Computation of Effective Ground Range Using an Oblate Earth Model
- PDF / 2,195,749 Bytes
- 15 Pages / 496.063 x 722.835 pts Page_size
- 42 Downloads / 211 Views
Computation of Effective Ground Range Using an Oblate Earth Model Bao U. Nguyen! and Murray E. Dixson' Abstract This paper documents a novel methodology used to improve the ground range calculation of a ballistic missile trajectory on a non-rotating Earth. The improvement is based on a more accurate modeling of the Earth's shape. This modeling assumes that the Earth is an oblate spheroid with eccentricity parameter e~ equal to 0.00669; that is, the Earth is compressed equally along the polar axis and maintains its circular shape on the equator. For scenarios of potential interest, this methodology shows that there is a difference of about 10 to 30 kilometers in ground range compared with a spherical Earth model. For example, a missile launched from country C1, with latitude (longitude) equal to 60 0 N (- 800 W ) , towards S1, with latitude (longitude) equal to 41°N (74 OW), has its ground range decreased by 23 km,
Introduction There is mounting political pressure within the United States to deploy the NMD
(National Missile Defense) system [1], which is now referred to as the IMD (Integrated Missile Defense) system. Such threats can be assessed by capability and intention, [2]. The ground range of a ballistic missile is one parameter that helps quantify these assessments. It determines how far the missile can reach and perhaps more importantly determines which specific targets could be hit. For this reason, evaluation of the ground range is for more than pure academic interest. For speed and simplicity, the Earth is often modeled as a perfect sphere but in reality the Earth resembles an oblate spheroid. An oblate spheroid is a circle in the equatorial plane and is an ellipse along the poles with the radius along the poles being less than that at the equator. For ballistic missile defense analysis purposes, we describe two distinct but equivalent algorithms for evaluating the ground range of a missile on an oblate spheroid even though these techniques also apply generally to an arbitrary ellipsoid. We will show that the difference in ground range between a perfect sphere and an oblate spheroid model of the Earth is about 10 to 30 kilometers. This more realistic calculation of a missile's ground range leads to 'Headquarters NORAD and US Northern Command Analysis. 2Canadian National Defence Headquarters, Operational Research Division.
291
Nguyen and Dixson
292
better estimates of areas that are within the range of the missile and overall, provide more accurate and credible ballistic missile defense analyses. For the purposes of this paper, we interpret "ground range" as follows. In the simplest case, Earth does not rotate and so the ground range is the length of the arc segment along the surface of the Earth between two points fixed to the surface (the ballistic missile launch and impact points for example). When the Earth rotates, things are more complicated. In this case we note that a ballistic missile trajectory is fixed in inertial space while the Earth rotates independently underneath. The ground range her
Data Loading...
