Dane BatemaBenoit Blier Drew Capps Patricia Roman Kyle Ryan Audrey Serra John TapeeCarlos Vergara Critical Design Review Team 1

AAE 451 Team 1 2 Mission Goal: High speed flight Design Mission –High speed dash (500 ft) –7 minute endurance flight Budget = $250 Carries 1 lb payload Stability –Dutch Roll damping > 0.8 Take-off/landing distance < 120 ft Minimum climb angle of 35 degrees Typical descent angle of 5.5 degrees V Stall ≤ 30 ft/sec

AAE 451 Team 1 3 Constraint Diagram C D 0 = C D 0 = C D 0 = CLIMB CRUISE (DASH) STALL C L max = 1.15 C L max = 1.25 C L max = 1.35 (L/D) max = 10 (L/D) max = 12 Design Point (1.2, 4.0) Power loading (lbf/hp) V dash = 90 mph (132 ft/s) V stall = 30 ft/s

AAE 451 Team 1 4 Graphic solution : Preliminary Weight Estimate 5 lbs

AAE 451 Team View Drawing

AAE 451 Team 1 6 AERODYNAMICS

AAE 451 Team 1 7 Wing Geometry 1.17 ft deg S = 4.16 ft 2 Wing 0.53 ft 4.90 ft Wing Airfoil MH 43 Aspect ratio5.76 Taper ratio0.45 Sweep angle (quarter chord) ° Dihedral angle 1.28 ° Span4.90 ft Area4.16 ft 2 Reynolds number626,773 Maximum velocity : 118 ft/s Aircraft wetted area : ft 2

AAE 451 Team 1 8 Tail Geometry Horizontal tail Airfoil NACA 0006 Aspect ratio5.44 Taper ratio0.6 Sweep angle (quarter chord) 7.85 ° Dihedral angle 0°0° Span2.01 ft Area0.74 ft 2 Reynolds number245,500 Maximum velocity : 118 ft/s Aircraft wetted area : ft ft deg S= 0.74 ft 2 Tail 0.28 ft 2.01 ft

AAE 451 Team 1 9 Mathematical Model Lift Coefficient 3D: (From the Roskam book)

AAE 451 Team 1 10 Elevator Effect on C L (From Flight Stability and Automatic Control, Robert C. Nelson)

AAE 451 Team 1 11 Mathematical Model Drag Coefficient 3D:

AAE 451 Team 1 12 C L vs Alpha and Drag Polar

AAE 451 Team 1 13 Flaps Needed C LMax C LMax from Lift Curve High speed dash Respect stall speed condition Minimum drag Maximum lift Flaps deg Needed w/o Flaps w/ Flaps

AAE 451 Team 1 14 Mathematical Model Moment Coefficient 3D: (From the Roskam book)

AAE 451 Team 1 15 Moment Coefficient

AAE 451 Team 1 16 PROPULSION

AAE 451 Team 1 17 Propeller Selection C P, C T,  found from gold.m Default inputs used due to empirical correction factor based on past experience 11 inch propeller selected to keep propeller speed below 10,000 RPM 11x10 and 11x11 both give similar high speed efficiency Power required increased by 1/0.75=33.3% per guidance from gold.m file.

AAE 451 Team 1 18 Battery Selection Procedure: –Tabulate total system cost and weight Different batteries Different power outputs Goals –Maximize Power Output –Minimize Cost Self-imposed limit: $50 Ensure motor can be purchased for < $100 (also self-imposed) –Based on supplied voltage and current selected system Max Power Output = 0.7 hp

AAE 451 Team 1 19 Max Speed (battery current limited) 118 ft/s ~ 80 mph Propeller –APC (LP11011) 11x Pattern Propeller ($7.95) Gearbox & Mounting Hardware –MP Jet (MP8104) 4.1:1 Gearbox for 480 Size ($19.90) –MP Jet (MJ8030) Short Prop Adapter for APC Props ($4.60) –MP Jet (MJ7250) 2" Black Lightweight Spinner ($3.20) Motor –MEGA ACn 16/25/3 ($84.00) Speed Controller –Castle Creations Phoenix-60 ($118.99) Batteries (in series) –2 x Apogee 3-Cell 11.1 V 1200mAh 20C LiPo (2 x $25.00) Total Propulsion Chargeable Cost = $ (neglects speed controller) Propulsion System

AAE 451 Team 1 20 Dash System Performance  =98%  =94% 426 W 0.57 hp  =65% 454 W 0.61 hp 502 W 0.67 hp  =90% 513 W 0.69 hp 278 W 0.37 hp 1.74 lbf Propeller power required increased by 1/0.75=33.3% per guidance from gold.m file.

AAE 451 Team 1 21 Loiter (Main_System_Design - Modified) –Estimated Loiter Time: 21.0 mins (3X requirement) –Motor Voltage input: 9.63 V –Motor Current input: 7.89 A –Motor RPM: 16,100 RPM –Motor  : 74.9% Motor/Battery Loiter Performance Stall P req > P avail (40,0.03) Loiter mission is steady turn at a 200 ft radius, 40 ft/s. Aircraft Constants: C D0 = e = 0.79 AR = 5.76 W = 5 lb S = 4.16 ft 2

AAE 451 Team 1 22 Motor/Battery Dash Performance Dash (Main_System_Design - Modified) –Motor Voltage input: 20.9 V –Motor Current input: 24.0 A* (Motor Max Continuous 30 A) –Motor RPM: 34,900 RPM (Motor Maximum 55,000 RPM) –Motor  : 90.3% –M tip,prop = 0.38 Vmax : ft/s Gear Ratio : Actual Gear Ratio: 4.1 Actual Vmax : ft/s Projected Time at Max Power: 3.1 min * Max battery continuous output 24 A Stall P req > P avail (118,0.37)

AAE 451 Team 1 23 Takeoff Cannot use 100% throttle except at high speed Reaches takeoff speed in much less than 120 ft

AAE 451 Team 1 24 STRUCTURES

AAE 451 Team 1 25 Wing Structure Aerodynamics gives the geometry Load case: Resist to 10g (47 ft radius at 80 mph) Materials 0.53 ft 2.45ft 1.17ft deg S wing = 4.16 ft 2 MH 43 Thickness:8.5% With a weight of 5 lb Wing should support 50 lb

AAE 451 Team 1 26 Analysis Method Discretization of the wingDetermination of the loads Quarter chord MAC: application of the lift For each part, we can figure out: The bending moment due to the lift The torque due to the aerodynamic moment Assumptions: Only bending loading Foam doesn’t carry the load Elliptical airfoil shape Only aerodynamic twist a b Calculations: Balsa will resist most of the load t is figured out from I G

AAE 451 Team 1 27 Calculation (cont.) M=L 1.d 1 + L 2.d 2 + ….. L1L1 L2L2 d1d1 d2d2 MAC Bending Moment: Twist: Deflection: Lift at MAC y y’ y’ with Thales theorem E balsa = psi

AAE 451 Team 1 28 Results for Wing Min. thickness.053 in Easy to built, but 70% heavier than discretized thickness Optimal thickness distribution Bending Results: Twist Results: Deflection Results: Max. Twist = -.3 deg Max. Deflection =.11 in

AAE 451 Team 1 29 Geometry Horizontal Tail Structure 0.46 ft 0.28 ft 2.01 ft NACA 0006, 6% thickness ratio S=0.74 ft 2 DATA Sref (ft²)0.68 lift force (lbf)1.87 Ult. Comp. Stress (psi)725.2 Vmax (ft/s)118 young modulus (ksi)185.6 shear modulus (psi)23060 balsa density (lb/ft 3 )6.2 wingspan (ft)2.01 root chord (ft)0.46 wingtip chord (ft)0.28 airfoil thickness (%)6 Results: Min. thickness: 1.38e-2 in Total deflection: 4.4e-1 in Very thin, impossible to find in the market so we will use 1/32 in Same method as the wing High speed dash + 20° of deflection

AAE 451 Team 1 30 Final tail structure layout Horizontal tail: Foam core + 1/32 in balsa sheet (similar to the wing) Vertical tail: The final geometry: We plan to make it in a full sheet of balsa sanded ft 0.32 ft 0.63 ft Same method as the wing High speed dash + 20° of deflection Min. thickness: 8.09e-4 in

AAE 451 Team 1 31 Landing Gear Roskam method for landing gear sizing: 1. Landing gear system: fixed 2. Landing gear configuration: taildragger 3. Locate c.g.: ft from the nose 4. Longitudinal tip over analysis 5. Lateral tip over analysis 15 deg 12 deg Ψ≤ 55 deg Main gear Tail gear

AAE 451 Team 1 32 Landing Gear 6. Ground clearance criteria 7. Landing gear material: 8. Number of wheels: 2 for main gear 1 for tail gear > 5 deg Glassfilled Nylon Lightweight Width:.177’’ Diameter: 2.25” OD Hayes Racing Wheels: Aluminum for main gear Piano wire for tail gear

AAE 451 Team 1 33 Wing-Fuselage Attachment Fuselage Rib Wing top view Carbon rod Nylon boltsL max /4

AAE 451 Team 1 34 Wing-Fuselage Attachment Nylon bolts: D =.2362 inLength = in Calculations: Carbon rod: D=.2362 int = thickness of rib =.2362 in Calculations: L max /4 Cross-sectional area Maximum force it will carry: F = n*W/4 Maximum stress: σ = F/A = psi Ultimate Tensile Strength for nylon = psi Margin=σ max / σ-1 Margin = 34 Carbon rod L max /4 t Front view Top view σ = F/(D*t) = psi Ultimate Compressive Strength of balsa = psi Margin = 2.2

AAE 451 Team 1 35 Component Layout Payload Battery (2) Motor and Gearbox Servos Speed Controller Receiver

AAE 451 Team 1 36 CG Location CG: 1.3 ft from nose CATIA Component Weight: 3.72 lbs Initial Sizing Historical Estimate: 5 lbs Leftover Weight for glue, ribs, fasteners: 1.28 lbs

AAE 451 Team 1 37 DYNAMICS & CONTROL

AAE 451 Team 1 38 Longitudinal Stability – Horizontal Tail Sizing Tail Sized using Class I Method (X-Plot) Initial Tail Size: Static margin - XPlot Static margin / Aircraft ~18% SM on XPlot

AAE 451 Team 1 39 Longitudinal Stability – Trim Diagram

AAE 451 Team 1 40 Lateral Stability – Directional Control Vertical Tail Sized using Class I Method (X-Plot) Minimum Vertical Tail Area: Actual Vertical Tail Area: Change of Yawing Moment with sideslip angle versus Vertical Tail area

AAE 451 Team 1 41 Longitudinal Stability – Elevator Sizing Elevator sized using Historical Data Our Tail volume ratio is: With Surface Ratio of: Current Elevator Area Elevator sized with historical data and Control Power

AAE 451 Team 1 42 Lateral Stability – Directional Control Rudder Sizing Wing Area Vertical Tail Area Rudder Area found by average & Control Power Analysis Rudder Area

AAE 451 Team 1 43 Lateral Stability – Roll Control Aileron Sizing Aileron Chord: Aileron Outboard Position Aileron Inboard Position Used historical data and Roll moment coefficient analysis

AAE 451 Team 1 44 Modes of Motion Longitudinal Motion Phugoid Mode (Long Period) Short Period

AAE 451 Team 1 45 Modes of Motion Lateral – Directional Motion Spiral Mode Roll Mode Dutch Roll

AAE 451 Team 1 46 Control System Root Locus General Block Diagram Rate Gyro Rudder Servo Yaw rate to rudder deflection Pilot Command Rudder Gain

AAE 451 Team 1 47 Compensated System Required Dutch Roll Damping Required Gain to achieve Dutch Roll Damping Natural Frequency at required Dutch Roll Damping Root Locus of Yaw rate to rudder deflection output Uncompensated Damping Ratio

AAE 451 Team 1 48 CONCLUSION

AAE 451 Team 1 49 Remaining Design Problems Servos –Control surface size is known –Margin of Safety Throttle limit –Need to physically test motor, gearbox, and propeller to determine current draw Rudder/Tailwheel attachment

AAE 451 Team 1 50 Final Design Max Speed: 118 ft/s Max Endurance: 21 min