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situation described in purple is where we increase the AOA at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EzYCZkZWx0YTtfXyZhbHBoYTtgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn . This situation is unstable because increasing the AOA will increase the lift that increase the AOA and so on...LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Stable 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situation described in purple is where we increase the AOA at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EzYCZkZWx0YTtfXyZhbHBoYTtgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn . This situation is stable because increasing the AOA will causes the damping. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYG1fXzBgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn - The contribution of body torque.
JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYE5fXzBgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn - The neutral point. The aerodynamic center. The point where the Net lift forces works.The moment equations: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Where: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Therefore, by devising the equation by 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 we will get the moment equations (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) :JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2I1EnYGNfX21gRictSSNtb0dGJDYtUSI9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctRiw2I1EqYGNfX21fXzBgRictRjA2LVEoJm1pbnVzO0YnRjNGNkY5RjtGPUY/RkFGQy9GRlEsMC4yMjIyMjIyZW1GJy9GSUZRLUYsNiVRJyYjOTE2O0YnLyUnaXRhbGljR0Y4RjMtSSZtb3ZlckdGJDYlLUYsNiVRInhGJy9GV1EldHJ1ZUYnL0Y0USdpdGFsaWNGJy1GIzYlLUYsNiVRIl9GJ0ZobkZqbkZobkZqbi9GREZpbi1GMDYtUScmc2RvdDtGJ0YzRjZGOUY7Rj1GP0ZBRkMvRkZRJjAuMGVtRicvRklGZm8tRiw2I1EnYGNfX0xgRidGMw==For static stability we want 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. 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
And therefore, for stability we will ask LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEnJiM5MTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JJm1vdmVyR0YkNiUtRiw2JVEieEYnL0YwUSV0cnVlRicvRjNRJ2l0YWxpY0YnLUYjNiUtRiw2JVEiX0YnRjtGPUY7Rj0vJSdhY2NlbnRHRjwtSSNtb0dGJDYtUSI+RidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS9GRUYxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGWS1JI21uR0YkNiRRIjBGJ0YyRjI=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1">Straight and horizontal flight</Text-field>For straight and horizontal flight as shown in the figure below, the forces and moment equations are:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
Qyg+SSwmU2lnbWE7Rl9feEc2Ii9JIlRHRiVJIkRHRiUhIiI+SSwmU2lnbWE7Rl9feUdGJS9JIkxHRiVJIldHRiVGKT5JLCZTaWdtYTtNX195R0YlLywmSShjX19tX18wR0YlIiIiKihJJkRlbHRhR0YlRjQtSSpjb25qdWdhdGVHJSpwcm90ZWN0ZWRHNiNJInhHRiVGNEklQ19fTEdGJUY0RikiIiFGKQ==print(); # input placeholderThe lift equation is:QyQ+SSJMRzYiLCQqKkkkcmhvR0YlIiIiSSJTR0YlRilJJUNfX0xHRiVGKUkidkdGJSIiIyNGKUYtISIiAnd therefore, the velocity and the lift coefficients are:QyYtSShpc29sYXRlRzYiNiRJLCZTaWdtYTtGX195R0YlKiRJInZHRiUiIiMiIiItRiQ2JEksJlNpZ21hO01fX3lHRiVJJUNfX0xHRiVGKw==print(); # input 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we can see, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRj4= related to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnJiM5MTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYkLUkmbW92ZXJHRiQ2JS1GLDYlUSJ4RicvRjBRJXRydWVGJy9GM1EnaXRhbGljRictRiM2JS1GLDYlUSJfRidGPUY/Rj1GPy8lJ2FjY2VudEdGPkYyLUYsNiNRIUYnRjI=, therefore,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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1">Forces equation</Text-field>The total lift forces are:QyQ+SSlMX190b3RhbEc2IiwoSShMX19ib2R5R0YlIiIiSShMX190YWlsR0YlRihJKExfX3dpbmdHRiVGKCEiIg==The lift that every aircraft part generate is:Qyg+SShMX19ib2R5RzYiLCQqKkkpJnJobztfX3dHRiUiIiJJJVNfX3dHRiVGKUkldl9fd0dGJSIiI0knQ19fTCxCR0YlRikjRilGLCEiIj5JKExfX3RhaWxHRiUsJCoqSSkmcmhvO19fdEdGJUYpSSVTX190R0YlRilJJXZfX3RHRiVGLEknQ19fTCxUR0YlRilGLkYvPkkoTF9fd2luZ0dGJSwkKipGKEYpRipGKUYrRixJJ0NfX0wsV0dGJUYpRi5GLw==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=The Lift coefficient of each part is:print(); # input placeholder
<Text-field style="Heading 2" bold="false" underline="true" layout="Heading 2"><Font bold="false" underline="false">Body lift coefficient</Font></Text-field>The body contribution include the positioning angle of the tail (LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2I1EnYGlfX3RgRidGLw== ) but for now the expression is:QyQ+SSdDX19MLEJHNiJJJkNfX0wwR0YlISIiLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 2" bold="false" layout="Heading 2"><Font bold="false">Tail lift coefficient</Font></Text-field>
The AOA that the tail having 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For small AOA, we get that QyQvSSsmYWxwaGE7X190RzYiKiZJJmFscGhhR0YlIiIiLCZGKEYoLi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiRJKiZlcHNpbG9uO0dGJUYnISIiRihGMA==print(); # input placeholderFor convenience, instead of writing 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 we will write LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1E1YCZlcHNpbG9uO19fJmFscGhhO2BGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=. Hence, QyQ+SSsmYWxwaGE7X190RzYiKiZJJmFscGhhR0YlIiIiLCZGKEYoSTMmZXBzaWxvbjtfXyZhbHBoYTtHRiUhIiJGKEYrLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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, the tail lift contribution is:PkknQ19fTCxURzYiLCYqJkkrJmFscGhhO19fdEdGJCIiIkkwQ19fTCwmYWxwaGE7X19UR0YkRihGKComSSsmZGVsdGE7X19lR0YkRihJMENfX0wsJmRlbHRhO19fZUdGJEYoRig=print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=For monoblock tail, the lift contribution is:PkkyQ19fTCxUX19tb25vYmxvY2tHNiItSShjb2xsZWN0R0YkNiQtSSVzdWJzRyUqcHJvdGVjdGVkRzYkL0kwQ19fTDsmZGVsdGE7X19lR0YkSTBDX19MLCZhbHBoYTtfX1RHRiRJJ0NfX0wsVEdGJEYuprint(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 2" layout="Heading 2"><Font bold="false">Wing lift coefficient</Font></Text-field>The wing lift contribution is depends of the real AOA:QyQ+SSdDX19MLFdHNiIqJkkwQ19fTCwmYWxwaGE7X19XR0YlIiIiSSZhbHBoYUdGJUYoISIiprint(); # input placeholderJSFHSo the total lift force is:SSlMX190b3RhbEc2Ig== = print(); # input placeholderAnd the lift coefficient is:PkklQ19fTEc2Ii1JKGNvbGxlY3RHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2JC1JJ2V4cGFuZEdGKDYjLUkoYWxnc3Vic0dGJDYkLywkKihJKSZyaG87X190R0YkIiIiSSV2X190R0YkIiIjLUkiL0dGJzYjLCQqJkkpJnJobztfX3dHRiRGNUkldl9fd0dGJEY3I0Y1RjdGNUY/SSRldGFHRiQtRiw2IyomSSlMX190b3RhbEdGJEY1LUY5NiMsJCooRj1GNUklU19fd0dGJEY1Rj5GN0Y/RjVJJmFscGhhR0Ykprint(); # input placeholderWe can define LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=QyQ+SS1DX19MLCZhbHBoYTtHNiIsKCoqSSVTX193R0YlISIiSSVTX190R0YlIiIiSTBDX19MLCZhbHBoYTtfX1RHRiVGK0kkZXRhR0YlRitGKyosRihGKUYqRitGLEYrSTMmZXBzaWxvbjtfXyZhbHBoYTtHRiVGK0YtRitGKUkwQ19fTCwmYWxwaGE7X19XR0YlRitGKQ==And therefore, PkkmQ19fTDFHNiIsKEkmQ19fTDBHRiQiIiIqJi5JLUNfX0wsJmFscGhhO0dGJEYnSSZhbHBoYUdGJEYnRicqJkkwQ19fTCwmZGVsdGE7X19lR0YkRidJKyZkZWx0YTtfX2VHRiRGJ0Ynprint(); # input placeholderWe also know that QyQ+SSZDX19MMEc2IiosSSRldGFHRiUiIiJJJVNfX3RHRiVGKEklU19fd0dGJSEiIkkwQ19fTCwmYWxwaGE7X19UR0YlRihJJWlfX3RHRiVGKEYrWhere LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYGlfX3RgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn is the tail installtion angle.JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=