Case Study Part $3$

Assume the parameters given for the Case Study as given in Part $1$ and Part $2,$ unless revised parameters are required as given below. You will need the following: $,K=0\mathrm{.}044.$

$1$ For the flaps and slats in the take off setting:

$C_{L_{\text{M}\text{a}\text{x}}}=2\mathrm{.}1$

Lift$-$off speed $=1\mathrm{.}2$ stall speed Full fuel load.

Calculate i$)$ the lift$-$off speed $($and give in units of $\frac{m}{s}$ and $kt),$ ii$)$ the ground run distance ignoring the drag and rolling resistance terms, for sea$-$level ISA conditions.

$[57\mathrm{.}8\frac{m}{s},112\mathrm{.}4kt,936m]$

$2$ Repeat the calculation of Question $1$ for an airfield at an altitude of $2500m,$ at ISA pressure and temperature. $($Use data from tables.$)$

$[65\mathrm{.}4\frac{m}{s},127\mathrm{.}2kt,1530m]$

$3$ Calculate the maximum climb angle assuming ISA sea$-$level conditions, flaps and undercarriage retracted, for a total weight of a$)88,000N,$ b$)55,000N.$

$7\mathrm{.}1,13\mathrm{.}4$

$4$ Using the atmospheric and weight conditions of Question $3$ calculate the climb angles for a range of speeds between $30$ to $220\frac{m}{s}.$ Use these to calculate the horizontal and vertical velocities $V_v$ and $V_h,$ and plot $V_h$ against $V_v.$ Use this plot to determine the maximum rate of climb and the corresponding climb angle and flight speed.

Use of a spreadsheet is recommended for this question.

$[$@ $W=88000N$:$13\mathrm{.}0\frac{m}{s},6\mathrm{.}0,124\frac{m}{s}]$

$[$@ $W=55000N$:$22\mathrm{.}4\frac{m}{s},10\mathrm{.}4,122\frac{m}{s}]$