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88 Rotor
fg =
⎧
1 −
1
(4zg/R) 2
3/2
1+1.5
⎪⎨
⎪⎩
σaλi 1
4CT (4zg/R) 2
−3/2
3/2 1.0991 − 0.1042/(zg/D)
1+(CT /σ)(0.2894 − 0.3913/(zg/D))
0.9926 + 0.03794
(zg/2R) 2
−1
0.0544
0.9122 +
(zg/R) −3/2 CT /σ
Cheeseman and Bennett
Cheeseman and Bennett (BE)
Law
Hayden
Zbrozek
These equations break down at small height above the ground, and so are restricted to zg/D ≥ 0.15;
however, the database for ground effect extends only to about z/D =0.3. Also, fg ≤ 1 is required.
Figure 11-2 shows T/T∞ = κg = f −2/3
g as a function of z/R for these models (CT /σ =0.05, 0.10, 0.15),
compared with test data from several sources.
11-4.1.3 Inflow Gradient
As a simple approximation to nonuniform induced velocity distribution, a linear variation over the
disk is used: Δλ = λxr cos ψ + λyr sin ψ. There are contributions to Δλ from forward flight and from
hub moments, which influence the relationship between flapping and cyclic. The linear inflow variation
caused by forward flight is Δλf = λi(κxr cos ψ + κyr sin ψ), where λi is the mean inflow. Typically κx
is positive, and roughly 1 at high speed; and κy is smaller in magnitude and negative. Both κx and κy
must be zero in hover. Based on references 5–8, the following models are considered:
15π
15π
Coleman and Feingold: κx0 = fx tan χ/2 =fx
32 32
κy0 = −fy2μ
√ √
White and Blake: κx0 = fx 2 sin χ = fx 2
κy0 = −2fyμ
μ
μ 2 + λ 2 + |λ|
μ
μ 2 + λ 2
where tan χ = |λ|/μ is the wake angle. Extending these results to include sideward velocity gives
κx =(κx0μx + κy0μy)/μ and κy =(−κx0μy + κy0μx)/μ. Forflexibility, the empirical factors fx and fy
have been introduced (values of 1.0 give the baseline model). There is also an inflow variation produced
by any net aerodynamic moment on the rotor disk, which can be evaluated using a differential form of
momentum theory:
Δλm =
fm
μ 2 + λ 2 (−2CMyr cos ψ +2CMxr sin ψ) =λxmr cos ψ + λymr sin ψ
including empirical factor fm. Note that the denominator of the hub-moment term is zero for a hovering
rotor at zero thrust; so this inflow contribution should not be used for cases of low speed and low thrust.