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Subject: great circle points
From: Paul Hirose (71202.2014@XXX.XXX)
Date: Sun Jul 25 1999 - 20:43:38 EDT
Lu and the group -
If you have a globe you can find intermediate points for a great
circle course with a string. Lat/lon readings by eye should get you
so close to a great circle as makes no difference.
HO 229 or similar sight reduction tables will also do the job. Just
pretend the destination is a star. Let's compute a great circle from
San Jose to Tokyo. I grew up in San Jose, and as I recall the
coordinates are 37N 122W. That will be the "assumed position". Tokyo
is at about 36N 140E. Difference in longitude is 98 degrees, which we
will treat as the "local hour angle". And of course the latitude of
Tokyo exactly corresponds to the declination of the "star".
We now have the data required to "reduce the sight". Pick up the HO
229 volume covering the latitude of San Jose, and turn to the LHA 98
page. In the column with the lat of San Jose, find the row with
Tokyo's "declination". According to the table, Hc = 15 17.8', Z =
56.2. Distance to the geographical position of a body is 90 - H, or
in this case, practically 74 42'. At 60 naut. miles per deg, that
works out to 4482 nm. Remembering that Z is measured east or west
from the elevated pole, and knowing that Tokyo is east of us, course
must be 360 - 56 = 304.
My GPS receiver says 4482 miles, 304 degrees!
Now to pick the intermediate points. Normally you would want one
every so many degrees of longitude. Suppose we make the segments 10
deg of longitude long. For the first point, turn to the LHA 10 page,
enter the column with San Jose lat as before, and find a "star" with
the same Z as we got for Tokyo (56 deg). Looks like 42N is the best
one. That's the latitude of the intermediate point. The longitude
would be San Jose + LHA, or 132W.
This method gives points to the nearest degree. You could
interpolate, but I don't think it's worth the trouble.
If you want to stay below, say, 45 north, just find the greatest LHA
that results in an intermediate point below 45N. From there you would
sail along the parallel. As LHA increases further, you'll the great
circle eventually drops back below 45N. At this point you can resume
the great circle.
HO 211 can also be used to compute points along a great circle. The
trick here is to space the points by distance, not longitude. If you
try to work in intervals of longitude, the solution has to be made by
interation. It's possible with pencil and paper, but a lot of work.
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