spring04_pset1

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Unformatted text preview: Massachusetts Institute of Technology Department of Aeronautics and Astronautics Cambridge, MA 02139 16.03/16.04 Unified Engineering III, IV Spring 2004 Problem Set 1 Time Spent (min) F1 Name: F2 Due Date: 2/10/04 M1 M2 Study Time Announcements: Good luck on your finals. Reminder: The unified final is on Monday, 12/15 at 9am Spring 2004 Uniﬁed Engineering Fluids Problems F1–F2 F1a. An aircraft’s wing is at zero angle of attack when all wheels are on the ground. Qualitatively describe the ﬂow b ehind the wing airfoil a short time after landing touchdown. Assume 2-D ﬂow. F1b. A short time after starting its motion at speed V , a 2-D airfoil of chord c has a circulation �, and its starting vortex is some distance d � c downstream. The ﬂuid is incompressible and inviscid. Determine the c� and cd of the airfoil, by convention taken p erpendicular and parallel to the direction of travel. How do these change in time? Hint: First determine the apparent freestream ﬂow velocity vector (magnitude and direction) seen by the airfoil. V � d F2a. Use Proﬁli or Xfoil to compute the “exact” inviscid cl (�) curves for the following airfoils, over the range � = 0� . . . 10� : 1) NACA 0010 2) NACA 0020 Also determine c� (�) using thin airfoil theory for: 3) Zero-camber airfoil Plot all three curves superimposed. Are the panel results and thin airfoil theory results consistent? Explain. F2b. Use Proﬁli or Xfoil to compute the following three p olars for the NACA 0010 airfoil, for � = 0� . . . 14� : 1) Inviscid 2) Viscous at Re = 106 3) Viscous at Re = 105 Plot the c� (cd ) drag p olars and the c� (�) curves overlaid, and comment on the validity of the inviscid approximation. Unified Engineering Spring 2004 Problem M1 This is question is designed to provide you with a chance to revise material we met last term, and an opportunity to start thinking about structural design. You are asked to design a minimum mass truss structure that will be attached at points A, and B, 1 m apart on a horizontal floor in order to support a vertical load of 10 kN, without exceeding the strength (assume that the tensile and compressive strengths are the same) of the bars, at a distance 2 m above the floor and 1m to the right of the right hand support point (B).. The truss will be made of constant cross-section members of whatever material you choose to select. All of the bars will have the same cross-section. The following materials are available for selection. Select a material, and then choose an appropriate truss configuration and then estimate the mass of the truss, such that it will meet the design requirement. Explain your thought processes at each step. Material Density, r, (Mg/m3) Modulus, E, CTE, a, Price , p, Tensile Strength, (GPa) x 10 -6 K-1 (\$/Mg) sf , (MPa) Mild Steel 7.9 203 12 300 220 Aluminum alloy (2000 series) 2.8 71 24 1500 350 Titanium alloy Ti-6Al4V 4.5 120 9.0 8000 850 Carbon fiber composite* 1.5 70 3.0 100000 700 Wood (e.g spruce)* 0.6 12 4.0 300 30 Silicon Carbide (SiC) 3.0 410 4.0 50000 300 Note. Although the design objective is to minimize the mass of the structure, the credit for the question will be based on demonstrating a logical approach to selecting a material and a truss configuration, and then obtaining an estimate for the mass of the truss. Do not spend more than an hour on this question, and do not analyze multiple truss configurations. A useful exercise is to estimate what you think the mass of the truss will be before you do any analysis - developing an intuition for the correct size for structures is a useful skill to cultivate. 2 Problem M2 A cable (i.e. a rope, string or chain) is a structural member that can only carry axial tensile loads (i.e the tension in the cable at a particular point acts in the direction of the cable at that point) . Nevertheless it can deflect in the transverse direction. The deflection is related to the load that it is carrying and the tension in the cable. a) A flexible cable weighing 10 N/m is stretched between two points at the same level 100 m apart. In addition to its weight it supports a vertical load of 500 N at a horizontal distance of 30 m from one end. The dip (distance below the horizontal) at that point being 1.9 m. Find (approximately) the horizontal component of the cable tension and the dip at midspan. b) If the cable has an effective cross-sectional area of 1000 mm2 and an effective Young’s modulus of 2 GPa, estimate the extension of the cable due to the loading in part (a). Would this extension affect the assumptions you made to evaluate the tension in the cable in part (a)?. 3 ...
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