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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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