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

#1 User is offline   robbymcdobby 

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Posted 27 November 2007 - 12:41 PM

I need some help. I've encountered several multi-caches that require me to calculate the coordinates to the final using an equation. Here's my question.

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 User is offline   admo1972 

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Posted 27 November 2007 - 12:49 PM

How many feet are we talking? You can simply go to that coordinate, walk however many feet along the given bearing, then search for the cache. You can also use the option in your GPS to project a waypoint. But neither case requires the Earth's radius. Of course, if the distance involved is so great that the curvature of the earth affects it...

#3 User is online   tozainamboku 

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Posted 27 November 2007 - 01:06 PM

Traveling at a constant bearing is called a rhumb line. I believe that fizzymagic's fizzycalc might be able to project a waypoint on a rhumb line.

#4 User is offline   DocDiTTo 

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Posted 27 November 2007 - 04:27 PM

View Postrobbymcdobby, on Nov 27 2007, 12:41 PM, said:

I need some help. I've encountered several multi-caches that require me to calculate the coordinates to the final using an equation. Here's my question.

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 User is offline   fizzymagic 

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Posted 27 November 2007 - 06:06 PM

Yeah, Fizzycalc can do both versions. I am betting that the multis the OP has seen are asking for a projection (head off in a straight line) rather than constant bearing (which eventually makes a spiral if you go far enough).

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.

Posted Image

Posted Image

#6 User is offline   tomfuller & Quill 

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Posted 27 November 2007 - 06:41 PM

If you don't like the fizzycalc, you can try Ed William's Great Circle Calculator. That is the best program to solve my A. Spring puzzle cache (GCWE3D). Solve this cache's location and PM me and I'll let you know if you're right. (Remember to use a colon: between degrees and decimal minutes.)

#7 User is offline   trainlove 

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Posted 29 November 2007 - 10:23 AM

If your GPS can't do 'Projections' then YOU can by using a calculator.
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 User is offline   trainlove 

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Posted 30 November 2007 - 10:35 AM

Without a topographic map you can actually calculate your grid variation using the following method.

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 User is offline   eagsc7 

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  Posted 16 December 2007 - 10:48 AM

View Postrobbymcdobby, on Nov 27 2007, 12:41 PM, said:

I need some help. I've encountered several multi-caches that require me to calculate the coordinates to the final using an equation. Here's my question.

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 User is offline   Harry Dolphin 

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Posted 16 December 2007 - 02:40 PM

Well, I've used the National Geodetic Survey's Forward program for getting coordinates for reference marks and azimuth marks. When the latest 'project two waypoints' cache appeared, I used the Forward program (though it did require converting feet into meters.) It was suggested that using Fizzy Magic would be more simple... At the cache site, I did use my new GPSr's Project a Waypoint ability. Both led me to approximately the same point. Of course, it took me two tries to find the cache. Sneaky hide!

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