## Convert distance and constant bearing into coordinate Calling all geo-mathematicians....

### #1

Posted 27 November 2007 - 12:41 PM

If given a starting GPS coordinate, a distance in feet, a degree of constant bearing, and the earth's radius in miles, can you come up with a final GPS coordinate?

The closest thing I can find is the Haversine formula, but that requires knowledge of the final coordinates--which I don't have in this case.

### #2

Posted 27 November 2007 - 12:49 PM

### #3

Posted 27 November 2007 - 01:06 PM

### #4

Posted 27 November 2007 - 04:27 PM

robbymcdobby, on Nov 27 2007, 12:41 PM, said:

If given a starting GPS coordinate, a distance in feet, a degree of constant bearing, and the earth's radius in miles, can you come up with a final GPS coordinate?

The closest thing I can find is the Haversine formula, but that requires knowledge of the final coordinates--which I don't have in this case.

Your GPS can probably do this. It's called projecting a waypoint. Fizzycalc is a great program for doing it on a computer though, as others have said.

### #5

Posted 27 November 2007 - 06:06 PM

I need to finish up my Web pages that illustrate the differences between geodesics (what on a sphere would be great circles) and rhumb lines. I did work up some neat graphics a while back, which I may as well include in this post! They are comparisons of the great circle and rhumb line paths between Los Angeles and London.

### #6

Posted 27 November 2007 - 06:41 PM

### #7

Posted 29 November 2007 - 10:23 AM

Set the GPS to UTM or MGRS if the area is small enough. Since only those are orthogonal.

Set your GPS to 'True' north not magnetic, or Grid north if yours can but I don't think any can do that. If his bearing is in magnetic units then you have to add or subtract the deviation, or is it variation? Can Dead Men Vote Twice, or True Virgins Make Dull Company and East is Least, or West is Most are standard ways to know to add or subtract.

Convert his given distance into meters.

Multiply that by the sin and cosine of his bearing.

Figure out which quadrant it's in, east of north, north of east, south of east, east of south, west of south, south of west, north of west and west of north. And add the sin or the cosince figure to the easting or the northing depending on which quadrant that can be sin for easting or cosine for easting...

But since UTM uses Grid north you will be a bit off. Depending on how far his distance is, it might not matter much since the difference from True to Grid is usually less than a degreee or so, but look at a topo of your area for a general figure you can use for more precision. I'm right at the edge of Zone 18/19 and I don't think the grid north is more than a degree from true, while magnetic is something like 16.75 degrees.

edited to fix a typo.

This post has been edited by **trainlove**: 29 November 2007 - 10:24 AM

### #8

Posted 30 November 2007 - 10:35 AM

Generate 2 waypoints in the area you are going to do your projection in.

One is right here at for example 19T 0265000E 4646000N, yes you have to be in UTM mode for this. The other is exactly 1 kilometer north, so it would be 19T 0265000E 4647000N. You have to have exactly the same easting.

Now go to Lat/Long and you will see that the west coords for both are not identical. Make a route with those 2 points and the bearing from the southern one to the northern one is your grid deviation.

The deviation will only be 0 if you are right in the middle of the zone and it does not matter if you are on the equator or near the pole. It will be the greatest if you are right at the boundary between zones, I'm not exactly sure but I think this will increase the closer you get to the pole.

Time to do an experiment.

### #9

Posted 16 December 2007 - 10:48 AM

robbymcdobby, on Nov 27 2007, 12:41 PM, said:

If given a starting GPS coordinate, a distance in feet, a degree of constant bearing, and the earth's radius in miles, can you come up with a final GPS coordinate?

The closest thing I can find is the Haversine formula, but that requires knowledge of the final coordinates--which I don't have in this case.

Here's a Great site from one of our local cachers...

http://home.comcast.net/~rosco_bookbinder/...onversions.html

The Steaks

### #10

Posted 16 December 2007 - 02:40 PM