Critical Design Review AAE451 – Team 3 Project Avatar December 9, 2003 Brian Chesko Brian Hronchek Ted Light Doug Mousseau Brent Robbins Emil Tchilian

Aircraft Name Avatar av·a·tar - n. - 1. <chat, virtual reality> An image representing a user in a multi-user virtual reality. Source: The Free On-line Dictionary of Computing http://wombat.doc.ic.ac.uk/foldoc/

Introduction Walk Around Design Requirements and Objectives Sizing Propulsion Aerodynamics Dynamics and Controls Structures Performance Cost Summary Questions

Aircraft Walk Around Wing Span = 14.4 ft Wing Chord = 2.9 ft A/C Length = 10 ft T-Tail – NACA 0012 Pusher Internal Pod Tricycle Gear Low wing – Clark Y

Design Requirements & Objectives Maximum weight < 55 lbs Cruise speed > 50 ft/sec Stall speed < 30 ft/sec Climb angle > 5.5° Operating ceiling > 1000 ft Flight time > 30 minutes Payload of 20 lbs in 14”x6”x20” pod Carry pitot-static boom Spending limit < $300 T.O. distance < 106 ft (~60% of McAllister Park runway length) Rough field capabilities Detachable wing Easy construction

Constraint Diagram

Propulsion

Ref. www.towerhobbies.com Chosen Engine O.S. Max 1.60 FX-FI 3.7 BHP @ 8500 RPM 1,800-9,000 RPM 2.08 lbs Fuel Injected Ref. www.towerhobbies.com

Chosen Propeller 4-blades Zinger 16X7 Wood Pusher Propeller 16 inches in diameter with 7 inch pitch 4 blades Ref. www.zingerpropeller.com

Ref. www.towerhobbies.com Chosen Fuel Tank Fuel tank chosen is: Du-Bro 50 oz. fuel tank Available from Tower Hobbies Located at the C.G. of aircraft Good for up to 32 min. of flight time (when completely full). Ref. www.towerhobbies.com

Takeoff EOM Integration Thrust Drag + Rolling Friction Position [ft] Velocity [ft/s] Velocity vs. Position at Takeoff Takeoff Distance Within Constraint

Max Velocity Maximum Velocity Thrust Thrust/Drag [lbf] Drag Flying Velocity [ft/s] Thrust/Drag [lbf] Maximum Velocity Thrust Drag

Aerodynamics

Wing Dimensions Prandtl’s Lifting line theory used for aerodynamic modeling of the lifting components Input parameters: AR, a0, aL=0, a. Lifting Line Model Gives CL, CDi at prescribed a CDvisc found using Xfoil which was used to obtain CD = CDi+CDvisc 5° Dihedral

Clark Y Airfoil has low drag over range of interest Airfoil Selection Region of Interest Clark Y Clark Y Airfoil has low drag over range of interest

Airfoil Selection Section Drag Coefficient Cd Section Lift Coefficient Cl Section Drag Coefficient Cd Angle of Attack (AOA) Section Lift Coefficient Cl

Wing Stall Performance CL needed = 1.19 Wing without flaps reaches CL at a=13° Wing stall possible Wing with 15° flap deflection reaches CL at 11° Required CL CL Angle of Attack (degrees) Flaperons necessary to meet stall requirements

Wing Performance Required CL at stall CD CL

Drag Build Up At Cruise Component CD Drag Wing 0.018 2.6 lbf Fuselage 0.0045 0.6 lbf Horizontal Tail 0.0043 Vertical Tail 0.0017 0.04 lbf

Wing Operating Parameters CL a (of wing) Flaperon Deflection CD L/D Stall 1.19 11° 15° 0.119 10 T/O 0.989 8° 0.084 12 Cruise 0.44 2.8° 0° 0.018 24

Dynamics and Controls

Center of Gravity & Aerodynamic Center Aircraft Center of Gravity is 3.2 ft from nose. Calculated from CAD program Pro-E Aircraft Aerodynamic Center is 3.7 ft from nose. Position where pitching moment of aircraft doesn’t change with angle of attack Calculated using Lift from Wing and Horizontal Tail Aerodynamic Center Center of Gravity

Aerodynamic Center of Aircraft Static Margin Desired Static Margin is 15% - 20% Dependent on C.G. and A.C. location Static Margin is 15% Contributes to Horizontal Tail Sizing Aerodynamic Center of Aircraft Static Margin = 20% Static Margin = 15% Center of Gravity

Horizontal Tail Sizing Tail sized based on desired static margin for static stability and take-off rotation ability  double-dot should be at least 10 deg/sec2 Ref. Roskam, Airplane Flight Dynamics Area 12 ft2 Span 6 ft Chord 2 ft 2 ft 6 ft

Vertical Tail Sizing Value of yawing coefficient due to sideslip angle should be approximately 0.001 = 10e-4 Tail area should be ~2 ft2 Ref. Roskam, Airplane Design Area 2 ft2 Span 1 ft Chord 2 ft 2 ft 1 ft

5° dihedral is a good compromise Dihedral Angle Recommendations Survey of Roskam data on homebuilt & agricultural low-wing aircraft: ~5° “Wing and Tail Dihedral for Models” - McCombs RC w/ailerons (for max maneuverability, low wing): 0-2° EVD (Equivalent V-Dihedral ≈ dihedral) Free Flight Scale model low wing: 3-8° EVD 5° dihedral is a good compromise

Control Surface Sizing Sizes calculate from traditional lifting device percentages. Ref. Roskam, Airplane Design Flaperon Elevator Rudder Chord 0.58 ft 0.6 ft Inboard Position 0.95 ft 0.2 ft 0.1 ft Outboard Position 7.2 ft 3 ft 1 ft 0.6 ft 0.58 ft 0.9 ft 6.25 ft 0.6 ft 2.8 ft

Trimming Incidence of Horizontal Tail calculated from trimmed flight during cruise (0 Angle of Attack) Analysis set incidence at -2

Structures

Wing Spar Design 2 Spar Design (at .15 & .60 chord): Resist Bending Assuming 5-g loading 53 lbf weight Safety factor of 1.5 Resist Torsion Less than 1o twist at tip under normal flight conditions Spar Results: Material of Choice: Bass or Spruce Wood Front Spar: 3.6” high (based on airfoil) 0.37” thick (0.73” at root) Rear Spar: 3” high (based on airfoil) 0.16” thick (0.25” at root)

Longitudinal Beam Design Resist Bending from: 20 lbf payload Horizontal tail loads Resist Torsion from: Rudder deflections Prop wash over tail Beam Results: Material of Choice: Bass or Spruce Wood Beam Dimensions: 3” high 0.25” thick 8” between the beams

Tail Structures Foam core with carbon fiber shell Horizontal and vertical tails comprised of carbon fiber w/ foam core Possible to make two foam cores, and cure entire tail at one time Control surfaces just need to be cut out of tail structure Tail spars allow attach points and transfer load to beams

Rear Gear Design Blue lines represent pin joints Black tie-downs absorb energy from landing Up to a 33 ft/sec “crash” from 5 feet high Need 18” relaxed length tie-down Square aluminum tube transfers landing load to tie-downs and surrounding structure 1” x 1” x 0.065” thick – 6063-T6

Front Gear Design Aluminum Bolt Elastic Band & Nylon Bolt Provides pivot for gear (does not break) Elastic Band & Nylon Bolt Elastic Band Absorbs some energy from landing Nylon bolt breaks during hard landing Front Gear Aluminum Tube Designed not to break Designed not to bend Al tube: 1” x 1” x 0.065” thick 6063-T6

Ref. www.towerhobbies.com Other Odds and Ends Covering for Wing: Coverite 21st Century Iron on Fabric 0.34 oz/ft2 Stronger, and resists tears better than MonoKote Covering for Fuselage: Fiberglass Either mold or foam core Not conductive – won’t interfere with internal electronics Ref. www.towerhobbies.com

Final Weight Estimate

Performance

Aircraft Performance (with 2.2lbf fuel) 90 ft/sec

Cost

Airframe Cost

Electronics Cost

Propulsion Cost

What Purdue Will Pay For This Project Total Aircraft Cost What Purdue Will Pay For This Project

Total Aircraft Value TOTAL AIRCRAFT VALUE = $106,341.15 Total Aircraft Value = (Engineering Pay) + (Cost) + (Value of Already Possessed Parts) Engineering Pay = 823.75 hr x $100/hour = $82,375 Aircraft Cost = $13,966.15 Value of Already Possessed Parts = $10,000 Micropilot = $5,000 Carbon Fiber & E-Glass = $5,000 (estimate) TOTAL AIRCRAFT VALUE = $106,341.15 What Purdue Would Pay to Outsource This Project

Summary

Summary – Internal View Internal Pod Camera View

Summary – 3-View

Summary -Major Design Points Aircraft Description Aspect Ratio = 5 Wing Span = 14.4 ft Wing Area ~ 42 ft2 Aircraft Length = 10 ft (not including air data boom) Engine = 3.7 hp O.S. 1.60 FX-FI – Fuel Injected Weight = 53 lbf Aircraft Configuration T-Tail Low Wing Pusher High Engine Tricycle Gear Internal Pod

Questions?

References (I) [1] MATLAB. PC Vers 6.0. Computer Software. Mathworks, INC. 2001 [2] Raymer, Daniel P., Aircraft Design: A Conceptual Approach, AIAA Education Series, 1989. [3] Roskam, Jan., Airplane Flight Dynamics and Automatic Flight Controls. Part I. DAR Corporation, Kansas. 2001 [4] Gere, James M., Mechanics of Materials. Brooks/Cole, Pacific Grove, CA. 2001 [5] Tower Hobbies. 9 December 2003. http://www.towerhobbies.com [6] XFoil. PC Vers. 6.94. Computer Software. Mark Drela. 2001. [7] Niu, Michael C., Airframe Structural Design, Conmilit Press Ltd. Hong Kong. 1995. [8] Halliday, et al., Fundamentals of Physics, John Wiley & Sons. New York. 1997. [9] Roskam, Jan, Airplane Design (Parts I-VIII), Roskam Aviation and Engineering Corp. Ottawa KS. 1988. [10] Kuhn, P., “Analysis of 2-Spar Cantilever Wings with Special Reference to Torsion and Load Transference”. NACA Report No. 508. [11] McMaster-Carr. 9 December 2003. http://www.mcmaster.com [12] Pro/ENGINEER. PC Release 2001. PTC Corporation. [13] Roskam, Jan., Methods for Estimating Stability and Control Derivatives of Conventional Subsonic Airplanes. Publisher Jan Roskam. Lawrence, KS. 1977.

References (II) [14] Zinger Propeller. 9 December 2003. http://www.zingerpropeller.com [15] McCombs, William F., “Wing and Tail Dihedral for Models”, Model Aviation. Dec. 1994. 104-112.

Appendix

SIZING

Cruise Speed

Stall Speed

Climb Angle

Ceiling

Endurance

Takeoff

Landing Distance

PROP

Appendix OS 1.60 FX-FI Consistency: The Fuel Injection system constantly supplies the correct air/fuel mixture to the engine, regardless of speed, altitude, or attitude. Recommended is a 450-550cc fuel tank that allows approximately 10 to 12 minute flights. = 30 min. with 50 oz. tank.

AERO

Aerodynamic Modeling Solving Prandt’s equation Substituting: Prandtl’s Lifting line theory used for aerodynamic modeling of the lifting components Solving Prandt’s equation Substituting: Equation to solve: Main Results CL = πAR*A1*(α- αLo) System of N equations with N unknowns (Solve N  N matix) Take N different spanwise locations on the wing where the equation is to be satisfied: 1, 2, .. N; (but not at the tips, so: 0 <  < ) The wing is symmetrical  A2, A4,… are zero Take only A1, A3,… as unknowns Take only control points on half of the wing: 0 < i  /2

Choice of main wing airfoil From lifting line with Initial parameters: Rectangular planform, 1000 ft a0 = 2pi, αL0 = 0, AR = 5; W/S = 1.28 (from sizing) CL = 0.4437 Cl distribution found at cruise Cl varies :0 to 0.58 Taking into account the Cl variation above, the need of an airfoil with a drag bucket at the specified Cl’s Xfoil utilized for different foils at the above conditions

Clark Y Airfoil Drag Bucket location fits best Airfoil Selection Region of Interest Clark Y Clark Y Airfoil Drag Bucket location fits best

ClarkY foil Xfoil runs of ClarkY foil at cruise and take-off Cruise: αL= -3.5deg Takeoff no flap: αL= -3.8deg Takeoff 10deg flap: αL= -7deg Takeoff 15deg flap: αL= -7.8deg In lifting Line Equation: a0 – updated depending on condition αL - updated according to above

Flaperons necessary to meet stall requirements Stall Performance CL needed = 1.19 Wing without flaps reaches CL at 13 deg aoa Wing stall possible Wing with 15 deg flap deflection reaches CL at 11 degrees Required CL Flaperons necessary to meet stall requirements

Stall Performance Drag Calculation CDtotal = CDinduced+CDvisc CDinduced – from Lifting line CD visc – integrated at the found Cls Required CL CD = 0.119 at required CL

Cruise Performance CL needed = 0.44 CL achieved at 2.8 deg Total Lift produced = 57lbf Total Drag = 2.6 lbf, L/D =21

Operating Parameters Stall 1.19 11 deg 15 deg 0.119 10 T/O 0.989 CL Aoa Flap Deflection CD L/D Stall 1.19 11 deg 15 deg 0.119 10 T/O 0.989 8. deg 0.084 12 Cruise 0.44 2.8 deg 0 deg 0.018 24

D & C

Center of Gravity Center of Gravity of Aircraft Weight of Horizontal Tail changes with area Note: 0.44 lbs/ft2 based on aircraft sizing code

Aerodynamic Center Aerodynamic Center as a function of Horizontal Tail Area Roskam Eq 11.1 Raymer Fig 16.12

Takeoff Rotation Equation This sizing based on angular acceleration during take-off rotation Ref. Roskam 421 book, pg 288-290 Variable definitions found in above reference

Yaw Moment due to Sideslip Vertical Tail sized from Coefficient of Yaw Moment due to Sideslip Roskam Eq 11.8 Vol 2 Due to Wing and Fuselage: Roskam Eq 10.42 Vol 6

Ref. McCombs, William F. “Wing and Tail Dihedral for Models.” Dihedral Angle EVD = A + kB A = 0° k = f(x/(b/2)) = 0.98 B = EVD / k ≈ EVD A=0° B X CL Ref. McCombs, William F. “Wing and Tail Dihedral for Models.”

Dynamics Short Period Mode Pole -14.391 ± 1.0079i Natural Frequency 14.431 (rad/s) Damping Ratio 0.99721 Phugoid Mode Pole -0.078823 ± 0.71828i Natural Frequency 0.72259 (rad/s) Damping Ratio 0.10908 Dutch Roll Mode Pole -1.1607 ± 2.4427i Natural Frequency 2.7045 (rad/s) Damping Ratio 0.42918 Spiral Mode Pole 0.29086 Roll Mode Pole -25.748 Ref. Purdue University AAE565, Matlab Predator Code

STRUCTURES

What Materials to Use Titanium Bass / Spruce

Ref. www.towerhobbies.com Material Properties Titanium = difficult to obtain Wood = not difficult to obtain Ref. 1999 Forest Products Laboratory Wood Handbook Ref. www.towerhobbies.com

Twist Constraint (<1o) Ref. Kuhn pg. 49 Where T = Torque (in-lbf) L = Length (in) l = f(B0, A0) (ref. Appendix) A0 = f(E, I) (ref. Appendix) B0 = f(G,J) (ref. Appendix) E = Young’s Modulus (psi) I = Moment of Inertia (in4) G = Torsional Stiffness (psi) J = Polar Moment of Inertia (in4) Assumptions: Small Deflections Spars & Ribs Carry all Torsion Span ~ 14.4 ft Chord ~ 2.9 ft Safety Factor = 1.5 G-Loading = 5.0 Weight = 53 lbs Ref. Gere

Twist at Tip

Twist at Tip (Zoom) Chosen Front Spar = 0.73” thick Chosen Rear Spar = 0.25” thick (note, this doesn’t include the step)

(based on span-wise lift distribution) Deflection at Tip a (in) L (in) Load (lbf) Ref. Gere pg. 892 Where Load = Weight*SF*G-loading (lbf) L = Length (in) E = Young’s Modulus (psi) I = Moment of Inertia (in4) Assumptions: Small Deflections NO TORSION Span ~ 14.4 ft Chord ~ 2.9 ft Safety Factor = 1.5 G-loading = 5.0 Weight = 53 lbs For this design: a ~ 3 ft or 36 in (based on span-wise lift distribution)

Chosen Spar Configuration Deflection at Tip Chosen Spar Configuration

(based on span-wise lift distribution) Is Stress too High? Load (lbf) Ref. Gere pg. 323 a (in) Where M = Weight*SF*G-loading*a (in-lbf) y = Maximum Dist from Neutral Axis (in) I = Moment of Inertia (in4) L (in) Assumptions: Span ~ 14.4 ft Chord ~ 2.9 ft Safety Factor = 1.5 G-loading = 5.0 Weight = 53 lbs For this design: a = 3 ft or 36 in (based on span-wise lift distribution)

Max Tension Stress

Max Compression Stress

Ref. www.towerhobbies.com Covering Traditional Monocote may not be strong enough for these large aircraft Coverite 21st Century Iron on Fabric is stronger, and resists tears much better 0.34 oz/ft2 Approx. 2 lbs for entire wing Ref. www.towerhobbies.com

Summary Main Wing Spruce or Bass wood Front Spar Rear Spar 0.73” thick by 3.6” high Rear Spar 3/8” thick by 3” high h t

Rear View of Tail NOTES Torsion can effectively be reduced with appropriate beam spacing Bending can be reduced by increasing moment of inertia of beams (not spacing) Some torsion is inherent, torsion can not be negated as it could in wing Side force from V-stab creates torsion effect on beams Downward force from H-stab creates bending moment on beams

Deflection at Tip (Rear of Tail) Load (lbf) Ref. Gere pg. 892 L (in) Where Load = (lbf) L = Length (in) E = Young’s Modulus (psi) I = Moment of Inertia (in4) Assumptions: Small Deflections Safety Factor = 1.5 G-loading = 3.0 Rectangular Beams Current Known Values: L = 6.2 ft Load ~ 8 lbf Moment of inertia of rectangular beam: I (in4) = (t)(h3)/12 t and h shown on next slide

Deflection at Tip (Rear of Tail) Green = spruce Black = bass h h=2 in t h=3 in

Deflection at Tip (Rear of Tail) Green = spruce Black = bass h h=2 in t h=3 in Required t ~0.55 in

Landing Gear Placement (I) θ = tipback angle = Landing gear placement based on guidelines found in Raymer

Landing Gear Placement (II) γ = overturn angle = Landing gear placement based on guidelines found in Raymer

Easily Obtainable Square Tubing Ref. www.mcmaster.com

Buckling of Rear Gear Load L Load For Rear Gear: L ~ 15.3 in Ref. Gere pg. 763 L Where L = Length (in) E = Young’s Modulus (psi) I = Moment of Inertia (in4) A = Cross Sectional Area (in2) Load Assumptions: Pinned-Pinned Column 1st Mode Buckling No Eccentricity For Rear Gear: L ~ 15.3 in

Compressive Failure of Rear Gear Load L Ref. MIL-HDBK-5H: 3-255 Where Load = (Weight)(S.F.)(Gloading) A = Cross Sectional Area (in2) Load Assumptions: Weight = 53 lbf Gloading = 10 S.F. = 1.5 Aluminum 6061-T6 No Buckling

Smallest easily obtainable tubing: 1” x 1” x 0.062” Stress on Rear Gear Smallest easily obtainable tubing: 1” x 1” x 0.062” t=0.062” t=0.125”

Great, what about the bungee? Consider worst reasonable landing situation Moving at (1.1)Vstall 5 feet above ground Aircraft falls out of the sky Can the bungee absorb the energy associated with this landing?

Great, what about the bungee? Assumptions: Weight = 53 lbf Vstall = 30 ft/sec Altitude = 5 ft Don’t want x to exceed 3 inches (beyond initial stretch) on landing

What Spring Constant is Needed? Required k ~ 3.75 lbf/in 1/k ~ 0.266 in/lbf

What is the Spring Constant? Relaxed Length ~18 inches

How Big is the Bolt? Diameter of nylon bolt = 0.5 in Load Reaction Ref. Gere pg 900 Load If load = (Weight)(S.F.)(Gloading) = 795 lbf Reaction = 1770 lbf (instantaneous) Need cross sectional area of bolt to be 0.197 in2 Diameter of nylon bolt = 0.5 in Reaction Assumptions: Weight = 53 lbf Gloading = 10 S.F. = 1.5 3.1” 6.9”

PERFORMANCE

Endurance Avg. Engine Fuel Consumption = 45.455 mL/min Endurance = Fuel / Consumptionfuel Avg. Engine Fuel Consumption = 45.455 mL/min Endurance = 30 min

Since this is RC, assume almost instaneous cruise conditions Range Since this is RC, assume almost instaneous cruise conditions L/D = 19 Cbhp = 1.5 lb/hr/bhp Prop eff = .67 Fuel Frac = 1.043

Minimum Flight Velocity Velocitymin= 29.95 ft/sec Weight = 53 lbf CLmax = 1.19 q =1.067 lbf/ft^2

Rate of Climb Vv= 7.5 ft/sec D = 6.5lbf hpengine = 3.7 hp W = 53 lbf Prop Eff = .3

Maximum Velocity Maximum Velocity Thrust Thrust/Drag [lbf] Drag Flying Velocity [ft/s] Thrust/Drag [lbf] Maximum Velocity Thrust Drag

Climb Angle Vv = 7.5 ft/sec V = 33 ft/sec