February 24, Dynamics & Controls 1 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

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Overview Tail Sizing (Class 1) Control Surface Sizing Tail Sizing (Class 2) Center of Gravity Aerodynamic Centers Static Margin Dihedral Angle Stability Longitudinal Static Stability and Modes Lateral Directional Stability and Modes

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Aircraft 3-View Mission Requirements 15 min. endurance Take-off distance ≤ 60 ft. V stall ≤ 15 ft./s V loiter ≤ 25 ft./s 35 ft. turn radius

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Tail Sizing (Class 1) Tail Areas  S HT = c HT C w S w /L HT  S VT = c VT b w S w /L VT c HT = Horizontal tail volume coefficient c VT = Vertical tail volume coefficient C w = Wing mean chord S w = Wing planform area L HT = Horizontal tail moment arm L VT = Vertical tail moment arm

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Tail Sizing (Class 1) Constants  c HT = 0.50  c VT = 0.05  C w = 1 ft  S w = 5.24 ft  L HT = 1.83 ft  L VT = 0.75 ft Horizontal tail  Area = ft 2 Vertical tail (canard)  Area = ft 2 (each)

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Control Surface Sizing Typical Values (Raymer)  Aileron 50-90% span & 15-25% chord  Elevator 90% span & 25-50% chord  Rudder 90% span & 25-50% chord

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Control Surface Sizing Span (ft)Chord (ft)Area (ft 2 ) Aileron Elevator Rudder (each)

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, 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

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Tail Sizing (Class 2) Horizontal Tail  Plot X cg and X ac versus S ht  S ht = ft 2 15%

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Tail Sizing (Class 2) Vertical Tail  Plot X cg and X ac versus S ht  S ht = ft 2

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Tail Sizing Comparison Class 1 SizingClass 2 Sizing Canard Area S ht ft ft 2 Vertical Tail Area S vt (each) ft ft 2

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Center of Gravity Canard/Batteries Propeller Motor Booms Receiver & Servos Wing Fuselage Speed Controller Vertical Tail CG CG at ft from leading edge

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Aerodynamic Centers Aerodynamic centers of wing and canard each at the quarter- chord position

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Aircraft Neutral Point C L  = Wing Lift curve slope X acw = Location of Wing Aerodynamic Center C m  fus =Fuselage pitching moment  h = Ratio of tail dynamic pressure to freestream dynamic pressure C L  h = Horizontal Tail Lift curve slope X ach = Location of Horizontal tail Aerodynamic Center

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Desired Static Margin Static Margin (Raymer)  Typical Fighter Jet: 0-5%  Typical Transport Aircraft = 5-10%  Model aircraft usually more stable Goal: Static Margin = 15%

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Actual Static Margin X cg = 1.70 ft X np = 1.85 ft Static Margin = 14.80%

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Dihedral Angle Equivalent V-Dihedral (EVD) It is helpful to express required and actual dihedral of an aircraft in terms of “Equivalent V-dihedral.”

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Dihedral Angle Outer Panel Dihedral Wing: 4 deg outer panel dihedral, B=4 deg and x at 0.9 ft Canard: -4 deg outer panel dihedral, B=4 deg and x at 0.08 ft

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Dihedral Angle EVD of the wing and canard: Wing EVD: Canard EVD:

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Effective Wing Area “Effective wing area that is contributing to the lift:

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Stability Characteristic Equation Roots of the characteristic equation,

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Stability Longitudinal Static Stability Lateral Directional Stability

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, 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)

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Longitudinal Static Stability Short Period Mode:

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Longitudinal Static Stability Phugoid Mode:

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Longitudinal Static Stability Short Period Mode Phugoid Mode

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, 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

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Lateral Directional Stability Dutch Roll mode:

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Lateral Directional Stability Dutch Roll mode: Spiral Mode: Roll Mode:

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Lateral Directional Stability Desired spiral mode time constant is excess of 20 seconds Desired roll mode time constant is 0.5 to 3 seconds

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Summary Tail Sizing (class 1 & 2) Control surface sizing Aerodynamic center and C.G. Locations Dihedral Angles Longitudinal Static Stability and modes Lateral Directional Stability and modes

[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface | Tail Sizing (Class 2) | CG | AC 1 2 | Static Margin 1 2 | Dihedral Angle | Stability 1 2 | Longitudinal | Lateral | Summary ]Overview3-View CG Summary February 24, Questions Polygonia interrogationis known as Question Mark