Another Waypoint Question

[+ScubaAl]

Ok folks,

Here is another waypoint question(I don't want the answer to a problem, just help in finding the solution). This problem involves 3 waypoints, two locations are know. From these 2 waypoints I'm given the heading from each to the new waypoint, but no distance. Also neither of the headings are 90's. So I need to find the distance from both to the third waypoint(where the 2 headings intersect).

I did place the 2 known waypoints on Mapsource and do waypoint projection out to a point that the 2 intersected, but don't think this is all that accurate.

Has anyone worked on this type of problem? I sure could use a bit of direction. Did check out google with not much luck.

If you are able to help, Thanks for your time, Al

[+webscouter.]

If the two points are reletivily close you can use basic trig to find the point. You can figure the distance between the two known points. You can also figure out the relative angle from 0 degrees between the points. (North is 0 or 360 degrees) Then by adding the heading to the found angle you will then know the angle degree to the unknown point. Then using your ASA math you can find the distance to the unknown.

 

Any way that is how I do it, if I have explained it at all.

[+Pasha]

Webscouter types faster than me. To flesh out what he said - you've got the right idea- where they intersect is the place you want to be. To get it exactly, what you need to do is figure out the distance between your first two waypoints as well as the exact angle that the bearings you're given make to the line between the first two waypoints. Then you can use the Law of Sines to figure out the distances between the first two waypoints and the third waypoint. The BBC has a nice page on the Law of Sines.

 

Converting those numbers to lat/long coordinates is another thing entirely, I guess.

[+ScubaAl]

Thanks for the quick replies,

 

Using Mapsource the distance between the 2 known points is 3.888 and the heading from the 1st to the 2nd is 101 degrees.

I guess in a perfect world there would be a website or program that I could just install the known info and have it spit out the needed information.

Maybe I need to shop for an idiots guide to trig.?

Al

[+CompuCash]

you could also do it with mapping software - and I belive it would be accurate.

 

placing the two known points would be easy.

 

Then when you draw a line it tells you your bearing for the line -

 

the intersection has to be accurate.

 

I use Delorme topo

 

cc

[+blindleader]

You can also do it mathematically in a number of ways:

1: Convert the coordinates of the two waypoints to some plane system such as UTM. Drag out your high school algebra knowledge and calculate the intersection of two lines. (don't forget to allow for the difference between grid North and True North). You can find the necessary formulas in numerous places by peeirng down the throat of Goggle.

2. Download compsys21 from the FAA and let it do any kind of intersection you want on a variety of versions of the Earth's surface.

[+EScout]

You can do this in the field with just your GPSr, and no compass or map or calculator. I am assuming the third point you are looking for is fairly close, not miles away.

1. Enter the two waypoints. Name them something like 001 and 002.

2. Write down the reciprical bearings of each. (Add 180 if the bearing is less than 180, subtract 180 if the bearing is over 180. For example if the bearing is 120, the reciprical is 300 degrees.)

3. On your Garmin, go to the find waypoints page and find your 2 waypoints. Starting at one waypoint, as you travel along its bearing toward the third point, you will keep the bearing shown on the page equal to its reciprical.

4. Scroll to the second waypoint on the find waypoints page. When the bearing shown on the page equals the reciprical bearing for this waypoint, then you are at the third waypoint.

 

Note: On the find waypoints page: Garmins update the bearing to a waypoint as you move. On Magellans, you need to scroll to another waypoint to get updated bearings as you move.

[+larsl]

Webscouter types faster than me.  To flesh out what he said - you've got the right idea- where they intersect is the place you want to be.  To get it exactly, what you need to do is figure out the distance between your first two waypoints as well as the exact angle that the bearings you're given make to the line between the first two waypoints.  Then you can use the Law of Sines to figure out the distances between the first two waypoints and the third waypoint.  The BBC has a nice page on the Law of Sines.

 

Converting those numbers to lat/long coordinates is another thing entirely, I guess.

...but remember that this only works when the three waypoints are so close together that the world is approximately flat between them, and even then it doesn't give an exact result.

[+Pasha]

Well... unless you're talking about 100 miles between waypoints, the error from using the law of sines would be well within the EPE of the GPSr. A significant elevation change between waypoints would also mess up the results.

 

That brings up an interesting question - do products such as Mapsource correct for earth curvature when doing waypoint projection and such? I assume they do since they're based on lat/long.

 

Practically speaking, I wouldn't bother with the math when faced with trying to find the cache at WP3; I'd just do what the OP did and fire up Mapsource or use the reciprocal bearing method. With most cache-related problems like this, the waypoints are within walking distance so the error introduced likely wouldn't matter much, but for longer distances... But he asked for a more precise method, so here we are.

[+ScubaAl]

Here is what I did, using Mapsource I entered the two known points. Using GeoCalc I did two waypoint projections using the given headings from said waypoint. I had to used 5 miles as the distance so I would be out past there intersection. I did the same projection using my Garmin 76cs is gave me a slightly different locations, so I ended up with different waypoints based on their intersections.

This morning I went out searching, no luck. We had about 8"of snow yesterday and this made the search a little harder. I did look around any near by places that had the right look to them, but with no luck.

I have been in contact with the cache owner and he did tell me I was in the right area. He also told me the cache was winter friendly. He also offered to evaluate my coordinates, but I wanted to do the search frist to see if I might be right.

So that is where I'm at. I will email the owner to see if I'm even close. Thanks again for everyones input.

Al

[+CharlieP]

Looks like everyone has a different way of doing this. I use the map page of my Garmin GPS76 and the Measure Distance function, which also does bearings. In a problem like this involving intersections, I get a general idea of where the intersection is on the screen, and then plot a couple of points on the bearing near the intersection to define a line from each of the 2 given waypoints. Then I can estimate where the lines cross and put a point there. You can check your accuracy by using the Measure Distance function to check the bearings from the intersection. I think this is similar to what you are doing and it works well if the distances involved are less than a mile. As the distance gets large, you need more than the .5 degree accuracy the GPS gives, since at one mile .5 degree is about 45 feet, at 5 miles 220 feet. When required, I swing the bearing around the point on the map page to see where it changes and use that to estimate fractions of a degree.

 

Oh yeah, make sure you are using True or Mag bearings as specified.

Edited March 20, 2005 by CharlieP