(EDITED) Running fixes

[HenryC]

Navigating with chart and compass should be part of every sailor's tool kit,  I suggest if you are rusty with the basics, you review my articles at

http://cpyoa.geekworkshosting.com/forum/index.php?topic=4274.0



Running Fix

If two landmarks on shore are not available for triangulating a position, the sailor often uses a technique called a running fix.  It is not necessarily an exact fix, or position, but it is usually a very good estimate, and it certainly is better than nothing!

If only one landmark on the chart is visible from your boat, take a bearing with your handheld compass ( or briefly point your bow at it and note your steering compass reading).  Draw that bearing on the chart to the landmark, using the compass rose to get the angle right.  At that moment in time, you are somewhere on that line, although you don't know exactly where. Note the time, and determine the speed of your boat as best you can, using your speed log or by dropping debris off the bow and timing how long it takes for it to drift past your stern.

Sometime later, after the bearing has changed substantially (at least 20-30 degrees) take another bearing and write it down, and the time.  Draw that bearing on the chart, and determine your distance traveled (distance = speed x elapsed time).  Now using your parallel rulers, advance your first bearing line along the course line (slide it down your course without changing the angle) for a distance corresponding to the time elapsed.  If you have stayed on course, and if your speed estimate has been accurate and constant, where the two lines cross will be your position.  (Of course, we are ignoring the effects of current and drift.)  Like I said, this is an estimated position, not a precise fix. If for some reason, you can't get a second bearing, advance your first bearing along your dead reckoning course line (using your parallel rulers and dividers) for a distance corresponding to the time interval you want.  Where it crosses your DR track is your estimated position.  Its not precise, or even as good as a two bearing running fix, but its better than nothing.

EDIT: A running fix can also be used to advance a Line of Position (LOP) from one bearing off a landmark to another LOP off ANOTHER landmark.  (It is assumed both landmarks are not visible simultaneously.)  In fact, you can advance LOPs from different observations hours or even days apart, developed with totally different methods.  I have used running fixes where LOPs were combined from Loran, Celestial, Radar and visual bearings taken over a course of many hours.

Doubling the Angle

However, there is also a type of running fix that requires neither chart nor compass.  It is suitable for rough eyeball navigation, or if you are in a boat with no navigational equipment aboard, such as a kayak.  However, it still relies on you being able to make a rough estimate of your speed.

Note the angle off the bow of some landmark on shore, say a tree or building.  If you don't have a compass, use a clock system (two o'clock, four o'clock, and so on).  Maintain your course and speed as closely as possible and some time later, when the angle has doubled,   your distance (as the crow flies) to the landmark is the same as the distance you traveled between the two measurements.  So if you traveled two miles in the time it took the bow angle to double, you are now two miles from the landmark

Bow and Beam Bearing.

A special case (actually, a simplified case) of Doubling the Angle is the Bow and Beam Bearing.  In this case, note the angle off the bow of the landmark, and mark the moment when that angle is 45 degrees off the bow (as viewed from the helm).  You can designate some item of deck hardware, a cleat or stanchion, to mark the angle and help you remember it.  Continue along your course and speed until the landmark is directly on the beam.  At that moment, the landmark will be as far away from you as the distance you traveled between observations.

Pep Talk and Obligatory Stern Warning

Both of these methods depend on trigonometry, but you don't need to know that.  Just study the pictures and think about it.  If you have even the simplest and most rudimentary equipment aboard, Bow and Beam and Doubling the Angle will be unnecessary, you will probably never need to know them.  However, I guarantee if you are a novice sailor just studying these examples and looking at the diagrams will give you an understanding of the piloting process that will come in extremely handy.  Running fixes are used with all navigation methods, even celestial, as advancing a line of position using dead reckoning.  It is a way of including at least one direct measurement into what would otherwise be just an estimate or educated guess.

When sailing on a small lake, it doesn't really matter all that much.  But on any large body of water, this knowledge could save your life.  You have no idea how quickly and completely you can get disoriented and sail off the edge of the earth.  Yes, it is flat, you know?



http://www.marshallmarinegroup.com/images/18b.jpg    (bow and beam bearing)
http://i.ytimg.com/vi/tmQRCHLSq0M/maxresdefault.jpg   (doubling the angle)

The links above will direct you to illustrations that will help explain the text.  Google them and the image feature will give you plenty of other diagrams and explanations

[GeeW]

Thank you for that. I enjoy your articles.

Gordon

[tmw]

Nice explanation.  It's pretty neat how isosceles triangles can help with navigation. 

The running fix is the one I remember most fondly in navigation class, although I understand it is difficult to do accurately, factoring tides into the speed.  Ironically, I thought I could just use a GPS tracker (via phone) to get a precise speed over ground for the running fix, although that defeats the purpose.

Thank you for sharing.

[HenryC]

 A GPS tracker, via phone?  Surely you're joking, Mr Feynman. Your giving this old Luddite fits!

If you have a cell phone on board, just call 911.  Tell the operator/dispatcher that your call is NOT an emergency, then ask him or her for your coordinates.  They will be glad to give you a lat and long.

This is not a bad idea to do from some remote outdoor location (not from the city), once a year or so, so you can test their positioning capability.  Most cell phones today are equipped with a GPS chip, and its a good idea to test this capability periodically in case you have to call in an emergency and don't know where you are, or are not capable of speech due to injury or some other reason.

If you call from the city, the computer at the dispatch end may only return a street address instead of geographical coordinates.  I used to work for my county's 911 system, but they are upgrading systems all the time so its a good idea to run an independent test every now and then.