# Find the stalling speed of an airplane.

Find the stalling speed of an airplane which has a wing area of \(17\,m^2\) and is flying at sea level with maximum lift coefficient of \(2.2\), flaps down. Weight of the airplane is \(8000\,N\).

Lift on an airplane is \[L = \frac{1}{2}{\rho _\infty }V_\infty ^2S{C_L}\]

Since, in a steady level flight , Lift = Weight, Therefore, \[L = W = \frac{1}{2}{\rho _\infty }V_\infty ^2S{C_L}\]

Stalling speed is when the coefficient of lift is maximum. Therefore, \[W = \frac{1}{2}{\rho _\infty }V_{Stall}^2S{C_{L,\max }} \Rightarrow V_{Stall}^2 = \frac{{2W}}{{{\rho _\infty }S{C_{L,\max }}}}\]

\[ \Rightarrow {V_{Stall}} = \sqrt {\frac{{2W}}{{{\rho _\infty }S{C_{L,\max }}}}} = \sqrt {\frac{{2 \times 8000}}{{1.225 \times 17 \times 2.2}}} = 18.69\,m/s\]