Case Study Part $6$

You will need to use data given previously

$[$i$.$e$.c=1\mathrm{.}82m,S_t=3m^2,a_t=0\mathrm{.}08$ per degree, $h_t=3\mathrm{.}5,\frac{\text{d}\text{e}\text{l}lon}{\text{d}\text{e}\text{l}{}_a}=0\mathrm{.}3].$

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

Moment of inertia:

Moment $I_y$

$0\mathrm{.}15$

$121{10}^{3}kgm{m}^2$

$1$

Calculate the frequency, $,$ and the damping factor, $,$ for the short period oscillation, for $100\frac{m}{s}$ EAS.

$1\mathrm{.}72ra\frac{d}{s},0\mathrm{.}129s^{-1}$

From your calculation, which is the most significant: pitch disturbance or rateof$-$pitch disturbance in determining the frequency?

$2$ Further to question $1$:

If the initial pitch disturbance is $10$ use $($preferably$)$ a spreadsheet to plot the decay of the oscillation. Do this for an elapsed time comparable with one period of the phugoid oscillation $($which is $45$ seconds at $100\frac{m}{s}).$

Note, to get reasonable definition in your plot of the short period oscillation you will need to use over $200$ values for the time $t.$

$3$ Further to question $1$:

What would be the effect of increasing the tail plane area by a factor $2$ on $$ and $?$

$2\mathrm{.}42ra\frac{d}{s},0\mathrm{.}25s^{-1}$