3 messages.-----------Johnnie
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>From: [log in to unmask]
>Date: Fri, 20 Oct 1995 13:25:00 -0700
>Subject: Re: Heading calculations....
According to DUTTON'S NAVIGATION AND PILOTING by Elbert S.
Maloney, your Heading is "the direction in which a ship
points or heads at any instant, expressed in angular units,
clockwise from 000[degrees] through 360[degrees]..." Check
the chapter under "Dead Reckoning" in this tome or the
AMERICAN PRACTICAL NAVIGATOR by Bowditch. I'm not sure I
understand the question, but if you want all the mathematics
you'll have to read the book(s). - PML
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>Date: Fri, 20 Oct 1995 16:49:34 -0500
>From: [log in to unmask] (Peter H. Dana)
>Subject: Re: Heading calculations....
Charles:
>I admit my brain hurts, but I have a simple problem, and I cannot
>locate a reference which satisfies me. I have points 1 and 2
>specified in lat/long. What is my heading if I wish to travel from
>point 1 to point2?
>
>I've been told that it's simple trig, but I don't think so.
>Can anyone post the proper equations?
Do you wish to travel over the surface of the earth along one
heading, travel over the surface of the earth along the shortest path
(requiring continually changing your "heading," or travel directly though
the earth from one point to the other along the shortest possible path?
The first is a "rhumb line" course with a single constant heading;
the second a "great circle" course or perhaps an "ellipsoidal geodesic"
depending on how much math you want to do; the third is a three dimensional
heading vector, not much use unless you want to dig.
Not a headache cure, but I think the best reference is "Spheroidal
Geodesics, Reference Systems & Local Geometry." P. D. Thomas, U. S. Naval
Oceanographic Office, Washington, DC. 1970. Rhumb line and great circle
heading calculations are also outlined in "The American Practical
Navigator," Publication No. 9, Defense Mapping Agency Hydrographic Center.
1977 (or later?), also known as Bowditch. This does not help with
ellipsoidal earth computations.
Peter
Peter H. Dana - Department of Geography - University of Texas at Austin
Austin, Texas 78712-1098 - Tel: (512) 869-1450 - Fax: (512) 869-0899
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>Date: Fri, 20 Oct 1995 21:00:24 -0400
>From: [log in to unmask] (Gerald I. Evenden)
>Subject: Re: Heading calculations....
> Date: Fri, 20 Oct 1995 16:10:39 EDT
> From: "Gilley, Charles" <[log in to unmask]>
> Subject: Heading calculations....
>
> I admit my brain hurts, but I have a simple problem, and I cannot
> locate a reference which satisfies me. I have points 1 and 2
> specified in lat/long. What is my heading if I wish to travel from
> point 1 to point2?
>
> I've been told that it's simple trig, but I don't think so.
> Can anyone post the proper equations?
>
> Regards,
> Charles Gilley
> AEL/Cross Systems
Presumable, you want to take the shortest path between the two points.
If so, the answer lies with the inverse solution of the equations
for the "geodesic" or "great circle" path. For the spherical Earth,
the solution is a fairly simple:
Az_12 = arctan{ cos(lat_2)*sin(del_lon) / [ cos(lat_1)*sin(lat_2) -
sin(lat_1)*cos(lat_2)*cos(del_lon) ] }
where Az_12 is the azimuth from point 1 to point 2 and
del_lon = lon_2 - lon_1. Use of the atan2 function is appropriate.
For the reverse azimuth from point 2 to point 1, exchange the
arguments in the equation.
Note also, that except for a couple of unique situations, the azimuth
of your path as you travel from point 1 to point 2 varies.
For the solution on an elliptical Earth, I suggest you use a program
like *geod* in the PROJ.4 distribution of kai.er.usgs.gov .
Gerald (Jerry) I. Evenden Internet: [log in to unmask]
voice: (508)563-6766 Postal: P.O. Box 1027
fax: (508)457-2310 N.Falmouth, MA 02556-1027
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