february 24, 20051 dynamics & controls 1 pdr michael caldwell jeff haddin asif hossain james...
DESCRIPTION
[ 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 radiusTRANSCRIPT
February 24, 2005
1
Dynamics & Controls 1 PDR
Michael CaldwellMichael CaldwellJeff HaddinJeff Haddin
Asif HossainAsif HossainJames KobyraJames KobyraJohn McKinnisJohn McKinnis
Kathleen MondinoKathleen MondinoAndrew RodenbeckAndrew RodenbeckJason TangJason TangJoe TaylorJoe TaylorTyler WilhelmTyler Wilhelm
AAE 451: Team 2AAE 451: Team 2
February 24, 2005
2[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
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
February 24, 2005
3[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Aircraft 3-View
Mission Requirements
15 min. endurance
Take-off distance ≤ 60 ft.
Vstall ≤ 15 ft./s
Vloiter ≤ 25 ft./s
35 ft. turn radius
February 24, 2005
4[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Tail Sizing (Class 1)
Tail Areas SHT = cHTCwSw/LHT
SVT = cVTbwSw/LVT cHT = Horizontal tail volume coefficient cVT = Vertical tail volume coefficient Cw = Wing mean chord Sw = Wing planform area LHT = Horizontal tail moment arm LVT = Vertical tail moment arm
February 24, 2005
5[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Tail Sizing (Class 1)
Constants cHT = 0.50 cVT = 0.05 Cw = 1 ft Sw = 5.24 ft LHT = 1.83 ft LVT = 0.75 ft
Horizontal tail Area = 1.432 ft2
Vertical tail (canard) Area = 0.915 ft2 (each)
February 24, 2005
6[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
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
February 24, 2005
7[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Control Surface Sizing
Span (ft) Chord (ft) Area (ft2)
Aileron 2.62 0.20 0.524
Elevator 1.92 0.33 0.634Rudder (each) 0.82 0.50 0.410
February 24, 2005
8[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Control Surface Comparison
Team 2 Spring 2005
Team 1Fall 2004
Team 4 Fall 2004
Aileron AreaWing Area 0.100 0.204 .0102
Elevator AreaCanard Area 0.442 0.198 0.258
Rudder AreaVtail Area 0.448 0.400 0.326
*Areas compared – Ongoing Research for Moments
February 24, 2005
9[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Tail Sizing (Class 2) Horizontal Tail
Plot Xcg and Xac versus Sht Sht = 1.557 ft2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25Horizontal Tail Sizing
Horizontal Tail Area Sht (ft2)
X ac a
nd X
cg
Xac
Xcg
15% Static Margin
15%
February 24, 2005
10[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Tail Sizing (Class 2) Vertical Tail
Plot Xcg and Xac versus Sht Sht = 0.912 ft2
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1Vertical Tail Sizing
Vertical Tail Area Svt (ft2)
Cn
Cn variation
Desired Cn
Size of Vertical Tail
February 24, 2005
11[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Tail Sizing Comparison
Class 1 Sizing Class 2 Sizing
Canard Area Sht 1.432 ft2 1.557 ft2
Vertical Tail Area Svt (each) 0.915 ft2 0.912 ft2
February 24, 2005
12[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Center of Gravity
Canard/Batteries Propeller Motor Booms Receiver & Servos Wing Fuselage Speed Controller Vertical Tail
CG
CG at 1.7077 ft from leading edge
February 24, 2005
13[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Aerodynamic Centers
Aerodynamic centers of wing and canard each at the quarter-chord position
February 24, 2005
14[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Aircraft Neutral Point
achh
Lw
hhL
achh
Lw
hhmacwL
np
XCSSC
XCSSCXC
X
h
hfus
CL = Wing Lift curve slope Xacw = Location of Wing Aerodynamic Center Cmfus=Fuselage pitching moment h = Ratio of tail dynamic pressure to freestream dynamic pressure CLh = Horizontal Tail Lift curve slope Xach = Location of Horizontal tail Aerodynamic Center
February 24, 2005
15[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
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%
February 24, 2005
16[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Actual Static Margin
Xcg = 1.70 ft Xnp = 1.85 ft Static Margin = 14.80%
February 24, 2005
17[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Dihedral Angle
Equivalent V-Dihedral (EVD)
It is helpful to express required and actual dihedral of an aircraft in terms of “Equivalent V-dihedral.”
February 24, 2005
18[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
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
kBAEVD
February 24, 2005
19[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Dihedral Angle
EVD of the wing and canard: Wing EVD:
Canard EVD:
deg 72.3)4)(93.0(093.0 ,25.0/
26.03166.0/08.0/
deg 36.3)4)(84.0(084.0 ,35.0/
35.062.2/9.0/
EVDckLxfor
Lx
EVDwkLxfor
Lx
February 24, 2005
20[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Effective Wing Area
“Effective wing area that is contributing to the lift:
99%
1002.62
2.6158 essEffectiven Area
ft Sq 2.6158 4cos)72.1((0.9)cos0
coso
2
o
eff aSS
February 24, 2005
21[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Stability
Characteristic Equation
02 22 nnss Roots of the characteristic equation,
12
442 & 2
222
21
nnnnnss
frequencynaturalUndampedratioDamping
where
n
,
February 24, 2005
22[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Stability
Longitudinal Static Stability Lateral Directional Stability
February 24, 2005
23[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Longitudinal Static Stability
Aircraft starting from straight, level, trimmed flight with small perturbations has twoindependent 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)
February 24, 2005
24[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Longitudinal Static Stability
Short Period Mode:
02 22 spsp nnsp ss
2
)( and 1
sp1 sp
spn
n
MUZM
MUMZ
February 24, 2005
25[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Longitudinal Static Stability
Phugoid Mode:
02 22 phph nnph ss
)(2
22
and 2
sp
11
DLn
u
un
CCX
Ug
UgZ
ph
ph
February 24, 2005
26[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Longitudinal Static Stability
Short Period Mode
Phugoid Mode
0.477 and 10.278 sp spn
0.113 and 0.166 ph phn
February 24, 2005
27[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Lateral Directional Stability
Lateral directional EOMs can be expressed bya second order differential equation and twofirst order differential equations.Lateral-directional Modes:1. Dutch Roll Mode2. Spiral Mode3. Roll Mode
February 24, 2005
28[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Lateral Directional Stability
Dutch Roll mode: 02 22
drdr nndr ss
z
nn I
SbqCDR
zn
nDR ICSbC
r
3
768.1
axis. z about the inertia ofMoment
rate. yaw toduet coefficienmoment yawin Change
angle. sideslip toduet coefficienmoment yawin Change
z
n
n
I
C
C
r
February 24, 2005
29[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Lateral Directional Stability
Dutch Roll mode:
Spiral Mode:
Roll Mode:
0.109 and 2.047 dr drn
01
s
s
01
r
s
ConstantTimeModeSpiraliss
ConstantTimeModeRollisr
February 24, 2005
30[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Lateral Directional Stability
Desired spiral mode time constant is excess of 20 seconds
Desired roll mode time constant is 0.5 to 3 seconds
February 24, 2005
31[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
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
February 24, 2005
32[ Overview | 3-View | Tail Sizing (Class 1) 1 2 | Control Surface 1 2 3 | Tail Sizing (Class 2) 1 2 3 | CG | AC 1 2 |Static Margin 1 2 | Dihedral Angle 1 2 3 4 | Stability 1 2 | Longitudinal 1 2 3 4 | Lateral 1 2 3 4 | Summary ]
Questions
Polygonia interrogationis known as Question Mark