In this series, I turn the tables and examine the opposite problem - namely you can identify landmarks and objects on a map, but don't know your position. You then use the bearings to known landmarks to identify your position.
Probably the most important concept in doing this is something called a line of postion (or LOP). A line of position is a line on the map on which you are located. You may not know precisely where along that line you are located, but you know you're on that line. Given a line of position, one more piece of information can help you fix your position. I'll consider a number of cases:
1.) A line of position is found by seeing to objects in the distance line up.
2.) Given a line of position that intersects with a natural feature that you're traveling on - say, a coastline, you can use the intersection of that line of position to find your position.
3.) The use of a magnetic compass to find a line of position
4.) The intersection of two lines of position to find a location - called triangulation.
To get you accustomed to the concept of a line of position, I draw your attention to a portion of a chart below that's a closeup of the area near Bar Harbor, Maine. Note the man-made feature of the breakwater extending from Bald Porcupine Island toward Mt. Desert Island (Bar Harbor).
Closeup of a chart showing a breakwater extending from Bald Porcupine Island.
Artist's rendition of a view of the breakwater extending from Bald Porcupine Island.
The navigation pole on the end of the breakwater and the northern tip of the island form a kind of line of position, highlighted by the linear construction of the breakwater itself. By comparing the view of the navigation pole, the breakwater, and Bald Porcupine, you can visually establish your approximate position on the chart. Since you're on the water and this line of position extends to a shoreline that runs perpendicular to this line-of-position, you can figure that you're just a bit south of the depth soundings marking "24" and "7" feet in Cromwell Cove.
Although the above exercise is really one of making a correspondence between what one sees in real life and what is on a chart, it demonstrates that we often establish lines of position visually (or can). Using a compass to extend a line of position is really doing much the same things, except now just using an instrument.
Look at a portion of the chart below. Let's say we start out from Bar Harbor, which is at the upper left-hand corner of the figure. If you look closely, you can see the portion of the chart above showing Bald Porcupine Island and the breakwater. So, you continue paddling south along the eastern coast of Mt Desert Island. This is the shore on the right hand side of the chart below. After paddling some distance, you wonder how much progress you've made.
Across Frenchman's Bay is a peninsula and one of the prominent headlands is called Schoodic Head on the Schoodic Peninsula. This is labeled on the chart below.
Frenchman's Bay, with the east coast of Mt. Desert Island on the left and Schoodic Head on the right.
You want to find your position along the coast, so you take out your compass and take a bearing to Schoodic Head. Your compass reads 100 degrees magnetic. You can use this information to create a line-of-position.
There's a concept called a back-bearing. This in the opposite direction (i.e. 180 degrees) of a bearing. The utility of a back-bearing is that it can be used from a bearing to establish your line of position. It's a fairly straightforward procedure to figure a back bearing. If the angle is less than 180 degrees, the back-bearing is 180 degrees plus your bearing. If the angle is greater than 180 degrees, the back-bearing subtract 180 degrees from your bearing.
So, with a bearing of 100 degrees magnetic, the back-bearing from Schoodic Head is 280 degrees.
Now, what good is the back-bearing? Imagine that you're standing at the top of Schoodic Head and looking at your present position - i.e. the opposite direction from your bearing. Your position lies on this line, which is your back bearing.
To establish this, you basically set-up a bearing on the chart from Schoodic Head that is 280 degrees magnetic and extend that line. This is shown on the figure below. Put the edge of the compass baseplate, and remember that you're now putting the bearing/direction-of-travel line as if you were taking a bearing on yourself from Schoodic Head. In this case, the compass dial is set at 280 degrees, and the parallel lines in the dial are oriented so that the dial is pointed along lines of magnetic north (assuming you prepared the chart as in the earlier discussions).
Back-bearing from Schoodic Head sets up a line of position.
Now, with this back-bearing, we have a line of position extending from Schoodic Head through Frenchman's Bay. Since you're traveling south along the coast of the Mt. Desert, the intersection of this line of position with with the eastern shoreline gives you your position. In this case, it's a point along the coast between Schooner Head and Old Whale ledges (see figure below).
Extension of the line-of-position from Schoodic Head to where it intersects the eastern coast of Mount Desert Island.
Triangulation
The above two examples showed you had to find your location using a line of position and a more-or-less linear feature in the environment: a shoreline. In other circumstances, other linear features could readily substitute for the role played by a shoreline. Examples include a river, a ridgeline, a trail, a road, or any equivalently linear feature. In these cases, you only need to find where a single line-of-position intersects the linear feature. Even something as simple as a contour line on a map when you have a known elevation can fulfill this role, in which case you only need one line of position to establish your location.
We often get into situations where we can't refer to a linear feature. This could be, for example, if you're some distance from land in the water, or if you're bushwhacking in flat woods, featureless woods. In this case, you can find your location if you can take bearings to two identifiable objects with your compass. This is called triangulation.
The concept in triangulation is much the same, except you're looking for the intersection of two lines-of-position. In the figure below, I show a person located at some unknown point in Blue Hill Bay, now to the west of Mt Desert Island. They take a bearing to a high point on the southwest end of Placentia Island. In the figure, the bearing to Placentia is 135 degrees magnetic. So, as before, to extract a line-of-position, we find the backbearing, which would be 180+135=315 degrees and draw a line from the high point we've spotted on Placentia.
Line of position of 315 degrees established from a back-bearing from the high point on the SW corner of Placentia Island.
In the figure below, I show not only the first line-of-position from Placentia, but a second line of position, which is to the northernmost point on the northeast corner of Swan Island. The compass bearing to this point is 180 degrees magnetic, so the back-bearing is 0 degrees (or 360 if you prefer that).
Back bearings from the NE tip of Swan and the high point on the SW corner of Placentia Islands form two lines of position. The intersection of the two lines of position give your location.
From the figure, you can see that the two back-bearings form two lines-of-position. The intersection of the two lines-of-position give your location.
Now, there is always some uncertainty in taking compass bearings. You can only take a bearing to a certain precision. My guesstimates for how precise I can take a bearing with a hand-held backpacker's compass is probably +/- 5 degrees. In this case, the lines-of-position you establish are only good to about this precision. The figure below shows how this translates into an uncertainty of position.
How the uncertainty in two lines-of-position create a "diamond" of uncertainty in position.
In the above figure you can see how the uncertainty in the two lines-of-position create a diamond shape where you're located. You typically can't do any better than this diamond of uncertainty. It does, however, illustrate how you can choose objects to take bearings to that help you figure out your position. If you choose two objects that are close together or are about 180 degrees apart, the diamond of uncertainty will be elongated in the direction of the bearings. On the other hand, if you choose two objects that are roughly 90 degrees apart, this will give you a stronger position from triangulation. Now, it's not always possible to find two objects that are exactly 90 degrees apart, but it helps to get as large an angular separation as possible between the objects to improve the estimate of your position.
The same issue of uncertainty arises when you are establishing your location from the intersection of a line of position with a linear feature, such as a coastline. In this case, the best way to minimize the uncertainty in position is to take a bearing to an object that is roughly perpendicular to the coastline, such as the choice of Schoodic Head in the one example above.
In the next section, I'll talk about range estimation using some simple tricks.
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