www.ijird.com August, 2018 Vol 7 Issue 8 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH & DEVELOPMENT DOI No. : 10.24940/ ijird/ 2018/ v7/ i8/ AUG18078 Page 293 Mathematical Model of Surface to Air Intercepting Missile I. Introduction Surface to air missiles (SAMs) are a powerful weapon in both defensive and offensive tactics. The purpose of the system is to detect and destroy enemy aircraft or missile approaching a defended area. The system must be capable of defending strategic areas against attack from high altitude, high speed enemy target that could cause damage. Missile systems can be categorized into two classes- strategic and tactical. Strategic missiles are designed to travel long distances towards known, stationary targets. Tactical missiles track or intercept shorter range, maneuvering and non-maneuvering targets where its guidance and control technologies turn out to be more critical. Strategic missiles primarily operate in exoatmospheric conditions while tactical missiles most commonly operate in endoatmospheric conditions. The missile type of interest in this study is the tactical missiles designed to intercept a non maneuvering target. Sophisticated missile launcher systems are used to point the missile to the target. Another classification of missiles includes: Surface-to-Surface Missiles (SSM), Surface-to-Air Missiles (SAM), Air- to-Air Missiles (AAM) and Air-to-Surface Missiles (ASM).The one of interest in this study is the Surface to Air Missiles (SAMs).This system consists of the Search radar, Missile Launch system and the Control Station. Figure 1 Sub-Systems of Surface to Air Missile ISSN 2278 – 0211 (Online) Bongdap Nanbol Keza PG Student, Department of Mechanical Engineering, Nigerian Defence Academy, Nigeria Abstract: The purpose of this design is to lay up a precised intercepting missile trajectory equations for military rapid response of counter attacks of enemies’ high invading targets. The set of non linear mathematical equations that model the trajectory of an intercepting missile is presented here with considerations to characteristics such as Angle of Attack (AoA), Lift off speed, Optimized flight direction (wind direction). A numerical solution using MATLAB is also derived for rapid computation and feed back into the missile launcher command computer system. This paper include scientific data for atmospheric variables such as pressure, density, gravity and temperature to an altitude below the tropopause (11km) beyond which the data seized to be true. An iterative computational process which divides the earth’s altitude into finite strata is used in MATLAB program to predict the flight parameters (AoA, lift off speed, intercept time) given input parameters (safe intercept position, speed of enemy’s target, position of enemy’s target) Keywords: Intercepting, missile, mathematical model, target