The Value of a Coordinate

Have you ever been out geocaching only to find that the advertised position of the cache is different from its location? Have you ever stood over a cache with your GPS and take new coordinates to send to the cache owner because they were different from what was advertised? Well, they might not have been that far off in the first place. With the following information, hopefully you will be able to figure out how far off the coordinates are by simply looking at the two different sets of coordinates.

Nothing is perfect. As great as we may think the GPS system is, it does have some errors. One error is caused by ionospheric interference. In the civilian world, radio waves from a GPS satellite are transmitted to us at about 1575 MHz. As these waves enter the atmosphere, they can be bent slightly and slowed. The military has the ability to pick up a second frequency, compare the two, and determine the amount of this error to cancel it out. In our civilian world the GPS system will try to predict the amount of error with an atmospheric model to reduce it. This error can change depending on the day, time of day, or even the position of the satellites you are receiving. Your GPS will not give you an indication as to the amount of this error.

A second error your GPS will have is caused by satellite geometry. The frequency we receive will only follow “line of sight.” It will not go through buildings, mountains, or even heavy foliage. If you are not receiving enough satellites, you will have some error. You need to be receiving at least two or three satellites to get a reading. Four is even better, which will then give you your altitude. We can determine how many satellites we are receiving and how well we are receiving each one by looking at the satellite page on your GPS.

A third error that we can experience is caused by reflected or multi-path signals. If you are caching in the vicinity of cliffs, mountains, or buildings, some of the radio waves may be reflected by these objects and cause your position to be less accurate than if you were on flat terrain.

So how far am I off if I come up with coordinates that are different from the published ones? I will use as an example a cache that I have with the coordinates of N44*53.343 W93*15.696 (I will use the “*” as the degrees symbol). This coordinate is given to us in degrees and minutes to the nearest thousandths of a minute (0.001). This is how Geocaching.com advertises a cache’s coordinates. Another way you can read this coordinate is in degrees - minutes - seconds to the nearest tenth of a second (0.1); such as N44*53’20.6” W93*15’41.8”. A third way to communicate the same coordinate is in degrees only to the nearest hundred thousandth of a degree (0.00001); such as N44.88904* W93.26160*.

The world is divided into 360 degrees around its edge, just like a compass. These consists of lines of longitude that go from the North to the South Poles. Starting at the Prime Meridian in Greenwich England, each one is measured west 180 degrees and east 180 degrees; for a total of 360. These degrees can be further divided into minutes. As in the example of a clock, there are 60 minutes in an hour. Each minute can be further divided into 60 seconds, giving us the three different ways to look at the same coordinates above.

In our degrees only,coordinate of N44.88904*, I can convert this coordinate to degrees - minutes by taking .88904 x 60 = 53.343. This gives us N44*53.343, the format we recognize at Geocaching.com. To look at it in degrees - minutes - seconds, take .343 x 60 = 20.6 seconds. This gives us N44*53’20.6”. I will use degrees - minutes, since that is what we most often use with geocaching.

Lines of latitude run parallel to the equator and are measured north and south of it 90 degrees each way. There are still 360 degrees around the world in this direction as well, but lines of latitude have no end to them, so we just look at them in 90 degree increments north and south of the equator. If there was a cache attached to the North Pole, its only coordinate it would be N90*. No longitude is needed because all lines of longitude meet at the North and South Poles.

How far is it between each degree? That can be a constant distance if you are looking at latitudes, but the distance between longitude varies depending on which latitude you are at, as these get closer to each other and eventually meet at the poles. One minute at the equator equals one nautical mile; which is 6076 feet. One degree would then equal 60 nautical miles; or 364,560 feet. Divide this number by 5,280 (which is feet in a statute mile) and you get 69.05 statute miles in one degree.

So if one minute equals 6076 feet, we can now continue dividing by the powers of ten to get this number even smaller. Basically, we are moving the decimal place to the left. Each tenth of a minute = 607.6 feet; each hundredth of a minute = 60.76 feet; and each thousandth of a minute = 6.076 feet. If your GPS gives you a latitude coordinate of N44*53.344 at my cache listed above, which is only .001 minute off the advertised coordinate of N44*53.343; the difference is only about 6 feet.

Remember how I said that the distance between degrees of longitude gets smaller as they near the poles. In my example cache location above, which is in the Minneapolis area, the latitude is almost 45 degrees north. This is about half way to the North Pole. According to my GPS (which is a Garmin eTrex Venture) it figures one degree of longitude in this area to be equal to about 259,200 feet. This, divided by 60, gives us 4,320 feet per minute. By dividing by the powers of ten again, each tenth of a minute = 432.0 feet; each hundredth of a minute = 43.20 feet; and each thousandth of a minute = 4.320 feet. In the coordinate above, if your GPS said W93*.15.697, which is .001 of a minute off the advertised cache coordinate of W93*15.696, there would only be a difference of about 4 feet.

Something else that you may find interesting; if the world is a circle, and if a circle has 360 degrees around it, and we know that each degree is about 69 statute miles, how far is it around the world? Take 360 x 69 = 24,840 statute miles around the world! How far is it straight through the world? If the circumference of the world is 24,840 statute miles, then we can divide the circumference by “Pi”, which is 3.1416..., and get a diameter of about 7,907 statute miles straight through the earth.

If I wanted to dig through the earth, where would I end up? All the cartoons we watched as kids led us to believe that we would end up in China. All we have to do is add or subtract 180 degrees. This takes some figuring since we do not measure the world in 360 degrees, but in sections of 180 east and west, and 90 degrees north and south. Using the cache coordinates above as an example (N44*53.343) the new latitude coordinates would be south of the equator at S44*53.343. And for longitude, my example cache is at W93*15.696; subtract 180*, which comes to E86*44.304. Where is this? It is southwest of Australia in the middle of the Indian Ocean. If your digging through the earth, as soon as you break through, your hole would fill up with water!

The next time you are out geocaching, keep in mind the errors that can affect your GPS. If your GPS is not getting you close to the advertised coordinates, check it for any indicated errors. Look around for any big objects that might also cause errors. Try to figure out how far off you are by looking at the differences between the coordinates your GPS is giving you and the advertised coordinates. If you find yourself off by a thousandth of a minute, relax, it is only 6 feet north or south, or 4 feet east or west (if you if you are in the Minneapolis area). If you are a hundredth of a minute off, you will be about 60 feet north or south, or 40 feet east or west of the cache.