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104 Rotor
vm = κ(KT / √ 2) (T1 + T2)/2ρA. The interference velocities are calculated separately for the two
rotors, with the correction factor ft: vint1 = ftκ T1/2ρA and vint2 = ftκ T2/2ρA. The sum vint1 + vint2
must take the required value. Below the non-overlap region, the component is in the wake of only one
of the rotors, so the interference velocity from the other rotor is zero, and thus ft =1. Below the overlap
region, the component is in the wake of both rotors, and the sum of the interference velocities equals vm
if
fth = KT / √ 2
√ τ1 + √ τ2
where τn = Tn/(T1 + T2) is the thrust ratio. For equal thrusts, fth = KT /2; orfth =1/ √ 2 for the
nominal velocity. The expression ft = fth cos 2 χ+sin 2 χ gives the required correction factor, with ft =1
in edgewise flight. Optionally the correction for twin rotors can be omitted (ft =1); nominal (KT = √ 2);
or use an input velocity factor in overlap region (KT ).
11–8 Drag
The rotor component includes drag forces acting on the hub and spinner (at zF hub ) and on the pylon
(at zF pylon ). The component drag contributions must be consistent. In particular, a rotor with a spinner
(such as on a tiltrotor aircraft) would likely not have hub drag. The pylon is the rotor support and the
nacelle is the engine support. The drag model for a tiltrotor aircraft with tilting engines would use the
pylon drag (and no nacelle drag), since the pylon is connected to the rotor shaft axes; with non-tilting
engines it would use the nacelle drag as well.
The body axes for the drag analysis are rotated about the y-axis relative to the rotor shaft axes:
C BF = C BS C SF , where C BS = Y−θref . The pitch angle θref can be input, or the rotation appropriate for
a helicopter rotor or a propeller can be specified.
a) Consider a helicopter rotor, with the shaft axes oriented z-axis up and x-axis
downstream. It is appropriate that the angle-of-attack is α =0for forward flight,
and α = −90 degree for hover, meaning that the body axes are oriented z-axis down
and x-axis forward. Hence θref = 180 degree.
b) Consider a propeller or tiltrotor, with the shaft axes oriented z-axis forward and
x-axis up. It is appropriate that the angle-of-attack is α =0in cruise and α =90
degree for helicopter mode (with a tilting pylon), meaning that the body axes are
oriented z-axis down and x-axis forward. Hence θref =90degree.
The aerodynamic velocity relative to the air is calculated in component axes, v B . The angle-of-attack
α and dynamic pressure q are calculated from v B . The reference areas for the drag coefficients are the
rotor disk area A = πR 2 (for hub drag), pylon wetted area Spylon, and spinner wetted area Sspin; these
areas are input or calculated as described previously.
The hub drag can be fixed, specified as a drag area D/q; or the drag can be scaled, specified as a
drag coefficient CD based on the rotor disk area A = πR 2 ; or the drag can be estimated based on the
gross weight, using a squared-cubed relation or a square-root relation. Based on historical data, the drag
coefficient CD =0.004 for typical hubs, CD =0.0024 for current low-drag hubs, and CD =0.0015 for
faired hubs. For the squared-cubed relation: (D/q)hub = k(WMTO/1000) 2/3 (WMTO is the maximum
takeoff gross weight; units of k are feet 2 /kilopound 2/3 or meter 2 /Megagram 2/3 ). Based on historical data,
k =1.4 for typical hubs, k =0.8 for current low-drag hubs, and k =0.5 for faired hubs (English units).
For the square-root relation: (D/q)hub = k WMTO/Nrotor (WMTO/Nrotor is the maximum takeoff gross