Case Study Part $4$

$($A spreadsheet is not needed for this task, though you could extend your spreadsheet to include the calculations required.$)$

The twin$-$engine aeroplane of this Case Study has the following parameters in addition to those given in Tutorial Set $4.$ Only those given here are needed for the calculations required in this task.

Overall:

Max. weight

Wing:

Wing area, $S_W$

Wing mean chord, $c$

Wing setting angle, $i_w$

Wing zero$-$lift angle, ${}_w$

Lift$-$curve slope, $a_w$

Moment Coeff. about a$.$c$.,C_{M_{W0}}$

Tail:

Tail area, $S_T$

Tail zero$-$lift angle, ${}_{To}$

Lift$-$curve slope, $a_T$

Tail distance, $h_T$

Tail setting angle, $i_T$

Downwash parameters:

del$\frac{}{d}el{}_a$

${}_o$

C$.$G$.$:

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

$1$ Calculate the tail$-$volume$-$ratio.

$88,000N$

$29\mathrm{.}5m^2$

$1\mathrm{.}82m$

$2$

$-3$

$0\mathrm{.}08$ per degree

$-0\mathrm{.}03$

$3\mathrm{.}0m^2$

$0$

$0\mathrm{.}08$ per degree

$3\mathrm{.}5$

variable $($see below$)$

$0\mathrm{.}3$

$1\mathrm{.}5$

$0\mathrm{.}15($only for Questions $1-3)$

$0\mathrm{.}341$

$2$ Plot $($or give a clear sketch with key numbers attached$)C_M$ against ${}_a$ in the range for three tail setting angles, $i_T=-4,0,+1.$

$]=-0\mathrm{.}00710.$ For $i_T=1,C_{Mo}=[+0\mathrm{.}0436$

$3$ From the results of Question $2$ find the trim angle, ${}_{a(\text{t}\text{r}\text{i}\text{m})}$ for the case $i_T=1,$ and find the EAS $($i$.$e$.,$ sea level speed$)$ for this trim condition.

$6\mathrm{.}1,72\mathrm{.}6\frac{m}{s}$

$4$ For $i_T=1$ calculate the new trim angle, ${}_{a(trim)},$ and the EAS if the $c.g$ position, $h,$ is changed to $h=0\mathrm{.}19.$

$16\mathrm{.}3,52\mathrm{.}1\frac{m}{s}$

$5$ Show how the value given for ${}_0$ is consistent with the rest of the wing parameters $a_w,i_w,{}_{wo},$del$\frac{}{d}el{}_a.$