An aircraft is performing a coordinated turn maneuver at a bank angle of 30 degree and forward speed of 100 m/s. Assume g=9.81 m/s^2 . What is the load factor and turn radius respectively?
An aircraft is performing a coordinated turn maneuver at a bank angle of \(30\) degree and forward speed of \(100\; m/s\).Assume \(g=9.81 \;m/s^{2}\) . What is the load factor and turn radius respectively?
Load factor is given as \(\frac{L}{W}\)
For a coordinated turn manoeuvre \[W=Lcos\phi\]
Load factor = \[\frac{L}{W}=n=\frac{L}{Lcos\phi}
\\\Rightarrow n=\frac{1}{cos\phi}=\frac{1}{cos30^{\circ}}
\\=\frac{2}{\sqrt{3}}\]
Turn radius will be given as \[\frac{mV^{2}}{R}=Lsin\phi
\\\Rightarrow Wtan\phi=\frac{mV^{2}}{R}
\\\Rightarrow R=\frac{mV^{2}}{Wtan\phi}=\frac{mV^{2}}{mg\;tan\phi}\]
\[\\=\frac{100\times 100}{9.81\times tan\;30^{\circ}}
\\=1.76\;km\]
