Modeling and Analysis of an Air-Breathing Flexible Hypersonic Vehicle

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td align="left">Terms </td><td align="center">Values</td><td align="center">Terms</td><td align="center">Values</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td align="left"><span style="width: 30.9px;"><svg height="20.1" id="M137" style="vertical-align:-4.11421pt" version="1.1" viewbox="0 0 30.9 20.1" width="30.9" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,12.05,20.037)"><path d="M559 163q-23 -66 -68 -163h-474l6 26q62 4 79.5 19.5t28.5 75.5l78 409q7 35 8.5 49t-8 25t-24 13t-51.5 5l5 28h266l-6 -28q-65 -5 -79.5 -18t-25.5 -74l-76 -406q-10 -57 14 -75q12 -13 96 -13q93 0 126 29q41 40 76 109z" id="x1D43F"></path></g><g transform="matrix(.012,-0,0,-.012,12.05,7.8)"><path d="M998 650l-8 -28q-71 -4 -86 -16t-22 -69l-50 -397q-3 -28 -4.5 -44t2 -29t6.5 -18.5t17 -10.5t24.5 -6.5t37.5 -3.5l-8 -28h-271l7 28q63 6 78 22t25 90l60 415h-2l-353 -552h-23l-130 536h-2l-70 -254q-44 -158 -47 -188q-5 -38 9 -51t71 -18l-6 -28h-241l8 28
q45 4 67 18.5t35 45.5q16 38 74 233l52 173q24 79 11.5 98t-89.5 26l6 28h177l136 -508l337 508h172z" id="x1D440"></path></g><g transform="matrix(.012,-0,0,-.012,24.199,7.8)"><path d="M483 97q-42 -50 -88.5 -79.5t-68.5 -29.5q-37 0 -17 93l22 102h-2q-54 -79 -144 -149q-59 -46 -100 -46q-24 0 -43 29t-19 86q0 78 34.5 153t94.5 120q41 31 94 51.5t98 20.5q29 0 72 -9q26 -6 39 -6l2 -4q-30 -117 -67 -323q-8 -41 2 -41q16 0 79 58zM374 387
q-32 15 -73 15q-52 0 -83 -23q-48 -36 -78 -108.5t-30 -152.5q0 -33 8.5 -50.5t20.5 -17.5q31 0 107 79t99 132q15 40 29 126z" id="x1D44E"></path></g>
</svg></span></td><td align="center">−0.00578253<br/></td><td align="center"><span style="width: 24.5625px;"><svg height="19.700001" id="M138" style="vertical-align:-4.52803pt" version="1.1" viewbox="0 0 24.5625 19.700001" width="24.5625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,14.6)"><path d="M682 629q-1 -16 -1.5 -72t-2.5 -86l-31 -4q-5 92 -51 129t-139 37q-100 0 -177 -49t-116 -125t-39 -162q0 -122 66 -201t182 -79q83 0 137 42.5t112 128.5l26 -15q-12 -31 -42.5 -88t-45.5 -75q-139 -27 -199 -27q-148 0 -243 81.5t-95 226.5q0 173 129.5 274.5
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<g transform="matrix(.012,-0,0,-.012,12.05,5.388)"><path d="M471 401q0 -32 -14 -91l-83 -376q-30 -146 -21 -180l-7 -15q-22 0 -47.5 23.5t-25.5 40.5q0 49 53 271l53 224q4 18 6.5 31t3.5 22.5t1 15t-2 9t-4.5 4.5t-6.5 1q-31 0 -100.5 -63.5t-126.5 -145.5q-16 -53 -40 -163q-48 -11 -74 -21l-7 8l82 341q9 36 -4 36
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<g transform="matrix(.008,-0,0,-.008,19.175,8.25)"><path d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" id="x33"></path></g>
<g transform="matrix(.012,-0,0,-.012,12.05,19.638)"><path d="M559 163q-23 -66 -68 -163h-474l6 26q62 4 79.5 19.5t28.5 75.5l78 409q7 35 8.5 49t-8 25t-24 13t-51.5 5l5 28h266l-6 -28q-65 -5 -79.5 -18t-25.5 -74l-76 -406q-10 -57 14 -75q12 -13 96 -13q93 0 126 29q41 40 76 109z" id="x1D43F"></path></g>
</svg></span></td><td align="center">−0.0954033<br/></td></tr><tr><td align="left"><span style="width: 19.525px;"><svg height="17.700001" id="M139" style="vertical-align:-4.11421pt" version="1.1" viewbox="0 0 19.525 17.700001" width="19.525" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,13.55)"><path d="M682 629q-1 -16 -1.5 -72t-2.5 -86l-31 -4q-5 92 -51 129t-139 37q-100 0 -177 -49t-116 -125t-39 -162q0 -122 66 -201t182 -79q83 0 137 42.5t112 128.5l26 -15q-12 -31 -42.5 -88t-45.5 -75q-139 -27 -199 -27q-148 0 -243 81.5t-95 226.5q0 173 129.5 274.5
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q-14 98 -31 149.5t-50 51.5q-49 0 -94 -70t-45 -164q0 -55 15.5 -86t40.5 -31q70 0 164 150z" id="x1D6FC"></path></g><g transform="matrix(.012,-0,0,-.012,12.05,17.638)"><path d="M559 163q-23 -66 -68 -163h-474l6 26q62 4 79.5 19.5t28.5 75.5l78 409q7 35 8.5 49t-8 25t-24 13t-51.5 5l5 28h266l-6 -28q-65 -5 -79.5 -18t-25.5 -74l-76 -406q-10 -57 14 -75q12 -13 96 -13q93 0 126 29q41 40 76 109z" id="x1D43F"></path></g>
</svg></span></td><td align="center">5.84425</td><td align="center"><span style="width: 24.5625px;"><svg height="21.9125" id="M140" style="vertical-align:-4.52803pt" version="1.1" viewbox="0 0 24.5625 21.9125" width="24.5625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,16.813)"><path d="M682 629q-1 -16 -1.5 -72t-2.5 -86l-31 -4q-5 92 -51 129t-139 37q-100 0 -177 -49t-116 -125t-39 -162q0 -122 66 -201t182 -79q83 0 137 42.5t112 128.5l26 -15q-12 -31 -42.5 -88t-45.5 -75q-139 -27 -199 -27q-148 0 -243 81.5t-95 226.5q0 173 129.5 274.5
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<g transform="matrix(.012,-0,0,-.012,17.5,7.475)"><path d="M-161 571q0 -21 -15 -36t-36 -15q-20 0 -35 15.5t-15 35.5q0 21 15 36.5t35 15.5q22 0 36.5 -15t14.5 -37z" id="x307"></path></g><g transform="matrix(.012,-0,0,-.012,12.05,7.613)"><path d="M471 401q0 -32 -14 -91l-83 -376q-30 -146 -21 -180l-7 -15q-22 0 -47.5 23.5t-25.5 40.5q0 49 53 271l53 224q4 18 6.5 31t3.5 22.5t1 15t-2 9t-4.5 4.5t-6.5 1q-31 0 -100.5 -63.5t-126.5 -145.5q-16 -53 -40 -163q-48 -11 -74 -21l-7 8l82 341q9 36 -4 36
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<g transform="matrix(.012,-0,0,-.012,12.05,21.85)"><path d="M559 163q-23 -66 -68 -163h-474l6 26q62 4 79.5 19.5t28.5 75.5l78 409q7 35 8.5 49t-8 25t-24 13t-51.5 5l5 28h266l-6 -28q-65 -5 -79.5 -18t-25.5 -74l-76 -406q-10 -57 14 -75q12 -13 96 -13q93 0 126 29q41 40 76 109z" id="x1D43F"></path></g>
</svg></span></td><td align="center">−0.00413381</td></tr><tr><td align="left"><span style="width: 24.275px;"><svg height="22.6875" id="M141" style="vertical-align:-4.52803pt" version="1.1" viewbox="0 0 24.275 22.6875" width="24.275" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,17.6)"><path d="M682 629q-1 -16 -1.5 -72t-2.5 -86l-31 -4q-5 92 -51 129t-139 37q-100 0 -177 -49t-116 -125t-39 -162q0 -122 66 -201t182 -79q83 0 137 42.5t112 128.5l26 -15q-12 -31 -42.5 -88t-45.5 -75q-139 -27 -199 -27q-148 0 -243 81.5t-95 226.5q0 173 129.5 274.5
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<g transform="matrix(.012,-0,0,-.012,12.05,8.538)"><path d="M494 514l-10 -15q-56 76 -106.5 117t-110.5 41q-45 0 -45 -30q0 -28 109 -152q59 -68 86 -118.5t27 -107.5q0 -62 -29.5 -119.5t-86.5 -96.5q-64 -45 -138 -45q-76 0 -121.5 53t-45.5 136q0 74 40.5 135t98.5 95q43 26 87 42q-40 59 -57.5 92t-17.5 62q0 46 39 77.5
t90 31.5q54 0 97.5 -35.5t65 -78.5t28.5 -84zM359 234q0 84 -90 191q-47 -17 -74 -47q-81 -89 -81 -200q0 -71 32.5 -109.5t72.5 -38.5q47 0 80 33t46.5 77.5t13.5 93.5z" id="x1D6FF"></path></g>
<g transform="matrix(.008,-0,0,-.008,19.437,11.388)"><path d="M391 364q0 -28 -20.5 -53.5t-50 -43.5t-70 -34t-73.5 -25t-68 -17v-29q0 -48 20 -81t65 -33q73 0 157 76l16 -23q-107 -113 -221 -113q-21 0 -40.5 6.5t-39 22t-31.5 47t-12 75.5q0 69 33.5 139.5t95.5 114.5q77 55 143 55q42 0 69 -24.5t27 -59.5zM313 350
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<g transform="matrix(.012,-0,0,-.012,12.05,22.625)"><path d="M559 163q-23 -66 -68 -163h-474l6 26q62 4 79.5 19.5t28.5 75.5l78 409q7 35 8.5 49t-8 25t-24 13t-51.5 5l5 28h266l-6 -28q-65 -5 -79.5 -18t-25.5 -74l-76 -406q-10 -57 14 -75q12 -13 96 -13q93 0 126 29q41 40 76 109z" id="x1D43F"></path></g>
</svg></span></td><td align="center">0.755975</td><td align="center"><span style="width: 19.525px;"><svg height="19.924999" id="M142" style="vertical-align:-4.14932pt" version="1.1" viewbox="0 0 19.525 19.924999" width="19.525" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,12.05,7.613)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.012,-0,0,-.012,12.05,19.863)"><path d="M559 163q-23 -66 -68 -163h-474l6 26q62 4 79.5 19.5t28.5 75.5l78 409q7 35 8.5 49t-8 25t-24 13t-51.5 5l5 28h266l-6 -28q-65 -5 -79.5 -18t-25.5 -74l-76 -406q-10 -57 14 -75q12 -13 96 -13q93 0 126 29q41 40 76 109z" id="x1D43F"></path></g>
</svg></span></td><td align="center">0.0621356</td></tr><tr><td align="left"><span style="width: 24.5625px;"><svg height="19.700001" id="M143" style="vertical-align:-4.52803pt" version="1.1" viewbox="0 0 24.5625 19.700001" width="24.5625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,12.05,5.388)"><path d="M471 401q0 -32 -14 -91l-83 -376q-30 -146 -21 -180l-7 -15q-22 0 -47.5 23.5t-25.5 40.5q0 49 53 271l53 224q4 18 6.5 31t3.5 22.5t1 15t-2 9t-4.5 4.5t-6.5 1q-31 0 -100.5 -63.5t-126.5 -145.5q-16 -53 -40 -163q-48 -11 -74 -21l-7 8l82 341q9 36 -4 36
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<g transform="matrix(.012,-0,0,-.012,12.05,19.638)"><path d="M559 163q-23 -66 -68 -163h-474l6 26q62 4 79.5 19.5t28.5 75.5l78 409q7 35 8.5 49t-8 25t-24 13t-51.5 5l5 28h266l-6 -28q-65 -5 -79.5 -18t-25.5 -74l-76 -406q-10 -57 14 -75q12 -13 96 -13q93 0 126 29q41 40 76 109z" id="x1D43F"></path></g>
</svg></span></td><td align="center">−0.0522466</td><td align="center"> </td><td align="center"> </td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mathematical Problems in Engineering

tab2

Table 2

Table 2: Modeling and Analysis of an Air-Breathing Flexible Hypersonic Vehicle 