An aircraft in a steady level flight at forward speed of \(50\; m/s\) suddenly rolls by \(180 ^{\circ}\) and become inverted. If no other changes are made to the configuration or controls of the aircraft , what will be the nature of the subsequent flight path taken by the aircraft and its characteristic parameter?
At first aircraft is flying at a steady level flight.Therefore the lift force will be equal to the aircraft’s weight.
After that aircraft rolls by \(180 ^{\circ}\) means the aircraft is now flying inverted down.This will make the angle of attack of the aircraft negative and Lift force will be acting in the downward direction.Since both lift and weight is acting in the downward direction and the aircraft is having a forward velocity, it will have a downward circular path.
The centripetal force will be equal to the sum of lift and weight forces.\[L+mg=\frac{mV^{2}}{R}
\\L=W
\\\Rightarrow mg+mg=\frac{mV^{2}}{R}
\\\Rightarrow R=\frac{V^{2}}{2g}
\\\Rightarrow R=\frac{50\times50}{2\times 9.81}
\\=127.4\;m\]
Therefore the aircraft will follow a downward circular path with a speed of 50 m/s and a radius of \(127.4\;m\).
