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Rotor 79
propulsion group. The drive-system state defines the gear ratio for dependent rotors and the engine
groups. From the rotor radius the rotational speed of the primary rotor is obtained (Ωprim = Vtip/R);
from the gear ratios, the rotational speed of dependent rotors (Ωdep = rΩprim) and the engine groups
(N = (60/2π)rengΩprim) are obtained; and from the rotor radius, the tip speed of the dependent rotor
(Vtip =ΩdepR) is obtained. The flight-state specification of the tip speed can be an input value; the
reference tip speed; a function of flight speed or a conversion schedule; or one of several default values.
These relationships between tip speed and rotational speed use the actual radius of the rotors in the flight
state, which for a variable-diameter rotor may not be the same as the reference, hover radius.
An optional conversion schedule is defined in terms of two speeds: hover and helicopter mode for
speeds below VChover, cruise mode for speeds above VCcruise, and conversion mode for speeds between
VChover and VCcruise. The tip speed is Vtip−hover in helicopter and conversion mode, and Vtip−cruise in
airplane mode. Drive-system states are defined for helicopter, cruise, and conversion-mode flight. The
flight state specifies the nacelle tilt angle, tip speeds, control state, and drive-system state, including the
option to obtain any or all of these quantities from the conversion schedule.
Several default values of the tip speed are defined for use by the flight state, including cruise,
maneuver, one-engine inoperative, drive-system limit conditions, and a function of flight speed (piecewise
linear input). Optionally these default values can be input as a fraction of the hover tip speed.
Optionally the tip speed can be calculated from an input CT /σ = t0 − μt1, from μ = V/Vtip, or from
Mat = Mtip (1 + μ) 2 + μ2 z; from which Vtip = T/ρAσt0 +(Vt1/2t0) 2 +(Vt1/2t0), Vtip = V/μ,or
Vtip = (csMat) 2 − V 2
z − V .
The sizing task might change the hover tip speed (reference tip speed for drive-system state #1),
the reference tip speed of a dependent rotor, a rotor radius, or the specification engine turbine speed
Nspec. In such cases the gear ratios and other parameters are recalculated. Note that it is not consistent
to change the reference tip speed of a dependent rotor if the gear ratio is a fixed input.
11–2 Geometry
The rotor rotation direction is described by the parameter r: r =1for counter-clockwise rotation,
and r = −1 for clockwise rotation (as viewed from the positive thrust side of the rotor).
The rotor solidity and blade mean chord are related by σ = Nc/πR; usually thrust-weighted values
are used, but geometric values are also required by the analysis. The mean chord is the average of
the chord over the rotor blade span, from root cutout to tip. The thrust-weighted chord is the average
of the chord over the rotor blade span r, from root cutout to tip, weighted by r 2 . A general blade
chord distribution is specified as c(r) =crefĉ(r), where cref is the thrust-weighted chord. Linear taper is
specified in terms of a taper ratio t = ctip/croot, or in terms of the ratio of thrust-weight and geometric
chords, f = σt/σg = c.75R/c.50R.
The rotor hub is at position zF hub . Optionally, a component of the position can be calculated,
superseding the location input. The calculated geometry depends on the configuration. For a coaxial
rotor, the rotor separation is s = |kT CSF (zF hub1 − zF hub2 )/(2R)| (fraction rotor diameter), or the hub
locations are calculated from the input separation s, and the input location midway between the hubs:
z F hub = z F center ± C FS
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sR