Capt. Dan's Coastal Navigation Course: Lines of Position, Fixes, Dead Reckoning

Take a look at the chart to the right; look at line #1. It's the easiest sort of LOP formed by the alignment of two landmarks. In this case, the landmarks are range marks deliberately set up to define this sort of line. When I see those range marks line up (or any two landmarks that I can identify on the chart), I can scribe a line between them and extend it to seaward.

What does that tell me?

It doesn't tell me exactly where I am, but I do know that I am somewhere on that line.

LOP based on a bearing

Unfortunately, pairs of range marks aren't always that easy to find, but you can use any single landmark that is identifiable on the chart. On the chart, Line #2 is just such a line based on a bearing line to a landmark.

The navigator sights the landmark using a hand-bearing compass or estimates the bearing with ship's compass. These are MAGNETIC bearings, which he converts to TRUE.

Remember, everything on the chart is TRUE.

Everything on the earth is referenced to MAGNETIC; however, since you can use the hand-bearing compass anywhere on the ship, we do not attempt to compensate for deviation. We just factor in variation.

How accurate is this procedure?

You'll be given bearings when you take the test, which are very accurate, but onboard, with the ship moving around, no deviation factored in - at best it's + or - a couple of degrees. Not that accurate.

Fixes

All you needed was two LOP's. The intersection was the fix. Draw a small circle around it and that's where you were. Approximately.

For better accuracy, a third LOP could be used. And we've done that with Line #3.

We no longer have a clean intersection but we have a small(we hope) triangle. The convention is bisect the legs of the triangle and draw lines at right angles to the legs into the middle. That's your statistical best estimate of position.

Other fixes

If you can identify two objects on your radar, you can get the range from each and scribe an arc the corresponding distances on the chart. The intersection of the arcs is your fix.

You can, much less accurately, estimate your position with any single LOP or range and the depth. Looking at the chart, if you're on Line #1 and the depth is 9, you know pretty well where you are (if you've figured in tide level).

Before LORAN, that was the best we could do.

Position Estimates

If you have only one identifiable landmark you have only one LOP. If that's all you've got, you can take a bearing and 20 minutes or so later, take another bearing on the same point. Advance the first line down your course based on your speed and where they cross is a rough idea of where you are. Very rough.

Run this short (homemade) movie and you'll get the idea.

BTW, the second LOP in the film just happens to go through a calculated DR point. It's a fluke. The second - or any LOP - could lie almost anywhere.

There's something even rougher called an estimated position, which uses a single LOP and your DR track. You know you're on the line. You hope you're near your DR. I'll show you, but just be glad you're navigating in the days of GPS.

Traditional Location Markings

A fix obtained by at least two LOPs, from GPS or Loran is marked with a circle

A Running fix or Estimated position is marked with a square.

A DR point is marked with a half circle.

All positions are marked with the time of the sighting.

Points to Ponder for Most Accurate Non-electronic Fixes

Take bearings from landmarks where the intersection of the LOPs is between 30 degrees and 90 degrees. (Think of what sort of fix you'd get with one landmark at 180 and the other at 360.

Use close objects rather than far distant ones. The close ones are easier to identify and the bearing is clearer when sighted through the hand bearing compass. Note that you'll have to average the swings, but it is possible to get readings within ą 2 degrees.

Use three LOPs whenever possible.

Do not replot DR from EP or Running Fix. Even a 2-bearing fix is dubious. Back it up with whatever is available including radar range, depth contour, RDF, bobbing the light or other means.

Don't let dark or fog set in without getting a good fix.

Don't approach port or a shoal area without precise knowledge of your position.

Always compare your fixes with your DR. I.e. replot a DR for the time of the fix. They should be very close.

Assume the worst. If you don't know your position with certainty, assume that you are closer to danger than estimated.

Take the conservative route.

What would Bowditch say?

Here's what the Bible of Navigation says about DR. Read all 6 pages and get ahead for next week or read the first two for another take on DR.

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