<Text-field style="Heading 1" layout="Heading 1">Lateral equilibrium equations</Text-field>

The side forces equation:

QyQ+SSpTaWRlRm9yY2VHNiIvSSVDX195R0YlLC4qJkknQ19feSxwR0YlIiIiSSJwR0YlRitGKyomSSdDX195LHJHRiVGK0kickdGJUYrRisqJkklYmV0YUdGJUYrSSxDX195LCZiZXRhO0dGJUYrRisqJkkrJmRlbHRhO19fYUdGJUYrSTBDX195LCZkZWx0YTtfX2FHRiVGK0YrKiZJKyZkZWx0YTtfX3JHRiVGK0kwQ19feSwmZGVsdGE7X19yR0YlRitGK0kmQ19feTBHRiVGKyEiIg==

The yawing moment equation:

QyQ+SSdZYXdpbmdHNiIvSSVDX19OR0YlLC4qJkknQ19fTixwR0YlIiIiSSJwR0YlRitGKyomSSdDX19OLHJHRiVGK0kickdGJUYrRisqJkklYmV0YUdGJUYrSSxDX19OLCZiZXRhO0dGJUYrRisqJkkrJmRlbHRhO19fYUdGJUYrSTBDX19OLCZkZWx0YTtfX2FHRiVGK0YrKiZJKyZkZWx0YTtfX3JHRiVGK0kwQ19fTiwmZGVsdGE7X19yR0YlRitGK0kmQ19fTjBHRiVGKyEiIg==

The rolling moment equations:

QyQ+SShSb2xsaW5nRzYiL0kqQ19fJkxzY3I7R0YlLC4qJkklYmV0YUdGJSIiIkkxQ19fJkxzY3I7LCZiZXRhO0dGJUYrRisqJkkicEdGJUYrSSxDX18mTHNjcjsscEdGJUYrRisqJkkickdGJUYrSSxDX18mTHNjcjssckdGJUYrRisqJkkrJmRlbHRhO19fYUdGJUYrSTVDX18mTHNjcjssJmRlbHRhO19fYUdGJUYrRisqJkkrJmRlbHRhO19fckdGJUYrSTVDX18mTHNjcjssJmRlbHRhO19fckdGJUYrRitJK0NfXyZMc2NyOzBHRiVGKyEiIg==

Now we will Analyze the force on the aircraft during turn:

The forces equations:

Qyg+SSRlcTFHNiIvLCgqJkkiTEdGJSIiIi1JJGNvc0dGJTYjSSRwaGlHRiVGKkYqSSJXR0YlISIiKiZJInlHRiVGKi1JJHNpbkdGJUYtRipGMCIiIUYwPkkkZXEyR0YlLywmKiZGKUYqRjNGKkYqKiZGMkYqRitGKkYqKihJIm1HRiVGKkkidkdGJUYqLUklZGlmZkclKnByb3RlY3RlZEc2JC1JJHBzaUdGJTYjSSJ0R0YlRkZGKkYwPkkkZXEzR0YlL0kickdGJSomRj9GKkYrRipGMA==

We will isolate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEkZXExRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0YzUSdub3JtYWxGJw== and place it in LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEkZXEyRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0YzUSdub3JtYWxGJw==:

LUkoaXNvbGF0ZUc2IjYkSSRlcTFHRiRJIkxHRiQ=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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PkkkZXE0RzYiLUkpc2ltcGxpZnlHRiQ2Iy1JJXN1YnNHJSpwcm90ZWN0ZWRHNiQvSSJMR0YkKiYsJkkiV0dGJCIiIiomSSJ5R0YkRjEtSSRzaW5HNiRGKkkoX3N5c2xpYkdGJDYjSSRwaGlHRiRGMUYxRjEtSSRjb3NHRjZGOCEiIkkkZXEyR0Yk

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlcTRHRigvKiYsJkkieUdGKCIiIiomLUkkc2luR0YlNiNJJHBoaUdGKEYySSJXR0YoRjJGMkYyLUkkY29zR0YlRjYhIiIqKEkibUdGKEYySSJ2R0YoRjItSSVkaWZmR0YmNiQtSSRwc2lHRig2I0kidEdGKEZFRjI3I0Yu

Now we isolate

LUklZGlmZkclKnByb3RlY3RlZEc2JC1JJHBzaUc2IjYjSSJ0R0YoRio= from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEkZXEzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0YzUSdub3JtYWxGJw== and place it in LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEkZXE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0YzUSdub3JtYWxGJw==:

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSVkaWZmR0YmNiQtSSRwc2lHRig2I0kidEdGKEYyRis=

LUkoaXNvbGF0ZUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkSSRlcTNHRictSSVkaWZmR0YlNiQtSSRwc2lHRic2I0kidEdGJ0Yw

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMvLUklZGlmZkdGJjYkLUkkcHNpR0YoNiNJInRHRihGMyomSSJyR0YoIiIiLUkkY29zR0YlNiNJJHBoaUdGKCEiIkYr

PkkkZXE1RzYiLUkpc2ltcGxpZnlHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2Iy1JJXN1YnNHRig2JC8tSSVkaWZmR0YoNiQtSSRwc2lHRiQ2I0kidEdGJEY1KiZJInJHRiQiIiItSSRjb3NHRic2I0kkcGhpR0YkISIiSSRlcTRHRiQ=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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Assuming small angles and divide the expression by 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 we get:

PkkkZXE2RzYiLUknZXhwYW5kRyUqcHJvdGVjdGVkRzYjLUklc3Vic0dGJzYlLy1JJGNvc0c2JEYnSShfc3lzbGliR0YkNiNJJHBoaUdGJCIiIi8tSSRzaW5HRi9GMUYyKiZJJGVxNUdGJEYzLUkiL0dGLzYjLCQqKEkkcmhvR0YkRjNJIlNHRiRGM0kidkdGJCIiIyNGM0ZBRjM=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlcTZHRigvLCYqLEkkcmhvR0YoISIiSSJTR0YoRjJJInZHRighIiNJJHBoaUdGKCIiIkkiV0dGKEY3IiIjKipGMUYyRjNGMkY0RjVJInlHRihGN0Y5LCQqLEYxRjJGM0YyRjRGMkkibUdGKEY3SSJyR0YoRjdGOTcjRi4=

PkkkZXE3RzYiLUkoYWxnc3Vic0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYkLywkKixJJHJob0dGJCEiIkkiU0dGJEYvSSJ2R0YkRi9JIm1HRiQiIiJJInJHRiRGMyIiIyomSSNtdUdGJEYzSShyX19ub3JtR0YkRjMtRiY2JC8sJCoqRi5GL0YwRi9GMSEiI0kieUdGJEYzRjVJJUNfX3lHRiQtRiY2JC8sJCosRi5GL0YwRi9GMUY+SSRwaGlHRiRGM0kiV0dGJEYzRjUqJkklQ19fd0dGJEYzRkZGM0kkZXE2R0Yk

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlcTdHRigvLCYqJkklQ19fd0dGKCIiIkkkcGhpR0YoRjJGMkklQ19feUdGKEYyKiZJI211R0YoRjJJKHJfX25vcm1HRihGMjcjRi4=

Where 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 .

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JSFH

<Text-field style="Heading 1" layout="Heading 1">Exercise 1</Text-field>

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Given an aircraft with two fuel tanks at the tip of it's wing (as it shown in the figure below).

-%'CANVASG6'-%)BOUNDS_XG6#,$-%&FloatG6#%)infinityG!""-%)BOUNDS_YGF'-%-BOUNDS_WIDTHG6#$"%+lF--%.BOUNDS_HEIGHTG6#$"%g_F--%)CHILDRENG6.-%%OVALG6'-%(OUTLINEG6#-%&COLORG6&%$RGBG$""!F-FGFG-%/LINE_THICKNESSG6#$"#5F--%(SPATIALG6&-%&TRANSG6#-%'VECTORG6$FGFG-%'ORIGING6#-%&POINTG6$$"%+IF-$"%&p#F--%&SCALEG6#-FU6$FLFL-%)ROTATIONG6#FG-%*LINESTYLEG6#FH-%%DATAG6%7$$"%SEF-$"$!eF-7$$"$?(F-$"%IUF-%'CLOSEDG-%%LINEG6'F@FI-FO6&FQ-FX6#-Fen6$$"%&["F-$"%bAF-F[oF`oFco-Fgo6&7$$"%!o#F-$"%+=F-7$$"$!HF-$"%+@F-7$$")/%35$!"'$"%!p#F-7$$"(K)RE!"%$"%5FF--Fep6'F@FI-FO6&FQ-FX6#-Fen6$$"%DXF-$"%lAF-F[oF`oFco-Fgo6&7$$"%SLF-$"%5=F-7$$"%+dF-$"%5@F-7$$"%5dF-$"%?FF-7$$"%!Q$F-Fdt-Fep6'F@FI-FO6&FQ-FX6#-Fen6$$"%+CF-$"%&e%F-F[oF`oFco-Fgo6&7$$"%!y#F-$"%qVF-7$$"%!z"F-$"%5XF-7$F]v$"%+[F-7$$"%5IF-Fbv-Fep6'F@FI-FO6&FQ-FX6#-Fen6$$"%:OF-$"%&f%F-F[oF`oFco-Fgo6&7$$"%?KF-$"%!Q%F-7$$"%5UF-F_v7$$"%?UF-$"%5[F-7$FevF`x-F>6'F@-FJ6#$"#?F--FO6&FQ-FX6#-Fen6$$"%+cF-$"%:CF-F[oF`oFco-Fgo6%7$$"%!\&F-$"%5?F-7$$"$?#F-$"$5)F-Fcp-Fep6'F@-FJ6#$"#gF--FO6&FQ-FX6#-Fen6$$"%&*HF-FawF[oF`oFco-Fgo6$7$$"%!*HF-$"%5WF-7$Fgn$"%!y%F--Fep6(F@-%/LINE_END_ARROWG6#Q*vee-arrow6"-FJ6#$"#:F--FO6&FQ-FX6#-Fen6$$"%0IF-$"%N8F-F[oF`o-Fdo6#""%-Fgo6$7$Fgn$"%5CF-7$Fgn$"$g#F--Fep6(F@Fi[lF^\l-FO6&FQ-FX6#-Fen6$$"%IXF-$"%0CF-F[oF`oF\]l-Fgo6$Fa]l7$$"%ggF-Fau-%/TEXT_CONTAINERG6(F^\l-FO6&FQ-FX6#-Fen6$$"%vKF-$"$I&F-F[oF`o-%,FIXED_WIDTHG6#%%trueG-%-FIXED_HEIGHTGFg_l-Fgo6%7$$"%!3$F-$"$]$F-7$$"$!RF-$"$g$F-Fcp-%*PARAGRAPHG6#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F]\l-Fi^l6(F^\l-FO6&FQ-FX6#-Fen6$$"%bhF-FarF[oF`oFe_lFi_l-Fgo6%7$$"%gfF-$"%?DF-7$Fc`l$"$S$F-Fcp-Fh`l6#Q[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]\l-F>6'F@Fex-FO6&FQ-FX6#-Fen6$$"$0%F-$"%&R#F-F[oF`oFco-Fgo6%7$$"$+$F-$"%!*>F-7$$"$5#F-F]zFcp

The surface of the fuel tanks is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYFNfX21gRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn and lift coefficient is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1ExYENfX0wsJmFscGhhOyxtYEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw== and they both given.

<Text-field style="Heading 2" layout="Heading 2">Art 1</Text-field>

Find the lift contribution to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYsNiNRNGBDX18mTGFwbGFjZXRyZjsscGBGJy8lK2V4ZWN1dGFibGVHUSV0cnVlRicvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0YrRjo= .

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

<Text-field style="Heading 3" layout="Heading 3">Solution</Text-field>

At first, we will check the influence of fuel tank on one wing:

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

So the contribution of two fuel tanks is:

QyQ+STMmRGVsdGE7Q19fJkxzY3I7LG1HNiIsJCoqSSVTX19tR0YlIiIiSSVTX193R0YlISIiSS9DX19MLCZhbHBoYTssbUdGJUYpSShwX19ub3JtR0YlRilGK0Yr

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

JSFH

So LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1E7YCZEZWx0YTtDX18mTGFwbGFjZXRyZjsscGBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic= is:

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print(); # input placeholder

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<Text-field style="Heading 2" layout="Heading 2">Art 2</Text-field>

What is the fuel tanks contribution to the side force as a result of sideslip angle? LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1E1YCZEZWx0YTtDX195LCZiZXRhO2BGJy1JI21vR0YkNi1RIj1GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRy1JJm10ZXh0R0YkNiRRIj9GJ0YzLUYsNiNRIUYnRjM=

<Text-field style="Heading 3" layout="Heading 3">Solution</Text-field>

The additional side force is:

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Now we need to find an expression to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EwYENfX3ksJmJldGE7LG1gRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn ( assuming the fuel tank is Spherical ) :

QyQ+SS5DX195LCZiZXRhOyxtRzYiLCRJL0NfX0wsJmFscGhhOyxtR0YlISIiRig=

So the side force is

SSwmRGVsdGE7Q19feUc2Ig==

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print(); # input placeholder

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And LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1E1YCZEZWx0YTtDX195LCZiZXRhO2BGJy1GLDYjUSFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic= is

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print(); # input placeholder

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Note that this is the contribution of only one fuel tank.

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