AAE 450 Spring 2008 Molly Kane March 20, 2008 Structures Group Inert Masses, Dimensions, Buckling Analysis, Skirt Analysis, Materials Selection

AAE 450 Spring 2008 Inert masses Group Name (i.e.Trajectory Optimization) Included in inert mass: Tanks Skirts Nose Cone Pressure addition Design/Stage Fuel Tank Mass (kg) Ox Tank Mass (kg)Skirt/Nose Cone Mass (kg)Pressure Tank Mass (kg) Total (kg) SB-HA-DA- DA MB-HA-DA- DA LB-HA-DA- DA Note: this is only the structural inert mass, and does not include engine or propellant mass

AAE 450 Spring 2008 Group Name (i.e.Trajectory Optimization) Dimensions 200g Payload : SB-HA-DA-DA StageStage Length (m)Nozzle Length (m)Skirt/Nose Cone Length (m)Fuel Tank Thick. (m)Ox Tank Thick. (m) StageStage Length (m)Nozzle Length (m)Skirt/Nose Cone Length (m)Fuel Tank Thick. (m)Ox Tank Thick. (m) kg Payload : MB-HA-DA-DA StageStage Length (m)Nozzle Length (m)Skirt/Nose Cone Length (m)Fuel Tank Thick. (m)Ox Tank Thick. (m) kg Payload : LB-HA-DA-DA

Backup Slides Design/StageFuel Tank Mass (kg)Ox Tank Mass (kg)Skirt/Nose Cone Mass (kg)Pressure Tank Mass (kg)Total (kg) SB-HA-DA-DA Stage Stage Stage MB-HA-DA-DA Stage Stage Stage LB-HA-DA-DA Stage Stage Stage

Other work MaterialTensile Strength (kPa)Density (g/cm^3)T_melt (deg C) Aluminum Titanium Magnesium Alloys Molybdenum Carbon-Carbon Hafnium Diboride Material Selection for Nose Cone  Aluminum – low heat applications, relatively inexpensive  Titanium – strong, high temperature usage  Magnesium Alloys – low density, low heat applications  Molybdenum – very high heat capabilities, maintains strength  Carbon-Carbon – ceramic, light, very expensive  Hafnium Diboride – ceramic, light, very high heat capabilities

Other Work (cont’d) steel titanium aluminum Thickness variations for skirts and its effect on pressure

Other Work (cont’d) 1/8 in. Nominal Area = 100 ft 2 = m 2 Maximum Area = ft 2 = m 2 Minimum Area = ft 2 = m 2 Divide nominal volume by thickness to get “area”. Add tolerances to area based on change in sample area. Multiply by thickness to get minimum/maximum volumes. Multiply by density to get masses. 10 ft 1/8 in. Tolerance (max) = Tolerance (min) = Tolerance calculations for skirts

AAE 450 Spring 2008 References Anonymous, “Titanium, Commercially Pure”, Aerospace Structural Metals Handbook, Setlak/CINDAS, West Lafayette, IN, Anonymous, “Magnesium, Mg-6Al-1Zn”, Aerospace Structural Metals Handbook, Setlak/CINDAS, West Lafayette, IN, Anonymous, “Aluminum, Al-2.5Mg-0.25Cr”, Aerospace Structural Metals Handbook, Setlak/CINDAS, West Lafayette, IN, Anonymous, “Carbon-Carbon Composite Thermal Protection System for Spacecraft from NextTechs Technologies,” NextTechs Technology c , [ Accessed 1/16/08] Buckman, R.W., “Molybdenum, Commercially Pure”, Aerospace Structural Metals Handbook, Setlak/CINDAS, West Lafayette, IN, Ewig, R. Sandhu, J. Shell, C.A., Schneider, M.A., Bloom, J.B., Ohno, S., “The K2X: Design of a 2 nd Generation Reusable Launch Vehicle,” 36 th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Huntsville, AL, 2000, pp Klemans, B., “The Vanguard Satellite Launching Vehicle” The Martin Company, Engineering Report No , April Group Name (i.e.Trajectory Optimization)

References, Cont’d Baker, E.H., Kovalevsky, L., Rish, F.L., Structural Analysis of Shells, Robert E. Krieger Publishing Company, Huntington, NY, 1981, pgs Brush, D.O., Almroth, B.O., Buckling of Bars, Plates, and Shells, McGraw Hill, 1975, pgs Grandt, A.F., AAE352 Class Notes, Spring 2007, Purdue University Jastrzebski, Zbigniew D., The Nature and Properties of Engineering Materials, 2 nd edition, SI Version, John Wiley & Sons, Inc. Wang, C.Y., Wang, C.M., Reddy, J.N., Exact Solutions for Buckling of Structural Members, CRC Press, Boca Raton, FL, Weingarten, V.I., Seide, P., Buckling of Thin-Walled Truncated Cones – NASA Space Vehicle Design Criteria (Structures), National Aeronautics and Space Administration, September Kverneland, K. O., Metric Standards for World Wide Manufacturing, The American Society of Mechanical Engineers, 1996, N.Y.,N.Y. Gilchrist Metal Fabricating,

AAE 450 Spring 2008 Backup Slides  Method 1 from Wang, Wang, Reddy N cr = 1 (Et 2 /R) √(3(1-ν 2 ))  Method 2 from Brush, Almroth P e a = [(πa/L) 2 + n 2 ] 2 *(n/a) 2 + (πa/L) 4. Eh n 2 12(1-v 2 ) (n 2 [(πa/L) 2 + n 2 ] 2 ) Where n is an integer representing the number of half – waves present in along the structure  Method 3 from Baker, Kovalevsky, Rish P cr = K c π 2 E (t/L) 2 Kc = 4√(3) γZZ = L 2 √(1- v 2 ) 12(1-v 2 ) π 2 Rt Where γ is representative of the R/t ratio. Structures Group

11 Critical Pressure – Axial Compression Structures Group = correlation factor to account for difference between classical theory and predicted instability loads E = Young’s modulus α = semivertex angle of cone ν = Poisson’s ratio t = thickness Slide by: Jessica Schoenbauer

12 Critical Moment - Bending Structures Group = correlation factor to account for difference between classical theory and predicted instability loads E = Young’s modulus α = semivertex angle of cone ν = Poisson’s ratio t = thickness r 1 = radius of small end of cone Slide by: Jessica Schoenbauer

13 Uniform Hydrostatic Pressure Pressure: Structures Group = correlation factor to account for difference between classical theory and predicted instability loads E = Young’s modulus t = thickness L = slant length of cone t = thickness Slide by: Jessica Schoenbauer

14 Torsion Structures Group = correlation factor to account for difference between classical theory and predicted instability loads E = Young’s modulus ν = Poisson’s ratio t = thickness l = axial length of cone t = thickness Slide by: Jessica Schoenbauer

Thickness (mm)Tolerance (mm) Table 11-2 from Kverneland

Backup Slides Table 10-2B from Kverneland