Table $1$: Cruise Data for Piston$-$Prop Aircraft

Number of engines & propellers $4$

Wing reference area $120$ m$2$

Total mass $30000$kg

Maximum lift coefficient $($CLmax$)1\mathrm{.}8$

Profile drag coefficientD$0$C $0\mathrm{.}025$

Maximum lift to drag ratio $12$

Propeller efficiency $92\%$

Specific fuel consumption $($s$.$f$.$c$.)1\mathrm{.}0$x$10-7$ kg J$-1$

Ambient density at cruise $0\mathrm{.}6$ kg m$-3$

$1.$ Explain briefly what a $$drag polar$$ is and explain how it relates to the performance of a

conventional aeroplane. Calculate the induced drag coefficient $($k$)$ consistent with the

data in Table $1.[10]$

$2.$ Calculate Vmd at the cruise configuration in Table $1.[10]$

$3.$ Estimate the mass of fuel required for a Gross Still$-$Air Range of $1000$km at cruise

altitude, assuming a true air speed $10\%$ higher than Vmd calculated in $(2).[20]$

$4.$ Estimate the total shaft power required to achieve a climb rate of $5$ m s$-1$ at a true

airspeed $10\%$ above VSTALL at ISA sea level conditions. $[20]$

$5.$ Estimate the total shaft power required to execute a $45$ degree correctly banked turn at

ISA sea level at a true airspeed $10\%$ above VSTALL.