An Autopilot to Make Anti-Missile Escape Manoeuvres: A preliminary Study

A missile has a high manoeuvrability, it can reach Gflyup=38g, but it also has a very high speed that can reach Mach 4. This means that the curvature radius of an actual missile is about Rmissile=(4 300)2 / (38 9.81)~5Km(!!!), and an F-16 at Mach 0.7 and Gflyup=9g will have a curvature radius Raircraft=(300 0.7)2 / (9 9.81)~0.5Km(!!!), so Rmissile / Raircraft~10. These numbers of radius of curvature mean that the aircraft has a much higher manoeuvrability than the missile. As in the Biblic story of David against the giant Golias, the much higher manoeuvrability of the aircraft will be the secret weapon against the missile. But this advantage of the aircraft over the missile only will be effective if in the moment at what the aircraft makes the escape manoeuvre the distance between the aircraft and missile is very small to take advantage of missile reaction time. This latter constraint implies a high accuracy in the estimation of this distance of the order of 2% of errors and 1% of errors in the estimation of missile speed. Since Raircraft << Rmissile, paradoxally as the distance between missile and aircraft reduces and simultaneously the aircraft speed decreases (which imply a decrease in the aircraft radius of curvature, Raircraft) the probability of survival increases. We will show that for a distance less than 300m the probability of the missile hitting the aircraft is very low and tends to zero with the decrease of this distance. If we consider that the missile has a small reaction time then this probability reaches the value 0 for distances smaller than a upper limit that decreases with the missile reaction time. We determine this upper limit through exhaustive simulation with detailed numerical simulation models of an air to air missile which reaches a speed of Mach 4 and maximum Gflyup=38g and a detailed model of an F16 aircraft. We also show that ideal descend angle of the aircraft is about 85 degrees. A missile has a high manoeuvrability, it can reach Gflyup=38g, but it also has a very high speed that can reach Mach 4. This means that the curvature radius of an actual missile is about Rmissile=(4 300)2 / (34 9.81)~5Km(!!!), and an F-16 at Mach 0.7 and Gflyup=9g will have a curvature radius Raircraft=(300 0.7)2 / (9 9.81)~0.5Km(!!!), so Rmissile / Raircraft~10. Since Raircraft << Rmissile, paradoxally as the distance between missile and aircraft reduces and simultaneously the aircraft speed decreases the probability of survival increases. We will show that for a distance less than 300m the probability of the missile hitting the aircraft is very low and tends to zero with the decrease of this distance. If we consider that the missile has a small reaction time then this probability reaches the value 0 for distances smaller than a upper limit that decreases with the missile reaction time. We determine this upper limit through exhaustive simulation with detailed numerical simulation models of an air to air missile which reaches a speed of Mach 4 and maximum Gflyup=38g and a detailed model of an F16 aircraft. We also show that ideal descend angle of the aircraft is about 85 degrees. Since the pilot has a reaction time varying between 0.5s and 2s to deal with state of the art missiles that implies to minimize the distance between aircraft and missile at which the aircraft begins the flyup to take advantage of missile reaction time it is inevitable to implement an autopilot since pilot reaction time is much greater than missile reaction time.