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for illustration, that the tailrotor thrust is the only agency balancing the main rotor
torque. The calculation of the rotor torque is discussed in the next section.
If the solidity, rotor area, and tip speed of the tailrotor are denoted by st, At and
(ΩR)t respectively, the corresponding thrust coefficient is defined by
tc Tt stAt Rt
2
t = /ρ (Ω )
Let us suppose that the tailrotor axis is perpendicular to the flight direction, i.e. the
incidence of the no-feathering axis of the tailrotor is zero. The only contribution to
the inflow ratio λ
t is the induced velocity ratio λit, which can be calculated from
4°
3°
2°
1°
0
–1°
–2°
–3°
0.1 0.2 0.3
–A1
b1
μ
φ
Fig. 4.12 Lateral control angles to trim
Trim and performance in axial and forward flight 127
λ it = ( t c /2), t √ s t in hovering flight
and λit = t c /2μt , t s t for μ
t > 0.05
Usually, the tip speeds of the main rotor and the tailrotor are the same, i.e. μ
t can
be taken as μ.
To calculate the collective pitch we can use eqn 3.33, where tc is referred to the nofeathering
axis, and obtain
θ
μ
0t = 3 2 c λ it
2(1 + 3 /2)
4
– a t
t 


(4.18)
Taking st = 0.1, Rt = 1.4 m, (ΩR)t = ΩR = 208 m/s, the tailrotor collective-pitch
angle to trim has been calculated and is shown in Fig. 4.13. The high values at
hovering and low speed are partly due to the high solidities typical of tailrotors
resulting in somewhat higher induced velocities than the main rotor.
4.3 Helicopter performance in forward flight
It is now possible to estimate the performance of the helicopter in forward flight, this
being the performance at a specific flight condition, or point on the flight envelope.
This should not be confused with the mission performance, which is aimed at assessing
the overall ability of the helicopter to complete a particular operational mission that
consists of a series of inter-related tasks.
The trim calculations of the previous sections give all the information needed for
calculating the power required for a given flight condition; in fact, using eqn 3.66,
the torque and power were calculated from the values of θ0 and λ was obtained from
the trim equations. For the performance alone, however, calculation of the trim
parameters is not necessary. A form of the torque equation for performance calculations
more convenient than eqn 3.66 can be obtained by considering the balance of forces
along the flight path in conjunction with eqn 3.66.
Referring to Fig. 4.1, we see that
TD sin αD + HD cos αD + W sin τc + D = 0
20°
16°
12°
8°
4°
0
0.1 0.2 0.3
θ0t
μ
Fig. 4.13 Tailrotor pitch angle to trim
128 Bramwell’s Helicopter Dynamics
Multiplying by ˆV V R = /Ω and remembering that ˆV sin αD = λD + λi gives
(λD + λi)TD + μHD + WVˆ sin τc+ DVˆ = 0
which can be written in non-dimensional form as
λD c μc λi c c τc
12
3
D D D 0 t + h = –( t + wVˆ sin + Vˆd)
Substituting for λD cD μcD t + h in eqn 3.66 gives
qc t w V V d
2
i c c c
12
3
= (1 + 3 )/8 + + sin + 0 D δ μ λ ˆ τ ˆ (4.19)
This expression for the torque coefficient can be regarded as the non-dimensional
form of an energy equation; the first term represents the power required to overcome
the profile drag of the blades, the second represents the induced power, the third
is the power required for climbing, and the last term is the power required to
overcome the fuselage drag. Of course, eqn 4.19 could have been derived from
energy considerations directly, but it is instructive to derive it from the balance of
forces.
Equation 4.19 has been derived from eqn 3.66 on the assumption that the induced
velocity was constant. Since the induced power in eqn 4.19 appears as a separate
term, it is a simple matter to include the effect of non-uniform induced velocity, as
mentioned in the previous chapter. Now, as we saw in Chapter 3, the induced power
can be expressed as (1 + k)Pi0, where Pi0 is the ‘ideal’ induced power for a constant
induced velocity distribution defined by vi0T and which, in non-dimensional form, is
represented by the second term of eqn 4.19. Values of k for the Mangler and Squire
　
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