February 17, 2005

1

Aerodynamics 2 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 17, 2005

2[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Overview

3-View Drawing Airfoil Selection Wing & Tail Geometry Control Surface Sizing & Effectiveness Twist Distribution Mathematical Model Launch Conditions L/DMAX & Endurance

February 17, 2005

3[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

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 17, 2005

4[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Selig 1210: M.S.Selig,J.J.Guglielmo,A.P.Broeren and P.Giguere,"Summary of Low-Speed Airfoil Data, Volume 1 – Wind Tunnel Data

SELIG 1210 AIRFOIL

Airfoil Selection: Wing

February 17, 2005

5[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

WORTMANN FX 63-137

Wortmann FX 63-137: M.S.Selig,J.F.Donovan and D.B.Fraser,"AIRFOIL AT LOW SPEEDS – Wind Tunnel

Airfoil Selection: Wing

February 17, 2005

6[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

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

February 17, 2005

7[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Airfoil Selection: Wing

Wortmann FX67-137

Wortmann FX 63-137: M.S.Selig,J.F.Donovan and D.B.Fraser,"AIRFOIL AT LOW SPEEDS – Wind Tunnel

February 17, 2005

8[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Airfoil Selection: Wing Wortmann FX 63-137

Lift Curve

-0.5

0

0.5

1

1.5

2

-10 -5 0 5 10 15 20

Alpha (deg)

Cl

XFOIL (Re=100800)

XFOIL (Re=155600)

Experimental (Re=100800)

Experimental (Re=155600)

Wortmann FX 63-137: M.S.Selig,J.F.Donovan and D.B.Fraser,"AIRFOIL AT LOW SPEEDS – Wind Tunnel

February 17, 2005

9[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Airfoil Selection: Wing

Wortmann FX 63-137: M.S.Selig,J.F.Donovan and D.B.Fraser,"AIRFOIL AT LOW SPEEDS – Wind Tunnel

Wortmann FX63-3137Drag Polar

-0.5

0

0.5

1

1.5

2

0 0.02 0.04 0.06 0.08 0.1 0.12

Cd

Cl

XFOIL (Re=100800)

XFOIL (Re=155600)

Experimental (Re=100800)

Experimental (Re=155600)

February 17, 2005

10[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Airfoil Selection: Wing

FX-63-137 XFOIL data

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

20,000 40,000 60,000 80,000 100,000 120,000 140,000

Reynolds number

CL

max

CLmax vs. Re

February 17, 2005

11[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Airfoil Selection: Canard

NACA 0012

February 17, 2005

12[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Airfoil Selection: CanardNACA 0012 Lift Curve

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-10 -5 0 5 10 15 20 25

Alpha (deg)

Cl

XFOIL (Re=98000)

XFOIL (Re=150000)

'XFOIL (Re=3000000)

Experimental (Re=3000000)

Abbott, I.H. & A.E. von Doenhoff, “Theory of Wing Sections”

February 17, 2005

13[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Airfoil Selection: CanardNACA 0012Drag Polar

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.01 0.02 0.03 0.04 0.05 0.06

Cd

Cl

XFOIL (Re=98000)

XFOIL (Re=150000)

XFOIL (Re=3000000)

Experimental (Re=3000000

Abbott, I.H. & A.E. von Doenhoff, “Theory of Wing Sections”

February 17, 2005

14[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Airfoil Selection: Vertical Tails

Flat Plate Non-Lifting Surface No Volume Needed Ease of Construction Light Weight

February 17, 2005

15[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Geometry

Wetted Area : 9.013 ft2

Wing Canard Vertical Tail (Individual)

Area (ft2) 5.24 1.2 0.64Chord (ft) 1 0.67 1.00Span (ft) 5.24 1.8 0.64

Aspect Ratio 5.24 2.69 0.64Taper Ratio 0.7 0.7 1

Dihedral Angle 4o -4o 0o

Sweep Angle 0o 0o 45o

February 17, 2005

16[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Control Surfaces: Aileron

Span: 2.26 ft Chord: 0.2 ft Area: 0.45 ft2

-20 -15 -10 -5 0 5 10 15 20-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25AILERON force vs. Deflection

Deflection (deg)

AIL

ER

ON

fo

rce

(lb

s)

15 ft/s

22 ft/s

AIL

ER

ON

forc

e (lb

f)

February 17, 2005

17[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Control Surfaces: Rudder (Single)

Span: 0.57 ft Chord: 0.35 ft Area: 0.20 ft2

-20 -15 -10 -5 0 5 10 15 20-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6RUDDER force vs. Deflection

Deflection (deg)

RU

DD

ER

fo

rce

(lb

s)

15 ft/s

22 ft/s

RU

DD

ER

forc

e (lb

f)

February 17, 2005

18[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Control Surfaces: Elevator

Span: 1.8 ft Chord: 0.23 ft Area: 0.42 ft2

-20 -15 -10 -5 0 5 10 15 20-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6ELEVATOR force vs. Deflection

Deflection (deg)

EL

EV

AT

OR

fo

rce

(lb

s)

15 ft/s

22 ft/s

ELE

VA

TO

R fo

rce

(lbf)

February 17, 2005

19[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Wing Twist Distribution

Root: 0.35o

Tip: -6.48o

February 17, 2005

20[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Wing Twist Distribution

*Neglecting Parasite Drag

*

February 17, 2005

21[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Mathematical Model

From Prandtl’s Classical Lifting-Line Theory

*LLL CCCo

615.0oL

C 1deg067.0 L

C

io DDD CCC 030.0

oDC

eAR

CC LDi

2

44.1cos9.0 25.0maxmax clL CC

February 17, 2005

22[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Mathematical Model

Re=147,820

February 17, 2005

23[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Mathematical Model

*MMM CCCo

087.0oM

C 1deg0.00025 M

C

2

2

cos2

cos

AR

ARCC

airfoilmoM

* Raymer, Daniel P., Aircraft Design: A Conceptual Approach p.493

February 17, 2005

24[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Mathematical Model

February 17, 2005

25[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Launch Conditions

Vtake-off = 1.2Vstall = 18 ft/s Climb Angle = 20o

Angle of Attack = 4.5o

αLo = -9.12o

February 17, 2005

26[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

L/DMAX

L/DMAX=10.75

αL/Dmax=0.60o

Re=147,820

February 17, 2005

27[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

L/DMAX

L/DMAX Velocity Loiter Straight:

VL/Dmax= 21.97 ft/s

Loiter Turn: VL/Dmax= 23.12 ft/s

Re=147,820

February 17, 2005

28[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Endurance

-6 -4 -2 0 2 4 6 8 10 120

5

10

15

20

25

30Endurance with Brushed Motor

Angle of Attack [deg]

End

uran

ce [

min

]

Brushed Motor

Brushless Motor

Re=147,820

Assumptions Level Flight No Acceleration Loiter~Straight Time =

Loiter~Turning Time

February 17, 2005

29[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Summary

3-View Drawing Airfoil Selection Wing & Tail Geometry Control Surface Sizing & Effectiveness Twist Distribution Mathematical Model Launch Conditions L/DMAX & Endurance Questions?

February 17, 2005

30[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Appendix

February 17, 2005

31[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Mathematical ModelNo Wing Twist: Re=147,820

February 17, 2005

32[ Overview | 3-View | Wing 1 2 3 4 5 6 7 | Canard 1 2 3 | Tails | Geometry | Control Surfaces 1 2 3 | Wing Twist 1 2

| Mathematical Models 1 2 3 4 | Launch Conditions | L/Dmax 1 2 | Endurance | Summary | Appendix 1 2 ]

Wing Twist Distribution