Structures and Weights Team One Speakers Todd Mostrog Chris Grupido Daniel Halla John Apostol Structures and Weights PDR 2 03 March, 2005

Overview Load Factor Selection Load Conditions Torsional Analysis Bending Analysis Structural Design Wing Fuselage Tail Section Weight Estimation Landing Gear Design

Load Factors Maximum Load Factor, nmax For CLmax of Wing = 1.24 and Wing Area = 2.2 ft2 Stall Speed : VSTALL = 20 ft/s : nmax = 1.00 Take-off Speed : VTO = 24 ft/s : nmax = 1.44 Turn Speed : VTURN = 25 ft/s : nmax = 1.56 Loiter Speed : VLOIT = 30 ft/s : nmax = 2.26 Max Speed : VMAX = 40 ft/s : nmax = 4.01

Load Factors Turn Considerations Bank Angle (deg) n Turn Radius (ft) 30 1.15 34.18 45 1.41 19.53 60 2.0 11.21 75 3.86 5.21

Load Factors Vertical Turn / Loop Considerations Considered for Loiter Speed : V = 30 ft./sec. For Pull – Up For Velocity Vector Vertical For Pull - Down

Load Factors Conclusions Load Factor of 2.4 chosen Aerobatics Performed at Loiter Speed or Below Max Speed for Level Dash Only Max Bank Angle of 60 degrees Turn Radius of 11.21 ft. Vertical Turn Radius: Pull-Up : 19.97 ft. Velocity Vector Vertical : 11.65 ft. Pull-Down : 8.22 ft.

Load and Moment Conditions For Maximum Load Factor of 2.4 and Weight of 1.3 lbf Maximum Load = 3.12 lbf Lift Distribution on Wing is 83% Elliptical - Centroid of Elliptical Parabolic Semisegment : x = 3/8 base - Assumed Resultant Loading at ½ Wing Section Span x = ½(b/2) = ½(3.85 ft. / 2) = 0.96 ft. Maximum Bending Moment at Root Chord M = 1.5 ft.-lbf = 17.97 in.-lbf

Torsional Analysis Twist Angle Equation For Root Chord = 5.04 in. For Twist of 1 deg : Twist Angle = 0.0015 rad/in. For Monokote Skin t = 0.001 in. and G = 406 ksi For Root Chord = 5.04 in. Shear Flow = 0.33 lb. \ in. Shear Stress = 330 psi Torque Applied = 9.52 lb.-in. For Tip Chord = 9.28 in. Shear Flow = 0.204 lb. \ in. Shear Stress = 204 psi Torque Applied = 0.47 lb.-in.

Modeling Assumptions Simplifying Assumptions Wing loading Concentrated lift force Centroid of a semi-segment of nth degree 3/8 span Originally modeled at .5 span -- maintained Effect of landing gear weight ignored Wing Geometry Sized from bending analysis Constant size spars

General Construction Wing and Fuselage Traditional rib and stringer construction Balsa leading edge All stringers are 0.125” square Tail Assembly Solid Balsa Monokote Covering 0.001 thick Grade “B” Balsa (trade study pending) Hidden fixed gear with 4 tires Foam main wheels 0.02 lbs (pair) Tail wheels Manufactured

Wing/Tail Properties Wing 3.7 ft. Span Weight =0.12 lbf Polar Moment of Inertia = 0.0074 in.4 Maximum Moment 17.97 in.-lbf (2.4 gs) 0.67 in. max deflection Spars (2) 0.125 X 0.5 (average) 20 Ribs 2.2 in. Separation 2 Stringers Solid Tail Section 31.74 in.3 0.17 lbf

Wing Geometry

Fuselage Properties 3 in. diameter 25 in. length Weight = 0.05 lbf Polar Moment of Inertia = 0.018 in4 Maximum Moment 19.2 in.-lbf J = 0.054 in4 0.36 degrees/inch of twist 6 Ribs 4.18 inches of Separation 12 stringers spaced 30 degrees apart

Fuselage Geometry

Landing Gear 1 ¾” diameter foam wheels (2) Fixed to wing ribs Designed for no failure Top half hidden in wing section picture of this below

Landing Gear Main Considerations Four points of contact Increases on ground stability Aft landing gear on tail Rudder mounted for ground directional control Forward landing gear in wing Simple structure attachment Reduce drag Four point landing gear, two forward two aft. Aft gear mounted on the bottom edges of the rudder. Allows for steering, so as rudders turn aircraft will turn. Forward landing gear mounted halfway into wing, in the bottom flat section of wing. Simple attachment, no real strut will be needed, direct axel design.

Landing Gear Main Concerns Forward tip over Rudder mounted aft gear Location of center of gravity close to location of forward point of contact Rudder mounted aft gear Strength of rudder to avoid failure In wing forward gear Limits allowable propeller size Forward tip over is important, making sure the center of gravity will be aft of the forward landing gear contact point. Rudder structure needs to be strong enough for tail strike on take off or rough landing. Rudder also needs to be strong enough to not break when rudder is moved. Rudder will be solid balsa structure and can be reinforced with small wire if necessary. The in wing mounted landing gear reduce propeller clearance and so a three blade propeller is being analyzed, slight adjustments can be made to wing to increase the distance from motor centerline to ground in rest position.

Landing Gear In wing mounted gear Tail mounted gear Tip-over Analysis Low center of gravity 5-10 degrees before wing strike Tail mounted gear Initial positive rest angle 5-10 degrees For tip over the in wing mounted gear will lower out center of gravity and cause the wingtips to touch long before the center of gravity passes over the point of contact. Between the radius of the tire and the wing dihedral there will be approximately 5-10 degrees before wing strike. So it will be stable on ground but will not allow for much roll on landing. Due to the aft landing gear being mounted in the rudders, there will be a slight nose up position when at rest at ground, this will help the nose tip over as it shifts the project center of gravity farther aft of the forward landing gear. This will also add propeller clearance when at rest, as aircraft accelerates on takeoff the tail will natural rise and thus moving the aircraft body line closer to parallel to the ground, this will also be looked at when deciding on wing incidence angle.

Center of Gravity Centers of Gravity Xc.g. = 0.20 * Aircraft Length Number Part 1 Motor 2 Batteries 3 Wing 4 Wheels 5 Aileron Servos 6 Speed Controller 7 Fuselage 8 Gyro 9 Mixer 10 Receiver 11 Tail Servos 12 Tail 13 Tail Gear Increasing Weight 13 9 11 7 12 8 5 6 10 4 3 1 2 Centers of Gravity Xc.g. = 0.20 * Aircraft Length Zc.g. = 0.55 * Aircraft Height

Mass Moments of Inertia Equations to solve MOI Mass Moments of Inertia Ixx = 0.0019 lb-ft2 Iyy = 0.041 lb-ft2 Izz = 0.0181 lb-ft2

Products of Inertia Since aircraft is symmetrical around y-axis plane: Equations to solve for POI Mass Product of Inertia Ixz = 0.0779 lb-ft2 Since aircraft is symmetrical around y-axis plane: Ixy = Iyz = 0

List of Parts Part Description Weight (lbs) Motor Graupner SPEED 500 7.2 V (ungeared) 0.36 Batteries Kokam Li-Poly 2-cell 1250 mAh x 2 0.365 Wing Grade B (Medium) Balsa Wood 0.09 Main Landing Gear LYT 1 ¾” Foam Wheels x 2 0.020 Aileron Servos JR Mini 311 x 2 0.082 Speed Controller Castle Creations PIXIE-20P 0.018 Fuselage 0.02 Gyro GWS PG03 Piezo Gyro 0.0125 Mixer Vee Tail OMNI 0.0126 Receiver JP 6-Channel 0.038 Tail Servos Tail 0.03 Tail Landing Gear Lexan EM1210 Polycarbonate x 2 0.0024

Parts Location Number Part Motor Batteries Wheels Aileron Servos Speed Controller Gyro Mixer Receiver Tail Servos Tail Gear

Questions or Comments?