1. The Theodorsen’s lift deficiency function is obtained for a pure harmonic excitatiuon of a pitching and plunging airfoil. The unsteady forces generated over the wing can be classified in circulatory and non circulatory foreces.

2. Articulated rotor

The body modes [eqn: w _{x}] and [eqn: w _{y}] cross the rotor’s lag mode of low-frequency. High-frequency lag mode is stable.

3. For a typical reduced frequency for a rotor blade,

[eqn: k`=` {wb} over {V} = {nc} over {2r}] for [eqn: w`=`n*OMEGA]

Then for a 1/rev motion and c/R=1/20, k =0.033 which is the magnitude of C(k) becomes 0.97. This means that quasi-steady assumption is quite adequate for 1/rev motion. However for a fixed wing, the free stream velocity V cannot be assumed as a steady one. It depends on the manuever of the airplane. The rotor is a trimmed condition will always achieve a periodic motion.

4. Loewy developed a 2-D model lfor unsteady aerodynamics of hovering rotor. And reduced frequency k is a function of w/[eqn: OMEGA] and wake spacing h. The Theodorsen’s lift deficiency function is also a function of h, but the k is a function of wb/U. In a Loewy’s function, the returning wake is modeled in a 2-D fashion,

[eqn: N _{b} h`=`V _{0} 2 pi / OMEGA ,`V _{0`} `:`steady``flow,# C`=` {1} over {1+ {pi ` sigma } over {4` lambda _{0}}}]

5. 1)flap-lag flutter

flap-lag flutter boundary is a function of thrust level for a hovering flight. For a particular thrust level [eqn: {G} over {sigma}], the blade is unstable inside the eliptic graph, which is the operation limit. The less damped lag mode becomes unstable for a fixed flap frequency, for varying lag frequencies. More thrust level has much more possibilities of instabilitiy.

2) pitch-flap flutter, divergence.

For stable hovering, the blade chordwise offset of the CG after aerodynamic center should be well-defined in a target operating speed

6. In a fixed wing, the torsional divergence is assessed by aerodynamic center offset from the elastic axis. However, in a rotary wing, the torsional divergence is determined by cg offset from the aerodynamic center.

7. The restricted spring in rigid flap-lag model represents the blade elastic stiffness of flap and lag wise direction. however, the restrained spring used in rigid torsion model represents the control system stiffness, which is much larger than the torsional elastic stiffness.

8. For a coupled flap-lag-torsion analysis, the coriolis force are considered in the modeling, giving a structural coupling term. For a single DOF model, the coriolis’ forces are neglected by a small angle assumption.

To investigae the coupled stability analysis such as flap-lag or flap-pitch flutter, the coriolis’ forces are included in the model.

However, to simplify analyze the ground resonance, the uncoupled lag equation is used. Also, the uncoupled flap eq. is used for simple trim calculation process.

9. The fixed frame hub loads are obtained from the rotating frame loads by the two steps.

1) Resolve the rotating frame loads of each blade in a fixed frame.

2) sum the fixed frame loads from all N blades

step1) redistributes the magnitudes of individual harmonics, but retaines all harmonics.

step2) filters out all non pN/rev harmonics by summation over all blades. under assumption of identical fully tracked rotor.

10. The Figure of Merit (F.M.) is defined as the ration of ideal power to the actual power.

[eqn: F.M.`=` {(C _{p`i} ) _{ideal}} over {(C _{p`i} ) _{actual} +C _{p0}}]

In momentum theory, ideal power is [eqn: lambda C _{T} `=`K _{h} sqrt {( {C _{T}} over {2} )} C _{T}]

However, considering the power loss in swirl flow, tip losses, non-uniform inflow, [eqn: lambda `=`K _{h} sqrt {( {C _{T}} over {2} )}]

[eqn: F.M.`=` {{C _{T}^{3/2}} over {sqrt {(2)}}} over {{C _{T}^{3/2}} over {sqrt {(2)}} K _{h} + {sigma} over {8} C _{d0}}]

which is not equal to 1.0 in practice.

Aifroil stall prevents the other factors from remaining constant.