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Russell Sher wrote:

> Does anyone know a simple way of calculating the closest point of approach
> between two vessels on given courses at given speeds?
> I would imagine that one method is to plot the courses and calculate which
> vessel will reach the point of intersection of the projected tracks first.
> The distance to the other vessel should give the CPA ( correct ?) There is
> no doubt a better method using the relative course - any input on this?
> I'm a bit suprisesd that few, if any, small-boat navigation books discuss
> this.

Russell,

Calculating CPA's is routine in the Navy and on other large ships at sea.  The
"secret" is to use a Maneuvering Board.  Maneuvering Boards are sold in pads
like plotting sheets and are published by the government (NIMA).  You can buy
them at many of the same kinds of places where you buy charts and plotting
sheets.

Everything you ever wanted to know about the subject (and more) can be found in
the Maneuvering Board Manual, Pub 217, available online from NIMA at

http://164.214.12.145/pubs/pubs_j_show_sections.html?dpath=MBM&ptid=8&rid=155

A Maneuvering Board is sort of like a radar screen.  Everything is relative.
You are in the center of what looks like a large compass rose with 000 relative
at the top.  There are concentric rings to indicate distance from you (range)
and radial lines to indicate relative bearing.  (For a picture of one, see the
Maneuvering Board Manual.)

The easiest way to use a Maneuvering Board is in conjunction with a radar.  To
figure CPA,  plot the range and relative bearing of the target and record the
time.  Wait a few minutes and repeat the process.  Now draw a line through the
two points and extend it past the center.  That line represents the relative
track of the target and where it passes closest to the center of the board is
the CPA.  To figure the time of the CPA, compute the relative speed based on the
time and distance between the two observations.

Obviously if the relative track extends through the center of the board, you are
on a collision course.  If you take a third range and bearing and it doesn't
fall on the previously plotted track, then either the target or you have turned
or changed speed and it's time to compute a new CPA.

On Navy ships at least some of the radar screens are set up so that you can plot
CPA's directly on the screen using a grease pencil.  (At least they used to
be.)

Regards,

Chuck Taylor
US Navy
(Retired)

   

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