Help with GPS coordinate projection

For a personal project (hobby) I’m trying to project lat/lon coordinates from a given starting point. This not really being my strong suit, I’ve been googling around a bit. There are apparently some online calculators that can help with this. Example:
http://www.gpsvisualizer.com/calculators
But I don’t really understand the math well enough to know if I’m using them correctly.

With further research, I stumbled across this (old, inactive) geocaching puzzle:
https://www.geocaching.com/geocache/GC1Q14Q_mga-5134?guid=9a31ba63-c4c8-4c56-9477-891f7d8b7498 which on the surface seems exactly what I want to do.
The problem is discussed in this thread:
http://forums.groundspeak.com/GC/index.php?showtopic=220496.

In post #3 someone suggests simply adding or subtracting the additional info to get the final coordinates. It’s later suggested that projection doesn’t work so simply.

In the end I’m more confused than ever.

My question, the problem as stated and proposed in the geocaching puzzle seems to be exactly like something I need if it is solved as simply as poster #3 suggests, is it?

Lat-long coordinates are simply angular measurements. If you add 3 degrees to a starting measurement of 41 degrees, you get 44 degrees. Exactly; projection is not relevant or involved.

If you’re using decimal degrees, make sure all your terms are expressed that way. If you’re using DD-MM-SS, make sure all terms are expressed that way and remember that 60 minutes rolls over to add one degree, just like 60 minutes of time rolls over to add one hour.

I’m not sure what you mean by “project lat/lon coordinates from a given starting point”. Projecting co-ordinates has a very specific meaning, basically changing the way that they are distorted to produce a 2d map from a 3d real world. That doesn’t seem to be what you want to do.

Do you just want to start at a given point, and then calculate the co-ordinates at a given angle and distance from that point?

What they said… there is no “projection” needed, just lon/lat math.

According to that page:

46° 05’ +14.787’ = 46° 19.787’ N
64° 46’ - 7.317’ = 64° 39.317’ W (you subtract to go East in the Western Hemisphere)

46° 19.787’ N, 64° 39.317’ W is in a field by some road. Seems like a plausible geocache location.

Not sure what the second location is for, but if you do the math (in reverse, starting from the cache you found just now), you get:

46° 6.03’ N, 64° 46.429’ W, which is in the middle of a road by a car dealership. shrug

Yes. You just add or subtract the numbers to get the new lat/long.

The following rules apply:

[ol]
[li]Only add/subtract lats to lats and longs to longs[/li][li]Keep all units the same. (21º 14’ 32" is not the same as 21º 14.32’)[/li][li]Northern hemisphere: Add north to north, subtract south from north.[/li][li]Southern hemisphere: Add south to south, subtract north from south.[/li][li]Western hemisphere: Add west to west, subtract east from west.[/li][li]Eastern hemisphere: Add east to east, subtract west from east.[/li][/ol]

That’s about it.

Nothing much to add to the other replies regarding degree units, but I will say this: if the offset you wished to add were in distances instead of angles, the problem becomes more difficult, because the miles/degree for east-west travel changes based on your latitude.

Among other things, this means there’s a difference between travelling 1000 miles north then 1000 miles east, versus travelling 1000 miles east and then 1000 north.

That seems way too complicated. You just need one rule:

  1. West and south are just the negative of the coordinate. All numbers add.

So instead of 121.9 degrees west, you convert to -121.9. If you want to travel 2 degrees west, you add -2.

Yes, you can do it like that if you wish.

Thanks, that’s what I needed.

To extend Dr. Strangelove’s comments:

We’ll all be better off when the world in general accepts that coordinates are best expressed as a pair of signed decimal numbers.

Yes, [Hemisphere] [Degrees] [Minutes] [Seconds] works, and always has. But -85.5853 is better than W 85-35-07 in pretty much every way except in terms of homage to tradition.

In support of this I’ll note that with little ill effect England some time ago gave up prices such as “6 pounds, 7 shillings, thruppence ha’penny”

I work in GIS and share quite a bit of point data. Decimal degrees is the standard now adays to the point that you don’t even need to ask what format someone wants it in.

For the OP, the last cite seems to be a curious discussion, possibly where some participant were trying to add correct but inappropriate, and thus confusing, information to the question. As pointed out above - if you are using spherical coordinates the question of adding a change in location is trivial if the change is also in spherical coordinates.

Where it all goes messy is where the change is specified as a bearing and a distance, or some other mix of things that involve distance. If I say the target location is 10 miles at 130 degrees true, there are complicating matters (and implicit assumptions) that lead to problems.

If you take out a compass (and ignoring for the moment the difference between magnetic and true north) and you walk or fly a constant bearing, you will trace out a Rhum Line on the face of the Earth. Rhum Lines are obviously useful ways of navigating, as they are easy if you have a compass. Also, if you have a Mercator projection map, all straight lines on the map are Rhumb Lines. However, a Rhum Line is not the shortest distance between two points on a sphere, and does define a straight line on a sphere. A Great Circle is a straight line on a sphere. But a great circle will, in general, require a constantly varying bearing (relative to north) as it is traversed. But it also makes perfect sense (on the surface of a sphere) to define a delta in position as a distance along a great circle. This will define the shortest path to the target location. So defining a delta in position by bearing and distance is potentially ambiguous, and one where the error in position depends upon where you are on the Earth and what direction you are travelling. Which is why, if you can, one avoids doing so. However lots of real world navigation has dealt with such issues on a daily basis for centuries.

The other problem you get is that the Earth is not actually a sphere. The next useful approximation is that it is an oblate spheroid - it is fatter at the equator. Again, if you define position only using spherical coordinates you don’t have any problems. But the moment distance comes into play you yet another source of error to handle. In order to cope, there is an internationally recognised definition of the shape of the Earth, and how it is to be used for defining position. This is the WGS 84. GPS satellites have their position defined relative to WGS 84, and the positions a GPS receiver provides are thus rooted to this definition of the Earth’s shape.

It does however get slightly worse. If you want to use a map, you need to take into account how the Earth is projected onto the flat surface that is the map. This is a huge area, and there is no right answer. However one constant is that a sphere is a rotten thing for many survey tasks, and a lot of the time people really would prefer to work in a coordinate system that is rectilinear. On a small enough scale treating a section of the Earth as flat mostly works, and maps and measurements work out, even when the spherical shape of the Earth is ignored. But you need to define how that flattening is done. And because you can only get away with such flattening for a limited distance, you need lots of places where such flattening is defined. These are the local datums, and every country on the planet has them. Big countries, have quite a few. Where you get into real trouble is in moving from one datum to another, because you inevitably have discontinuities in your locations as you cross. But printed maps are mostly projected using these local datums. These datums provide a local rectilinear coordinate system. (The grid is defined as made up of “eastings” and “northings”, and can be on a feet or metre pitch) Many GPS receivers can automatically provide locations in these coordinates, and are programmed to convert from datum to datum as appropriate. Defining a delta position here is not a trivial issue. Within a single datum it does make sense to talk about x miles east, and y miles north as a delta. If the delta takes you into another datum it gets awful.

As much as you can you always want to work in spherical coordinates, but the grim reality is that there are many tasks for which this still isn’t the best, and coping with local datums and Mercator projections will remain.

For geocaching, it is possible that the issues involved could be enough to render the location of a cache in error enough to matter.

Nitpick: rhumb

A rhum line would likely have something to do with a distilled spirit - perhaps implying that it would not be particularly straight.

:smack: Of course it is. What is worse, I believed the spell checker when I first wrote “rhumb”.
Also, a missing “not” in the following:

“However, a Rhum Line is not the shortest distance between two points on a sphere, and does define a straight line on a sphere”

Clearly a rhumb line does not define a straight line on a sphere.