Three-dimensional Model of Maritime Search

Abstract

This paper establishes a three-dimensional maritime search and rescue plan by integrating a differential equation model, a global optimal model and an area partition algorithm. Based on the data of flight data and the loss time of communication for MAS MH370, we establish a differential equation model to determine the search scope of the sea area, and determine the place where the plane fall into water. After the plane falls into water, the plane will be moving in the water due to the effect of sustained ocean currents, thereby we establish a differential equation model. By solving this model, we obtain that the search scope is a circular area of 2000 square miles with a coordinate of circle center. Introduction With the development of economy, the plane has gradually become one of the convenient traffic. Plane flying does not be limited from the mountains, rivers, deserts, oceans and other geographical conditions, and can increase the number of plane according to the passenger source and the supply quantity. According to the statistics data from International Civil Aviation Organization, the average number of deaths in per one km is 0.04 people, and it is safer way than the train transportation. The plane’s disadvantage is expensive, and heavily influenced by weather. Although the plane accident rate is very low, once the plane crash happens, very few people survived or even no survivors. Therefore, maritime search and rescue is a very complex and vital activity. When distress target location is unknown, we must carry out maritime search and rescue. Search operation is the most expensive, the most dangerous and the most complex part in the whole search and rescue process, is also the only way to find and rescue the survivors. Making process of search action plan of the sea are generally considered more complex, so this paper takes a Boeing 737 crashed plane as an example, the searching process of sea action plan is divided into three steps: 1) Determine the specific scope of search area (i.e. to determine what kind of search power to participate in the action); 2) Determine the search partition and search way (i.e., to determine how these search powers act). And then we design a search plan after these three steps. The model In order to determine the specific scope of search area, the whereabouts process of plane is divided into two stages: (1) The falling process of the plane in the sky. In this stage, we will determine the place where fall into water. (2) The falling process of the plane in the water. Considering the sea buoyancy and the effect of ocean currents, we will determine the specific scope of search area. Due to too many indexes for crash problem of different type plane, in order to simplify the problem, we take the Boeing 737 plane as an example. Suppose that the plane lost power at one point from A to B over the sea, the airplane flying in the air and generate the resistance f with the opposite direction of its movement. Because of the Earth's gravity, the plane has the gravity G. And upper and lower wing surface flow velocity are inconsistent, so that the wing generates lift F. The projected point of the plane on the sea as the origin, northeast 45° is the X-axis, and the vertical direction is Y-axis. In 4th International Conference on Mechatronics, Materials, Chemistry and Computer Engineering (ICMMCCE 2015) © 2015. The authors Published by Atlantis Press 1384 this coordinate system the initial coordinates of the plane is (0,10000) , and the initial plane velocity is parallel to the X-axis direction. After plane lost power, speed and direction of movement, posture, air resistance and aerodynamic plane are changes over time change, so this is a typical problem of fluid dynamics. However, in order to simplify the model, we suppose that lift F is a given value, and the direction is always perpendicular to the direction of motion of the plane. Usually, when the object is not large and the moving speed is relatively low, we can suppose that the resistance is proportional to the speed if the object speed is less than 10 m/s, and in general within the range of considerable velocity and size of the object, it can be assumed that the resistance is proportional to the square of the speed from 10 m/s to approach or exceed the speed of sound. If the object speed exceeds the speed of sound, then a sharp increase in resistance, and the resistance is proportional to high power of the speed [1]. The relative literature data are listed in the following Table 1. Table 1. Air density data under certain altitude Altitude (m)