Jayme Zott 2-28-08 Aerothermodynamics Aerodynamic Loads Special thanks to Alex Woods, CJ Hiu and the entire trajectory group AAE 450 Spring 2008

**Note: Rocket is out of atmosphere before first stage drops off Moments Outputs of call_aerodynamics.m Mach # Cd Normal Force (to be used as Lift) Bending Moment Pitching Moment Shear Center Of Pressure Location **Note: Rocket is out of atmosphere before first stage drops off AAE 450 Spring 2008 Aerothermodynamics

**Less than Vanguard max aerodynamic loading Other Aero Loads Xcp (measured from nose): 500g 43.8% length of rocket 1 kg 40.4% length of rocket 5 kg 33.2% length of rocket Future Work Figure out why roger.ecn hates me Begin CFD for final design Begin writing for final report **Less than Vanguard max aerodynamic loading AAE 450 Spring 2008 Aerothermodynamics

References Ashley, Holt, Engineering Analysis of Flight Vehicles, Dover Publications Inc., New York, 1974, pp. 303-312 Woods, Alex for original code and extra help analyzing results The Martin Company, “The Vanguard Satellite Launching Vehicle”, Engineering Report No. 11022, April 1960. AAE 450 Spring 2008

5kg AAE 450 Spring 2008 5kg M Cd Xcp [m] Normal Force [N] Pitching Moment [Nm] Shear (1) [N] Shear (2) [N] Shear (3) [N] Bending Moment (1) [Nm] Bending Moment (2) [Nm] Bending Moment (3) [Nm] 0.45 0.332646 0.001413 0.008648839 0.026130105 -0.0225522 -0.02312887 -0.02314879 -0.101802721 -0.10172681 -0.03035144 0.01203 0.627135193 1.894717648 -1.63528066 -1.67709561 -1.67853975 -7.381807783 -7.376303411 -2.200810507 0.022814 2.254322893 6.810820723 -5.87823912 -6.02854866 -6.03373981 -26.53491378 -26.51512756 -7.911113206 0.033764 4.934423611 14.90801282 -12.8667113 -13.1957196 -13.2070824 -58.08152214 -58.03821265 -17.31641191 0.044882 8.711096019 26.31819668 -22.714539 -23.2953613 -23.3154208 -102.5355252 -102.4590678 -30.56991834 0.056168 13.62739393 41.17144763 -35.5339869 -36.4426088 -36.4739894 -160.4036954 -160.2840877 -47.82272157 0.067624 19.72572583 59.59589136 -51.4356366 -52.7508718 -52.7962953 -232.1852098 -232.0120769 -69.22364607 0.079251 27.04782767 81.71762161 -70.5283166 -72.3317612 -72.3940457 -318.3713287 -318.1339297 -94.91915612 0.09105 35.63475083 107.6606639 -92.9190698 -95.2950573 -95.3771154 -419.4452549 -419.1324883 -125.0533137 0.10302 45.52686752 137.5469919 -118.713169 -121.748724 -121.853561 -535.8821967 -535.4826069 -159.7677972 0.094861 38.3711082 115.9278201 -100.054234 -102.612671 -102.70103 -451.6540423 -451.3172587 -134.6560343 0.107189 48.89014225 147.7082076 -127.483045 -130.742851 -130.855433 -575.4702278 -575.0411185 -171.5705639 0.119712 60.84323258 183.8212044 -158.651217 -162.708008 -162.848115 -716.1662311 -715.6322095 -213.5176386 0.132428 74.27138704 224.3907044 -193.665678 -198.617808 -198.788836 -874.2247425 -873.5728618 -260.6411675 0.145332 89.21518497 269.5393071 -232.632243 -238.580766 -238.786207 -1050.123408 -1049.340366 -313.0835561 0.158425 105.7149177 319.3887417 -275.65597 -282.704633 -282.948068 -1244.336485 -1243.408624 -370.986199 0.171704 123.810768 374.0604094 -322.84164 -331.096864 -331.381969 -1457.336952 -1456.250263 -434.49011 0.18517 143.5430339 433.6760597 -374.29433 -383.865225 -384.195769 -1689.599142 -1688.339263 -503.736707 0.198823 164.9524025 498.3586179 -430.120134 -441.118523 -441.498368 -1941.601973 -1940.154184 -578.8687742 0.212662 0.412249 188.0802822 568.2331875 -490.427026 -502.967492 -503.400595 -2213.832848 -2212.182065 -660.0316257 0.226689 0.410851 212.9691992 643.4282505 -555.325895 -569.525858 -570.016274 -2506.79233 -2504.923097 -747.3744996 0.240903 0.40951 239.6632709 724.077095 -624.931778 -640.911599 -641.463485 -2820.99971 -2818.896183 -841.052217 0.255306 0.408231 268.208765 810.3195065 -699.365321 -717.248445 -717.866064 -3156.999591 -3154.64552 -941.2271457 0.269898 0.407021 298.65476 902.3037624 -778.754498 -798.667643 -799.355372 -3515.369661 -3512.748365 -1048.071518 0.28468 0.405889 331.0539227 1000.188981 -863.23664 -885.310036 -886.072372 -3896.729843 -3893.824179 -1161.770156 0.299652 0.404841 365.4634225 1104.147883 -952.960817 -977.328506 -978.170079 -4301.75306 -4298.545383 -1282.523687 0.314817 0.403886 401.9460068 1214.370045 -1048.09065 -1074.89085 -1075.81644 -4731.177891 -4727.650006 -1410.552309 0.330174 0.403032 440.5712675 1331.065717 -1148.80759 -1178.18318 -1179.19771 -5185.823481 -5181.956583 -1546.100243 0.345724 0.402287 481.4171346 1454.470345 -1255.31486 -1287.4139 -1288.52248 -5666.607119 -5662.381716 -1689.440968 0.361469 0.401662 524.5716418 1584.849899 -1367.842 -1402.81841 -1404.02637 -6174.565022 -6169.960851 -1840.883422 0.377409 0.401165 570.1350212 1722.507201 -1486.65038 -1524.66478 -1525.97766 -6710.876987 -6705.872906 -2000.779351 0.393546 0.400808 618.2221967 1867.789464 -1612.03966 -1653.26032 -1654.68394 -7276.895751 -7271.469608 -2169.532057 0.40988 0.4006 668.9657676 2021.0973 -1744.35559 -1788.95964 -1790.50011 -7874.182094 -7868.310575 -2347.606873 0.426413 0.400554 722.519594 2182.895555 -1883.99938 -1932.1742 -1933.83798 -8504.547056 -8498.205494 -2535.543741 0.443066 0.400679 778.7156996 2352.676735 -2030.53303 -2082.45478 -2084.24797 -9166.013442 -9159.178646 -2732.75318 0.459751 0.400983 837.3046348 2529.687195 -2183.30607 -2239.13431 -2241.06242 -9855.645059 -9848.296028 -2938.359794 AAE 450 Spring 2008

1kg AAE 450 Spring 2008 1 kg M Cd Xcp [m] Normal Force [N] Pitching Moment [Nm] Shear (1) [N] Shear (2) [N] Shear (3) [N] Bending Moment (1) [Nm] Bending Moment (2) [Nm] Bending Moment (3) [Nm] 0.45 0.404338 0.001413 0.0034678 0.00875932 -0.00310658 -0.00332069 -0.00333155 -0.011837695 -0.017351214 -0.00553263 0.01203 0.251452758 0.63514483 -0.22526012 -0.24078534 -0.24157321 -0.858360036 -1.258149409 -0.401175101 0.022814 0.903875857 2.283101137 -0.8097234 -0.86553061 -0.86836268 -3.085473863 -4.522562742 -1.442070037 0.033764 1.978449354 4.997367653 -1.77236367 -1.89451734 -1.9007163 -6.753641803 -9.899214883 -3.156476092 0.044881 3.492653838 8.822098619 -3.12884066 -3.34448453 -3.35542786 -11.92253566 -17.47557034 -5.572282312 0.056167 5.463716678 13.80080867 -4.89458723 -5.23192871 -5.24904786 -18.65096283 -27.33782664 -8.716973744 0.067622 7.908595074 19.97633001 -7.08479424 -7.57308771 -7.59786726 -26.99680848 -39.5708295 -12.6176044 0.079247 10.84396443 27.39078308 -9.7144001 -10.3839295 -10.4179063 -37.01699585 -54.2580147 -17.30077872 0.091044 14.28621288 36.08556266 -12.7980859 -13.680147 -13.7249092 -48.76746748 -71.48138056 -22.7926428 0.103013 18.25144276 46.10134169 -16.3502766 -17.4771594 -17.5343456 -62.30319041 -91.32149553 -29.11888678 0.094851 15.38179579 38.85289687 -13.7795471 -14.7292519 -14.7774468 -52.50735322 -76.96315375 -24.54056788 0.107176 19.59809516 49.50285263 -17.5566546 -18.7666826 -18.8280882 -66.90012785 -98.05950043 -31.26737548 0.119696 24.38892095 61.60400539 -21.8484428 -23.3542666 -23.430683 -83.25410796 -122.0305027 -38.91079939 0.132408 29.77061136 75.19762379 -26.669548 -28.5076488 -28.6009274 -101.6250656 -148.9579091 -47.49690601 0.145308 35.759317 90.32450272 -32.0344386 -34.2422948 -34.3543374 -122.0681326 -178.9225296 -57.05146253 0.158395 42.37105658 107.0251039 -37.9574646 -40.5735437 -40.7063025 -144.6379906 -212.0045141 -67.60002567 0.171669 49.62178815 125.3397356 -44.4529219 -47.5166765 -47.6721537 -169.3891138 -248.2837091 -79.16805535 0.185128 57.52749795 145.3087777 -51.5351314 -55.0870014 -55.267249 -196.3760731 -287.8401021 -91.78105651 0.198772 66.10430944 166.9729564 -59.2185371 -63.2999577 -63.5070785 -225.6539076 -330.7543671 -105.464753 0.212602 0.412255 75.3686151 190.3736774 -67.517824 -72.1712425 -72.4073907 -257.2785746 -377.1085243 -120.2452978 0.226619 0.410858 85.3372344 215.5534252 -76.4480595 -81.7169617 -81.984344 -291.3074891 -426.9867304 -136.1495252 0.240822 0.409517 96.0276017 242.5562371 -86.024862 -91.9538102 -92.254688 -327.8001652 -480.4762185 -153.2052506 0.255212 0.408239 107.4579886 271.4282653 -96.2645997 -102.899284 -103.235976 -366.8189748 -537.6684107 -171.4416248 0.26979 0.40703 119.6477661 302.2184392 -107.184626 -114.571933 -114.946819 -408.4300429 -598.6602306 -190.8895531 0.284556 0.405898 132.6177132 334.9792446 -118.803555 -126.991655 -127.407178 -452.7043009 -663.5556466 -211.582187 0.299512 0.404851 146.3903798 369.7676401 -131.141588 -140.180042 -140.638718 -499.7187249 -732.4674869 -233.555503 0.314658 0.403895 160.9905127 406.6461337 -144.220895 -154.160791 -154.665213 -549.5577909 -805.5195732 -256.848983 0.329995 0.403041 176.4455575 445.6840504 -158.066061 -168.960185 -169.513031 -602.3151872 -882.8492301 -281.5064145 0.345524 0.402296 192.7862498 486.959025 -172.704621 -184.607653 -185.2117 -658.0958329 -964.6102435 -307.5768339 0.361245 0.40167 210.0473135 530.558767 -188.167681 -201.136449 -201.794578 -717.0182618 -1050.976356 -335.1156409 0.37716 0.401172 228.2682888 576.5831511 -204.490664 -218.584433 -219.299653 -779.2174486 -1142.145407 -364.1859191 0.39327 0.400813 247.4945174 625.1467055 -221.714188 -236.995025 -237.770486 -844.8481714 -1238.344265 -394.8600078 0.409575 0.400603 267.7783193 676.3815855 -239.885122 -256.418325 -257.257339 -914.0890301 -1339.834714 -427.2213798 0.426077 0.400553 289.1804071 730.4411454 -259.057856 -276.912469 -277.818541 -987.1472737 -1446.920531 -461.366898 0.442699 0.400674 311.6357998 787.1612494 -279.174177 -298.415233 -299.391664 -1063.801083 -1559.276583 -497.1928898 0.459349 0.400973 335.0380606 846.2730488 -300.138735 -320.824697 -321.874453 -1143.687124 -1676.37031 -534.5295427 0.476172 0.401462 359.7132572 908.6001582 -322.243634 -344.453095 -345.580164 -1227.918464 -1799.833199 -573.8970746 0.493166 0.402153 385.7613137 974.394976 -345.578388 -369.396111 -370.604795 -1316.836203 -1930.165223 -615.4549075 0.510333 0.403057 413.3007455 1043.956861 -370.249168 -395.767234 -397.062206 -1410.844906 -2067.959376 -659.3921242 0.527672 0.404188 442.4726774 1117.642279 -396.382398 -423.701601 -425.087976 -1510.426317 -2213.921779 -705.9338795 0.545182 0.405559 473.4458783 1195.877525 -424.129267 -453.360822 -454.844243 -1616.156546 -2368.896871 -755.3494321 0.562863 0.407183 506.4231299 1279.174806 -453.671435 -484.939075 -486.525822 -1728.727811 -2533.899276 -807.962306 0.580715 0.409074 541.6493696 1368.152808 -485.228324 -518.670908 -520.368027 -1848.976229 -2710.154541 -864.1632814 0.598737 0.411246 579.4222168 1463.563289 -519.066553 -554.841312 -556.656783 -1977.917755 -2899.151814 -924.427189 0.61693 0.413715 620.1057497 1566.325875 -555.512276 -593.798922 -595.741864 -2116.795209 -3102.712766 -989.3348899 0.635291 0.416496 664.1487762 1677.574209 -594.967549 -635.973506 -638.054445 -2267.140642 -3323.083018 -1059.602425 0.653822 0.419604 712.1094211 1798.718061 -637.932361 -681.89951 -684.130722 -2430.859272 -3563.055161 -1136.120244 0.672521 0.423056 764.6887459 1931.528242 -685.034747 -732.248255 -734.644211 -2610.344243 -3826.136969 -1220.00684 0.691389 0.426869 822.7775411 2078.254801 -737.072708 -787.872742 -790.450704 -2808.636362 -4116.785534 -1312.683407 AAE 450 Spring 2008

200g AAE 450 Spring 2008 200 g M Cd Xcp [m] Normal Force [N] Pitching Moment [Nm] Shear (1) [N] Shear (2) [N] Shear (3) [N] Bending Moment (1) [Nm] Bending Moment (2) [Nm] Bending Moment (3) [Nm] 0.45 0.438355126 0.001413 0.003586752 -0.000350932 -0.00046729 -0.000468683 -0.004736151 -0.005341605 -0.0012573 0.01203 0.260077744 -0.025446321 -0.03388353 -0.033984542 -0.343421421 -0.387323242 -0.091167633 0.022814 0.934876366 -0.091469434 -0.121797855 -0.122160953 -1.234463837 -1.392273477 -0.327711493 0.033764 2.04629422 -0.200211901 -0.266595944 -0.267390707 -2.702043079 -3.047463036 -0.717307827 0.044881 3.612397721 -0.353441361 -0.47063153 -0.472034554 -4.770015066 -5.379797498 -1.266289635 0.056166 5.650985378 -0.552899243 -0.736223446 -0.738418239 -7.461881962 -8.415783462 -1.980896004 0.067621 8.179569861 -0.800299007 -1.065653281 -1.068830155 -10.80076849 -12.18150184 -2.867265825 0.079245 11.21536559 -1.097324932 -1.46116377 -1.46551972 -14.80940554 -16.70258936 -3.931433439 0.091041 14.77528266 -1.445631523 -1.924958 -1.930696592 -19.51012219 -22.00422956 -5.179326512 0.103008 18.87592807 -1.846843629 -2.459199569 -2.466530816 -24.92484722 -28.11115455 -6.616766456 0.094846 15.90755993 -1.556414901 -2.072473702 -2.07865206 -21.00524538 -23.6904842 -5.576234904 0.107169 20.26771871 -1.983018108 -2.640525272 -2.648397079 -26.76264661 -30.18389193 -7.104644646 0.119688 25.22187542 -2.467738791 -3.285964267 -3.295760224 -33.30439643 -37.5619167 -8.841274376 0.132397 30.78689339 -3.012226879 -4.01098768 -4.022945042 -40.65276214 -45.84967239 -10.79203537 0.145295 36.97943471 -3.618112611 -4.817766286 -4.832128778 -48.82974533 -55.07197317 -12.96276836 0.15838 43.81601754 -4.287012142 -5.708452109 -5.725469871 -57.85715748 -65.25341885 -15.3592636 0.171651 51.31308953 -5.020534732 -6.685187989 -6.705117548 -67.75671703 -76.41850428 -17.98728668 0.185107 59.48711959 -5.820291718 -7.750119532 -7.773223814 -78.55017045 -88.59175591 -20.85261058 0.198748 68.3547103 -6.687907516 -8.90540976 -8.931958137 -90.25944074 -101.7978993 -23.96105518 0.212574 0.412258 77.93273396 -7.625032934 -10.15325684 -10.18352523 -102.906807 -116.0620617 -27.3185349 0.226586 0.410861 88.23849557 -8.633361112 -11.4959153 -11.53018636 -116.5151198 -131.4100147 -30.93111583 0.240784 0.40952 99.28992664 -9.714646493 -12.9357213 -12.97428464 -131.1080569 -147.8684631 -34.80508367 0.255169 0.408242 111.1058146 -10.87072726 -14.47512251 -14.51827505 -146.7104263 -165.465386 -38.94702418 0.269741 0.407034 123.7060731 -12.10355179 -16.11671333 -16.1647597 -163.3485231 -184.2304403 -43.36391788 0.284501 0.405902 137.1120602 -13.41520978 -17.86327634 -17.91652947 -181.0505497 -204.1954335 -48.06325163 0.29945 0.404855 151.3469521 -14.80796882 -19.71783098 -19.77661283 -199.8471092 -225.394881 -53.0531496 0.314589 0.403899 166.4361825 -16.28431736 -21.68369081 -21.74833318 -219.7717857 -247.8666601 -58.34252731 0.329917 0.403045 182.4079589 -17.84701529 -23.76453079 -23.83537647 -240.8618263 -271.6527794 -63.94127268 0.345437 0.4023 199.2938721 -19.49915345 -25.96446661 -26.04187062 -263.1589448 -296.8002854 -69.86045944 0.361149 0.401673 217.1296139 -21.244224 -28.28814832 -28.37247958 -286.7102711 -323.3623327 -76.1125991 0.377054 0.401175 235.9558301 -23.08620376 -30.7408713 -30.8325145 -311.5694759 -351.3994534 -82.71193955 0.393152 0.400815 255.8191327 -25.02965331 -33.32870831 -33.42806625 -337.7981086 -380.9810649 -89.67482021 0.409446 0.400604 276.7733109 -27.07983544 -36.05866711 -36.16616347 -365.4671952 -412.187273 -97.0200963 0.425935 0.400553 298.880784 -29.24285734 -38.93887985 -39.05496255 -394.659158 -445.1110367 -104.7696483 0.442545 0.400672 322.0759665 -31.51230204 -41.96080186 -42.08589338 -425.2873939 -479.6546816 -112.9004859 0.459181 0.400969 346.245085 -33.87703783 -45.10961053 -45.24408912 -457.2016704 -515.6487702 -121.3727269 0.475989 0.401456 371.7262194 -36.37014283 -48.42935165 -48.57372689 -490.8484071 -553.5967907 -130.3048819 0.492968 0.402143 398.6220809 -39.00166645 -51.9334067 -52.08822806 -526.3632298 -593.6517071 -139.7329553 0.510119 427.0544824 -41.78352699 -55.63764573 -55.80350999 -563.9069872 -635.9949301 -149.6996472 0.527441 0.404172 457.1684599 -44.72991497 -59.56096437 -59.73852464 -603.671193 -680.8424562 -160.2557987 AAE 450 Spring 2008

Fluent – subsonic case AAE 450 Spring 2008

Fluent – subsonic case AAE 450 Spring 2008