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96 Rotor
11-5.1.1 Induced Power
11-5.1 Energy Performance Method
The induced power is calculated from the ideal power: Pi = κPideal = κfDTvideal. Reference
values of κ are specified for hover, axial cruise (propeller), and edgewise cruise (helicopter): κhover,
κprop, κedge. Two models are implemented: constant model and standard model. The constant model
uses κ = κhover if μ = μz =0;orκ = κprop if |μ| < 0.1|μz|; orκ = κedge otherwise.
The standard model calculates an axial-flow factor κaxial from κhover, κclimb, and κprop. Let Δ=
CT /σ − (CT /σ)ind. For hover and low-speed axial climb, including a variation with thrust, the inflow
factor is
κh = κhover + kh1Δh + kh2Δ 2 h +(κclimb − κhover) 2
π
tan−1 ((|μz|/λh)/Maxial) Xaxial
where |μz|/λh = Maxial is the midpoint of the transition between hover and climb and Xaxial is large
for a fast transition. Figure 11-4 illustrates κ in hover (with a minimum value). Figure 11-5 shows the
behavior of this function for a helicopter in climb (Xaxial =0.65). A polynomial describes the variation
with axial velocity, scaled so κ = κh at μz =0and κ = κp at μz = μzprop, including a variation with
thrust:
κp = κprop + kp1Δp + kp2Δ 2 p
κaxial = κh + ka1μz + S(ka2μ 2 z + ka3μ Xa
z )
where S =(κp−(κh+ka1μzprop))/(ka2μ2 zprop+ka3μ Xa
zprop); S =0if ka2 = ka3 =0(not scaled); κaxial = κh
if μzprop =0. A polynomial describes the variation with edgewise advance ratio, scaled so κ = κaxial at
μ =0and κ = foffκedge at μ = μedge. Thus the induced power factor is
κ = κaxial + ke1μ + S(ke2μ 2 + ke3μ Xe )
where S =(foffκedge − (κaxial + ke1μedge))/(ke2μ2 Xe
edge + ke3μedge ); S =0if ke2 = ke3 =0(not scaled);
κ = κaxial if μedge =0. The function foff =1− ko1(1 − e−ko2ox ) accounts for the influence of lift offset,
ox = rMx/T R =(Khub/T R)βs. Figure 11-6 illustrates κ in edgewise flight. Minimum and maximum
values of the induced power factor, κmin and κmax, respectively, are also specified.
11-5.1.2 Profile Power
The profile power is calculated from a mean blade drag coefficient: CPo =(σ/8)cdmeanFP . Since the
blade mean lift coefficient is cℓ ∼ = 6CT /σ, the drag coefficient is estimated as a function of blade loading
CT /σ (using thrust-weighted solidity). With separate estimates of the basic, stall, and compressibility
drag, the mean drag coefficient is:
cdmean = χS (cdbasic + cdstall + cdcomp)
where χ is a technology factor. The factor S =(Reref/Re) 0.2 accounts for Reynolds number effects on
the drag coefficient; Re is based on the thrust-weighted chord, 0.75Vtip, and the flight state; and Reref
corresponds to the input cd information. The following models are implemented for the basic drag:
a) Array model: The basic drag cdbasic is input as a function of CT /σ; the array is linearly interpolated.
b) Equation model: The basic drag cdbasic is a quadratic function of CT /σ, plus an additional term
allowing faster growth at high (sub-stall) angles of attack. Let Δ = |CT /σ − (CT /σ)Dmin|, where