Question

The overall drag coefficient of an aircraft of weight W and wing area S is given by

$C_D=a+b{C}_L^2$

Where 'a' and 'b' are constants. The maximum drag in horizontal flight will be

• A. $W\sqrt{ab}$
• B. $2W\sqrt{ab}$
• C. $4W\sqrt{ab}$
• D. $6W\sqrt{ab}$

Answer 1

The correct option is B $2W\sqrt{ab}$

$Theliftforce,F_L=C_{L}S\left(\frac{\rho V^2}{2}\right)$

$Thedragforce,F_D=C_{D}S\left(\frac{\rho V^2}{2}\right)$

The weight of aircraft shall be equal to the lift force

$C_{L}S\left(\frac{\rho V^2}{2}\right)=W$

$\therefore Dragforce,F_D\left(\frac{C_D}{C_L}\right)W$

$Itwillbemaximumwhen\frac{C_D}{C_L}ismaximum$

$Given{C}_D=a+b{C}_L^2$

$\therefore \frac{C_D}{C_L}=\frac{a}{C_L}+b{C}_L$

$\frac{d\left(C_D/C_l\right)}{d{C}_L}=-\frac{a}{C_L^2}+b=0$

$C_L=\sqrt{\left(a/b\right)}$

$\therefore Maximumdrag=[\frac{a}{\sqrt{a/b}}+b\sqrt{a/b}]w$

$=2W\sqrt{ab}$