Problem $1$: Aircraft wing Analysis

The objective is to identify the cross sectional properties and analyze following torsional load

cases for an aircraft wing previously analyzed for bending loads in Phase $1.$ The wing

geometry and lift distribution remain unchanged.

Torsion: maneuver $(+3$g pull$-$up$)$

Torsion: runway taxi $(-3$ g dead weight$)$

The airfoil cross$-$section is assumed to consist of stringers, as depicted in the figure

below. Vertex coordinates of the stringers are provided in the code.

Torsion load

The NACA $641212$ airfoil creates lift and moment acting at the quarter$-$chord. $1$ For stability

the elastic axis must lie behind $($downstream of$)$ of the aerodynamic center $(25\%$ chord$).$ The

sectional twisting moment $($torque$)$ per unit span wise length about the elastic axis is

m$\_($T$)($x$)=$m$\_($ea$)($e$-$c$\_($s$)//20)$w$($x$)$

where e is the distance from the aerodynamic center to the elastic axis, c$\_($s$)$ is the structural

chord perpendicular to the elastic axis. Note bomb is placed such that it induces negligible

torsional moment in the wing.

Extend the provided code to compute results for the wing analysis under torsional loads.

P$.$S$.$ For polar moment of inertia, you can just simple use the formula, J $=$ I$\_$yy $+$ I$\_$zz

$1.$ Calculate centroidal coordinate yc at x$=8\mathrm{.}4$m$.$

Express your answer in$$ ft up to $3$ places of decimals.

$2.$ Calculate centroidal coordinate zc$$at x$=1\mathrm{.}9$m$.$

Express your answer in$$ft up to $3$ places of decimals.

$3.$ Calculate Second moment of area about yy axis at x$=5\mathrm{.}0$m$.$

Express your answer in$$ ft$4$ up to $2$ places of decimals.

$4.$ Calculate second moment of area about zz axis at x$=4\mathrm{.}0$m$.$

Express your answer in$$ ft$4$ up to $3$ places of decimals.

Calculate product of Inertia at x$=4\mathrm{.}5$m$.$

Express your answer in$$ ft$4$ up to $3$ places of decimals.

$5.$ Calculate product of Inertia at x$=4\mathrm{.}5$m$.$

Express your answer in$$ ft$4$ up to $3$ places of decimals.

$6.$ Calculate polar moment of Inertia at x$=7\mathrm{.}1$m$.$

Express your answer in ft$4$ up to $3$ places of decimals.

$7.$ For load case $2,$ Calculate twist at x$=12\mathrm{.}4$m

Express your answer in degrees up to $2$ places of decimals.