FLIGHT DYNAMICS AND CONTROL OF A ROTORCRAFT TOWING A SUBMERGED LOAD

FLIGHT DYNAMICS AND CONTROL OF A ROTORCRAFT TOWING A SUBMERGED LOAD Ananth Sridharan Ph.D. Candidate Roberto Celi Professor Alfred Gessow Rotorcraft Center Department of Aerospace Engineering University of Maryland, College Park Presented 16 th October 2013 to the Federal Chapter of the American Helicopter Society

Research supported by the Army/Navy/NASA VLRCOE program Discussions with Mr. Mike Fallon, NAVAIR, and Mr. Alan Schwartz, NSWC, Carderock gratefully acknowledged

Outline Motivation Previous Work Outline Motivation and Objectives Previous Work Steady forward flight Tear-drop maneuver Future steps

Outline Motivation Previous Work Motivation and Objectives Motivation Certain naval missions require towing a submerged load along a prescribed path Hydrodynamic forces limit flight envelope: power Operating at unfamiliar attitudes: pilot fatigue Objectives Formulate a mathematical model of a helicopter towing a fully submerged body Identify means to reduce cable force, power Study behavior of helicopter-load combination during maneuvers Tow-tank model in the photograph courtesy of Dr Jaye Falls, USNA

Outline Motivation Previous Work State-of-the-art Surface-based towing Strandhagen (1963) Curved cable and load hydrodynamics (steady) Knutson (1991) Ship-based towing of passive load (steady) Buckham (2003) PID control of towed body (semi-submersible) Grosenbaugh (2007) Transient behavior of curved cables Helicopter-based towing Kennedy (1973) H-53 helicopter towing oil spill containment barrier Ludwig (1976) HH-3F helicopter towing hydroplaning sled consistent nose-down pitch attitude of less than -6 o leads to pilot fatigue Hong (2003) Helicopter with towed body analysis [Trim, OEI]

Rotorcraft Cable / Towed body Trim formulation Maneuvering flight Mathematical model Helicopter

Rotorcraft Cable / Towed body Trim formulation Maneuvering flight Mathematical model Curved cable

Rotorcraft Cable / Towed body Trim formulation Maneuvering flight Mathematical model Towed body

Steady Forward Flight Steady Turning Flight Tear-drop Towed body trim characteristics Sling cable V Towed body θ CG

Steady Forward Flight Steady Turning Flight Tear-drop Towed body : longitudinal dynamics Sling cable D : Drag force T : Cable force T sin(θ) V T cos(θ) Towed body θ CG D

Steady Forward Flight Steady Turning Flight Tear-drop Towed body : longitudinal dynamics Sling cable D : Drag force T : Cable force T sin(θ) V T cos(θ) Towed body θ CG D As speed increases, hydrodynamic drag increases

Steady Forward Flight Steady Turning Flight Tear-drop Towed body : longitudinal dynamics Sling cable D : Drag force T : Cable force T sin(θ) V T cos(θ) Towed body θ CG D As speed increases, hydrodynamic drag increases T cos(θ) increases nose down pitching moment

Steady Forward Flight Steady Turning Flight Tear-drop Towed body : longitudinal dynamics Sling cable D : Drag force T : Cable force T sin(θ) V T cos(θ) θ CG D Towed body As speed increases, hydrodynamic drag increases T cos(θ) increases nose down pitching moment

Steady Forward Flight Steady Turning Flight Tear-drop Towed body : longitudinal dynamics Sling cable T sin(θ) D : Drag force T : Cable force L T : Tail force V T cos(θ) θ CG D Towed body L T As speed increases, hydrodynamic drag increases T cos(θ) increases nose down pitching moment Tail generates down-force nose up moment

Steady Forward Flight Steady Turning Flight Tear-drop Towed body : longitudinal dynamics Sling cable T sin(θ) D : Drag force T : Cable force L T : Tail force L F : Hydrofoil force V T cos(θ) θ CG D Towed body L F L T As speed increases, hydrodynamic drag increases T cos(θ) increases nose down pitching moment Tail down-force nose up moment Main fin negative incidence down-force

Steady Forward Flight Steady Turning Flight Tear-drop Effect of cable attachment point on rotor power required Power reqd (hp) +4 inch +2 inch baseline Higher offset creates nose-down moments, hydrofoil down-force Total rotor thrust increases, power draw increases

Steady Forward Flight Steady Turning Flight Tear-drop Trim depth of towed body Depth (ft) Helicopter altitude Water surface Total depth depends on hydrodynamic drag and down-force (speed)

Steady Forward Flight Steady Turning Flight Tear-drop Varying vertical separation in forward flight θ F Water surface Utilize fin pitch angle to vary vertical separation 310 ft 280 ft 250 ft

Steady Forward Flight Steady Turning Flight Tear-drop Main rotor power required for various vertical separations Power reqd (hp) 310 ft Zero pitch 250 ft 280 ft Nose-up fin pitch less down-force less rotor thrust less power Smaller vertical separation for reducing power required

Rotorcraft Towed body Trim formulation Maneuvering flight Maneuvering flight General unsteady flight condition Computed by numerical integration of ODEs Here, use a pseudo-fcs that generates controls to minimize deviation from target trajectory LQR-based controller to track prescribed trajectory (role of pilot) Generate initial guess for optimization process Same pseudo-fcs can be used stand-alone with restrictions Gentle maneuvers (small accelerations) Speed changes during maneuver are gradual

Rotorcraft Towed body Trim formulation Maneuvering flight Example maneuver: tear-drop Steady turns with lead-in and leadout from forward flight Sequence of heading changes Nose-left : -Δψ Fwd. flight Left turn 0 Right turn 5 Nose right : π+2δψ Nose left : -Δψ Total : 180 o Fwd. flight 1 4 Left turn 2 3

Steady Forward Flight Steady Turning Flight Tear-drop : Tear-drop (movie)

Steady Forward Flight Steady Turning Flight Tear-drop : Tear-drop (movie)

Steady Forward Flight Steady Turning Flight Tear-drop : Tear-drop (movie)

Summary Interactions with USNA Future Work Future work Improve model fidelity Cable curvature Free-vortex wake for rotors Cable torsion, asymmetric cross-sections Ongoing: Implement fin pitch control system for towed body depth regulation Study interactions and coordinate with helicopter trajectory controller Trajectory optimization

FLIGHT DYNAMICS AND CONTROL OF A ROTORCRAFT TOWING A SUBMERGED LOAD Ananth Sridharan Ph.D. Candidate Roberto Celi Professor Alfred Gessow Rotorcraft Center Department of Aerospace Engineering University of Maryland, College Park

Steady Forward Flight Steady Turning Flight Tear-drop QUESTIONS?

BACKUP SLIDES

Rotorcraft Cable / Towed body Trim formulation Maneuvering flight Mathematical model Rotorcraft Rotorcraft model UH-60 like configuration Main rotor : Flexible rotor blades : Euler-Bernoulli beams (FEM),dynamic inflow Fuselage, empennage: Rigid-body with table look-up aerodynamics Tail rotor: Actuator disk with dynamic inflow Trim Flight condition defined by speed, altitude, turn rate and flight path angle Unknowns: Rotor harmonic mode coefficients, control inputs, attitudes, rotor inflow Equations: Vehicle force and moment equilibrium Turn co-ordination and sideslip Rotor response periodicity

Rotorcraft Cable / Towed body Trim formulation Maneuvering flight Mathematical model Cable Straight cable [v1.0] Straight and active in tension Simplified axially flexible formulation Force proportional to extension (tension only) Captures first-order cable slackening Curved cable [v2.0]: Beam within a beam Multiple interconnected beam segments Finite elements with cascading reference frames Applicable to rotor blades and wings as well Large global deformations, small angles in segments Hydrodynamic forces (lift, drag, moment, buoyancy)

Rotorcraft Cable / Towed body Trim formulation Maneuvering flight Mathematical model Towed body Cylindrical hull and five fins Hull experiences gravity, drag and buoyancy Fins : hydrodynamic lift and drag (tables) (2) Main fins pitch about mounting axes No control system Cavitation effects neglected Optionally replace with experimental data All dimensions in cm