Aircraft Flight Dynamics Robert F Stengel Lecture10 Linearized Equations and Modes of Motion

Aircraft Flight Dynamics Robert F. Stengel Lecture10 Linearized Equations and Modes of Motion

... Spring"Spring Force vs. Displacement"Spring" Damper"Displacement"Rate of Change" Linearized Equations   and Modes of Motion   Robert Stengel, Aircraft Flight Dynamics MAE ... matrix!Rigid-Body Equations of Motion (Scalar Notation)"•  Rate of change of Translational Position "•  Rate of change of Angular Position"•  Rate of change of Translational Velocity ... longitudinal motion& quot;Effects of longitudinal perturbations on lateral-directional motion& quot;Effects of lateral-directional perturbations on longitudinal motion& quot;Effects of lateral-directional...

Aircraft Flight Dynamics Robert F. Stengel Lecture7 Gliding, Climbing, and Turning Performance

... Glide"Climbing Flight Gliding, Climbing, and Turning Flight Performance  Robert Stengel, Aircraft Flight Dynamics, MAE 331, 2012!Copyright 2012 by Robert Stengel. All rights reserved. For educational ... reversal of direction"•  Kinetic-/potential-energy exchange"•  Yaw maneuver at low airspeed"•  X-31 performing the maneuver"Next Time: Aircraft Equations of Motion Reading Flight ... Maximum Steady Rate of Climb: "Jet-Driven Aircraft& quot;•  Condition for a maximum at constant thrust and cos2γ ~ 1"•  Airspeed for maximum rate of climb at maximum thrust,...

Aircraft Flight Dynamics Robert F. Stengel Lecture15 Transfer Functions and Frequency Response

... }Δu(s)Transfer Function Matrix"•  Frequency-domain effect of all inputs on all outputs"•  Assume control effects do not appear directly in the output: Hu = 0"•  Transfer function ... ejφα(ω)Bode Plot(Frequency Response of a Scalar Transfer Function)Angle and Rate Response of a DC Motor over Wide Input-Frequency Range "!  Long-term response of a dynamic system ... Transfer Function Matrix "•  With Hx = I, and assuming"–  Elevator produces only a pitching moment"–  Throttle affects only the rate of change of velocity"–  Flaps...

Aircraft Flight Dynamics Robert F. Stengel Lecture1 Introduction to Flight Dynamics

... Aerodynamics of Airplane Configurations!  Cruising Flight Performance!  Gliding, Climbing, and Turning Performance!  Nonlinear, 6-DOF Equations of Motion !  Linearized Equations of Motion !  ... vehicles.! Understanding of aircraft equations of motion, configuration aerodynamics, and methods for analysis of linear and nonlinear systems.! Appreciation of the historical context within which past aircraft ... Velocity"Normal "Velocity"Phases of Flight& quot; Flight of a Paper Airplane Flight of a Paper Airplane Example 1.3-1, Flight Dynamics& quot;•  Red: Equilibrium flight path"• ...

Aircraft Flight Dynamics Robert F. Stengel Lecture2 PointMass Dynamics and Aerodynamic Thrust Forces

... F aerodynamics+ F thrust⎡⎣⎤⎦IRate of change of position!Rate of change of velocity!Vector of combined forces! Equations of Motion for a Point Mass " ˙ x (t) =dx(t)dt= f[ x(t) ,F] •  ... Frame"CXCYCZ⎡⎣⎢⎢⎢⎤⎦⎥⎥⎥B=axial force coefficientside force coefficientnormal force coefficient⎡⎣⎢⎢⎢⎤⎦⎥⎥⎥CDCYCL⎡⎣⎢⎢⎢⎤⎦⎥⎥⎥=drag coefficientside force coefficientlift coefficient⎡⎣⎢⎢⎢⎤⎦⎥⎥⎥•  ... "q Equations of Motion for a Point MassNewtonian Frame of Reference"•  Newtonian (Inertial) Frame of Reference"–  Unaccelerated Cartesian frame whose origin is referenced...

Aircraft Flight Dynamics Robert F. Stengel Lecture3 Aviation History Mythology to 1990

... effects"•  Short-Takeoff -and- Landing (STOL) aircraft augment takeoff/landing lift in many ways, e.g.,"–  Full-span ﬂaps"–  Deﬂected thrust"Grumman F8 F!Grumman F4 F!GB R1!CTo,CTV,CTδT,CLδTWorld ... (1864-1928)!–  Longitudinal equations of motion (with W.E. Williams, 1903)!–  Full equations of motion and linearized equations (1911)!Comfort and Elegance by the End of the Decade!•  Boeing ... largest aircraft of its time!•  Sud-Aviation Caravelle (1959)!–  1st aircraft with twin aft-mounted engines!Small Commercial Jets of the 1960s!•  Preponderance of aft-mounted 2- and 3-engine...

Aircraft Flight Dynamics Robert F. Stengel Lecture5 Configuration Aerodynamics 2.

... Axes" f B=XBYBZB!"###$%&&&mB=LBMBNB!"###$%&&&Force Vector"Moment Vector" r × f =i j kx y z f x f y f z= yfz− zfy( )i + zfx− xfz( )j + xfy− yfx( )km =yfz− zfy( )zfx− xfz( )xfy− yfx( )#$%%%%&'((((=rf ... Dihedral effect"•  Vertical tail effect"Rolling Moment due to Sideslip Angle!•  Crossﬂow effects depend on vertical location of the wing"Example of Conﬁguration and Flap Effects!NACA ... maximum for a given polar"–  Two solutions for lower L/D (high and low airspeed)"Newtonian Flow and High-Angle -of- Attack Lift and Drag•  Aerodynamics analogous to those of the...

Aircraft Flight Dynamics Robert F. Stengel Lecture6 Cruising Flight Performance

... Cruising Flight Performance  Robert Stengel, Aircraft Flight Dynamics, MAE 331, 2012!Copyright 2012 by Robert Stengel. All rights reserved. For educational use only.!http://www.princeton.edu/ ~stengel/ MAE331.html!http://www.princeton.edu/ ~stengel/ FlightDynamics.html!•  ... Pressure and Mach Number"ρ= air density, functionof height=ρsealevele−βha = speed of sound= linear functionof height Dynamic pressure = q ρV22Mach number = V aDeﬁnitions of ... 1Typical Effects of Altitude and Velocity on Power and Thrust"•  Propeller"•  Turbojet"Thrust of a Propeller-Driven Aircraft& quot;T =ηPηIPengineV=ηnetPengineV•  Efﬁciencies...

Aircraft Flight Dynamics Robert F. Stengel Lecture8 Aircraft Equations of Motion 1

... theorem"•  Model in Pro/ENGINEER, etc." Aircraft Equations of Motion - 1  Robert Stengel, Aircraft Flight Dynamics,  MAE 331, 2012"•  6 degrees of freedom"•  Angular kinematics"•  ... solutions"•  Linear equations of motion& quot;–  Simplify computation of flight paths and solutions"–  Define modes of motion& quot;–  Provide basis for control system design and flying qualities ... Equations of Motion? "dx(t )dt= f x(t),u(t),w(t ),p(t),t[ ]dx(t )dt= F x(t ) + G u(t) + L w(t)Translational PositionCartesian Frames of Reference"•  Two reference frames of...

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