March 10, Dynamics & Controls 2 PDR Michael Caldwell Jeff Haddin Asif Hossain James Kobyra John McKinnis Kathleen Mondino Andrew Rodenbeck Jason Tang Joe Taylor Tyler Wilhelm AAE 451: Team 2

[ ] March 10, Overview Aircraft 3-View Trim Diagram Loop Closure Description Block Diagram Aircraft Transfer Function Pitch Rate Gyro Transfer Function Servo Transfer Function Gain Calculation Root Locus, Bode, and Nyquist Plot

[ ] March 10, Mission Requirements 15 min. endurance Take-off distance ≤ 60 ft. V stall ≤ 15 ft/s V loiter ≤ 25 ft/s 35 ft. turn radius Aircraft 3-View

[ ] March 10, Effect of Control Surface Deflection: Lift Roskam,Jan, Airplane Design PartVI: Prelimenary Calculation of Aerodynamic, Thrust, and Power Characteristics, 2000

[ ] March 10, Effect of Control Surface Deflection: Pitching Moment Roskam,Jan, Airplane Design PartVI: Prelimenary Calculation of Aerodynamic, Thrust, and Power Characteristics, 2000

[ ] March 10, Trim Diagram C L Max Trimmed Maximum C L (x ref = x cg ) α CL Max α = 0 o

[ ] March 10, Loop Closure Description Pitch Rate feedback to the Elevator Objectives: 1) Establish longitudinal stability by using pitch rate feedback by varying damping ratio of the short period mode from 0.83 to ) Numerical values for all physical constants in the transfer functions.

[ ] March 10, Block Diagram H e (s) q(s)/  e (s) H (s)K  Pilot Input Elevator Servo Aircraft  e (s ) q(s) + _ Pitch Rate Gyro Feedback Gain

[ ] March 10, Dynamic Models Aircraft Transfer Function

[ ] March 10, Longitudinal Non-Dimensional Stability Derivatives Pitching moment coefficient due to elevator deflection Pitching moment coefficient due to angle of attack Pitching moment coefficient due to rate of change of angle of attack Pitching moment coefficient due to pitch rate Lift coefficient due to elevator deflection = = = = = Equation Description Value

[ ] March 10, Longitudinal Dimensional Stability Derivatives Pitch angular acceleration per unit elevator angle Vertical acceleration per unit elevator angle Pitch angular acceleration per unit angle of attack Pitch angular acceleration per unit rate of change of AOA Vertical acceleration per unit angle of attack Pitch angular acceleration per unit pitch rate Equation Description Value = [(rad/s 2 )/rad] = [(ft/s 2 )/rad] = [(rad/s 2 )/rad] = [(rad/s 2 )/(rad/s)] = [(ft/s 2 )/rad] = [(rad/s 2 )/(rad/s)]

[ ] March 10, Dynamic Models Aircraft Transfer Function (short Period Approx.) Aircraft Transfer Function (Flat Earth Predator)

[ ] March 10, Natural Frequency and Damping Ratio Undamped Natural Frequency Damping Ratio

[ ] March 10, Dynamic Models Pitch Rate Gyro Transfer Function Futaba GYA350 Gyro :  The Gyro Mixer  The Gyroscope or Sensor  The Switch/Gain Control Unit (SW Unit)

[ ] March 10, Dynamic Models Servo Transfer Function Hitec HS-55 Economy Sub Micro Servos The servo is used to convert voltage (  v ) to elevator deflection (  e )

[ ] March 10, Gain Calculation, k First Trial: Determine k by trial and error: - Using the modified DesignPitch.m file - Matlab code to approximate short period mode Second Trial: - Flat Earth Predator - SISOTOOL k =

[ ] March 10, Root Locus

[ ] March 10, Root Locus

[ ] March 10, Gain Calculation, k For k = 0 For k =

[ ] March 10, Bode Plot

[ ] March 10, Nyquist Plot

[ ] March 10, Questions ?

[ ] March 10, Appendix

[ ] March 10, Tail Sizing Comparison Class 1 SizingClass 2 Sizing Canard Area S ht ft ft 2 Vertical Tail Area S vt (each) ft ft 2

[ ] March 10, Control Surface Sizing Span (ft)Chord (ft)Area (ft 2 ) Aileron Elevator Rudder (each)

[ ] March 10, Control Surface Comparison Team 2 Spring 2005 Team 1 Fall 2004 Team 4 Fall 2004 Aileron Area Wing Area Elevator Area Canard Area Rudder Area Vtail Area *Areas compared – Ongoing Research for Moments

[ ] March 10, Actual Static Margin X cg = 1.70 ft X np = 1.85 ft Static Margin = 14.80%

[ ] March 10, Variation of Yawing Moment Coefficient with Sideslip Angle Roskam,Jan, Methods for Estimating Stability and Control Derivatives of Conventional Subsonic Airplanes, 1977

[ ] March 10, Variation of Rolling Moment Coefficient with Sideslip Angle Roskam,Jan, Methods for Estimating Stability and Control Derivatives of Conventional Subsonic Airplanes, 1977

[ ] March 10, Variation of Pitching Moment Coefficient with Elevator Angle Roskam,Jan, Methods for Estimating Stability and Control Derivatives of Conventional Subsonic Airplanes, 1977

[ ] March 10, Variation of Yawing Moment Coefficient with Rudder Deflection Roskam,Jan, Methods for Estimating Stability and Control Derivatives of Conventional Subsonic Airplanes, 1977

[ ] March 10, Variation of Rolling Moment Coefficient with Aileron Deflection Roskam,Jan, Methods for Estimating Stability and Control Derivatives of Conventional Subsonic Airplanes, 1977

[ ] March 10, Longitudinal Static Stability Aircraft starting from straight, level, trimmed flight with small perturbations has two independent natural motions acting about an aircraft’s pitch axis. Longitudinal Modes: 1. Short Period Mode (Heavy damping and high frequency) 2. Phugoid Mode (Less damping and low frequency)

[ ] March 10, Longitudinal Static Stability Short Period Mode:

[ ] March 10, Longitudinal Static Stability Phugoid Mode:

[ ] March 10, Longitudinal Static Stability Short Period Mode Phugoid Mode

[ ] March 10, Lateral Directional Stability Lateral directional EOMs can be expressed by a second order differential equation and two first order differential equations. Lateral-directional Modes: 1. Dutch Roll Mode 2. Spiral Mode 3. Roll Mode

[ ] March 10, Lateral Directional Stability Dutch Roll mode:

[ ] March 10, Lateral Directional Stability Dutch Roll mode: Spiral Mode: Roll Mode:

[ ] March 10, Lateral Directional Stability Desired spiral mode time constant is excess of 20 seconds Desired roll mode time constant is 0.5 to 3 seconds