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Analysis and Sizing of Wing and Tail Boom Structures for Aerodynamic Efficiency

This document details the analysis and sizing of wing and tail boom structures designed for optimal aerodynamic performance. It covers materials selection, wing analysis, tail boom sizing, and center of gravity estimation, emphasizing minimizing weight while maximizing stress loading capacity. Calculations include the sectional lift coefficient, bending moments, and the mechanical properties of selected materials. The report concludes with discussions on torsion constraints, geometry of components, and weight distribution across landing gear systems, aiming to enhance design accuracy in aviation structures.

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Analysis and Sizing of Wing and Tail Boom Structures for Aerodynamic Efficiency

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  1. STRUCTURES & WEIGHTS PDR 1 TEAM 4 Jared Hutter, Andrew Faust, Matt Bagg, Tony Bradford, Arun Padmanabhan, Gerald Lo, Kelvin Seah October 28, 2003

  2. OVERVIEW • Materials • Wing Analysis • Tail Boom Sizing • C-G Determination • Landing Gear

  3. Material Properties Sources: - www.matweb.com - US Dept. of Agriculture

  4. Wing Analysis • Procedure • Calculated sectional lift coefficient • Evaluated sectional wing bending moment • Sized I-beam to desired proportions • Trade Study • Minimize material weight • Maximize stress loading capacity • Selected most suitable material and thickness

  5. Wing Analysis Root Bending Moment = 508.5 ft-lbf Actual bending moment at each point along spar Based on lifting line theory

  6. Wing Analysis

  7. Wing Analysis

  8. Wing Analysis 508.5 ft-lbf

  9. Wing Analysis • Single spar wing structure selection • I-beam • Material: BALSA (Ochroma Pyramidale) 12% • Height = 0.357 ft = 4.28 in • Base = 0.216 ft = 2.59 in • Thickness = 0.051 ft = 0.61 in • Weight = 11.0 lbf

  10. Tail Boom Sizing • Cylindrical tubes • Availability • More efficient than solid rods • Used twist and deflection constraints • Appropriately sized inner diameters • Found corresponding outer diameters

  11. Tail Boom Sizing • Equation for Deflection • I: moment of inertia (in4) • P: estimated maximum aerodynamic load applied to end of boom (lbf) • E: modulus of elasticity (ksi) • L: length of tail boom (in) • d: deflection of end of boom (in)

  12. Tail Boom Sizing • Equation for Twist • f: angle of twist (rad) • T: applied torque (ft-lbf) • L: length of tail boom • G: shear modulus (ksi) • J: torsion constant (in4) • Torsion Constant J For circular tube: • t: thickness (in) • r: radius of tube (in)

  13. Tail Boom Sizing • Twist • T = 15 ft-lbf • L = 5 ft • G = 3920 ksi • set f = 5 deg = 0.0873 rad • Known Constants • Deflection • P = 26.73 lbf • L = 5 ft • E = 10500 ksi • set d = 2 in

  14. Tail Boom Sizing • Set inner diameter to be 1.6 in • Solve for the outer diameter that satisfies both constraints • Outer diameter = 1.7 in • Thickness = 0.05 in • Weight for both booms = 5.04 lbf

  15. Tail Boom Sizing

  16. C.G. LOCATION ESTIMATION • This figure shows the approximate weights and C.G. locations of the main components: z x Wing W = 12.04 lb x = 1.55 ft z = 0 ft Avionics Pod W = 20 lb x = -1.44 ft z = - 0.58 ft Tail Section W = 2.3 lb x = 8.23 ft z = 0.075 ft Main Gear W = 3 lb x = 0 ft z = -1.25 ft Tail Booms W = 5.94 lb x = 4.05 ft z = 0 ft Engines, Fuel, Casings W = 12.72 lb x = -0.3 ft z = -0.5 ft Tail Gear W = 0.5 lb x = 8 ft z = -0.21ft NOT TO SCALE

  17. C.G. LOCATION ESTIMATION LIFT • Total Weight: W = 54.5 lb • C.G. Location: x = 0.47 ft, z = -0.38 ft • Wing M.A.C.: x = 0.775 ft • Static Margin: SM = 10.0% z x WEIGHT SM = – (xCG – xMAC) / c NOT TO SCALE

  18. Represents C.G. location TAILDRAGGER LANDING GEAR CONSTRAINTS RAYMER 11.2 3.1 ft 0.47 ft Z 0.38 ft X 18.80 deg. (16 - 25 deg) 1.35 ft 1.42 ft 10.04 deg. (10 - 15 deg) 8 ft NOT TO SCALE

  19. Wx FB = x + y WEIGHT DISTRIBUTION Center of Gravity FA W = 54.5 lbf FB Main Gear Tail Gear y = 7.43 ft x = 0.70 ft Wy 49.81 lbf FA ∑MB = 0 = =  91% of weight carried by main gear 9% by tail gear x + y ∑MA = 0 4.68 lbf  = NOT TO SCALE

  20. FOLLOW-UP ACTIONS • Torsion constraint on spar • Geometry of wing ribs • Geometric layout of tail • Moments and products of inertia

  21. QUESTIONS?

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