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Thanks to all who participated in the discussion of balistic missile
submarines, and pointed to me
the directions of search. Following these directions, I found and
read some literature and discovered a lot of interesting things
about gyroscopes, missiles, etc.

There are two things which are directly related
to Cel Nav, and which I want to bring to the attention of the list.

1. Gyroscopic devices can determine two things without any external
checks: the direction of the Earth rotation axis is space, and
the vertical direction.
(This is because they can be made to "feel" the Earth
rotation and gravity). These data do not deteriorate with time, and this
is why a gyrocompass and gyrohorizon are possible. They can be made accurate
enough. It follows that one CAN determine the lattitude,
as 90d minus the angle between these two directions.

But one cannot determine longitude by gyroscopes.
So in the end of XX century
they had a problem exactly similar to that in the beginning of XVIII century:-)
The probem of Longitude.

2. Pure inertial systems require external
checks less than 1 day before launch.
(Actually 8 hours before lunch to ensure the advertised accuracy for
Polaris missiles). Several systems were used for these checks:
Loran C, Transit and Omega (Very Low Frequency).
Loran C and Transit do not work to more than few meters depth.
Omega works up to
100 m depth, but has smaller accuracy. There definitely was some research
on using pre-surveyed sea bottom features,
but I am not sure that this was actually used, sounds quite implausible.
Loran C was apparently the main system, according to some authors.
Its hudge disadvantage is that it requires stations on foreign territory.

So they indeed resorted to Cel Nav:-)
But Cel Nav for the missile, not for the submarine.
This is called a Stellar-inertial system, and it is used on all
submarine-launched missiles after Polaris. When the missile is already high
enough, a star sight is taken from the missile.
And the navigational data are corrected,
shortly before the engine is off.
This was an extremely hard technical problem (engineering AND mathematical).

One would naturally suppose that TWO star sights are needed.
And all literature until 1982 mentions two sights.
Soviet missiles apparently take two sights.
However, in 1982, a paper was published (I have it) which made the point
that ONE sight is enough. This is called the Unistar Principle.
The details were never published completely, but the Principle says
that "Whatever you can achieve with two (or more) stars, you can also
achieve with one star, if the star is properly selected".
(It is selected from a star catalog  which is maintained on the submarine
few minutes before the launch.)

It took me 4 days thinking to convince myself that this
Unistar Principle is probably correct:-)
I can explain more detail if anyone is interested.
(This is pure Cel Nav, after all, but not of the kind usually discussed
on the list:-)

The literature on the subject is scarce. Some papers of 1960-s
and 70-s are available. Some books are available as well,
but they are mostly written
by "social scientists" and political "scientists",
and like, who hardly understand what they are talking
about when they mention technical matters.
The few old papers which come from the real developers, usualy do not
mention a single number or a single formula:-(
Just words. In addition to these sources there are quite a lot of
modern Chinese articles on the subject (in English!) but they consist
of purely theoretical guessing, and poor math.

Alex.

   

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