Download - NASA

84 Rotor
The force includes a term proportional to the rotor thrust and an input blockage factor fB =ΔT/T ≥ 0.
This term accounts for blockage or download, as an alternative to including the drag of the fuselage
or a lifting surface in the aircraft trim. For example, fB can model the tail-rotor blockage caused by
operation near the vertical tail. The rotor loads in aircraft axes acting at the center of gravity are then:
where Δz F = z F hub − zF cg.
F F = C FS F S
M F = C FS M S + Δz F F F
The wind axis lift L and drag X are calculated from the net rotor-hub force F F and the rotor velocity
v F . The velocity relative to the air gives the propulsive-force direction ep = v F /|v F | (no interference)
and the velocity magnitude V = |v F |. The drag and lift components of the force are X = −e T p F F and
L = |(I −epe T p )F F |, respectively. Thus XV = −(v F ) T F F and L 2 = |F F | 2 −|X| 2 . The rotor contribution
to vertical force is the z-axis component of the force in inertial axes, FV = −k T C IF F F .
11–4 Aerodynamics
The rotor velocity relative to the air is vF = vF AC + ωF ACΔzF in aircraft axes. The velocities in shaft
axes are
v S = C SF v F ⎛
=ΩR⎝
−μx
⎞
rμy ⎠
μz
ω S = C SF ω F ⎛ ⎞
r ˙αx
AC =Ω⎝
˙αy ⎠
r ˙αz
where ΩR is the rotor tip speed. The advance ratio μ, inflowratio λ, and shaft angle-of-attack α are
defined as
μ =
μ 2 x + μ 2 y
λ = λi + μz
α = tan −1 (μz/μ)
The blade velocity relative to the air has the maximum amplitude (advancing tip velocity) of μat =
(1 + μ) 2 + μ 2 z, from which the advancing tip Mach number is Mat = Mtipμat, using the tip Mach
number Mtip =(ΩR)/cs. The rotor thrust coefficient is defined as CT = T/ρA(ΩR) 2 . The dimensionless
ideal induced velocity λi is calculated from μ, μz, and CT ; then the dimensional velocity is vi =ΩRλi.
The ideal induced power is then Pideal = Tvi. Note that for these inflow velocities, the subscript “i”
denotes “ideal.” The ideal induced velocity could be solved based on the reference velocity vh rather
than the tip speed ΩR, but the advance ratio is required for other purposes as well.
11-4.1 Ideal Inflow
The ideal wake-induced velocity is obtained from the momentum theory result of Glauert:
λi =
CT
2 λ2 sλ
=
+ μ2 2 h
λ2 + μ2 where λ = λi + μz, λ 2 h = |CT |/2 (λh is always positive) and s = sign CT . This expression is generalized
to
λi = λh sF(μ/λh,sμz/λh)