# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Navigating Projectiles**

**From:**Charles Seitz

**Date:**2004 Nov 23, 22:04 -0500

There appears to be some interest about the Fire Control problem here. If we stretch the point, its also a navigation problem! We must methodically fire the ordnance from Point A to Point B. See http://dcoward.best.vwh.net/analog/ford.htm for some information on Chuck Taylor's electro-mechanical computer that computed ballistics for naval gunfires. My understanding is the Mark 1 was to be replaced by a digital computer when the Iowa class battle ships were recommissioned. However, the digital computers provided no increase in firing accuracy so the analog computers were retained. Analog computers represent a computational variable in a physical manner such as a voltage, current, shaft rotation angle etc. All of these analogs are cleverly manipulated through adders, differential drives shaped cams gear trains and the list goes on. Interestingly, there is usually only a small latency in the solution because the computer is continuously working as the input variables change . I worked with an analog computer for the M60A3 battle tank and I have a lot of respect for the analysts who designed these kinds of systems. Using a digital computer, 'navigating' a projectile from here to there is an iterative process that refines a best guess firing elevation and direction until the computed impact point is within the kill radius of the munition. There is no closed form solution for calculating a trajectory in air. Mathematically, trajectory segments dy/dx are integrated to construct the trajectory. Each segment is calculated using ballistics parameters customized to a particular type of projectile. Adjustments are made for air density, mach number, acceleration of gravity and flow direction of the air mass. For long range firings, coriolis force must be considered. There are several classes of trajectory models: 1) A point mass model considers the projectile to be cencentrated into a single point . 2) A modified point mass model applies rudimentary corrections for the angle the projectile body makes with respect to a line tangent to the trajectory. If I remember correctly, this angle is called the Yaw of Repose. 3) A six degree of freedom model (6 DOF) simulates pitch, yaw and roll in 3D space. These are full solution models used by those who design projectiles. The ENIAC digital computer (1948) was designed for the US Army to solve trajectory ballistics problems. The general trajectory software (GTRAJ modified point mass model ) in use today as a NATO standard, is traceable to that era. --- CHAS