$\%\%$ DOUGLAS A$-4$E$/$F SKYHAWK $[$LONGITUDINAL$]$

M $=0\mathrm{.}6$;

rho $=2\mathrm{.}3769*10^-3$;

a $=1116\mathrm{.}45$; $\%$all unit in english unit, speed of sound

uo $=$ M$*$a;

S $=260$;

c $=10\mathrm{.}8$;

b $=27\mathrm{.}5$;

AR $=($b$^2)/$S;

Ix $=8090$;

Iy $=25900$;

Iz $=29200$;

g $=32\mathrm{.}174$;

m $=17578/$g;

Q $=0\mathrm{.}5*$rho$*($uo$^2)$; $\%$dynamic pressure

alpha $=0$;

e $=0\mathrm{.}8$; $\%$oswald efficiency

CL $=0\mathrm{.}1268$; $\%$ from calculations

CD $=0\mathrm{.}037$; $\%$ from calculations

$\%\%$ Lift Coefficient Derivatives

CDu $=0$; $\%$ for jet assume zero

CTu $=0$; $\%$ for jet assume zero

CDo $=$ CD; $\%$ assume same

CLo $=$ CL; $\%$ assume same

CDalpha $=0\mathrm{.}1$; $\%$from graph

CLalpha $=3\mathrm{.}6$; $\%$from graph

$\%\%$ Longitudinal Stability Dimensionless Drivatives, not follow NELSON but dr document

CXu $=-($CDu$+2*$CDo$)+$CTu

CXalpha $=($CLo$-((2*$CLo$*$CLalpha$)/($pi$*$e$*$AR$)))$

CZu $=-((($M$^2)*$CLo$)/(1-$M$^2))-2*$CLo

CZalpha $=-($CLalpha$+$CDo$)$

CZalphadot $=0\mathrm{.}82$; $\%$assume equal to CLalphadot

CZq $=0$; $\%$assume since no graphs exist

CZdeltae $=0\mathrm{.}4$; $\%$CZdeltae$=-$CLdeltae

CMu $=0$; $\%$assume $0$ due to low speed flight

CMalpha $=-0\mathrm{.}39$; $\%$CMalpha to CMdeltae taken from graph

CMalphadot $=-1\mathrm{.}3$;

CMq $=-3\mathrm{.}9$;

CMdeltae $=-0\mathrm{.}6$;

$\%\%$ Longitudinal Stability Dimensional Derivatives

Xu $=($CXu$*$Q$*$S$)/($m$*$uo$)\%$checked

Xalpha $=($CXalpha$*$Q$*$S$)/$m $\%$checked

X

Xw $=(-($CDalpha$-$CLo$)*$Q$*$S$)/($m$*$uo$)$

Zu $=($CZu$*$Q$*$S$)/($m$*$uo$)\%$checked

Zw $=(-($CLalpha$+$CDo$)*$Q$*$S$)/($m$*$uo$)$

Zalpha $=($CZalpha$*$Q$*$S$)/$m $\%$checked

Zalphadot $=($CZalphadot$*$c$*$Q$*$S$)/(2*$m$*$uo$)\%$checked

Zq $=($CZq$*$c$*$Q$*$S$)/(2*$m$*$uo$)\%$checked

Zdeltae $=(-$CZdeltae$*$Q$*$S$)/$m $\%$checked

Mu $=($CMu$*$Q$*$S$*$c$)/($uo$*$Iy$)\%$checked

Mw $=($CMalpha$*$Q$*$S$*$c$)/($uo$*$Iy$)\%$checked

Mwdot $=($CMalphadot$*$Q$*$S$*($c$^2))/(2*($uo$^2)*$Iy$)\%$checked

Malpha $=$ uo$*$Mw $\%$checked

Malphadot $=$ uo$*$Mwdot $\%$checked

Mq $=($CMq$*$Q$*$S$*($c$^2))/(2*$uo$*$Iy$)\%$checked

Mdeltae $=($CMdeltae$*$Q$*$S$*$c$)/$Iy $\%$checked

$\%$State$-$ Space Matrix

format long

A $=[$Xu$,$ Xw$,0,-$g;

Zu$,$ Zw$,$ uo$,0$;

Mu$+($Mwdot$*$Zu$),$ Mw$+($Mwdot$*$Zw$),$ Mq$+($Mwdot$*$uo$),0$;

$0,0,1,0]$

B $=[0$;

Zdeltae;

Mdeltae$+($Mwdot$*$Zdeltae$)$;

$0]$

C $=$ eye$($size$($A$))$

D $=$ zeros$($size$($B$))\%$zero matrix

$[$num$,$ den$]=$ ss$2$tf$($A$,$ B$,$ C$,$ D$,1)$

numu $=$ num$(1,$:$)$

numw $=$ num$(2,$:$)$

numq $=$ num$(3,$:$)$

numtheta $=$ num$(4,$:$)$

t $=0$:$0\mathrm{.}01$:$20$;

impulse$($A$,$ B$,$ C$(4,$:$),$ D$(4,$:$),1,$ t$)$;

title$(\text{'}$Longitudinal Pitch Attitude $(\backslash$theta$)$ without Controller'$)$;