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    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.
    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

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