March 24, 20051 Critical Design Review Michael Caldwell Jeff Haddin Asif Hossain James Kobyra John...
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Transcript of March 24, 20051 Critical Design Review Michael Caldwell Jeff Haddin Asif Hossain James Kobyra John...
March 24, 2005
1
Critical Design ReviewCritical Design Review
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
March 24, 2005 2[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Overview
Walkaround Aircraft 3-View Constraint Diagram Physical Properties Aerodynamics Dynamics & Controls Structures, Weights, & Landing Gear Propulsion Unique Aspects of the Design Constraint Diagram Revisited
March 24, 2005 3[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Walkaround
March 24, 2005 4[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
5.24
ft
3.00 ft
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
Weight 1.96 lbs
Wingspan 5.24 ft
Length 3.00 ft
Height 1.50 ft
Aspect Ratio 5.24
Cruise Speed 23 ft/s
Max Thrust 1.00 lb
March 24, 2005 5[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Constraint Diagram
Design Space
Design Point
Wing Loading: 0.376 lbf/ft2
Power Loading: 32.74 lbf/hp
LiPoly Weight: 1.97lbf
Wing Area: 5.24 ft2
Power: 0.060 hp
Takeoff
March 24, 2005 6[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Tabular Summary of Parameters
Wing Area 5.24 ft2
Canard Area 1.432 ft2
Tail Area (each) 0.915 ft2
Wetted Area 23.08 ft2
Mean Chord 1.00 ft Wing Taper Ratio 0.7 Landing Gear Skis (interchangeable) Motor Type Brushless Wing Dihedral 4º Canard Dihedral -4º Center of Gravity 1.70 ft Neutral Point 1.85 ft Static Margin 14.80% Foam & Balsa Construction Pitch Rate Feedback to Elevator
March 24, 2005 7[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Concept Selection Objectives
Selected mission objectives Assigned rankings (out of 120 possible points)
Objectives Team Ranking % of votes
Endurance (high AR, fuselage - batteries) 5 8.85
Manuverability (position of control surfaces) 8a 8.13
Lightw eight 6 8.75
Robust/Accessibility 4 9.48
Low Speed 3 10.10
Cost 12a 5.00
Stylish 2 10.21
Stable (CG vs. AC) 7 8.54
Easy To Fly (size) 8b 8.13
Technically Simple 1 10.31
High Lift (w ing area/lif t distribution) 10 7.50
Ground Clearance (props, tail) 12b 5.00
March 24, 2005 8[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Weighted Objectives
For each design, objectives are ranked either: 1 - Poor, 3 - Average, 9 - Excellent
Each objective score is multiplied by corresponding weighted average
Scores for each design concept are totaledObjectives 1 2 3 4 5 6 7
Technically Simple 9 9 3 3 1 3 3
Stylish 3 9 3 3 9 9 3
Low Speed 3 3 9 1 3 3 3
Robust/Accessibility 9 9 9 3 3 3 9
Endurance (high AR, fuselage - batteries) 3 3 3 9 3 9 3
Lightweight 9 9 1 3 1 3 9
Stable (CG vs. AC) 9 3 3 9 1 9 9
Manuverability (position of control surfaces) 9 1 3 9 1 3 3
Easy To Fly (size) 3 9 3 3 9 9 3
High Lift (wing area/ lift distribution) 9 9 3 3 9 9 9
Cost 3 3 3 3 1 3 3
Ground Clearance (props, tail) 9 9 3 1 9 9 9
Total 53.86 53.34 33.33 35.24 33.63 49.12 44.64
March 24, 2005 9[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Pugh’s Method
ConceptsObjectives
1 2 3 4 5 6 7 8 9
Technically Simple S - - - - - S S
Stylish + - S + + S S +
Low Speed S - S + + - - -
Robust/Accessibility S S S + + S S +
Endurance (high AR, fuselage - batteries) S - S + + S S -
Lightweight S - - - - S S +
Stable (CG vs. AC) S - + - S S + +
Manuverability (position of control surfaces) - S S - S S S -
Easy To Fly (size) + S S + + S S -
High Lift (wing area/lift distribution) S - S + + - - -
Ground Clearance (props, tail) S - S - + S S -
S + 2 0 1 6 7 0 1 4
S - 1 8 2 5 2 3 2 6
S s 8 3 8 0 2 8 8 1Total 1 -8 -1 1 5 -3 -1 -2
D
A
T
U
M
All other designs’ objectives are compared to design 1 (datum) + (better), - (worse), s (same)
Sum of each scoring criteria taken Design strengths and weaknesses determined
March 24, 2005 10[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Aerodynamics Overview
Airfoil Selection Twist Distribution Mathematical Model Launch Conditions L/DMAX
March 24, 2005 11[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
SELIG – WORTMANN COMPARISON
Selig 1210: M.S.Selig,J.J.Guglielmo,A.P.Broeren and P.Giguere,"Summary of Low-Speed Airfoil Data, Volume 1 – Wind Tunnel DataWortmann FX 63-137: M.S.Selig,J.F.Donovan and D.B.Fraser,"AIRFOIL AT LOW SPEEDS – Wind Tunnel
Airfoil Selection: Wing
March 24, 2005 12[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Airfoil Selection: Wing
Wortmann FX63-137
Wortmann FX 63-137: M.S.Selig,J.F.Donovan and D.B.Fraser,"AIRFOIL AT LOW SPEEDS – Wind Tunnel
March 24, 2005 13[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Airfoil Selection: Canard
NACA 0012
March 24, 2005 14[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Airfoil Selection: Vertical Tails
Flat Plate Non-Lifting Surface No Volume Needed Ease of Construction Light Weight
March 24, 2005 15[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Wing Twist Distribution
Root: 1o
Tip: -7o
March 24, 2005 16[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Mathematical Model Prandtl’s Classical Lifting Line Theory
Elliptical Loading
Parasite Drag – Component Buildup Method
22
1
-b
yo
-- 2
2
2
2
)()(b
b
b
bdyyVdyyLL
)()( yVyL
SV
LCL
2
21
eAR
CCC L
LiDi
2
- -
2
24
1)( b
bo
oi dy
yy
dyd
VV
yw
misc
cc
o Dref
wetccfD C
S
SQFFCC
S
March 24, 2005 17[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Mathematical Model
From Prandtl’s Classical Lifting-Line Theory
*LLL CCCo
615.0oL
C 1deg067.0 -L
C
io DDD CCC 0.043
oDC
eAR
CC L
Di
2
44.1cos9.0 25.0maxmax clL CC
March 24, 2005 18[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Mathematical Model
Re=147,820
March 24, 2005 19[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Mathematical Model
*4
MMM CCCoc
033.0-oMC
1deg014.0 --MC
cohowfoo MMMM CCCC
0MM
MM
MMM
o
o
fowowfo C
CCCC
CMo calculated using Roskam Vol. VI and CMα calculated from flatearth.m
March 24, 2005 20[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Launch Conditions
αLo = -9o
Vtake-off = 1.2Vstall = 18 ft/s Climb Angle = 20o
Angle of Attack = 4.5o
-9o
20o
4.5o
March 24, 2005 21[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
L/DMAX
L/DMAX=10.75
αL/Dmax=0.60o
Re=147,820
March 24, 2005 22[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
L/DMAX
L/DMAX Velocity Loiter Straight:
VL/Dmax= 21.97 ft/s
Re=147,820
Operation Point
March 24, 2005 23[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Dynamics & Controls Overview
Tail Sizing Control Surface Sizing Static Margin Trim Diagram Dihedral Angle Feedback System
March 24, 2005 24[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
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 (canard) Area = 1.432 ft2
Vertical tail Area = 0.915 ft2 (each)
March 24, 2005 25[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Tail Sizing (Class 2) Vertical Tail
Plot Cnβ versus Svt Svt = 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
March 24, 2005 26[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Tail Sizing (Class 2) Horizontal Tail
Plot Xcg and Xac versus Sht
Sht = 1.36 ft2
March 24, 2005 27[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Canard & Tail Sizing
Class 1 Sizing Class 2 Sizing
Canard Area Sht 1.43 ft2 1.36 ft2
Vertical Tail
Area Svt (each)0.92 ft2 0.91 ft2
March 24, 2005 28[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Control Surface Sizing
Span (ft) Chord (ft) Area (ft2)
Aileron (each) 1.40 0.20 0.28
Elevator 1.00 0.33 0.33
Rudder (each) 0.75 0.58 0.44
March 24, 2005 29[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
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%
March 24, 2005 30[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Actual Static Margin
Xcg = 1.70 ft
Xnp = 1.85 ft Static Margin = 14.80%
March 24, 2005 31[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
-5 0 5 10 150
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
(deg)
CL
c=-10o
c=-5o
c=0o
c=5o
c=10o
-0.3-0.2-0.100.10.20.30
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
CM
Xref
CL
CL Max
Trimmed Maximum CL
(xref = xcg)
α CL Max
α = 0o
Trim Diagram
March 24, 2005 32[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
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
Dihedral Angle
kBAEVD
March 24, 2005 33[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Dihedral Angle
EVD of the wing and canard: Wing EVD:
Canard EVD:
deg 72.3)4)(93.0(0
93.0 ,25.0/
26.03166.0/08.0/
deg 36.3)4)(84.0(0
84.0 ,35.0/
35.062.2/9.0/
EVDc
kLxfor
Lx
EVDw
kLxfor
Lx
March 24, 2005 34[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Loop Closure Description
Pitch Rate feedback to the Elevator
Objective: Establish longitudinal stability by
using pitch rate feedback by varying damping ratio of the short period mode from 0.83 to 0.99.
March 24, 2005 35[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Block Diagram
He(s) q(s)/e(s)
H (s)K
S
PilotInput
ElevatorServo Aircraft
e(s) q(s)
+ _
Pitch RateGyro
FeedbackGain
March 24, 2005 36[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Aircraft TF / Natural Frequency and Damping Ratio
Aircraft Transfer Function (Flat Earth Predator)
Undamped Natural Frequency (Short Period)
Damping Ratio (Short Period)
004912.06.14387.939.23236.25
10147.101007.09.3815.61821.90
)(
)(2345
19234
-----
-
sssss
ssss
s
sq
e
rad/sec 16.201 1
- MU
MZ qnsp
0.836 2
1
-
spn
q
sp
MUZ
M
March 24, 2005 37[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Gain Calculation, k
Gain Calculation: - Flat Earth Predator
- SISOTOOL k = 0.0857 - Root Locus Plot
For k = 0 For k = 0.0857
%83.0
sec/ 15
836.0
p
n
M
rad
%0
sec/ 5.16
99.0
p
n
M
rad
March 24, 2005 38[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Root LocusRoot Locus
Real Axis
Imagin
ary
Axis
-18 -16 -14 -12 -10 -8 -6 -4 -2 0 2-10
-8
-6
-4
-2
0
2
4
6
8
100.160.340.50.640.760.86
0.94
0.985
0.160.340.50.640.760.86
0.94
0.985
24681012141618
System: untitled1Gain: 0Pole: -12.5 + 8.2iDamping: 0.836Overshoot (%): 0.83Frequency (rad/sec): 15
March 24, 2005 39[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Root LocusRoot Locus
Real Axis
Imagin
ary
Axis
-18 -16 -14 -12 -10 -8 -6 -4 -2 0 2-10
-8
-6
-4
-2
0
2
4
6
8
100.160.340.50.640.760.86
0.94
0.985
0.160.340.50.640.760.86
0.94
0.985
24681012141618System: untitled1Gain: 0.0857Pole: -16.3 + 2.27iDamping: 0.99Overshoot (%): 0Frequency (rad/sec): 16.5
March 24, 2005 40[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Gyro and Servo Selection
Futaba GYA350 gyro Weight: 0.92 ounces Remote gain function
JR S241 sub micro servos Weight: 0.32 ounces Torque: 17 oz/in
March 24, 2005 41[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Structures Overview
Material Properties Structures Landing Gear Center of Gravity Weight and Cost Estimation V-n Diagram Wing Loading Analysis
March 24, 2005 42[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Material Properties
Density (lbf/ft3) Young’s Modulus (ksi) Yield Stress (psi)
Balsa 11 625 1725
Spruce 34 1500 8600
EPS Foam 1.5 320-360 72.5
EPP Foam 1.3 1000 4000
Epoxy 0.0625 lb/ft2 500 14500
Ultrakote 0.0156 lb/ft2 N/A N/A
Values from Fall ’04 AAE 451 projects and http://www.matweb.com
March 24, 2005 43[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Structural Geometry
Primarily EPP Foam Balsa fuselage structures
March 24, 2005 44[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Wing – Fuselage Attachment
March 24, 2005 45[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Fuselage Structure
Formers Outer Fuselage (each):
Three - 1” radius Main Fuselage:
Four - 2” radius
Stringers Outer Fuselage (each):
Seven – 1/8” x 1/8” x 36” One – 3/8” x 1/2” x 36” (for landing gear mounts)
Main Fuselage:Eight – 1/4” x 1/4” x 20”
March 24, 2005 46[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Tail Structure
Flat Plate Non-Lifting Surface No Volume Needed Ease of Construction 1/8” Balsa –
Lightweight EPP Foam Rudder
March 24, 2005 47[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Landing Gear
Wire mounting Rigid Lightweight Inexpensive Easy to construct
Interchangeable Smooth takeoff and
landing on AstroTurf®Pictures courtesy of http://www.dubro.com
March 24, 2005 48[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]
Location Front gear by canard Back gear by wing
Configuration Wire strut attached to
stringer in outer fuselage with mounting bracket
Interchangeable with wheels, skis, and floats attached to mounting blocks
Gear Configuration
Pictures courtesy of http://www.dubro.com
Fuselage Attachment Wheel/Ski/Float Attachment
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Weight Estimation
Weight (lbf)Wing 0.6460
Fuselages 0.4260Tail 0.1493
Canard 0.1190Landing Gear 0.0625
Motor 0.1250Batteries 0.1125
Servos 0.0675Rate Gyro 0.0573
Speed Controller 0.0469Receiver 0.0400
Propellers 0.0060Misc 0.1000
Total 1.9580
Tail 8%
Wing 35%Fuselages 23%
Propellers 0%
Receiver 2%
Rate Gyro 3%Speed
Controller 3%
Canard 6%
Landing Gear 3%
Motor 7%
Batteries 6% Servos 4%
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Cost Estimation
CostsMotor and Controller $134.00
Gyro $124.99Receiver $69.00
Servos $65.96Battery $29.90
EPP Foam $60.00Propellers $22.00Ultrakote $18.00
Balsa $15.00Landing Gear $15.00
Total $553.85(Team Cost) $130.00
(Purdue Cost) $423.85
Balsa12%
Landing Gear12%
Propellers17%
EPP Foam45%
Ultrakote14%
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V-n Diagram Level Flight
Turning Flight
Max Load Factor
Vdive ~ 50% higher than Vcruise
nmax=2.7778-g @ Vloiter = 25 ft/sec
22max stallVVn
W
SVCnL L
22
1
maxmax
SVCWL stallL2
21
max
Typical limit load factors for general aviation (npositive = 3.0-g, nnegative = -1.5-g)from Raymer, Daniel P., Aircraft Design: A Conceptual Approach p.407
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Wing Loading Analysis
Analysis Load Distribution and Maximum Wing
Loading Maximum Wing Root Bending Moment Maximum Torsional Moment Maximum Wing Tip Deflection Maximum Bending Stress
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Bending
Worst case simplification Cantilevered beam Negligible weight, outer fuselage mass/support Elliptical load distribution
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Twisting
Moment due to lift found from moment coefficient
212 mM C V S
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Constraints
Twisting: less than one degree of twist
Bending: bending stress less than EPP foam yield stress (w/ safety factor of 2)
ML
GI 21
2 mM C V S
My
I
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Analysis
Maximum wing load: 1.97 lbs of lift, elliptical loading, load
factor of 2.77 yields 5.45 lbs Maximum bending moment (at root):
3.623 ft-lbs
Maximum torsional moment (from Cm): 0.194 ft-lbs
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Results
Maximum wing stress: 361.80 psi
Maximum tip deflection: 0.16 in.
Maximum rotation: 0.13 degrees
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Moments and Products of Inertia
Balsa Components:
Volume = 86.51099 (+/- 0.00014) cubic inches
Volume Centroid = 4.025129,2e-007,1.06559 (+/- 8.6e-006,2.2e-006,1.2e-005)
Volume Moments:
Volume Moments of Inertia about World Coordinate Axes Ix: 3479.97 (+/- 0.0035) Iy: 9483.726 (+/- 0.014) Iz: 11292.75 (+/- 0.012)
Volume Moments of Inertia about Centroid Coordinate Axes Ix: 3381.738 (+/- 0.011) Iy: 7983.872 (+/- 0.045) Iz: 9891.13 (+/- 0.035)
Foam Components:
Volume = 1048.1777 (+/- 0.00012) cubic inches
Volume Centroid = 2.468645,1.1e-005,0.7137613 (+/- 3.5e-006,2.7e-006,2.4e-006)
Volume Moments:
Volume Moments of Inertia about World Coordinate Axes Ix: 222524.954 (+/- 0.0066) Iy: 98029.872 (+/- 0.043) Iz: 317314.68 (+/- 0.042)
Volume Moments of Inertia about Centroid Coordinate Axes Ix: 221990.954 (+/- 0.017) Iy: 91108.06 (+/- 0.11) Iz: 310926.87 (+/- 0.097)
Calculated from CAD Model Multiply by material density to determine
Mass MOI
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Propulsion Overview
Propeller Selection Component Trade Study Motor & Battery Selection
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Prandtl & Goldstein
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.05
0.1
0.15Radial Thrust Distribution
dC
Td
x
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.02
0.04
0.06
0.08Radial Power Distribution
nondimensional radial location
dC
Pd
x
PrandtlGoldstein
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0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9Effect of Advance Ratio on Propeller Efficiency
Advance Ratio
Pro
pe
ller
Effi
cie
ncy
2 Blade3 Blade
Propeller Efficiency and Advance Ratio
Operation Range J = 0.35 - 0.45
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Thrust Coefficient and Advance Ratio
0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.60
5
10
15
20
25Effect of Advance Ratio on Thrust Coefficient
Advance Ratio
Th
rust
[oz]
2 blades3 blades
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Propeller Efficiency and Advance Ratio
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9Effect of Advance Ratio on Propeller Efficiency
Advance Ratio
Pro
pe
ller
Effi
cie
ncy
2 Blade3 Blade
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Propeller Selection
2 Blades 8 in Diameter 5 in Pitch
Phase Flight Speed
[ft/s] Thrust [oz]
% Throttle *
Propeller Efficiency
Power [W] **
Take-off 18 3.15 50% 63% 10 Climb 18 4.00 55% 59% 14 Level Flight 22 2.93 51% 70% 10 Turn 23 3.24 54% 70% 12
Aerobatic 25 8.00 77% 59% 38 3 Blades 8 in Diameter 6 in Pitch Take-off 18 3.15 40% 65% 10
Climb 18 4.00 44% 61% 13 Level Flight 22 2.93 41% 72% 10 Turn 23 3.24 43% 69% 12
Aerobatic 25 16.00 83% 49% 92 * max motor RPM is 9350, direct drive ** power required from the battery (assumes75% motor efficiency)
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Component Trade Study• Graupner Speed 500 60% too powerful, unreliable data
• Each “Tier” represents a battery / motor combination
• More selection with Li & Brushless
• Connectors for brushed motors and Li batteries are not compatible. It would not be wise to have a Li & brushed combination.
• Our Aircraft needs to weigh less than 32 oz
Battery & Motor Weight vs Total Aircraft Weight
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 20 40 60 80 100 120
Total Aircraft Weight (oz)
Est
imat
ed C
om
po
nen
t W
eig
ht
(lb
)
Brushless & Li Brushed & Ni Brushed & Li
www.hobby-lobby.comwww.balsapr.com
Our Aircraft
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Thrust, Power, and Endurance
Δt
EP
E
)req(input)req(input
tNN
Preqinput
propmotor
reqoutput
..
..)(
mAhΔtVolts
WattsmAh hoursbrushless 300
Phase Time (s) Energy (ft-lb) Power (hp) Power (W) mAhTake-off 5 27 0.01 7.29 1.37Climb 5 36 0.01 9.72 1.82
Level Flight 445 2791 0.01 8.50 142.05Turn 445 3119 0.01 9.50 158.73Total 900 5973 N/A N/A 303.97
Brushless Nmotor=85%, Nprop=74%
Phase Speed Friction Coefficient Thrust Required (oz)Take Off N/A 0.3 2.4Take Off N/A 0.5 3
Climb 18 N/A 4Loiter 20 N/A 3Turn 20 N/A 3.2
Airspeed
Amps
“Sedate” Mission 15min
Airspeed
Amps
“Trainer” Mission 23min
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Motor & Battery Selection
ComponentsProp 2 Code• Calculates near 900mAh necessary to fly mission
• Fails to include component energy requirements
• Components need approximately 150mAh across our mission
• 1050mAh battery necessary
• Kokam 1200mAh battery chosen on grounds of weight & preferred vendors
Component Product Name Weight (oz) PriceMotor AXI 2212/20 2.00 $58.20
Speed Controller Jeti 18amp 0.32 $75.80Prop Graupner 2 Blade 0.10 $4.50Prop Graupner 3 Blade 0.14 $6.50
Battery Kokam 1200mAh 1.80 $29.90Total 4.22 $185.90
Brushless Motor Selection
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Unique Aspects of the Design
Twin Boom Design EPP Foam Robust Interchangeable Landing Gear Brushless Motor 3-Bladed Prop Alternative
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Remaining Design Problems
Updating SURFCAM Possible Wing Area Updates Landing Gear Position
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Constraint Diagram Revisited
Design Space
Current Design Point
Weight: 2.06 Lbf
Wing Area 5.30 ft2
Power: 0.06 hp
Wing Loading: 0.39 lbf/ft2
Power Loading: 34.33 lbf/hp
Desired Design Point
Takeoff
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Summary
Walk Around Aircraft 3-View Constraint Diagram Physical Properties Aerodynamics Dynamics & Controls Structures, Weights, & Landing Gear Propulsion Unique Aspects of the Design Constraint Diagram Revisited
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Questions?
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Appendix
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Turning Conditions
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L/D Mathematical Model
41
22
2
2
***
-
turn
LL
turn
rgCCS
WV
o
2
222 ***
2
1* turnL
turn
turnturn VCSg
r
VWL
* Raymer, Daniel P., Aircraft Design: A Conceptual Approach p.493
***
21
LL
straight
CCS
WV
o
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L/DMAX
L/DMAX Velocity Loiter Straight:
VL/Dmax= 21.97 ft/s
Loiter Turn: VL/Dmax= 23.12 ft/s
Re=147,820
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Effect of Control Surface Deflection: Lift
ic c
cL c L
SC C
S
1 slipc
cc
Sx
S
c ic c
L LC a C
'L
c Theory
Theory c l
l Cb l
l l C
aC ka K C
C C a
Roskam,Jan, Airplane Design PartVI: Prelimenary Calculation of Aerodynamic, Thrust, and Power Characteristics, 2000
CTL ic cL L c L cC C i C
CTLo LLLL CCCC
*
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Effect of Control Surface Deflection: Pitching Moment
ctl ic cM M c M cC C i C
ic cM L c cC C V
c
cc ac cg
SV x x
S
c ic c
M MC a C
Roskam,Jan, Airplane Design PartVI: Prelimenary Calculation of Aerodynamic, Thrust, and Power Characteristics, 2000
CTLorefx MMMM CCCC
*