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
Introduction
Modeling
Results
Conclusions
Presented 16th 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
Introduction
Modeling
Results
Conclusions
Outline
• Motivation and Objectives
• Previous Work
• Results
– Steady forward flight
– Tear-drop maneuver
• Future steps
Introduction
Modeling
Results
Conclusions
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
Introduction
Modeling
Results
Conclusions
Outline
Motivation
Previous Work
Tow-tank model in the
photograph courtesy of
Dr Jaye Falls, USNA
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 -6o leads to pilot fatigue”
– Hong (2003) Helicopter with towed body analysis [Trim, OEI]
Introduction
Results
Conclusions
Outline
Motivation
Previous Work
Modeling
Mathematical model
Introduction
Results
Conclusions
Rotorcraft
Cable / Towed body
Trim formulation
Maneuvering flight
Modeling
Helicopter
Mathematical model
Introduction
Results
Conclusions
Rotorcraft
Trim formulation
Maneuvering flight
Modeling
Curved cable
Cable / Towed body
Mathematical model
Introduction
Results
Conclusions
Rotorcraft
Trim formulation
Maneuvering flight
Modeling
Towed body
Cable / Towed body
Introduction
Modeling
Results
Conclusions
Steady Turning Flight
Towed body trim characteristics
Tear-drop
Steady Forward Flight
Sling cable
CG
θ
V
Towed body
Introduction
Modeling
Results
Conclusions
Steady Turning Flight
Towed body : longitudinal dynamics
Tear-drop
Steady Forward Flight
Sling cable
CG
T sin(θ)
T cos(θ)
•D : Drag force
•T : Cable force
V
θ
Towed body
D
Introduction
Modeling
Results
Conclusions
Steady Turning Flight
Towed body : longitudinal dynamics
Tear-drop
Steady Forward Flight
Sling cable
CG
•As speed increases, hydrodynamic drag increases
T sin(θ)
T cos(θ)
•D : Drag force
•T : Cable force
V
θ
Towed body
D
Introduction
Modeling
Results
Conclusions
Steady Turning Flight
Towed body : longitudinal dynamics
Tear-drop
Steady Forward Flight
Sling cable
•As speed increases, hydrodynamic drag increases
•T cos(θ) increases nose down pitching moment
T cos(θ)
D
CG
•D : Drag force
•T : Cable force
T sin(θ)
V
θ
Towed body
Introduction
Modeling
Results
Conclusions
Steady Turning Flight
Towed body : longitudinal dynamics
Tear-drop
Steady Forward Flight
Sling cable
CG
•As speed increases, hydrodynamic drag increases
•T cos(θ) increases nose down pitching moment
T sin(θ)
T cos(θ)
D
•D : Drag force
•T : Cable force
V
θ
Towed body
Introduction
Modeling
Results
Conclusions
Steady Turning Flight
Towed body : longitudinal dynamics
Tear-drop
Steady Forward Flight
Sling cable
Towed body
•As speed increases, hydrodynamic drag increases
•T cos(θ) increases nose down pitching moment
•Tail generates down-force nose up moment
T sin(θ)
T cos(θ)
V
θ
LT
•D : Drag force
•T : Cable force
•LT : Tail force
CG D
Introduction
Modeling
Results
Conclusions
Steady Turning Flight
Towed body : longitudinal dynamics
Tear-drop
Steady Forward Flight
Sling cable
• 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
T sin(θ)
T cos(θ)
V
θ
LF
•D : Drag force
•T : Cable force
•LT : Tail force
•LF : Hydrofoil force
LTTowed body
CG D
Introduction
Modeling
Results
Conclusions
Steady Turning Flight
Effect of cable attachment point on rotor power required
Tear-drop
• Higher offset creates nose-down moments, hydrofoil down-force
• Total rotor thrust increases, power draw increases
Steady Forward Flight
baseline
+2 inch
+4 inch
Power
reqd
(hp)
Introduction
Modeling
Results
Conclusions
Steady Turning Flight
Trim depth of towed body
Tear-drop
Steady Forward Flight
• Total depth depends on hydrodynamic drag and down-force (speed)
Helicopter altitude
Water surface
Depth
(ft)
Introduction
Modeling
Results
Conclusions
Steady Turning Flight
Varying vertical separation in forward flight
Tear-drop
Steady Forward Flight
Water surface
• Utilize fin pitch angle to
vary vertical separation280 ft 250 ft
θF
310 ft
Introduction
Modeling
Results
Conclusions
Steady Turning Flight
Main rotor power required for various vertical separations
Tear-drop
Steady Forward Flight
• Nose-up fin pitch less down-force less rotor thrust less power
• Smaller vertical separation for reducing power required
250 ft280 ft
310 ft
Zero pitch
Power
reqd
(hp)
Introduction
Modeling
Results
Conclusions
Rotorcraft
Towed body
Maneuvering flight
Trim formulation
• 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
Maneuvering flight
Introduction
Modeling
Results
Conclusions
Rotorcraft
Towed body
Example maneuver: tear-drop
Trim formulation
Maneuvering flight
1
2
3
45
0 Right turn
Left turn
Left turn
• Steady turns with lead-in and lead-
out from forward flight
• Sequence of heading changes
– Nose-left : -Δψ
– Nose right : π+2Δψ
– Nose left : -Δψ
– Total : 180o
Fwd. flight
Fwd. flight
Introduction
Modeling
Results
Conclusions
Steady Turning Flight
Results: Tear-drop (movie)
Tear-drop
Steady Forward Flight
Introduction
Modeling
Results
Conclusions
Steady Turning Flight
Results: Tear-drop (movie)
Tear-drop
Steady Forward Flight
Introduction
Modeling
Results
Conclusions
Steady Turning Flight
Results: Tear-drop (movie)
Tear-drop
Steady Forward Flight
Introduction
Modeling
Results
Conclusions
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
Summary
Conclusions
Interactions with USNA
Future Work
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
Introduction
Modeling
Results
Conclusions
Introduction
Modeling
Results
Conclusions
Steady Turning Flight
QUESTIONS?
Tear-drop
Steady Forward Flight
BACKUP SLIDES
Mathematical model – Rotorcraft
Introduction
Modeling
Results
Conclusions
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)
Introduction
Modeling
Results
Conclusions
Rotorcraft
Cable / Towed body
Trim formulation
Maneuvering flight
• 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
Mathematical model – Towed body
Introduction
Results
Conclusions
Rotorcraft
Maneuvering flight
Modeling Cable / Towed body
Trim formulation
All dimensions in cm