fig. 4.7.
0 0.1 0.2 0.3
–2°
–4°
–6°
–8°
–10°
–12°
–14°
–16°
Fuselage attitude, θ
f = 0
f = 0.01
f = 0.02
e = 0
e = 0.04
μ
Fig. 4.6 Fuselage angle in trimmed flight
Trim and performance in axial and forward flight 123
4.2.2 Effect of tailplane on trim
Let us suppose that the pitching moment of the tailplane can be calculated in isolation
from the fuselage on which it is mounted. The fuselage datum line for referring
angles is a line perpendicular to the rotor hub axis. If the no-lift line of the tailplane
makes an angle αT0 to the datum line it can be seen from Fig. 4.8 that the tailplane
incidence αT is given by
αT = αD + B1 – a1 + αT0 – ε = θ – τc + αT0 – ε
where ε is the downwash angle at the tailplane relative to the undisturbed flow.
If ST is the tailplane area, aT is the lift slope and lTR is the tail arm, the pitching
moment MT is
MT VS l Ra B a
12
2
= – T T T(D – 1 + 1 + T – ) 0 ρ α α ε
If this moment can be added independently to the basic fuselage pitching moment
Mf, the equation for the longitudinal cyclic pitch to trim, eqn 4.13, can be modified
to become
B a
M H hR WfR M
1 1 WhR M
f D T
s
= +
+ – +
+
= +
+ – – ( + – + – )
1 +
c c
12
2
T T D 1 1 T
c
f D 0
s
a
C h h wf Va B a
w h C
m
m
μ α α ε
8°
6°
4°
2°
0
–2°
–4°
0.1 0.2 μ 0.3
c.g. 3.0 cm forward of shaft
c.g. 7.4 cm forward of shaft
c.g. 12.7 cm forward of shaft
Theory (no fuselage moment)
B1
Fig. 4.7 Measured longitudinal control to trim; Sikorsky S–51, level flight 172 rev/min
V
a1 – B1
Vertical
τc ε
Rotor
hub axis
αD
θ
αT0
Fig. 4.8 Determination of tailplane incidence
124 Bramwell’s Helicopter Dynamics
where VT = STlT/sA is the tail volume ratio.
This equation can be arranged to give
B a
C h h wf Va
k w h C
m
1 1
c c
12
2
T T D T
T c m
= +
+ – – ( + – )
( + ).
f D 0
s
μ α α ε
(4.15)
where kT Va w h Cm
12
2
= 1 + T T/( c + ). s μ The equation may be compared with eqn
4.14 for the no-tailplane case.
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