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    Re: Navigating Projectiles
    From: Mike Boersma
    Date: 2004 Nov 23, 23:35 -0500

    To be somewhat closer to the intent of the list discussion and given that the
    subject of the list is navigation, perhaps we should discuss torpedo fire
    control solutions rather then artillery fire control solutions. After all, a
    torpedo is (apart from manned suicide versions) an unmanned submarine. My copy
    of the maneuvering board manual includes use of the maneuvering board to solve
    torpedo fire control problems. Obviously, the point here is to contact the
    target with the torpedo rather than to avoid collision.
    Michael Boersma
    Charles Seitz wrote:
    > 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

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