CRITICAL DESIGN REVIEW AAE 451 CRITICAL DESIGN REVIEW TEAM 4 Jared Hutter, Andrew Faust, Matt Bagg, Tony Bradford, Arun Padmanabhan, Gerald Lo, Kelvin Seah December 9, 2003

OVERVIEW Introduction Aerodynamics Propulsion Structures Aircraft Walk-Around Design Requirements Constraint Analysis Aerodynamics Propulsion Structures Dynamics and Control Cost and Performance Summary

INTRODUCTION

AIRCRAFT WALK-AROUND Empennage High Wing Avionics Pod Twin Booms S = 39.3 ft2 b = 14.0 ft, c = 2.8 ft AR = 5 Twin Booms 3 ft apart; 5.7 ft from Wing MAC to HT MAC Twin Engine 1.8 HP each Avionics Pod 20 lb; can be positioned front or aft depending on requirements Empennage Horizontal with Single Elevator; Two Vertical Tails with One Rudder Each

Single Engine Performance Twin Engine Performance DESIGN REQUIREMENTS Parameter Single Engine Performance Twin Engine Performance Customer Requirement Endurance – 30 minutes 15 minutes Payload Weight (Avionics Pod) 20 lbs Gross Take-Off Weight 55 lbs Climb Angle > 0° 5.5° Maximum Cruise Speed  30 ft/s 60 ft/s 50 ft/s Minimum Stall Speed 28 ft/s 30 ft/s Maximum Operational Altitude (ASL) 2000 ft 1000 ft

CONSTRAINT ANALYSIS Original Numbers Final Numbers CL0= 0.30 CLMax= 1.3 CD0 = 0.03 ηp = 0.6 Final Numbers CL0 = 0.39 CLMax = 1.58 CD0 = 0.0208 ηp = 0.7

ORIGINAL CONSTRAINT DIAGRAM

FINAL CONSTRAINT DIAGRAM (TWIN ENGINE)

AERODYNAMICS

AIRCRAFT CL AND CM Lift Coefficient CL = CL + CLe elevator + CL0 CL = 5.176 [rad-1]  + 0.4283 [rad-1] elevator + 0.398 Moment Coefficient CM = CM + CMe elevator + CM0 CM = -2.7029 [rad-1]  + (-0.9338) [rad-1] elevator + 0.0

CL vs  & CL vs CMc/4

TRIM DIAGRAM

DRAG BREAKDOWN Part CD Main Wing 0.0132 Fuselage 0.0033 Tail 0.0108 Landing Gear 0.0008 Engines 0.0001 Stationary Propeller 0.0012

DRAG POLAR Coefficient of Lift, CL Coefficient of Drag, CD

PROPULSION

WHY TWIN ENGINES ? Clean Air for Air Data Boom Unobstructed View for Camera Survivability of the Pod

ENGINE SELECTION AND CHOICE Sized engine based off of constraint diagram Verified with thrust analysis Engine Choice: Saito FA-100 Specifications: Four Stroke Engine Weight: 20.8 oz Practical RPM: 2,100 - 9,300 Power: 1.8 BHP @ ~9100 RPM Fuel Consumption Rate: 1 oz/min @ max. RPM Source: http://www.saitoengines.com

FUEL SYSTEM Tank located in wing Filled from the top Dimensions: 3.25” high 4” wide 8” long VP-20 Oscillating pump: Weight: 0.882 oz Max. Flow Rate: 3.5 oz/min Fuel lines run externally underneath the wing

REQUIRED THRUST FOR SINGLE ENGINE CLIMB Test for minimum requirement: Flight Path Angle,  = 0.5 Drag = 7.5 lbf Weight = 50.2 lbf Thrust = Drag + Weight  sin() = 8 lbf  W T D L V PROPELLER SELECTION PROCEDURE Ran various propeller geometries in Gold.m to meet thrust and horsepower requirements. Chose propeller with highest propeller efficiency.

PROPELLER CHOICE Master Airscrew Propeller Made of glass-filled Nylon Diameter: 16” Pitch: 6” Made of glass-filled Nylon

PROPELLER PARAMETERS T = 10.7 lbf T = 3.44 lbf /engine  6.88 lbf Single Engine Climb (V = 33.6 ft/s) CP = 0.0274 CT = 0.0619 J = 0.1662 rev-1 HP = 1.74 @ 9100 RPM  = 37.5% T = 10.7 lbf Twin Engine Cruise (V = 60 ft/s) CP = 0.0185 CT = 0.0337 J = 0.3857 rev-1 HP = 0.54 @ 7000 RPM  = 70% T = 3.44 lbf /engine  6.88 lbf

STRUCTURES

AIRCRAFT V-N DIAGRAM Load Limit at Max Speed 1-g at Level Flight Stall Speed Load Limit at Max Speed CLmax Constraints Structural Constraints

MAIN WING Both box beams and I-beam configurations considered Various materials analyzed bitch Final spar dimensions Main: 3.7 in high by 2.0 in wide by 0.7 in thick Rear: 1.8 in high by 0.9 in wide by 0.6 in thick

TAIL SECTION Modeled as beams under a distributed load For rectangular beams: Vertical Stabilizer Deflection Horizontal Stabilizer Deflection q1 q2

TAIL SECTION Deflection Curves 1 in  0.5 in 1 in  0.5 in

LANDING GEAR MAIN Purchasing all landing gears REAR

LANDING GEAR Tip Over Analysis 14.03 ft 43 ° 43 ° 25 ° 10.1 ° Raymer Range: > 25 ° Raymer Range: 16 ° - 25 ° 25 ° 10.1 ° Raymer Range: 10 ° - 15 °

TAIL BOOMS Cylindrical Tubes Final tail boom dimensions: Sized according to bending and torsional constraints Bending: Twist: Set d = 2 in Set f = 5 deg Final tail boom dimensions: Inner diameter: 1.6” Outer diameter: 1.7” Thickness: 0.05” Length: 6.10 ft

POD ATTACHMENT Four different analysis considerations in pod attachment (from Gere, Mechanics of Materials) : 1) allowable tensile stress in main base of connecting rail 2) allowable tensile stress around bolt holes 3) allowable shear stress in bolts 4) allowable shear stress in connecting rail Only the 2) and 4) analyses are demonstrated

POD ATTACHMENT Tensile stress in bolt holes Shear stress around bolt holes = allowable shear stress of spruce (580 psi) P = load we are designing for d1 =width of hole section = 1.25 in d2 =hole diameter = 3/8 in t = rail thickness = 3/8 in h = rail height = ¾ in = 178 psi < 580 psi = 370 psi (for spruce, tension perpendicular to grain) = 152.4 psi < 370 psi

AIRCRAFT LAYOUT Total Weight = 50.21 lbs

POD INTERNAL LAYOUT Avionics + Structure = 20 lbs

POD ATTACHMENT METHOD

WING CONSTRUCTION Wing + Required Structure = 13.1 lbs

CENTRAL WING INTERNAL LAYOUT

DETACHABLE SECTION INTERNAL LAYOUT

DETACHABLE SECTION INTERNAL LAYOUT

TAIL SECTION INTERNAL LAYOUT Tail Section + landing gear = 1.59 lbs

REAR LANDING GEAR CONNECTION

WEIGHTS SUMMARY Component Weight (lbf) Wing & Structure 13.1 Tail Section & rear gear 1.59 Tail Booms 4.70 Basic Flight Systems 0.849 Propulsion & Fuel 6.61 Avionics & Structure 20 Main Landing Gear 2.36 Fiber-glass & Mylar Skin 1 Total Weight 50.21

DYNAMICS & CONTROL

MODIFIED CLASS 1 TAIL SIZING Tail Volume Coefficient Approach (Raymer, p.124). Equation used to find Horizontal Tail (HT) and Vertical Tail (VT) Areas: Iterated until the following conditions are satisfied: Stability and control derivatives fall within recommended range. Ability to trim in yaw with rudder under OEI flight conditions. Results to be verified with stability in aircraft responses. where HT Volume Coefficient VT Volume Coefficient Wing Chord, 2.8 ft Wing Area, 39.3 ft2 Wing Span, 14.0 ft Moment Arm, 6.1 ft

CLASS 1 CONTROL SURFACE SIZING Chord-wise Span-wise Ailerons 0.15 cW ~ 0.25 cW 0.5 bW ~ 0.9 bW Elevator 0.25 cHT ~ 0.5 cHT ~ 0.9 bHT Rudder 0.25 cVT ~ 0.5 cVT ~ 0.9 bVT Raymer: Choice of Values: Chord-wise Span-wise Ailerons 0.20 cW 12.97 ft Elevator 0.50 cHT 2.67 ft Rudder 0.35 cVT 0.9 bVT

TAIL SIZING RESULTS HORIZONTAL TAIL VERTICAL TAIL Chord-wise Span-wise SHT = 9.01 ft2 1.01 ft 1.68 ft ½ = 2.03 ft2 = 0.6 1.51 ft 1.19 ft 3.0 ft 1.19 ft AR = 3.2 5.37 ft 1.68 ft Volume Coefficients: = 0.50 = 0.045 Chord-wise Span-wise Aileron 0.56 ft 10.0 ft Elevator 0.84 ft 2.67 ft Rudder 0.35 cVT 2.42 ft

RUDDER DEFLECTION IN OEI CONDITIONS Roskam (AAE 421 Textbook) Required rudder deflection: = 28 ft/s Deflection Limit: = 25° FAR 23, 25 requires that for  = 0° In this case, = 28.56 ft/s Max Deflection FAR 23, 25 Limit 1.2 Stall Speed

C.G. LOCATION ESTIMATION Aircraft C.G. location: x Wing W = 13.1 lb x = 0.50 ft Tail Gear W = 0.55 lb x = 7.0 ft Avionics Pod W = 20 lb x variable Main Gear W = 2.3 lb x = 0 ft Tail Booms W = 4.7 lb x = 3.80 ft Engines, Fuel & Casings W = 6.6 lb x = -0.10 ft Tail Section W = 1.0 lb x  7.0 ft

STATIC MARGIN CALCULATIONS Aircraft aerodynamic center was calculated using: Static margin: Static Margin is a function of payload C.G. location. Sensitivity study was conducted to examine the effect of the payload C.G. location on static margin. 0.810 [ fraction of MAC ]

SENSITIVITY STUDY Nominal Design Point where SM = 15% MAC Payload of 20 lb, with its C.G. @ x = +2.9 ft

MODAL ANALYSIS Lateral-Directional Subsystem Longitudinal Subsystem Mode Poles Natural Frequency (rad/sec) Damping Ratio Dutch Roll -3.89 ± j 2.00 4.37 0.89 Roll -1.56 Spiral -0.37 Mode Poles Natural Frequency (rad/sec) Damping Ratio Phugoid -0.06 ± j 0.60 0.607 0.093 Short Period -7.36, -73.3

6-DOF SIMULATION WITH ELEVATOR STEP INPUT 5° Phugoid Mode Short Period Mode (non-oscillatory in this case)

6-DOF SIMULATION WITH AILERON STEP INPUT Roll Mode t a 5°

6-DOF SIMULATION WITH RUDDER DOUBLET INPUT 5° -5° Dutch Roll Mode

PERFORMANCE AND COST

PERFORMANCE - LEVEL FLIGHT Min Thrust Required = 4.7 lb @ 50 ft/s Min Power Required = 0.38 HP @ 38 ft/s Max Speeds Twin = 60 ft/s (limited by structures) Single = 51 ft/s Min Speeds Twin = 28 ft/s (limited by stall) Single = 38 ft/s

PERFORMANCE - LEVEL FLIGHT Assume 1oz/min and 2.34 lb Fuel Range Endurance Max Range = 16 miles @ 65 ft/s Range at Min Thrust = 14.2 miles @ 50 ft/s Range at Min Power = 9.6 miles@ 38 ft/s Max Endurance = 25 min @ 50 ft/s Endurance at Min Power = 22 min @ 38 ft/s

PERFORMANCE Climb Glide Climb Angle () At Best Rate of Climb: 14.4 ft/s (Twin) 15o 4.8 ft/s (Single) 5.5o At Best Angle of Climb: 11.4 ft/s (Twin) 19o 4.3 ft/s (Single) 6.3o Best Glide @ 50 ft/s (L/D)max = 10.5 CL = 0.43

COST Propulsion 2 x Engine (Saito FA-100) 560 2 x Prop (Master 16 x 6) 19.8 Fuel (per gallon) 16.95 Fuel Tank (50 oz.) 11.49 2 x Fuel Feed Line (2 ft.) 3.7 2 x Engine Mounts 53.98 Total Propulsion $665.92 Structure 2 x Main Gear (Robart #682) 150 2 x Tail Gear & Wheel Set 27.98 2 x Main Wheels 23.7 Total for Landing Gear 201.68 Monocoat (15 ft x 27 in.) / roll (need 89.58 ft^2) 61.5 Balsa (3x3x6 in) block (need 5.33 ft^3) 128.25 Spruce (need 0.184 ft^3) 40.63 Fiberglass (50wide x 36vary in) 10 2 x Aluminum Booms (6061 T6) 8 ft each 51.2 Total Materials 291.58 Total Structure $493.26 Controls Futaba 9CAP 9ch PCM with 4 S3001 servos 479.99 Servos 3xS3001 79.97 Total Controls $559.96

COST Total Aircraft Cost $15100.94 Total Payload 12321.8 Total Propulsion 665.92 Total Structure 493.26 Total Controls 559.96 Total Labor (No Engineering) 960.00 Total Miscellaneous (Nuts, Bolts, Hinges, etc.) 100.00 Total Aircraft Cost $15100.94

TOTAL COST

SUMMARY

TOP VIEW 14.03 ft 2.81 ft AR = 5 3.00 ft 6.10 ft 5.37 ft 1.68 ft

PROFILE VIEW 1.01 ft 1.51 ft 2.81 ft 1.74 ft 6.10 ft

FRONT VIEW 14.03 ft 3.00 ft

QUESTIONS?

APPENDIX

Modulus of Elasticity (ksi) MATERIAL PROPERTIES Material Density (lb/ft3) Modulus of Elasticity (ksi) Al 2024-T6 178.2 10500 Balsa 11 490 Basswood 24.9 1500 Spruce 24.5 1230 Foam 1.43 - Sources: - www.matweb.com - US Dept. of Agriculture

WING ANALYSIS Actual bending moment at each point along spar Root Bending Moment = 508.5 ft-lbf Actual bending moment at each point along spar Based on lifting line theory

WING ANALYSIS

WING ANALYSIS 508.5 ft-lbf

TAIL BOOM SIZING

VERTICAL TAIL Bending moment decreases from root to tip Increasing deflection Deflection greatest at tip

POD ATTACHMENT Tensile Stress in Main Base As seen from left rear view of pod Tensile Stress in Main Base where: P = load we are designing for = allowable tensile stress in material A = area under inspection d2= hole diameter t = rail thickness = 370 psi (for spruce, tension perpendicular to grain) d2= 3/8 in t = 3/8 in P = 50 lbf

POD ATTACHMENT Solve for and make sure it’s less than that for spruce =355.6 psi < 370 psi

POD ATTACHMENT Shear stress experienced in bolts As seen from left rear view of pod Shear stress experienced in bolts where = allowable shear stress in bolts n = number of bolts required = 91 psi from plasticnutsandbolts.com

POD ATTACHMENT This time, solve for n and find how many bolts are required for the given allowable shear stress and load P n = 5, but use 6 for symmetry

LANDING GEAR ANALYSIS Gear modeled as spring-mass damper Mass, m Spring constant, k Damping constant, c Mass, m

LANDING GEAR ANALYSIS Equation of motion: State space representation: Where d2x/dt2 = vertical acceleration dx/dt = vertical velocity x = vertical position k = spring constant c = damping coefficient State space representation: Used values of: k = 305 lbm/s2 c = 40 lbm/s m = 1.70 lbm (W = 54.6 lbf) to be verified with manufacturer

LANDING GEAR ANALYSIS State space representation modeled in MATLAB Use ode45 to obtain position, velocity, and acceleration data Find the vertical force applied to the 2 main gears

LANDING GEAR ANALYSIS Modeled vertical velocity = 6 ft/s Maximum displacement = 2.1 in

LANDING GEAR ANALYSIS - Modeled vertical velocity = 6 ft/s

LANDING GEAR ANALYSIS - Modeled vertical velocity = 6 ft/s

LANDING GEAR ANALYSIS Design joint for 240 lb vertical compressive load - Modeled vertical velocity = 6 ft/s

LANDING GEAR – SCHEMATIC

RUDDER DEFLECTION IN OEI CONDITIONS ref. “Airplane Flight Dynamics and Automatic Flight Controls” (Roskam) Section 4.2.6 [rad] where @ 2,000 ft  [slug/ft3] V [ft/sec] P [hp] yT [ft] for fixed pitch

AIRCRAFT AERODYNAMIC CENTER The following equation was used: ref. “Airplane Flight Dynamics and Automatic Flight Controls” (Roskam) Equation 3.38 where = 0.25 = 2.78 = 6.19 rad-1 = 6.01 rad-1 = 0.45 = 9.01 ft2 = 39.34 ft2 = 2.22 ref. “Airplane Design, Volume VI” (Roskam) Equation 8.45

MIL-F-8785C GUIDELINES Lateral-Directional Subsystem Longitudinal Subsystem Mode Poles Natural Frequency (rad/sec) Damping Ratio Dutch Roll -3.89 ± j 2.00 4.37 0.89 Roll -1.56 Spiral -0.37  0.4, OK!  0.08, OK! Stable, non-oscillatory – OK! Stable, does not diverge – OK! Mode Poles Natural Frequency (rad/sec) Damping Ratio Phugoid -0.06 ± j 0.60 0.607 0.093 Short Period -7.36, -73.3 “Must be heavily damped” – OK!

PERFORMANCE APPENDIX

PERFORMANCE APPENDIX

COST BREAKDOWN