ROTORCRAFT DYNAMICS RICHARD L. BENNETT, Ph.D.1705 Deauville CtFort Worth, TX 76112rlbennett@sbcglobal.net

Penn State UniversityState College, PA August, 2013

LECTURE OBJECTIVESOverview of Rotorcraft TechnologyConfigurations, Dynamics, AerodynamicDispel Some MythsCalibration SignalsInspect HardwareExpose Mathematical Foundations

VEHICLE COSTS

COMPLEXITY COMPARISONBoeing 747 circa 196711 Months between First Test FlightAnd First Commercial Flight

Bell Model 222 Helicopter circa 198042 Months between First Test FlightAnd Type Certificate

ROTORCRAFT SALES1972 Bell Helicopter Produced 230 helicopters/month (Viet Nam war)2007 Bell Produced

HELICOPTER MYTHS4 Bladed helicopters fly faster than 3 bladed helicopters.Helicopter rotors increase the thrust by increasing the rotation speed.Changing the blades airfoil will make a significant change in the rotors aerodynamic performance in hover.The fuselage vibrations are independent of the type of rotor.

MYTHSRandom airloads are an important consideration in the design of helicopters.All helicopters are subject to ground resonanceOnly aerodynamic forces acting on the rotor influence the rotors dynamic behavior.Component lifes are determined by the number of take off/landings.Tilt rotor aircraft are not subject to helicopter type fuselage vibrations in in airplane mode flight

MYTHSThe HP rating of the transmission must exceed the HP rating of the engine.The operating aerodynamic environment (mach, angle of attack) of the helicopter rotor blade is similar to that of a fixed wing aircraftIncreasing the number of blades will increase the maximum hover thrust.The rigid body simulation of a helicopter uses only the same rigid body equations as used for a fixed wing aircraft

HELICOPTER ENGINEERING 101

LIFTING AIRFOIL

HOVERING ROTOR BALANCING ACTOLIFT (L)rmBCENTRIFUGALFORCE (CF)MOMENT DUE TO CENTRIFUGAL FORCE BALANCESMOMENT DUE TO AERODYNAMIC LIFT

DRAG ON MAIN ROTOR PRODUCESMAIN ROTOR TORQUEMain Rotor TorqueBlade RotationDRAGDRAGDRAGDRAG

TAIL ROTOR THRUST OPPOSES MAIN ROTOR TORQUEMain Rotor TorqueBlade RotationTail RotorThrustTAIL ROTOR NOT REQUIRED AT HIGH FORWARD SPEED

Hover Tip Speed (HTP) ~ 500 miles/hr ~700 ft/secBlade Rotation (RPM) ~300 rev/min = 5 rev/secHTPHTPHTP

HTPBlade RotationIN HOVER: WIND VELOCITY IS CONSTANT AROUND AZIMUTH

Hover Tip Speed =500 mphHelicopterForward Speed: V~ 140 mphHTPHTPAdvancing Blade: HTP +V = 500 +140= 640 mph= 0.86 MachRetreating Blade HTP-V =500-140 =360 mph = 0.48 MachReversed Flow AreaBlade RotationIN FORWARD FLIGHT: WIND VELOCITY DEPENDS ON AZIMUTH

HelicopterForward Speed: V~ 140 mphHTPReversed Flow AreaAERODYNAMIC CONSTRAINTS LIMITFORWARD SPEEDRetreating Blade StallAdvancing Tip Mach # (Drag Divergence)

HELICOPTER PROBLEM Aerodynamic Box

HELICOPTER PROBLEM Harmonic External Aerodynamic Forces

HELICOPTER PROBLEM #2

dD

r

Blade aerodynamic forces are harmonic functions of rotor speed

HELICOPTER PROBLEM- PART1

Top View of Helicopter in Forward Flight

V: Fwd Speed

R

Adv Tip MachCompressibility Effects

Stall Region

Reversed Flow

THE DYNAMICS PROBLEMOSCILLATORY AERODYNAMIC FORCES AT FREQUENCIES AT OR NEAR THE NATURAL FREQUENCIES OF THE ROTOR AND/OR FUSLEAGE CAN PRODUCE FATIQUE LOADS ON THE ROTOR FUSELAGE VIBRATIONS NOISE REDUCED COMPONENT LIFE

HELICOPTER PROBLEM Rotor Harmonic Forces Transmittedto Fuselage

Frequencies of the Steady State Rotor Harmonic Forces are Integer Multiples of Rotor RPM 1/Rev 2/Rev 3/Rev etc

THE HELICOPTER PROBLEMSHAKE, RATTLE, AND ROLL

EARLY ATTEMPTSAIRPLANE PROPELLORS ARE UNSTABLE IN EDGEWISE FLOW DUE TO DISSIMILAR AERODYNAMIC ENVIRORNMENT ON ADVANCING AND RETREATING BLADE

HELICOPTER vs. AIRPLANESAirplanes are subject to Steady Air loads Random Air loadsHelicopters are subject to Steady Air load Harmonic Air loads Periodic but Not Harmonic Random Air loads

FIXED WING BASICS(P-51)1. Propeller Blades are cantilevered to drive shaft2. Propeller Tip Path Plane (TPP) always perpendicular to shaft3. Propeller thrust always along shaft4. Propeller thrust ~ Aircraft drag5. Orientation of propeller shaft controlled by Aileron, rudder, etc6. Blade pitch is independent of blade azimuth7. Propeller thrust controlled by RPM and blade pitch8. Aerodynamic forces acting on blades are:Steady State orRandom (Gust)9. Propeller transmits steady forces to fuselageAerodynamic Gyroscopic

FIXED WING BASICS(P-51)Rigid body airplane has 6 rigid body degrees of freedomFore/aft translationVertical translationLateral translationYawPitchRoll

HELICOPTER BASICS1. Blades are attached to shaft via flapping hinge to permit rigid body blade motion parallel to mast2. Blade tips form a Tip Path Plane (TPP)3. Rotors resultant aerodynamic force is perpendicular to TPP4. TPP is free to tilt relative to mastFore/Aft tiltLateral tilt5. Rotors resultant aerodynamic force is controlled by blade pitch (RPM is held constant)

HELICOPTER BASICS 6. Rotor force must:Overcome gravity and fuselage dragProvide maneuverabilityProvide helicopter stability7. TPP location controlled totally by aerodynamic forces acting on blade8. Blades geometric pitch is function of blade azimuth9. Aerodynamic forces on blades are:SteadyHarmonicPeriodic but not harmonic

HELICOPTER BASICS 10. Harmonic aerodynamic forces on blades transmit harmonic forces to fuselage causing fuselage vibrations.11. Rigid body helicopter has 10 rigid body degrees of freedom:Fore/aft translationLateral translationVertical translationYawPitchRollMain RotorFore/aft tiltLateral tiltTail RotorFore/aft tiltLateral tilt

REQUIREMENTS FORHELICOPTER FLIGHTConfiguration for Anti-torqueMoveable and Controllable Tip Path PlanesRotor Control SystemStructure able to withstand large oscillatory forcesFlight mode controllability/stabilityEfficient Power Source