Aircraft Flight Dynamics Robert F Stengel Lecture14 RootLocus Analysis of Parameter Variations

Aircraft Flight Dynamics Robert F. Stengel Lecture14 RootLocus Analysis of Parameter Variations

... Locus Analysis of Parameter Variations Robert Stengel, Aircraft Flight Dynamics MAE 331, 2012"•  Effects of system parameter variations on modes of motion"•  Root locus analysis& quot;–  ... Variation in aircraft aerodynamic conﬁguration"–  Effect of feedback control, i.e., control of pitching moment (via elevator) that is proportional to pitch rate"Effect of Parameter Variations ... Number of zeros of the numerator = q"Spirule"Origins of Roots (for k = 0)"Δ(s) = d(s) + kn (s)k → 0# →## d(s)•  Origins of the roots are the Poles of d(s)"Effect of a0...

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

... 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"•  ... a sound footing for the development of future aircraft. More Learning Objectives"!  Detailed evaluation of the linear and nonlinear flight characteristics of a specific aircraft type."! ...

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

... =vxvyvz⎡⎣⎢⎢⎢⎢⎤⎦⎥⎥⎥⎥ F I= f x f y f z⎡⎣⎢⎢⎢⎢⎤⎦⎥⎥⎥⎥I= F gravity+ F aerodynamics+ F thrust⎡⎣⎤⎦IRate of change of position!Rate of change of velocity!Vector of combined forces!Equations of ... Frame"CXCYCZ⎡⎣⎢⎢⎢⎤⎦⎥⎥⎥B=axial force coefficientside force coefficientnormal force coefficient⎡⎣⎢⎢⎢⎤⎦⎥⎥⎥CDCYCL⎡⎣⎢⎢⎢⎤⎦⎥⎥⎥=drag coefficientside force coefficientlift coefficient⎡⎣⎢⎢⎢⎤⎦⎥⎥⎥•  ... "qEquations of Motion for a Point MassNewtonian Frame of Reference"•  Newtonian (Inertial) Frame of Reference"–  Unaccelerated Cartesian frame whose origin is referenced to an...

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 ... wings!–  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- ... Sabreliner!Commercial Transport Aircraft Commercial Aircraft of the 1940s!•  Pre-WWII designs!•  Derivatives of military transport and bomber aircraft of WWII!–  Convair 240 (> C-131,...

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 ... =Surface∫LBMBNB"#$$$%&''' f B= f x f y f z!"####$%&&&&dx dy dzSurface∫=XBYBZB!"###$%&&&Configuration Aerodynamics - 2  Robert Stengel, Aircraft Flight...

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!•  ... tubes on Fouga Magister"Cessna 172 pitot tube"X-15 Q Ball" Flight Testing Instrumentation"•  Air data measurement far from disturbing effects of the aircraft& quot;z ... CT12ρV3S ≈ independent of airspeedThrust = T = CT12ρV2S ≈ independent of airspeed•  Throttle Effect"T = TmaxδT = CTmaxδTqS, 0 ≤δT ≤ 1Typical Effects of Altitude and Velocity...

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 ... Flight Envelope Flight Envelope Determined by Available Thrust"•  Flight ceiling deﬁned by available climb rate"–  Absolute: 0 ft/min"–  Service: 100 ft/min"–  Performance: ... stall"•  Flow-separation buffet"–  Angle of attack"–  Local shock waves"Piper Dakota Stall Buffet"http://www.youtube.com/watch?v=mCCjGAtbZ4g!Boeing 787 Flight Envelope...

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

... Construct aircraft moments and products of inertia from components using parallel-axis theorem"•  Model in Pro/ENGINEER, etc." Aircraft Equations of Motion - 1  Robert Stengel, Aircraft ... Rate"Rate of Change of Angular Momentum•  Moments and products of inertia tabulated for geometric shapes with uniform density"Moments and Products of Inertia"(Bedford & Fowler)"•  ... sequences of 3 rotations can be chosen; however, once sequence is chosen, it must be retained"Effects of Rotation on Vector Transformation from Inertial to Body Frame of Reference"Yaw...

Aircraft Flight Dynamics Robert F. Stengel Lecture9 Aircraft Equations of Motion 2

... sinγ!"###$%&&&Relationship of Inertial Axes to Velocity Axes" Aircraft Equations of Motion - 2  Robert Stengel, Aircraft Flight Dynamics, MAE 331, 2012"•  Rotating frames of reference"•  ... IB−1MB−ωBIBωB( )•  Rate of change of Translational Position "•  Rate of change of Rotation Matrix "•  Rate of change of Translational Velocity "•  Rate of change of Angular Velocity ... )•  Rate of change of Translational Velocity "•  Rate of change of Angular Velocity "Mirror symmetry, Ixz ≠ 0# FLIGHT - Computer Program to Solve the 6-DOF Equations of Motionhttp://www.princeton.edu/ ~stengel/ FlightDynamics.html!FLIGHT...

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

... 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 ... )det A(n × n)(1 × 1)=CTdet A; C = matrix of cofactorsCofactors are signed minors of A"ijth minor of A is the determinant of A with the ith row and jth column removed"y ... Numerically"–  First differences in f( x,u,w)"•  Analytically"–  Symbolic evaluation of analytical models of F, G, and L" F( t ) =∂ f ∂xx =xN(t )u = uN(t )w = wN(t )G(t ) =∂ f ∂ux...

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