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How to calculate new waypoint from coords?


ZeMartelo
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Hi there,

 

I need someone to explain how a new set of coords can be calculated given existing coords and the distance from it in minutes format.

IE

Lets say original position is @ N46° 25.000 W064° 26.000 and the new coords are 14.877 minutes North and 7.137 minutes East of it.

 

What are the new coords and how is it calculated?

 

Thanks.

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Isn't that just a matter of adding/subtracting the offset values to the original coordinate?

 

Which would yield:

 

N46° 25.000 + 14.877 minutes = N 46° 39.877 (add, since both the coordinate and offset are Northings)

W064° 26.000 - 7.137 minutes = W 64° 18.863 (subtract, since it is the coordinate is given in degrees and minutes West and the offset is to the East)

 

Projections given a direction and distance are less trivial and are better handled by a special calculator or your GPSr if it supports that. But that's a different problem from what the topicstarter mentions.

Edited by Orion84
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Isn't that just a matter of adding/subtracting the offset values to the original coordinate?

 

You would think but I dont think it is correct, I have done that but I am not getting the correct results.

 

Thanks for sugesting Fizzycalc Pdop's but it doesnt do this math just the traditional projection based on distance and bearing...

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Ignore the last entry. I added on the West instead of subtracting.

 

Try N46 40.112 W64 18.859

 

I added the offset to the North coordinates and drew a line along that point. I then subtracted the offset from the West and drew a second line. The intersection point should be correct.

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Very very easy to convert decimal value to angle value(deg-min-sec) :

 

14.877 minutes North = 14 minutes 53 sec North

 

7.137 minutes East = 7 minutes 8 sec East

 

Note:

 

0.877 x 60 = 53 sec (round of 52.62)

 

0.137 x 60 = 8 sec (round of 8.22)

 

 

N46° 25.000 = N 46° 15 min 00 sec

 

W064° 26.000 = W 064° 15 min 00 sec

 

Note :

 

0.25 x 60 = 15 min

 

0.26 x 60 = 15 min ( round of 15.6)

 

 

And finally use angle addition rule as usual to find your final coordinates.

Edited by shivia
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the new coords are 14.877 minutes North and 7.137 minutes East of it.
Nobody knows the answer until you explain what you mean by a minute. The first guess would be 14.877 minutes of latitude and 7.137 minutes of longitude, but you're saying that won't give the "correct" results. So what are the "correct" results?
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Yeah, it's not the math, it's the puzzle. The reference to the "wrong" answer is because the cache description is linked to geochecker.com, which allows cachers to check the answers to puzzle caches before actually tromping off through the woods.

 

Interesting puzzle.

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GC1Q14Q is the geocache in question. I'm not that good at solving puzzle caches but once you figure out what they mean by "First Location" and "Second Location", it should be an easy addition/subtraction to get the final coords.

 

JetSkier

 

I would expect First Location to be the posted coordinates... Second location would be the results of the first calculation.

 

I don't agree that it is simple add/subtact. I think you have to create two lines based on the information and find the intersection of those two lines.

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Ignore the last entry. I added on the West instead of subtracting.

 

Try N46 40.112 W64 18.859

 

I added the offset to the North coordinates and drew a line along that point. I then subtracted the offset from the West and drew a second line. The intersection point should be correct.

Call me stupid, but isn't that intersection of lines exactly the same point which you would get if you simply add/subtract the offsets from the coordinate?

 

Let me try to refrase your method in a slightly more formal way (hope I understand it correctly):

The first line you drew is a line that consists of all the points that have N46° 25.000 + offset as their latitude. The second line you drew contains all points that have W064° 26.000 - offset as their longitude. As such the intersection you found has N46° 25.000 + offset as latitude and W064° 26.000 - offset as longitude. Which is exactly the same as what I calculated.

 

I guess you just made a slight error in adding/subtracting, or in drawing these lines and determinating the intersection? How did you do that exactly anyway?

Edited by Orion84
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GC1Q14Q is the geocache in question. I'm not that good at solving puzzle caches but once you figure out what they mean by "First Location" and "Second Location", it should be an easy addition/subtraction to get the final coords.

 

JetSkier

 

I would expect First Location to be the posted coordinates... Second location would be the results of the first calculation.

 

I don't agree that it is simple add/subtact. I think you have to create two lines based on the information and find the intersection of those two lines.

Consider these two coordinates:

 

1) N28 47.000, W81 21.000

2) N28 50.200, W81 19.500

 

What is the North and East Offset from #1 to #2? Would it be as simple as adding/subtracting the values? Would the answer be N 13.2 minutes and E 1.5 minutes? I'm pretty sure it would be.

 

JetSkier

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Consider these two coordinates:

 

1) N28 47.000, W81 21.000

2) N28 50.200, W81 19.500

 

What is the North and East Offset from #1 to #2? Would it be as simple as adding/subtracting the values? Would the answer be N 13.2 minutes and E 1.5 minutes? I'm pretty sure it would be.

 

JetSkier

 

You probably meant N 3.2?

Anyway, that is what I am trying to find out. These coords is it really just a matter of adding/subtracting or theres more to it?

Once I know how the math works I can try to figure out the puzzle.

I didnt mean to bring that puzzle cache into this discussion as it seems that there is an aversion in this forum to talk about any kind of help to solve puzzles.

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There is nothing magic about the math. The coordinates and offsets given are all in degrees and decimal minutes -- dd* mm.mmm. So it really IS just a matter of adding or subtracting once you decide what to add or subtract. No coordinate conversion is required.

 

Since the minutes are in decimal fractions, you really can just add or subtract unless there is overflow/underflow from the "whole" part of the minutes. Just remember that there are 60 minutes in a degree (not 100).

 

Latitude increases as you go north (in the northern hemisphere). Latitude is measured from the equator and will be between 0 and 90 degrees. Longitude increases as you go west (in the western hemisphere). Longitude is measured from the prime meridian (through Greenwich) and will be between 0 and 180 degrees.

 

Now all you need to do is solve the puzzle. And yes, it's poor form to ask for assistance on a puzzle cache in the forums. Not that any of us knows the answer anyhow :rolleyes:

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There is something nonsensical about the math. I know what the puzzle maker probably meant, but unfortunately the way he chose to express it is not correct.

 

Here's a simple little demonstration. Use something accurate like FizzyCalc.

 

Start at N 46 05.000, W 064 40.000.

 

Go 10 miles due East (azimuth 90). Then go 10 miles due North (azimuth 0). Where are you?

 

Now start at the same position and go 10 miles due North. Then go 10 miles due East. Now where are you? Is it the same point? If not, why not?

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No one is talking about miles, and directions. We are talking about coordinates.

 

The reason for getting slightly different results (0.023 minutes offset in longitude) in your example is a standard effect of projecting using a distance and direction. You can simply check this on a slightly bigger scale using a piece of string and a globe. Starting at some point, go one length of string North and then the same length of string West and repeat that the other way around (first West then North), you clearly end up somewhere completely different, because the "circumference" of the earth at a higher latitude is smaller. (Lines of constant longitude converge, lines of constant latitude are parallel)

 

But I don't see the relevance of that in the situation discussed here, which only deals witch coordinates and offsets in degrees (and minutes). Because if you go X degrees to the West and then Y degrees to the North you end up in exactly the same place as when you would go Y degrees to the North and then X degrees to the West (again, easily checked on a globe).

Edited by Orion84
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But I don't see the relevance of that in the situation discussed here, which only deals witch coordinates and offsets in degrees (and minutes). Because if you go X degrees to the West and then Y degrees to the North you end up in exactly the same place as when you would go Y degrees to the North and then X degrees to the West (again, easily checked on a globe).

 

Not true.

 

It requires a larger scale, but the same effect enters. Unless you follow rhumb lines. But your method, with a string, would show the effect. Problem is that going due East is not following a parallel.

 

Doesn't matter for this puzzle in any case.

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I didnt mean to bring that puzzle cache into this discussion as it seems that there is an aversion in this forum to talk about any kind of help to solve puzzles.

 

the aversion is to sharing answers to puzzles for the purpose of avoiding solving them yourself. This is an intillectual conversation regaerding the mathematics of GPS coordinates. IMHO 2 separate issues and perfecectlty acceptable. After all, the puzzle answer may have nothing to do with what you are discussing. Only the CO and previous finders would know for sure.

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Not true.

 

It requires a larger scale, but the same effect enters. Unless you follow rhumb lines. But your method, with a string, would show the effect. Problem is that going due East is not following a parallel.

 

Doesn't matter for this puzzle in any case.

Measuring degrees with a piece of string seems a bit hard to me, since the number of degrees longitude the string covers depends on the latitude.

 

Furthermore: if two people are walking due East (or West), one on X degrees latitude and the other on Y degrees latitude, I would say their paths are in parallel. For instance, one might be walking along the equator, the other along one of the tropics. They would both be walking due East (or West), and for as far as I know, these lines are definitely parallel? Correct me if I'm wrong, but please explain it, in stead of just saying it's not true, so we can all learn something ;)

Edited by Orion84
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Furthermore: if two people are walking due East (or West), one on X degrees latitude and the other on Y degrees latitude, I would say their paths are in parallel. For instance, one might be walking along the equator, the other along one of the tropics. They would both be walking due East (or West), and for as far as I know, these lines are definitely parallel?

You are correct that if two people are walking at the same longitude due East they have parallel paths. At that instant. However, if they keep walking straight their paths will eventually cross.

 

Of course, since they are confined to the surface of the Earth their paths cannot be straight. By "straight" I mean this: suppose Oscar is at the Equator and Joe is at 45 degrees North. Each points a laser due East parallel to the surface of the Earth. The two laser beams are parallel. They each start walking in a line such that their laser beam is always either directly overhead or directly underneath. Their paths will quickly be non-parallel, and in fact will cross in 6000-plus miles.

 

In order for their paths to remain parallel, Joe has to keep turning to the left so that he is always walking along the same latitude. That path is known as a "rhumb line" and is not straight.

 

It's not easy to visualize, but it's true! Spherical geometry can be non-intuitive, which is why UTM is so popular. Unfortunately, the Earth is (approximately) a sphere, so we are stuck with it.

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It's not easy to visualize, but it's true! Spherical geometry can be non-intuitive, which is why UTM is so popular. Unfortunately, the Earth is (approximately) a sphere, so we are stuck with it.

True. What I am really having a hard time visualizing is the meaning of an offset in degrees (minutes in this case) when traveling along the straight line due east (rather than along the rhumb line, which is what everybody initially assumes). Any suggestions?

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It's not easy to visualize, but it's true! Spherical geometry can be non-intuitive, which is why UTM is so popular. Unfortunately, the Earth is (approximately) a sphere, so we are stuck with it.

True. What I am really having a hard time visualizing is the meaning of an offset in degrees (minutes in this case) when traveling along the straight line due east (rather than along the rhumb line, which is what everybody initially assumes). Any suggestions?

Me too, hence my comment. The puzzle author's statement doesn't make sense unless he meant rhumb line.

 

BTW, rhumb lines are straight on Mercator and related projections. People tend to think in those projections, so we tend to think along rhumb lines.

 

Here's a neat one to ask people: what direction is it from London to Los Angeles? That is, if you had a laser that could go through the Earth, what direction would you point it from London to hit LA? (ignore the up-down component).

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You are correct that if two people are walking at the same longitude due East they have parallel paths. At that instant. However, if they keep walking straight their paths will eventually cross.

 

Of course, since they are confined to the surface of the Earth their paths cannot be straight. By "straight" I mean this: suppose Oscar is at the Equator and Joe is at 45 degrees North. Each points a laser due East parallel to the surface of the Earth. The two laser beams are parallel. They each start walking in a line such that their laser beam is always either directly overhead or directly underneath. Their paths will quickly be non-parallel, and in fact will cross in 6000-plus miles.

 

In order for their paths to remain parallel, Joe has to keep turning to the left so that he is always walking along the same latitude. That path is known as a "rhumb line" and is not straight.

 

It's not easy to visualize, but it's true! Spherical geometry can be non-intuitive, which is why UTM is so popular. Unfortunately, the Earth is (approximately) a sphere, so we are stuck with it.

What you are saying is that walking due East (or West) is not the same as walking along a line of constant latitude?

 

That does not seem to match what I read at wikipedia:

All rhumb lines spiral from one pole to the other unless the bearing is 90 or 270 degrees, in which case the loxodrome is a line of constant latitude, such as the equator.

 

If you walk along a line of constant latitude, that means that only your longitude changes. That is what I would call walking due East (or West) (since the N part of your position does not change, only the E (or W) part). And The Wikipedia article on rhumb lines seems to agree with me there? Or are you saying that these rhumb lines are not an accurate representation of spheric geometry?

 

Edit 1: I just did some projections using fizzycalc. Projecting at a 90 degree bearing for large distances, and indeed, latitude changes, as you mentioned. So according to FC you would be right and my definition of walking due East is incorrect...

 

Edit 2: My GPSr shows the same phenomenon and creating two waypoints in Mapsource that are on the same latitude does not result in a 90° bearing from one to the other. So apparently following a 90° bearing is indeed not the same as following a line of constant latitude. I still can't really grasp why, but I do see that something might be wrong in my original idea of "going due East" :D

 

Well, never to old to learn something new, ey ;)

 

Anyway, I guess we can safely asume that if someone gives you such an offset in degrees, you can just determine the destination by adding/subtracting. Either because the scale is to small to show significant error, or because that is exactly the way the offset is calculated in the first place.

Edited by Orion84
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What you are saying is that walking due East (or West) is not the same as walking along a line of constant latitude?

Yes. A line of constant latitude requires that you continually turn.

 

That does not seem to match what I read at wikipedia:
All rhumb lines spiral from one pole to the other unless the bearing is 90 or 270 degrees, in which case the loxodrome is a line of constant latitude, such as the equator.

It does match, as it is describing rhumb lines.

 

The problem is that North always points at the North pole. As you walk in a straight line, the position of the North pole changes in relation to you, so the direction of North (and thus the other directions) change as well.

 

To always be heading East, you always have to have the North pole on your left; as you walk, it moves and you have to turn to keep it on your left.

 

The answer to the question I posed in my last post is: Los Angeles is northeast of London. That seems very counterintuitive, but it is true; if you were to point straight at LA while standing in London, you would point somewhat down in a northeast direction! I made a couple of images that help illustrate this. Here is a Mercator projection of paths between London and LAX:

MapSm.jpg

 

The "straight" line looks like the yellow one, right? Now look at it on a sphere:

GreatCircle1Sm.jpg

 

And another view that makes it clear why the great circle is "straight:"

GreatCircle2Sm.jpg

 

I hope these are helpful...

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