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Rotor 87
The velocity ratio is fW =(fW λi)/λi, and
fT = μz + fW λi/2
fVzμz + λi
is the thrust ratio. However, physical problems and convergence difficulties are encountered with this
approach in descent, if an arbitrary value of fT is permitted. From the expression for fT , fT should
approach 1/fVz at high rates of climb or descent. To avoid problems with an arbitrary value of fT ,itis
assumed that the input value of fT defines the velocity ratio fW =2fT in descent. So in descent μz is
not replaced by μz/fT .
11-4.1.2 Ground Effect
The wake-induced velocity is reduced when the rotor disk is in the proximity of the ground plane.
Ground effect in hover can be described in terms of the figure of merit M =(T3/2 / √ 2ρA)/P as a function
of scaled rotor height above the ground, zg/D = zg/2R. Usually the test data are given as the ratio of the
thrust to out-of-ground-effect (OGE) thrust, for constant power: T/T∞ =(M/M∞) 2/3 = κg ≥ 1. The
effect on power at constant thrust is then P = P∞fg, where fg = κ −3/2
g ≤ 1. Ground effect is generally
negligible at heights above zg/D =1.5and at forward speeds above μ =3λh.
The ground plane is assumed to be perpendicular to the inertial-frame z-axis. The ground normal
(directed downward) is k F g = C FI k in airframe axes, or k S g = C SF k F g in rotor-shaft axes. The height
of the landing gear above ground level, hLG, is specified in the flight state. The height of the rotor hub
above ground level is then
zg = hLG − (k F g ) T (z F hub − z F LG)+dLG
where z F LG is the position of the landing gear in the airframe and dLG is the distance from the bottom of
the gear to the location zLG. From the velocity
v S =
⎛
⎝ μx
the angle ɛ between the ground normal and the rotor wake is evaluated: cos ɛ =(k S g ) T v S /|v S | (ɛ =0for
hover, ɛ =90degree in forward flight). Note that if the rotor shaft is vertical, then cos ɛ = λ/ μ 2 + λ 2 (see
ref. 1). The expressions for ground effect in hover are generalized to forward flight by using (zg/ cos ɛ)
in place of zg. No ground-effect correction is applied if the wake is directed upward (cos ɛ ≤ 0), or if
zg/ cos ɛ>1.5D. From zg/D cos ɛ, the ground-effect factor fg = κ −3/2
g is calculated. Then
is the effective ideal induced velocity.
−rμy
−λ
⎞
⎠
(λi)IGE = fg (λi)OGE
Several empirical ground-effect models are implemented: from Cheeseman and Bennett (ref. 1,
basic model and using blade-element (BE) theory to incorporate influence of thrust); from Law (ref. 2);
from Hayden (ref. 3); and a curve fit of the interpolation from Zbrozek (ref. 4):