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Rotor 103
The wake is a skewed cylinder, starting at the rotor disk and with the axis oriented by eP w. The
interference velocity is required at the position zF B on a component. Whether this point is inside or
outside the wake cylinder is determined by finding its distance from the wake axis, in a plane parallel to
the rotor disk. The position relative to the rotor hub is ξP B = CPF (zF B − zF hub ); the corresponding point on
the wake axis is ξP A = ePwζw. Requiring ξP B and ξP A have the same z value in the tip-path plane axes gives
ζw = (kP ) T C PF (z F B − zF hub )
(k P ) T e P w
from which fz, fw, fa, and Rc are evaluated. The distance r from the wake axis is then
r 2 = (i P ) T (ξ P B − ξ P A) 2 + (j P ) T (ξ P B − ξ P A) 2
The transition from full velocity inside the wake to zero velocity outside the wake is accomplished in
the distance sRc, using
fr =
⎧
⎨ 1 r ≤ Rc
1 − (r − Rc)/(sRc)
⎩
0 r ≥ (1 + s)Rc
(s =0for an abrupt transition, s large for always in wake).
The interference velocity at the component (at z F B ) is calculated from the induced velocity vF ind ,
the factors fW fz accounting for axial development of the wake velocity, the factor fr accounting for
immersion in the wake, and an input empirical factor Kint:
v F int = Kint fW fzfrft v F ind
An additional factor ft for twin rotors is included. Optionally the development along the wake axis
can be a step function (fW fz =0, 1, fW above the rotor, on the rotor disk, and below the rotor disk,
respectively); nominal (t =1); or use an input rate parameter t. Optionally the wake immersion can use
the contracted radius Rc or the uncontracted radius R; can be a step function (s =0,sofr =1and 0
inside and outside the wake boundary); can be always immersed (s = ∞ so fr =1always); or can use
an input transition distance s. Optionally the interference factor Kint can be reduced from an input value
at low speed to zero at high speed, with linear variation over a specified speed range.
To account for the extent of the wing or tail area immersed in the rotor wake, the interference
velocity can be calculated at several of points along the span and averaged. The increment in position
is Δz F B = CFB (0 Δy 0) T ; where Δy =(b/2)(−1+(2i − 1)/N ) for i =1to N, and b is the wing span.
For twin main rotors (tandem, side-by-side, or coaxial), the performance may be calculated for
the rotor system, but the interference velocity is still calculated separately for each rotor, based on
its disk loading. At the component, the velocities from all rotors are summed, and the total used to
calculate the angle-of-attack and dynamic pressure. This sum must give the interference velocity of
the twin-rotor system, which requires the correction factor ft. Consider differential momentum theory
to estimate the induced velocity of twin rotors in hover. For the first rotor, the thrust and area in the
non-overlap region are (1 − m)T1 and (1 − m)A, hence the induced velocity is v1 = κ T1/2ρA; similarly
v2 = κ T2/2ρA. In the overlap region the thrust and area are mT1 + mT2 and mA, hence the induced
velocity is vm = κ (T1 + T2)/2ρA. So for equal thrust, the velocity in the overlap region (everywhere
for the coaxial configuration) is √ 2 larger. The factor KT is introduced to adjust the overlap velocity: