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Rotor 95
(all equal to 1 for μz =0). Hence
for tip-path plane command; or
(θ0.75)n+1 =(θ0.75)n − f
e0
θc θc
= −
θs θs
f
eθ
n+1
(θ0.75)n+1 =(θ0.75)n − f
βc
βc
= +
βs
n+1
βs
n
n
Et
e0
f
e2 β + n2
Et
Ec
Es
n −eβ
n
eβ
Ec
for no-feathering plane command. Alternatively, the derivative matrix dE/dv can be obtained by numerical
perturbation. Convergence of the Newton–Raphson iteration is tested in terms of |E| 1). For a ducted fan, fD = fW /2 is
introduced. The induced power at zero thrust is zero in this model (or accounted for as a profile power
increment). If κ is deduced from an independent calculation of induced power, nonzero Pi at low thrust
will be reflected in large κ values.
The profile power is calculated from a mean blade drag coefficient: Po = ρA(ΩR) 3 CPo, CPo =
(σ/8)cdmeanFP . The function FP (μ, μz) accounts for the increase of the blade section velocity with rotor
edgewise and axial speed: CPo = 1
2 σcdU 3 dr = 1
2 σcd(u 2 T + u2 R + u2 P )3/2 dr; so (from Harris)
FP =4 1
2π
2π 1
0
∼= 1+V 2
0
Es
2 2 2 3/2
(r + μ sin ψ) +(μcos ψ) + μz dr dψ
1+ 5
2 V 2 + 3
8 μ2 4+7V 2 +4V 4
(1 + V 2 ) 2
3
+
2 μ4z + 3
2 μ2zμ 2 + 9
16 μ4
9 μ
−
16
4
1+V 2
√
1+V 2 +1
ln
V
with V 2 = μ 2 + μ 2 z. This expression is exact when μ =0, and fP ∼ 4V 3 for large V .
Two performance methods are implemented, the energy method and the table method. The induced
power factor and mean blade drag coefficient are obtained from equations with the energy method, or
from tables with the table method. Optionally κ and cdmean can be specified for each flight state,
superseding the values from the performance method.