Method of Calculating the Probability of a Safe Landing for Ship-Based Aircraft

We propose the method for calculating the probability of a safe landing for ship-based aircraft. We define a safe landing as the event that the initial touch of the landing surface by an aircraft occurs on a given segment of the deck, and at the time of this contact, the phase coordinates of the aircraft (elevation angle, banking angle, vertical velocity, and so on) are within the specified limits. We propose a formula for estimating the desired probability and a formula for determining the maximum possible error <inline-formula><tex-math notation="LaTeX">$\Delta P$</tex-math></inline-formula> of this estimate: If <inline-formula><tex-math notation="LaTeX">$ P$</tex-math></inline-formula> is an unknown exact value of the desired probability and <inline-formula><tex-math notation="LaTeX">$\hat{P}$</tex-math></inline-formula> is an approximate calculated value, then <inline-formula><tex-math notation="LaTeX">$|P-\hat{P}|\leq \Delta P$</tex-math></inline-formula>. We implement the method on the example of the automatic landing of a MiG-29 K aircraft on the aircraft carrier “Admiral Kuznetsov.” Random perturbations are caused by an atmospheric turbulence and ship’s motions. We present and discuss the calculation results. These results show that the error <inline-formula><tex-math notation="LaTeX">$\Delta P$</tex-math></inline-formula> is negligible, so that the proposed formula for <inline-formula><tex-math notation="LaTeX">$\hat{P}$</tex-math></inline-formula> determines the desired probability <inline-formula><tex-math notation="LaTeX">$P$</tex-math></inline-formula> almost exactly.