Great Circle route difficulty

[BigBill]

I was brushing up on the procedure for figuring the great circle route, the one in the 50 year almanac by Kolbe and had some troubles. Maybe  I was just tired and the tv was on but 2 attempts at fairly close destinations, both under 400 NM just didn't work. Once I chose someplace more distant, about 2900 NM it worked fine. Is it possible to be too close to use? TIA

[P.Rutherford]

I was brushing up on the procedure for figuring the great circle route, the one in the 50 year almanac by Kolbe and had some troubles. Maybe  I was just tired and the tv was on but 2 attempts at fairly close destinations, both under 400 NM just didn't work. Once I chose someplace more distant, about 2900 NM it worked fine. Is it possible to be too close to use? TIA

BigBill,

Are you trying to plot waypoints along a great circle route?

Or, are you trying to get the distance from departure to destination?  If so- this is the formula you need;

https://thenauticalalmanac.com/Formulas....estination

To get the initial bearing use this formula;

Azimuth to Destination

NOTE- LHA= Present Longitude – Destination Longitude

Z = tan-1(sin (LHA) ÷ (cos (LHA) x sin(Your present Latitude) – cos(Your present Latitude) x tan(Destination Latitude))

Then to put Z into the right quadrant, apply the following rules-

If answer is negative, add 180º to Z
LHA is NEGATIVE if it's less than 180º .


Yes, a very short distance route, Great circle or Rhumb line, aren't significantly different. Great Circle routes less than about 1,500 miles aren't much different than Rhumb line.

Using OpenCPN, a computer chart plotting program, you can create a Great Circle route, get multiple waypoints and visually see how it compares to a Rhumb line route.

Paul

[CarlosPindle]

BigBill,

This might not help you directly but have you read Bowditch Chapter 24, "The Sailings"?

Get it here- The Sailings

It covers the Great Circle route (and others) planning.

It's good reading.

Carlos

P.S.  I just edited this post to add the link to Bowditch Chapter 24.

[BigBill]

I don't use a calculator, I run through the tables or do the basic math.

The procedure as described was the the Lat of the destination is the Declination, the Longitude of destination is the GHA and the assumed lat and long are used with the sight reduction tables in the usual way. The out put is the initial course and Hc which 60(90 - Hc) = distance to destination.

Maybe I'll just try running the two examples in question again. I was pretty tired when I tried before which now that I'm alert, maybe I should have done that before bothering everybody!

Oh to answer, not plotting waypoints, just doing the problem as far as getting initial heading and distance. 

As I said, the routine worked fine for the far destinations but close ones the math didn't work. I was getting values for f in excess of 90° and azimuths all over the place.

[BigBill]

I got it figured  out. Just a couple of dumb mistakes I was making in the almanac. f was about 94° and I wasn't reading back up to the value thinking it stopped at 90°, at an f greater than 90° z2 becomes negative accounting for the azimuth problems. Once I realized that it all fell into place.

By the way I was using this site to check my work.
http://www.gpsvisualizer.com/calculators