Case Study Part $5$

The twin$-$engine aeroplane of the earlier Case Studies has the following parameters relating to lateral stability. You will need to use some of the data given previously degree, $[$:$W_{\text{m}\text{a}\text{x}}=88000(N),K=0\mathrm{.}044\}.$

Wing:

Sweep $,0$

Dihedral angle, $,2$

Effective centre, $\frac{?}{\text{b}\text{a}\text{r}}(y),3\mathrm{.}7m$

Aileron:

Aileron lift$-$curve slope, $a_a,0\mathrm{.}01$ per degree

Effective centre, $y_a,6\mathrm{.}5m$

Fin:

Fin area, $S_F,2\mathrm{.}0m^2$

Fin distance, $h_F($to effective centre$),3\mathrm{.}8$

Fin height, $l_F($above $c.g.),0\mathrm{.}6$

Fin lift$-$curve slope, $a_F,0\mathrm{.}06$ per degree

Rudder lift$-$curve slope, $a_R,0\mathrm{.}02$ per degree

c$.$g$.$ position, $h$

$0\mathrm{.}15$

Engine:

Moment arm, $y_E,$

$2\mathrm{.}0m$

$1$ Calculate the following $($non$-$dimensional$)$ lateral moment and force stability derivatives, $\frac{?}{\text{b}\text{a}\text{r}}(L{)}_v\frac{,}{b}ar(N{)}_v\frac{,}{b}ar(Y{)}_v\frac{,}{b}ar(L{)}_{}\frac{,}{b}ar(N{)}_{}\frac{,}{b}ar(Y{)}_{}.$

$-0\mathrm{.}0157,0\mathrm{.}0956,-0\mathrm{.}2331,0\mathrm{.}00521,-0\mathrm{.}0319,0\mathrm{.}0777$

$2$ If$,$ at altitude, the port engine should fail calculate the non$-$dimensional yawing moment caused by the remaining engine if its thrust is $5221N$ and the aircraft EAS is $85\frac{m}{s}.$ Calculate: i$)$ the side$-$slip angle for no deflection of the rudder and ii$)$ the rudder deflection required to bring the side slip to zero. Ignore the rolling moment equation and take $=0.$

$-0\mathrm{.}00494,3\mathrm{.}0,-8\mathrm{.}9$