16  Rotary Wing

16.1 Principal Aeroderivatives

16.1.1 Control Power

Derivative	Common Name	Principal Contributors	Typical Sign
\(M_{B_1}\)	Pitch control power	MR thrust vector Mast bending moment Control gearing Rotor type Effective hinge offset	-
\(L_{A_1}\)	Roll control power	MR thrust vector Mast bending moment Control gearing Rotor type Effective hinge offset	-
\(N_{\theta_{\text{TR}}}\)	Yaw control power	TR thrust TR moment arm Control gearing	-
\(Z_{\theta_C}\)	Heave control power	MR thrust Control gearing	-

16.1.2 Static Stability

Derivative	Common Name	Principal Contributors	Typical Sign
\(M_u\)	Speed stability	MR flap back Mast bending moment Horizontal tailplane	+
\(M_w\)	Static / Incidence / Angle of Attack stability	MR flap back Mast bending moment Horizontal tailplane Fuselage
\(L_v\)	Lateral static stability (dihedral effect)	MR ‘flap back’ TR vertical moment arm Fuselage	-
\(N_v\)	Directional static stability (weathercock effect)	TR thrust Vertical tailplane Fuselage	+

16.1.3 Damping

Derivative	Common Name	Principal Contributors	Typical Sign
\(X_u\)	Drag damping	Rotor drag Fuselage drag	-
\(Y_v\)	Side force	Rotor drag Fuselage drag	-
\(Z_w\)	Heave damping	MR characteristics	-
\(L_p\)	Roll damping	Main rotor Effective hinge offset	-
\(M_q\)	Pitch damping	Main rotor Effective hinge offset Horizontal tailplane	-
\(N_r\)	Yaw damping	Tail rotor Vertical tailplane Fuselage	-

16.1.4 Cross Coupling

Derivative	Common Name	Principal Contributors	Typical Sign
\(L_{\theta_{\text{TR}}}\)	Tail rotor roll	Tail rotor vertical position	+
\(M_{\theta_C}\)	Pitch change with power	Forward speed Main rotor	+
\(N_{\theta_C}\)	Torque reaction	Torque
\(Y_{\theta_{\text{TR}}}\)	Tail rotor drift	Tail rotor

16.2 Forward Flight Static And Dynamic Stability 

Stability Characteristic	Principal Influences	Typical Test	Role Relation
Longitudinal Static Stability	\(M_w\) \(M_u\) \(M_{\theta_C}\) \(M_{\theta_{TR}}\)	Trimmed flight control positions Trimmed flight control positions - collective Apparent static stability Collective fixed static stability	Control margins Control inputs progressive, predictable, and in correct sense Speed selection Speed maintenance
Manoeuvre Stability	\(M_w\) \(M_q\) \(M_{\theta_C}\)	Apparent manoeuvre stability Collective fixed manoeuvre stability Pull-ups/push-overs	Aggressive turning and manoeuvring flight
Longitudinal Dynamic Stability	\(M_w\) \(M_u\) \(M_q\)	Excitation of dynamic long term mode Natural turbulence, release to trim, pulse input	IMC flight Transit Nuisance mode
Lateral-Directional Static Stability	\(L_v\) \(N_v\) \(Y_v\)	Trimmed flight control positions Steady heading sideslip (SHSS)	Control margins Control inputs progressive, predictable, and in correct sense Sideforce cues Maintaining balanced flight
Lateral Static Stability (Dihedral)	\(L_v\)	SHSS Turns on one control – pedal	Transit Lateral and out-of-wind transitions Instrument approaches
Directional Static Stability	\(N_v\)	SHSS Turns on one control - cyclic	Transit Instrument approaches
Lateral-Directional Dynamic Stability Oscillations (Dutch Roll Mode)	\(L_v\) \(N_v\)	Excitation of LDO via doublet, pulse, or SHSS release to trim	IMC flight Transit Nuisance mode
Lateral-Directional Dynamic Stability Spiral Stability	\(L_v\) \(N_r\) \(N_v\) \(L_r\)	Turns on one control – cyclic Time to half/double bank angle	IMC flight Turns Lateral gust response

16.3 References

Cooke, A., Fitzpatrick, E., (2002), Helicopter Test and Evaluation, Wiley Blackwell, UK.

Leishman, J.G., (2006), Principles of Helicopter Aerodynamics, 2nd Edition, Cambridge University Press, UK.

Padfield, G.D., (2007), Helicopter Flight Dynamics, 2nd Edition, Blackwell Publishing, UK.