*Flight Dynamic Modeling and Trim Analysis of Mini HelicopterB.SeenuY5101004Department of Aerospace EngineeringIndian Institute of TechnologyKanpurThesis SupervisorProf. C. Venkatesan

*Introduction

Coordinate Systems

Blade Inertia/Aerodynamic Loads

Blade Flap Equation

Flight Dynamic Equations

Trim Equations

Results and Discussions

Conclusion/ Future workCONTENTS

*INTRODUCTION

UAVs

Fixed WingRotary Wing

*Advantages of UAVs:Military surveillancesRemote sensing/Agricultural sprayingMeteorological measurements at high altitudeAircrew training and support costsThey reduce the aircrew risk

Features of Mini Helicopter:Variable rpmStabilizer bar to increase the stabilityVTOL, Hovering

*Literature ReviewKim et. al.,(1998) Developed a non-linear model, particularly focused on effect fly bar on helicopter stability.

Cunha et. al.,(2003)-Developed a mathematical model for model scale helicopter with interaction between main rotor and stabilizer bar. Hover flight test.

Mini helicopter development in IIT-KanpurPrasanth (2004)- Developed the flight dynamic equation for autonomous mini helicopter. Obtained only trim results for hover flight.

Pradeep (2005)- He extended the previous work and obtained the trim and stability results for hover and forward flight conditions. Flap dynamics not included in the formulation.

*My work:Flight dynamic model for general maneuvering flightRotor flap dynamicsDynamic inflow model (radius, azimuth angle, time)Gust effectsSteps:Blade inertia loadsBlade aerodynamic loadsBlade flap equationForces and moments acting at the C.G. of the fuselageMain rotor loadsTail rotor loadHorizontal tail plateVertical tail plate

*HELICOPTER DYNAMICSVERTICAL FINHORIZONTAL PLATETAIL ROTORMAIN ROTORDRAG FORCEHub Loads Due to All BladesBlade Root LoadsSectional Inertia & Aerodynamic Loads on BladeForces and Moments on Fuselage STABLIZER BAR

*Idealizations of the Model Helicopter

Blades are assumed symmetric airfoil cross section

Fuselage and rotor shaft are rigid

Blade is modelled as rigid blade with hinge offset (e)

Root spring attached at hinge undergoing only flap motion

Drees inflow model

Vertical fin and Tail plate with symmetric airfoil

*Coordinate Systems

R - Hub fixed inertial system

l - Non-inertial hub fixed non rotating system

2K - Hub fixed rotating system. Rotates with Kth blade

3K - Origin at hinge offset, parallel to 2-system. system rotates with Kth blade

4K - Origin on elastic axis of Kth Blade and positioned in cross section of blade

- Origin at elastic axis of Kth blade and positioned in cross section of blade

s1- Origin at CG of the Helicopter. Parallel to 1 system

*R - Hub fixed inertial systemCoordinate Systems1 and 2K systems3K and 4K systems1-Non inertial hub fixed non rotating system

*Coordinate SystemsBody fixed coordinate system2k and 3k coordinate systems

*Coordinate Systems

4k and coordinate systems with origin on elastic axis

*Blade Inertia LoadsPosition vector of point PAcceleration of point PAccl. of hub centreRel accl. of point P Coriolis AccelerationAngular AccelerationCentripetal Acceleration

*Blade Inertia loadsDistributed inertia forces Inertia forces at blade root Inertia moments at blade root

*Blade Inertia LoadsTransforming these loads into 1-syatem

These loads are acting at the origin of the 1-system. Total load due to all the blades are obtained by summing up the loads due to all blades

*Blade Inertia LoadsThe average inertia loads acting at the hub in one revolutionSince 1-system s1 system are parallel, the main rotor inertia loads actingat CG of the helicopter in s1 can be written asThe distance from CG to hub centre,

*Blade Aerodynamic LoadsExpression for Circulatory and Non-circulatory Lifts and Moment (Theodorsons unsteady aerodynamic theory )Drag force is given by

*Blade Aerodynamic Loads

Drees Inflow Model is the mean induced velocity is the advance ratio

*Blade Aerodynamic LoadsAerodynamic Loads at Blade Rootwhere

*Blade Aerodynamic LoadsMean aerodynamic loads acting at hub is obtained as The main rotor aerodynamic loads acting at CG of helicopter

* The geometric pitch angle is defined asThe blade flap response is represented byMoment equilibrium at the hinge of the main rotor bladeFlap Equation Motion

*Flap equation of MotionSubstituting in flap equation then apply the operator method, one obtains the flap response coefficients and

Where

*Forces and Moments on Fuselage

Tail rotor thrust The moment at the CG due to tail rotor thrust

*Forces and Moments on Fuselage

Horizontal plate and Vertical fin systemForces and Moments using lift expression Parasite drag Drag force acts in the direction opposite to the velocity vectorFuselage frontal area

Fuselage drag coefficient

*Forces and Moments on Fuselage

External Force at the CG of the helicopter External Moment at the CG of the helicopter

*Flight Dynamic EquationsHelicopter is treated as a rigid body doing a complicated manoeuvre flightGeneral manoeuvring flight condition

*Flight Dynamic Equations

Kinematic relationsYAWPITCHROLL

*Flight Dynamic Equations

Force EquationsMoment Equations

*Trim Equations

Perturbation approach

All the degrees of freedom are expressed as constant and time varying terms

These are substituted in force and moment equations.

Trim equations are obtained by separating the constant terms

*Trim Equations

Trim EquationsBlade Equilibrium Equation

*Trim Analysis

Input data,Forward speedControl and attitude anglesSolve the Inflow EquationSolve the Blade Flap EquationSolve the Force and Moment equations Check the Trim condition

*Mini Helicopter data

Mass ( kg)8.2 Radius main rotor (m)0.8(rad/s)146Ixx (kg m2)0.21Radius tail rotor (m)0.15(rad/s)628Iyy (kg m2)0.41Chord main rotor (m)0.064e0.085Izz (kg m2)0.65Chord tail rotor (m)0.03a 5.73Ixz (kg-m2)0.0 hz(m)-0.3250.01Fuselage frontal area0.0704 hx,hy (m)0.01.0 (Hz)11Mass of the blade (kg)0.186

*Results

Rigid Blade with no flapping motion:Control angles and attitude variation with forward speed

*Results

Total inflow and Power required variation with forward speed Rigid blade with no flapping motion:

*Results

Rigid blade with flapping motion:Control angles and attitude variation with forward speed =189.54Nm11Hz

*Results

Effect of flap stiffness on power required

*ResultsEffect of fuselage frontal area:

Fuselage frontal area =

=1 Fuselage drag coefficientFor big helicopter (Fuselage frontal area/Rotor area)Based on this ratio the new frontal area is calculatedPower = Parasite power (fuselage drag) + Induced power + Tail rotor power

*Results

Control angle variation with and blade flapping

*Results

Variation in pitch attitude due to fuselage frontal area

*Results

Variation in power required due to fuselage frontal area

*Concluding Remarks

Developed a flight dynamic equations for a mini helicopter, from first principles.

Using the dynamic equations the trim characteristics of mini helicopter is analyzed.

The results of the present study indicate that

The blade flapping decreases the pitch attitude of the helicopter by a small amount at all forward speeds.

The reduction in fuselage frontal area is affecting significantly pitch attitude and the power required for flight.

The increase in non-rotating flap frequency shows that the trim settings approach those corresponding to rigid blade condition in an asymptotic manner.

*Future work

Wind tunnel test is to be carried out to estimate the drag characteristics of the mini helicopter fuselage.

Using the dynamic equations of motion one can do stability analysis of mini helicopter.

Model can be used for flight control studies.

Development of a simulator model for autonomous flight.

*References

Venkatesan, C., Lecture notes on Helicopter Technology, Department of Aerospace Engineering, IIT Kanpur 2001.

Padfield, G., Helicopter Flight dynamics: The Theory and Application of Flying Qualities and Simulation Modeling, AIAA Education Series, U.S.A.1996

Kim, S.K. and Tilbury, D.M., Mathematical Modeling and Experimental Identification of a Model Helicopter, AIAA Modeling and Simulation Technologies Conference and Exhibit, Boston, MA, Aug. 10-12, 1998

Cunha, R. and Silvestre, C., SimModHeli: A dynamic Simulator for Model-Scale Helicopter, The 11th IEEE Mediterranean Conference on Control and Automation, Rhodes, Greece, June18-20, 2003.

Venkatesan, C. and Friedmann, P., Aeroelastic Effects in Multi-Rotor Vehicles with Application to a Hybrid Heavy Lift System, NASA CR- 3822, 1984.

Pradeep, Y., Flight Dynamic Modeling and Analysis of a Mini Helicopter for Trim and Stability, M.Tech Thesis, Department of Aerospace Engineering, July2006, IIT Kanpur.

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Thank you

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