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a
a
1
0 D 1
2 =
2 (4 /3 + – )
1 – /2
μ θ λμ
μ
remembering that this is still with reference to the plane of no-feathering. On solving
for a1 we get
a1
0 D
2 =
2 (4 /3 + )
1 + 3 /2
μ θ λ
μ
(3.60)
The coning angle a0 becomes
a0 0 a
2
= D 1
8
(1 + ) +
4
3
–
4
3
γθ μ λ μ 
 
 
and on substituting eqn 3.60 we have
a0 0
2 4
2 D
2
2 =
8
– 19 /18 + 3 /2
1 + 3 /
+ 4
3
– /2
+ 3 /2
γ θ μ μ
μ
λ μ
μ
1
2
1
1

   
(3.61)
The lateral flapping coefficient b1 remains unaltered:
b
a
1
0
1/2
i
2 =
4( + 1.1 )/3
1 + /2
μ ν λ
μ
(3.57)
Rotor aerodynamics and dynamics in forward flight 109
The thrust coefficient can be written
tc tc a 0 a
2
D D 1 = =
4
2
3
(1 + 3 /2) + – θ μ λ μ 
 
 
(3.62)
and on substituting for a1 we have
t a
c 0
2 4
2 D
2
D 2 =
4
2
3
– + 9 /4
1 + 3 /2
+
– /2
+ 3 /2
θ μ μ
μ
λ μ
μ
1 1
1

 

 
(3.63)
The H-force coefficient takes the simple form
h
a
c a
1
4
D 12
D 1 0 = +
4
μδ λ [ – μθ ] (3.64)
which can also be written as
h
a
c
1
4
D 0
2
2
D
D 2 = +
4
( /3)(1 – 9 )
1 + 3 /2
+
1 + 3 /2
μδ μ λ θ μ
μ
λ
μ
 /2
 

 
(3.65)
Finally, the torque coefficient can easily be seen to have the same form as
eqn 3.43, that is
qc t h
2
= (1 + 3 )/8 – D c – c D D δ μ λ μ (3.66)
On considering the resultant blade flow velocity and induced power coefficient we
also have the same result as eqn 3.44, i.e.
qc t h k t
2
= (1 + 4.7 )/8 – D c – c + i c D D δ μ λ μ λ (3.67)
3.14 Comparison with experiment
In order to arrive at fairly simple formulae for the force and flapping coefficients, a
number of simplifying assumptions were made in the analysis and it is important to
test the accuracy of the results by comparisons with experimental data. Squire et al.18
have conducted wind tunnel tests on a 3.65 m diameter rotor and compared the
results with theoretical values. Generally speaking, the agreement was found to be
good. Since the ranges of parameters in Squire’s tests were arbitrary, many of the
combinations were outside the range of normal helicopter operations. Much more
recently, Harris19 has conducted tests on a 1.53 m diameter rotor which contains a
large number of cases in which the collective pitch was adjusted so that the thrust
coefficient was kept constant at a value typical of steady flight. Thus, the variation of
μ in the tests corresponded to a helicopter changing its forward speed under conditions
of trim. Harris also measured the coning angle and other quantities not considered in
Squire’s tests.
The force and flapping coefficients contain two quantities, namely, the blade lift
110 Bramwell’s Helicopter Dynamics
slope a and the drag coefficient δ, which are not known for a particular rotor although,
of course, in the absence of data, reasonable assumptions can be made. In the tests
described by Harris, the thrust and torque were measured over a range of collective
pitch angles at a nominal tip speed ratio of 0.08. Now we saw earlier in this chapter
that the mean induced velocity can be found from
vi0 = T/2ρAV
which can be expressed as
λi
= stc/2μ
provided V > 1, or as μ > λ
i, hov. This inequality is satisfied for the tests made at
μ = 0.08 referred to above.
The thrust coefficient can be written from eqn 3.33 as
t a st
c 0
2
nf
　
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本文鏈接地址：Bramwell’s Helicopter Dynamics(58)