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

2. 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- DA119.186656.030116.224312.664204.105 MB-HA-DA- DA76.449736.294912.63048.211297.0892 LB-HA-DA- DA280.7421155.540531.329735.7067503.319 Note: this is only the structural inert mass, and does not include engine or propellant mass

3. 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) 14.94291.70411.77890.0037 21.76780.46451.14000.00550 30.98740.12390.33750.00220 StageStage Length (m)Nozzle Length (m)Skirt/Nose Cone Length (m)Fuel Tank Thick. (m)Ox Tank Thick. (m) 14.15551.35221.58670.0032 21.48160.38560.78520.00460 31.05540.13520.35960.00240 1kg Payload : MB-HA-DA-DA StageStage Length (m)Nozzle Length (m)Skirt/Nose Cone Length (m)Fuel Tank Thick. (m)Ox Tank Thick. (m) 17.07142.53042.89650.0052 22.19210.61221.53800.00670 31.00240.13040.34080.00220 5kg Payload : LB-HA-DA-DA

4. 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-DA119.186656.030116.224312.664204.105 Stage 168.052856.030111.074512.664147.8214 Stage 247.983403.3991051.3825 Stage 33.150401.750704.9011 MB-HA-DA-DA76.449736.294912.63048.2112133.5862 Stage 144.116436.29498.46678.211297.0892 Stage 228.520102.1202030.6403 Stage 33.813202.043505.8567 LB-HA-DA-DA280.7421155.540531.329735.7067503.319 Stage 1191.9896155.540524.245435.7067407.4822 Stage 285.508305.2916090.7999 Stage 33.244201.792705.0369

5. Other work MaterialTensile Strength (kPa)Density (g/cm^3)T_melt (deg C) Aluminum234.42.68649 Titanium896.34.511649 Magnesium Alloys303.41.8525 Molybdenum689.510.222622 Carbon-Carbon1.52000-7000 Hafnium Diboride10.53250 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

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

7. Other Work (cont’d) 1/8 in. Nominal Area = 100 ft 2 = 9.290304 m 2 Maximum Area = 100.208 ft 2 = 9.30966888 m 2 Minimum Area = 99.7918 ft 2 = 9.27095928 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) = 0.019365 Tolerance (min) = 0.019345 Tolerance calculations for skirts

8. AAE 450 Spring 2008 References Anonymous, “Titanium, Commercially Pure”, Aerospace Structural Metals Handbook, Setlak/CINDAS, West Lafayette, IN, 2002. Anonymous, “Magnesium, Mg-6Al-1Zn”, Aerospace Structural Metals Handbook, Setlak/CINDAS, West Lafayette, IN, 2002. Anonymous, “Aluminum, Al-2.5Mg-0.25Cr”, Aerospace Structural Metals Handbook, Setlak/CINDAS, West Lafayette, IN, 2002. Anonymous, “Carbon-Carbon Composite Thermal Protection System for Spacecraft from NextTechs Technologies,” NextTechs Technology c. 2000- 2008, [http://www.azom.com/details.asp?ArticleID=3904. Accessed 1/16/08] Buckman, R.W., “Molybdenum, Commercially Pure”, Aerospace Structural Metals Handbook, Setlak/CINDAS, West Lafayette, IN, 2002. 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. 11-12. Klemans, B., “The Vanguard Satellite Launching Vehicle” The Martin Company, Engineering Report No. 11022, April 1960. Group Name (i.e.Trajectory Optimization)

9. References, Cont’d Baker, E.H., Kovalevsky, L., Rish, F.L., Structural Analysis of Shells, Robert E. Krieger Publishing Company, Huntington, NY, 1981, pgs. 229-240. Brush, D.O., Almroth, B.O., Buckling of Bars, Plates, and Shells, McGraw Hill, 1975, pgs. 161-165. 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, 2005. Weingarten, V.I., Seide, P., Buckling of Thin-Walled Truncated Cones – NASA Space Vehicle Design Criteria (Structures), National Aeronautics and Space Administration, September 1968. Kverneland, K. O., Metric Standards for World Wide Manufacturing, The American Society of Mechanical Engineers, 1996, N.Y.,N.Y. Gilchrist Metal Fabricating, www.gmfco.com

10. 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. 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. 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. 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. 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

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

16. Backup Slides Table 10-2B from Kverneland