LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTA==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1">Mathematical Model</Text-field>
<Text-field style="Heading 2" layout="Heading 2">Question 1</Text-field>We asked to calculate the aileron lift and rolling moment efficiency. The aileron is at the rear 20% of the chord, at 0.8-0.95 of the wing span.By adding an aileron, the change will be in the AFC matrix: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 , where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EuYENfX0wmZGVsdGE7YEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw== describe the aileron.From here, the whole process is the same as it was in home assignment 1.JSFHJSFH
<Text-field style="Heading 2" layout="Heading 2">Question 2</Text-field>Trimmed flight is when the sum of the forces at the vertical direction is zero, and the moment around the center of gravity is zero.In this question, the aircraft is trimmed by the Elevator . 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write the equation of motion by using Lagrange equations: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 LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXJvd0dGJDYkLUkjbWlHRiQ2JVEpJmRlbHRhO3hGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjZRJ25vcm1hbEYnRjg= mean's each of the DOF we will use.Assumptions:The aircraft center of gravity coincides with the elastic axis. Linear torque 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There are no ailerons.3 DOF model 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.At straight flight there is no kinetic energy LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjS0VGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSI9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYkUSIwRidGOUY5.The reference plane goes through the center of gravity, hence 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 .The virtual work is done by LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2I1EnYExfX1RgRictSSNtb0dGJDYtUSJ+RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkctRjA2LVEiLEYnRjNGNi9GOlEldHJ1ZUYnRjtGPUY/RkFGQ0ZFL0ZJUSwwLjMzMzMzMzNlbUYnRi8tRiw2I1EnYExfX3dgRidGL0ZKRi8tRiw2JVEiV0YnLyUnaXRhbGljR0ZOL0Y0USdpdGFsaWNGJ0Yz, as a result of shifting in each of the DOF. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY8LUkjbWlHRiQ2JVEoJiM5NDg7d0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYjUSdgTF9fVGBGJy1GNjYtUScmc2RvdDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GVi1JKG1mZW5jZWRHRiQ2JC1GIzYpLUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkhGVUZXLUYsNiNRLWAmZGVsdGE7X19oYEYnLUY2Ni1RKCZtaW51cztGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GYW8tRiw2I1EzYCZkZWx0YTtfXyZhbHBoYTtgRidGUi1GLDYjUSdgbF9fVGBGJ0Y5RjlGXW8tRiw2JVEiV0YnRi9GMkZSRmpuLUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkhGYG9GYm8tSSNtbkdGJDYkUSIyRidGOUZSLUkobXN1YnN1cEdGJDYnLUY2Ni1RJiZpbnQ7RidGOUY7Rj4vRkFGMUZCL0ZFRjFGRkZIRlVGVy1GIzYnLUZgcDYkUSIwRidGOUYvLyUrZm9yZWdyb3VuZEdRLFsxMjgsMCwxMjhdRicvJSxwbGFjZWhvbGRlckdGMUYyLUYjNiUtRiw2JVEibEYnRi9GMkYvRjIvJTFzdXBlcnNjcmlwdHNoaWZ0R0ZfcS8lL3N1YnNjcmlwdHNoaWZ0R0ZfcS1GLDYlUSJxRidGL0YyRlItRiw2JVEiY0YnRi9GMkZSLUYsNiNRLmBDX19MJmFscGhhO2BGJ0ZSLUZZNiQtRiM2Jy1GLDYlUScmIzk0NTtGJy9GMEY9RjlGXHAtRiw2JVEnJiM5NTI7RidGXnNGOS1GWTYkLUYjNiQtRiw2JVEieUYnRi9GMkY5RjlGOUY5RlItRlk2JC1GIzYsRmpuRlxwRmNvRlItRiw2I1EnYGxfX3dgRidGXHAtRiw2JVEiZUYnRi9GMkZSLUYsNiNRNmAmZGVsdGE7X18mdGhldGE7X19UYEYnRjlGOUZnbi1GNjYtUTAmRGlmZmVyZW50aWFsRDtGJ0Y5RjtGPkZARkJGREZGRkhGVUZXRmZzRjk=.Let open the expression for virtual work: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And after solving the integrals: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 the algebraic subtitling LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RJyZzZG90O0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZMLUYsNiVRImxGJ0YvRjItRjY2LVEiPUYnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yNzc3Nzc4ZW1GJy9GTkZWLUYsNiVRIlNGJ0YvRjJGOQ== we get: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For each DOF we solve the Lagrange equation: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And by placing the expression of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYExfX1RgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn in the equation of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EzYCZkZWx0YTtfXyZhbHBoYTtgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn we got 2 equation with two variables, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjY2LVEifkYnRjJGOS9GPEYxRj5GQEZCRkRGRkZIL0ZMRkotRiw2I1EtYCZ0aGV0YTtfX1RgRidGMg== .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And from this system of equations we get the expressions for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EtYCZ0aGV0YTtfX1RgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn :LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JJm1mcmFjR0YkNigtRiM2KC1GLDYlUSJXRicvRjBRJXRydWVGJy9GM1EnaXRhbGljRictRjY2LVEnJnNkb3Q7RidGMkY5RjtGPUY/RkFGQ0ZFL0ZIUSYwLjBlbUYnL0ZLRmZuLUZNNigtRiw2I1EnYGxfX1RgRictRiM2JkZqbi1GNjYtUSIrRidGMkY5RjtGPUY/RkFGQ0ZFL0ZIUSwwLjIyMjIyMjJlbUYnL0ZLRmNvLUYsNiNRJ2BsX193YEYnRjIvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRl1wLyUpYmV2ZWxsZWRHRjFGWC1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiNRIUYnLUYjNi8tRk02KC1JI21uR0YkNiRRIjJGJ0YyLUYjNiQtRl9xNiRRIjNGJ0YyRjJGaG9GW3BGXnBGYHBGWC1GNjYtUSJ+RidGMkY5RjtGPUY/RkFGQ0ZFRmVuRmduLUYsNiVRInFGJ0ZURlZGWC1GLDYlUSJTRidGVEZWRlgtRiw2I1EuYENfX0wmYWxwaGE7YEYnRlgtRiw2JVEiZUYnRlRGVi1GNjYtUSgmbWludXM7RidGMkY5RjtGPUY/RkFGQ0ZFRmJvRmRvLUZNNigtRiM2JkZecUZYLUYsNiVRI0dKRidGVEZWRjItRiM2JC1GLDYlUSJsRidGVEZWRjJGaG9GW3BGXnBGYHBGMkZncEYyRjJGMi1GIzYpRmdwLUYjNihGanFGWEZdckZYRmByRjJGZ3BGWC1GY3A2JC1GIzYwLUZNNigtRiM2JS1GX3E2JEZqb0YyRlRGVkZicUZob0ZbcEZecEZgcEZYRmdxRmpxRlhGXXJGWEZgckZYRmNyRmZyLUZNNigtRiM2Jy1GX3E2JFEiNEYnRjJGWEZncUZdc0YyRmBzRmhvRltwRl5wRmBwRlRGVkYyRlRGVkZob0ZbcEZecEZgcEZncC1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR0Zmbi8lJmRlcHRoR0ZfdS8lKmxpbmVicmVha0dRKG5ld2xpbmVGJ0ZncUZqdEZncS1GLDYjUS1gJnRoZXRhO19fVGBGJ0Y1LUZNNigtRiM2Ji1GNjYtUSomdW1pbnVzMDtGJ0YyRjlGO0Y9Rj9GQUZDRkVGYm9GZG8tRiM2JkZRRlhGaG5GMkZncEYyLUYjNi4tRk02KC1GIzYkRmF0RjJGYnFGaG9GW3BGXnBGYHBGWEZncUZqcUZYRl1yRlhGYHJGZnItRk02KEZldC1GIzYmRmJzRlhGY3JGMkZob0ZbcEZecEZgcEZURlZGaG9GW3BGXnBGYHBGZ3BGMg==Divergence occur when LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EtYCZ0aGV0YTtfX1RgRictSSNtb0dGJDYtUS0mUmlnaHRBcnJvdztGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdRJXRydWVGJy8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSC1GMDYtUSgmaW5maW47RidGM0Y2RjkvRjxGOEY+RkBGQkZEL0ZHUSYwLjBlbUYnL0ZKRlBGMw==, soLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZELUkmbWZyYWNHRiQ2KC1GIzYkLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Y0LUYjNiQtRjE2JFEiM0YnRjRGNC8lLmxpbmV0aGlja25lc3NHRjMvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGQC8lKWJldmVsbGVkR1EmZmFsc2VGJy1JI21vR0YkNi1RJyZzZG90O0YnRjQvJSZmZW5jZUdGRS8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZaLUZHNi1RIn5GJ0Y0RkpGTEZORlBGUkZURlZGWEZlbi1JI21pR0YkNiVRInFGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNVEnaXRhbGljRidGRi1GW282JVEiU0YnRl5vRmFvRkYtRltvNiNRLmBDX19MJmFscGhhO2BGJy1GRzYtUSgmbWludXM7RidGNEZKRkxGTkZQRlJGVEZWL0ZZUSwwLjIyMjIyMjJlbUYnL0ZmbkZdcC1GLDYoLUYjNictRjE2JFEiNEYnRjRGRkZnbi1GW282JVEjR0pGJ0Zeb0Zhb0Y0LUYjNiYtRltvNiVRImxGJ0Zeb0Zhb0ZGLUZbbzYlUSJlRidGXm9GYW9GNEY8Rj5GQUZDLUZHNi1RLSZSaWdodEFycm93O0YnRjRGSkZML0ZPRmBvRlBGUkZURlYvRllRLDAuMjc3Nzc3OGVtRicvRmZuRmZxLUYxNiRRIjBGJ0Y0LUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHRlovJSZkZXB0aEdGYHIvJSpsaW5lYnJlYWtHUShuZXdsaW5lRidGZ25GW3ItRkc2L0Zpbi8lJWJvbGRHRmBvL0Y1USVib2xkRicvJStmb250d2VpZ2h0R0Zdc0ZKRkxGTkZQRlJGVEZWRlhGZW4tRkc2L1EzJkRvdWJsZVJpZ2h0QXJyb3c7RidGanJGXHNGXnNGSkZMRmRxRlBGUkZURlZGZXFGZ3FGaHJGaHItRltvNiNRJ2BxX19EYEYnLUZHNi1RIj1GJ0Y0RkpGTEZORlBGUkZURlZGZXFGZ3EtRiw2KC1GIzYmLUYxNiRRIzEyRidGNEZGRmZwRjQtRiM2K0ZbcUZGRl5xRkZGY29GRkZmb0Zeb0Zhb0Y8Rj5GQUZDLUZbbzYjUSFGJ0ZbckZockZgc0ZockZoci1GW282I1EnYHZfX0RgRidGZnMtSSZtc3FydEdGJDYjLUYjNictRiw2KC1GIzYpLUYxNiRRIjJGJ0Y0RkZGY3NGXm8vJStmb3JlZ3JvdW5kR1EsWzEyOCwwLDEyOF1GJy8lLHBsYWNlaG9sZGVyR0Zgb0Zhby1GIzYlLUZbbzYlUScmIzk2MTtGJy9GX29GRUY0Rl5vRmFvRjxGPkZBRkNGXm9GZHVGZ3VGYW9GZnMtRml0NiMtRiM2Jy1GLDYoLUYjNiktRjE2JFEjMjRGJ0Y0RkZGZnBGXm9GZHVGZ3VGYW8tRiM2LUZbcUZGRl5xRkZGY29GRkZbdkZGRmZvRl5vRmFvRjxGPkZBRkNGXm9GZHVGZ3VGYW9GNA==Calculating LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NDg7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy at trim: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Using the lift definitions: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and so: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
<Text-field style="Heading 1" layout="Heading 1">Question 1</Text-field>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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1">Wing Data</Text-field>The given data of the wing:
The wing area, S, is defined by the integral 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 for a square wing, were the chord is constant, the expression is reduced to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiU0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRImNGJ0YvRjItRjY2LVEnJnNkb3Q7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORlYtRiw2JVEibEYnRi9GMi1GNjYtUSI6RidGOUY7Rj5GQEZCRkRGRkZIRkpGTQ==For the given straight wing we add aileron at 0.8-0.95 wingspan, at the rear 20% of the chord. The aileron connected through rigid connector.
An element stiffness matrix:print(); # input 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 = print(); # input placeholderJSFHAt first, we set the number of elements (equal elements):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 = print(); # input placeholderThe length and the surface area of each element is:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EnYGxfX2VgRictSSNtb0dGJDYtUSomY29sb25lcTtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRy1JJm1mcmFjR0YkNigtRiw2JVEibEYnLyUnaXRhbGljR1EldHJ1ZUYnL0Y0USdpdGFsaWNGJy1GIzYjLUYsNiVRIk5GJ0ZQRlMvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmluLyUpYmV2ZWxsZWRHRjgtRiw2I1EhRic= = print(); # input 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 = print(); # input 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 = print(); # input placeholderJSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 2" layout="Heading 2">Art 1</Text-field>Find the aileron lift efficiency and rolling torque efficiency at the root of the wing. Check it in the range of velocity from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYjUSdgdl9fRGBGJ0Y5 .
<Text-field style="Heading 3" layout="Heading 3">Solution</Text-field>JSFH
<Text-field style="Heading 4" layout="Heading 4"><Font bold="true">Stiffness Matrix</Font></Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Let, the Total Stiffness Matrix, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EiVEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2Iy1GLzYlUSNTTUYnL0Y2RjQvRjlRJ2l0YWxpY0YnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRic= , a N x N matrix over the Real Domain be assembled by the following process:#Stiffness Matrix Procedure
#This procedure recived the number of elements and an element...
#...stiffness matrix and gives us the total stiffness matrix
StiffMat := proc (N::anything, K__e::Matrix)
local j, n, k, Rng, T__SM;
T__SM := Matrix(3*N, 3*N, 0);
for j to 3 do
for n to 3 do
T__SM[j, n] := T__SM[j, n]+K__e[j+3, n+3]:
end do;
end do;
for k from 0 by 3 to 3*N-6 do
Rng := 1+k .. 6+k;
T__SM[Rng, Rng] := T__SM[Rng, Rng]+K__e;
end do;
return T__SM;
end proc:
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 4" layout="Heading 4"><Font bold="true">AFC Matrix</Font></Text-field>Now we need to build the AFC matrix:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Note, the aileron is between 0.8-0.95 wing span, at the rear 20% of the chord.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFH#AFC matrix assembly
AFCtotal := Matrix(2*N, 2*N):
for k from 0 by 2 to 2*N-2 do
rng := 1+k .. 2+k;
if `or`(((2+k)*(1/2))*l__e <= .8*l, (1/2)*k*l__e >= .95*l) then
AFCtotal[rng, rng] := eval(AFC, `C__L δ` = 0);
else
AFCtotal[rng, rng] := eval(AFC, `C__L δ` = 2*Pi);
end if;
end do:JSFHJSFH%;LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 4" layout="Heading 4"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font bold="true"> and </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2I1EpYFRfX0Esc2BGJy1JI21vR0YkNi9RIn5GJy8lJWJvbGRHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjgvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTEYvRjMvJStleGVjdXRhYmxlR0Y1LyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJ0Y2Rjk=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2I1EpYFRfX0Esc2BGJy1JI21vR0YkNi9RIn5GJy8lJWJvbGRHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjgvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTEYvRjMvJStleGVjdXRhYmxlR0Y1LyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJ0Y2Rjk=</Equation><Font bold="true">Matrix</Font></Text-field>We build a procedure that calculate the transformation matrix as a function of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5MjM7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy.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print(); # input placeholderJSFHJSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=#Transformation Matrix assembly
TransMatrix := proc (T_As::Matrix,T_as::Matrix )
local i, j, n;
local TotalT__as := Matrix(2*N, 3*N);
local TotalT__As := Matrix(2*N, 3*N);
for i to N do
if i = 1 then
for j to 2 do
for n to 3 do
TotalT__as[2*i-2+j, 3*i-3+n] := T_as[j, n+3]:
TotalT__As[2*i-2+j, 3*i-3+n] := T_As[j, n+3]:
end do:
end do:
else
for j to 2 do
for n to 6 do
TotalT__as[2*i-2+j, 3*i-6+n] := T_as[j, n]:
TotalT__As[2*i-2+j, 3*i-6+n] := T_As[j, n]:
end do:
end do:
end if:
end do:
return TotalT__as, TotalT__As;
end proc:JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=After having all the relevant matrix we can build the SIC matrix:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEqUHVsbEFuZ2xlRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYkUSIwRidGOS1GNjYtUSI6RidGOUY7Rj5GQEZCRkRGRkZIRkpGTQ==JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY3LUkjbWlHRiQ2I1EoYFRfX1NNYEYnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctRiw2JVEpU3RpZmZNYXRGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNFEnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUSJORidGTUZQLUYwNi1RIixGJ0YzRjYvRjpGT0Y7Rj1GP0ZBRkMvRkZRJjAuMGVtRicvRklRLDAuMzMzMzMzM2VtRictRiw2I1EnYEtfX2VgRidGMy1GMDYtUSI6RidGM0Y2RjlGO0Y9Rj9GQUZDRkVGSC1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR0Zpbi8lJmRlcHRoR0Znby8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GLDYlUSZldmFsZkYnL0ZORjhGMy1GUzYkLUYjNiMtRiw2JVEpQUZDdG90YWxGJ0ZicEYzRjNGX29GYm8tRiw2I1EvYFRfXyZhbHBoYTssc2BGJ0YvLUYsNiVGYXBGTUZQLUZTNiQtRiM2JC1GLDYlUSxUcmFuc01hdHJpeEYnRk1GUC1JJW1zdWJHRiQ2JS1GUzYkLUYjNictRiw2JVElZXZhbEYnRk1GUC1GUzYkLUYjNictRiw2I1EtYFRfX0EscyxvbmVgRidGWi1GLDYlUSkmTGFtYmRhO0YnRmJwRjMtRjA2LVEiPUYnRjNGNkY5RjtGPUY/RkFGQ0ZFRkgtRiw2JVEqUHVsbEFuZ2xlRidGTUZQRjNGWkZdci1GUzYkLUYjNictRiw2I1EzYFRfXyZhbHBoYTsscyxvbmVgRidGWkZnckZqckZdc0YzRjMtRiM2Iy1JI21uR0YkNiRRIjFGJ0YzLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGMy1GMDYtUSI7RidGM0Y2RmduRjtGPUY/RkFGQ0ZobkZIRmJvLUYsNiNRKWBUX19BLHNgRidGL0ZdcS1GUzYkLUYjNiVGY3EtRmdxNiUtRlM2JC1GIzYlLUYsNiNRIUYnLUYjNidGXXItRlM2JC1GIzYnRmRyRlotRiw2JVEpJkxhbWJkYTtGJ0ZicEYzRmpyRl1zRjNGWkZdci1GUzYkLUYjNidGZHNGWkZpdUZqckZdc0YzRmB1RjMtRiM2Iy1GanM2JFEiMkYnRjNGXXQtRjA2LVEifkYnRjNGNkY5RjtGPUY/RkFGQ0Zobi9GSUZpbkYzRl9vprint(); # input 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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=And the eigenvalues vector of the multiplication of the AFC matrix by the SIC matrix are: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print(); # input placeholderUsing the largest eigenvalue to find the Divergence pressure and velocity: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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 = print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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 = print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=We want to examine the influence of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NDg7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy on the wing, therefore we will set LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy to be zero.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, we build the velocity vector which changes from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EnYHZfXzBgRictSSNtb0dGJDYtUSI9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctSSNtbkdGJDYkUSIwRidGM0Yz to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EnYHZfX25gRictSSNtb0dGJDYtUSI9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctRiw2I1EnYHZfX2RgRictRjA2LVEoJm1pbnVzO0YnRjNGNkY5RjtGPUY/RkFGQy9GRlEsMC4yMjIyMjIyZW1GJy9GSUZRLUYsNiVRKCYjMTAxMztGJy8lJ2l0YWxpY0dGOEYzRjM=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print(); # input placeholderWe use the rigid body AOA, AFC, SIC to calculate the Forces and moments vector.
<Text-field style="Heading 4" layout="Heading 4"><Font bold="true">The calculating</Font></Text-field>JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFH#Building alpha rigid
`α__R` := `<,>`(seq(0, i = 1 .. 2*N))^%T:
for i from 2*N-7 to 2*N-1 do
if type(i, even) = true then
`α__R`[i] := delta:
else
`α__R`[i] := 0:
end if:
end do:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=#Efficiencies Proc
Efficiencies := proc (N, rho, a_R, e, l_e, v::list, AFC::Matrix, SIC::Matrix)
local F_Rigid, F, M_Rigid, M, Imatrix, ForcesRigid, MForcesRigid, Forces, MForces, h_c1, h_cm, i, k;
F_Rigid := Vector[column](0, 2*N);
F := Vector[column](0, 2*N);
M_Rigid := Vector[column](0, 2*N);
M := Vector[column](0, 2*N);
Imatrix := IdentityMatrix(2*N);
for i from 1 to 2*N do
F_Rigid := (1/2)*rho*v[i]^2*(AFC.Transpose(a_R));
F := MatrixInverse(evalf(Imatrix-(1/2)*rho*v[i]^2*AFC.SIC)).F_Rigid;
M_Rigid := F_Rigid*(i*l_e-(1/2)*l_e);
M := F*(i*l_e-(1/2)*l_e);
ForcesRigid := 0;
Forces := 0;
MForcesRigid := 0;
MForces := 0;
for k to 2*N do
ForcesRigid := ForcesRigid+F_Rigid[k];
Forces := Forces+F[k];
MForcesRigid := MForcesRigid+M_Rigid[k];
MForces := MForces+M[k];
end do;
h_c1[i] := Forces/ForcesRigid;
h_cm[i] := MForces/MForcesRigid;
end do;
h_c1 := `<,>`(seq(h_c1[i], i = 1 .. 2*N));
h_c1[1] := 1;
h_cm := `<,>`(seq(h_cm[i], i = 1 .. 2*N));
h_cm[1] := 1;
return h_c1, h_cm;
end proc:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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%;JSFHprint(); # input 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%;LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
From the figures above you can see that the efficiency is positive until 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 and from there, the efficiency is negative. The reason for that is because at 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 there is aileron reversal point. Near to the divergence velocity, the efficiency decrease is exponential.Adding ailerons will reduce the wing lift because they generate negative torsion on the wing. JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 2" layout="Heading 2">Art 2</Text-field>Repeat article 1 for pulled backward and pulled forward wing (the pull angle is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbW5HRiQ2JFEjMjBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JS1GLzYkUSIwRidGMi8lJ2l0YWxpY0dRJXRydWVGJy9GM1EnaXRhbGljRicvJTFzdXBlcnNjcmlwdHNoaWZ0R0Y5RjI=).
<Text-field style="Heading 3" layout="Heading 3">Solution</Text-field>JSFH
<Text-field style="Heading 4" bold="true" layout="Heading 4"><Font bold="true">Wing pulled forward </Font><Equation executable="false" style="Heading 4" input-equation="" display="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">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</Equation></Text-field>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print(); # input 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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=After having all the relevant matrix we can build the SIC matrix:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=And the eigenvalues vector of the multiplication of the AFC matrix by the SIC matrix are: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print(); # input placeholderUsing the largest eigenvalue to find the Divergence pressure and velocity: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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 = print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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 = print(); # input placeholderJSFHFor straight wing the AOA is constant along the wing.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, we build the velocity vector which changes from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EnYHZfXzBgRictSSNtb0dGJDYtUSI9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctSSNtbkdGJDYkUSIwRidGM0Yz to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EnYHZfX25gRictSSNtb0dGJDYtUSI9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctRiw2I1EnYHZfX2RgRictRjA2LVEoJm1pbnVzO0YnRjNGNkY5RjtGPUY/RkFGQy9GRlEsMC4yMjIyMjIyZW1GJy9GSUZRLUYsNiVRKCYjMTAxMztGJy8lJ2l0YWxpY0dGOEYzRjM=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%;We use the rigid body AOA, AFC, SIC to calculate the Forces and moments vector.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
JSFH
<Text-field style="Heading 4" bold="true" layout="Heading 4"><Font bold="true">Wing pulled backward </Font><Equation executable="false" style="Heading 4" input-equation="" display="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">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</Equation></Text-field>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(); # input 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(); # input placeholderJSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=After having all the relevant matrix we can build the SIC matrix:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=And the eigenvalues vector of the multiplication of the AFC matrix by the SIC matrix are:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEmZXZhbGNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSNSZUYnL0YwUSZmYWxzZUYnL0YzUSdub3JtYWxGJy1GNjYkLUYjNiUtRiw2JVEsRWlnZW52YWx1ZXNGJ0YvRjItRjY2JC1GIzYlLUYsNiNRIUYnLUYjNiQtRiw2JVEpc2ltcGxpZnlGJ0YvRjItRjY2JC1GIzYlLUYsNiVRKUFGQ3RvdGFsRidGL0YyLUkjbW9HRiQ2LVEiLkYnRj8vJSZmZW5jZUdGPi8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0Zpby1GLDYlUSRTSUNGJ0YvRjJGP0ZMRj9GTEY/Rj9GTC1GZm42LVEifkYnRj9GaW5GW29GXW9GX29GYW9GY29GZW9GZ29Gam8=print(); # input placeholderUsing the largest eigenvalue to find the Divergence pressure and velocity: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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 = print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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 = print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=For straight wing the AOA is constant along the wing.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEoJmFscGhhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSomY29sb25lcTtGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1GLDYlUSZldmFsZkYnL0YwUSV0cnVlRicvRjNRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtSSZtZnJhY0dGJDYoLUYjNiMtSSNtbkdGJDYkUSMxMEYnRjItRiM2Iy1GaG42JFEkMTgwRidGMi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGZW8vJSliZXZlbGxlZEdGMS1GNjYtUScmc2RvdDtGJ0YyRjlGO0Y9Rj9GQUZDRkUvRkhRJjAuMGVtRicvRktGXnAtRiw2JVElJnBpO0YnRi9GMkYyLUY2Ni1RIjpGJ0YyRjlGO0Y9Rj9GQUZDRkVGR0ZKLUYsNiNRIUYnNow, we build the velocity vector which changes from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EnYHZfXzBgRictSSNtb0dGJDYtUSI9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctSSNtbkdGJDYkUSIwRidGM0Yz to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EnYHZfX25gRictSSNtb0dGJDYtUSI9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctRiw2I1EnYHZfX2RgRictRjA2LVEoJm1pbnVzO0YnRjNGNkY5RjtGPUY/RkFGQy9GRlEsMC4yMjIyMjIyZW1GJy9GSUZRLUYsNiVRKCYjMTAxMztGJy8lJ2l0YWxpY0dGOEYzRjM=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkobWZlbmNlZEdGJDYmLUYjNiQtRiw2JVEkc2VxRidGL0YyLUZQNiQtRiM2LS1GLDYlUSJpRidGL0YyLUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkgvRktRJjAuMGVtRicvRk5RLDAuMzMzMzMzM2VtRidGZW4tRjY2LVEiPUYnRjlGO0Y+RkBGQkZERkZGSEZKRk0tSSNtbkdGJDYkUSIwRidGOS1GNjYtUSMuLkYnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZdby1GLDYjUSdgdl9fZGBGJy1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIRmpvL0ZORltwLUZkbzYkUSQwLjFGJ0Y5RmhuLUkmbWZyYWNHRiQ2KEZdcC1GIzYlLUZkbzYkUSIyRidGOS1GNjYtUScmc2RvdDtGJ0Y5RjtGPkZARkJGREZGRkhGXG9GXHAtRiw2JVEiTkYnRi9GMi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGanEvJSliZXZlbGxlZEdGPUY5RjkvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRictRjY2LVEiOkYnRjlGO0Y+RkBGQkZERkZGSEZKRk0=print(); # input placeholderUsing the rigid body AOA, AFC, SIC to calculate the Forces and moments vector.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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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%;LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
As we can see from the figures above, the efficiency increase when the velocity increase. The reason for this is because the pulled forward lift contribution is greater than the aileron influence of the wing. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1">Question 2</Text-field>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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFH
<Text-field style="Heading 1" layout="Heading 1">Wing Data</Text-field>The aircraft weight is QyQ+SSJXRzYiIiNdISIiNewton. The aircraft is trimmed by Elevator. The distance from the center of gravity to where the force works on the Elevator is QyQ+SSVsX190RzYiJCIiJiEiIkYo meter. The distance from the wing aerodynamic center to the center of gravity is QyQ+SSVsX193RzYiJCIiJiEiIyEiIg== meter.The given data of the straight wing (without the aileron):
PkkiU0c2IiomSSJjR0YkIiIiSSJsR0YkRic= = print(); # input placeholderPkklU19fdEc2IiomSSJTR0YkIiIiLUkiL0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjJCIjOiEiIkYn = print(); # input placeholderPkkiZUc2Ii1JJGFic0clKnByb3RlY3RlZEc2IywmSSZ4X19lYUdGJCIiIkkmeF9fYWNHRiQhIiI= = print(); # input placeholderJSFHJSFH
<Text-field style="Heading 2" layout="Heading 2">Art 1</Text-field>Find the Divergence velocity of the trimmed aircraft.
<Text-field style="Heading 3" layout="Heading 3">Solution</Text-field>We need to find the dynamic pressure in order to find the divergence velocity:JSFHPkklcV9fREc2Ii1JJmV2YWxmRyUqcHJvdGVjdGVkRzYjLCQqLEkjR0pHRiQiIiJJImxHRiQhIiJJImVHRiRGLkkiU0dGJEYuSS1DX19MfiZhbHBoYTtHRiRGLiIjNw==print(); # input placeholderPkkqdl9fRCx0cmltRzYiLUkmZXZhbGZHJSpwcm90ZWN0ZWRHNiMtSSVzcXJ0R0YkNiMsJComSSVxX19ER0YkIiIiSSRyaG9HRiQhIiIiIiM=print(); # input placeholderThe velocity is in [m/sec]JSFH
<Text-field style="Heading 2" layout="Heading 2">Art 2</Text-field>Find the trim AOA, the Elevator trim angle and the tip of the wing torque angle at the velocity range from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYjUStgdl9fc3RhbGxgRidGOQ== to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRJDAuOEYnRjktRjY2LVEifkYnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZXLUYsNiNRLGB2X19ELHRyaW1gRidGOQ== .JSFH
<Text-field style="Heading 3" layout="Heading 3">Solution</Text-field>The Stall velocity:Pkkpdl9fc3RhbGxHNiItSSZldmFsZkclKnByb3RlY3RlZEc2Iy1JJXNxcnRHNiRGJ0koX3N5c2xpYkdGJDYjLCQqKkkiV0dGJCIiIkkkcmhvR0YkISIiSSJTR0YkRjNJKUNfX0x+bWF4R0YkRjMiIiM= = print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFHWe build a sequence of the dynamic pressure that changes from the stall velocity to 80% from the divergence velocity:QyQ+SSJxRzYiNyMtSSRzZXFHJSpwcm90ZWN0ZWRHNiQsJComSSRyaG9HRiUiIiJJInZHRiUiIiMjRi5GMC9GLztJKXZfX3N0YWxsR0YlLCRJKnZfX0QsdHJpbUdGJSQiIikhIiJGOQ==print(); # input placeholderNow, we build a loop which find AOA, Torsion angle and delta for different 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%;Qyw+SSdhbHBoYTFHNiItSShjb252ZXJ0RyUqcHJvdGVjdGVkRzYkSSZhbHBoYUdGJUklbGlzdEdGKCEiIj5JJ3RoZXRhMUdGJS1GJzYkSSZ0aGV0YUdGJUYrRiw+SSdkZWx0YTFHRiUtRic2JEkmZGVsdGFHRiVGK0YsPkkicUdGJS1GJzYkKiZGOCIiIkklcV9fREdGJUYsRitGLD5JI1YxR0YlNyMtSSRzZXFHRig2JEkidkdGJS9GRDtJKXZfX3N0YWxsR0YlLCRJKnZfX0QsdHJpbUdGJSQiIilGLEYs%;LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=The plotting:print(); # input 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%;From the figures above we can see that when LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEicUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RLSZSaWdodEFycm93O0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiNRK2BxX19zdGFsbGBGJy1GNjYtUSJ+RidGOUY7Rj4vRkFGPUZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORldGOQ==than LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RLSZSaWdodEFycm93O0YnRjIvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R1EldHJ1ZUYnLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZKLUY2Ni1RKCZpbmZpbjtGJ0YyRjlGOy9GPkYxRkBGQkZERkYvRklRJjAuMGVtRicvRkxGUkYy. When the aircraft reduces his speed (LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEicUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTEY5 decrease), In order to stay trimmed, there is need for larger LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIn5GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSUYy. Even if LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIn5GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSUYyis small and negative, we still get's Lift, this is because the wing torque (the third figure).In the second figure (LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NDg7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy ) we see an reversed tendency from the first figure (LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy). In order to get trimmed aircraft we need to inflect the elevator in reversed angle of the AOA. As the dynamic pressure increase, the torsion angle increase, and at divergence, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RLSZSaWdodEFycm93O0YnRjIvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R1EldHJ1ZUYnLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZKLUY2Ni1RKCZpbmZpbjtGJ0YyRjlGOy9GPkYxRkBGQkZERkYvRklRJjAuMGVtRicvRkxGUkYy.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFH