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