Bye, Bye, Birdie Part III Robert Reeder
In the past two installments of Bye, Bye Birdie we have used onboard electronic tools to derive our position in the absence of GPS. For this column, we will get back to the basics of paper charts and conventional tools and some navigation fundamentals which are often glossed over in books written for larger vessels—visual bearing fixes.
What follows are three different methods of obtaining a fix from visual bearings to three objects on shore. For these examples I used three prominent landmarks around downtown Seattle. For expedience I took these sights from the small jetty park at Duwamish Head in West Seattle. As it is not possible to determine in any meaningful way what the magnetic deviation will be for a hand bearing compass on a small boat, I will also not account for the magnetic deviation imparted from the concrete and steel construction of the jetty. As we will see, this is quite significant, and reasonably simulates the magnetic deviation you would encounter on board your own yacht.
My three objects for both fixes are the Smith Tower, the Space Needle, and the middle tower of the three television towers on Queen Anne Hill.
Visual Fix with a Hand-Bearing Compass
For the first fix we will use a standard “hockey puck” style handbearing compass. It is important to note that many books on navigation (and most USCG licensing exams) presume that the navigator is using an alidade mounted on the ship’s steering compass to obtain visual bearings. While this arrangement allows for excellent information on the magnetic deviation affecting the visual bearings, rarely are steering compasses on small boats mounted in such a way as to make this possible.
For this reason we must utilize a hand-bearing compass. Because it is impossible to hold the compass in exactly the same location relative to various magnetic disturbances on the boat (i.e. electromagnetic fields and structural metal) while taking all of your sight fixes, it is also impossible to create an accurate deviation table for your hand-bearing compass. Absent that, we must simply proceed as though there were no magnetic deviation, even though this is rarely the case; the errors introduced this way can be significant.
I will first demonstrate the “standard” method of plotting a three-bearing fix with a hand-bearing compass. Then we’ll do the same sights again using a sextant and a three-arm protractor. Lastly, we’ll synthesise these two techniques, to obtain a much easier and more accurate fix from our hand-bearing compass than is possible with the standard method.
Method 1: Hand Bearing Compass
We begin by simply shooting the three bearings with our handbearing compass and recording them. Smith Tower bears 063° Space Needle bears 029° Middle of the three towers on Queen Anne bears 005°
Using NOAA’s Nautical Chart 18450, we can calculate that our magnetic variation in 2017 is 15° 50’ East (in 2012 it was 16° 45’ East, decreasing annually by 11’ as noted in the charts compass rose). We round this up to 16° East, and add this East variation to
our compass bearings. Remember the mnemonic Can Dead Men Vote Twice at Elections (Compass, Deviation, Magnetic, Variation, True, Add East). When correcting from Compass bearings to True bearings, we add East deviation and variation, and subtract West deviation and variation. As we have eliminated deviation from our calculation, simply add East variation and subtract West variation. We’ll discuss deviation and variation in greater detail in another article, but for now just remember that variation is in the world around us and deviation is on our boat with us.
So, our compass bearings corrected for magnetic variation but not deviation are: Smith Tower 069° True Space Needle 035° True Queen Anne Hill 021° True
We plot these using a parallel ruler from the nearest compass rose. We must use the outer, True ring of the compass rose. The inner Magnetic ring is only valid for the year in which it is printed, and in this particular case is in error by one degree; in many cases the error is quite a bit more.
The first Line of Position is drawn across the entire span of Elliot Bay from Smith Tower. In real life we would not need or want to draw this much. Conveniently there is a compass rose right next to Smith Tower on the chart.
We then draw the next two Lines of Position from the Space Needle and the middle TV tower on Queen Anne Hill. These are also drawn spanning the entire bay, for clarity’s sake only.
We immediately see two problems.
The first, which is not insurmountable, is that our position triangle is relatively huge; about a half-mile on the longest axis, for three objects which were all a little more than two miles away. We can still roughly guess the center of that triangle, or with best practices graphically trisect it to determine the geometric center.
The second problem is much more serious and only readily apparent because we are doing a dockside fix and actually do know where we were standing when we took the bearings. This fix is in error by more than an half-mile, which in open ocean would be fine but inside a small bay such as this one, is unacceptable. Worse
yet, if we did not have a position reference external to this fix (the dock printed on the chart, or GPS) we would have no easy way of knowing this. This fix is essentially useless.
This error is due entirely to magnetic deviation caused, in this case, by the steel supports of the concrete dock upon which I was standing to take my bearings, but could just as easily have been caused by something on the boat (anchor gear, electrical current, radio speakers, or any other form of electromagnetic interference). And again, because this is not my actual steering compass, I would be none the wiser until my fix fell apart, and then I would have no safe means of correcting it.
Method 2: Horizontal Sextant Angles
So far we have only used a hand-bearing compass and a set of parallel rulers or other means of moving a parallel line on the chart, both of which are presumably on board most cruising boats even if only stuffed unceremoniously into the navigation table.
Now we are going to add two new tools, which may not yet exist on your boat.
The first is a sextant. Yes, for real, a sextant should be part of the navigation equipment of any vessel venturing far enough away from their home dock that they can no longer see it on a clear day.
That said—and this is a purely philosophical point—if you are using a sextant only as a redundant system to your GPS for navigation, it does not make sense to spend much more on that sextant than you would spend on a small handheld GPS receiver.
The good news is, you can get a perfectly functional Davis Mark 3 sextant brand new for about $60. The better news is, this sextant you get for $60 for obtaining terrestrial bearing fixes in inland and near-coastal waters, is perfectly functional for your celestial offshore navigation. The bad news? None, really, except that the Mark 3 is made of stamped plastic held together with model-airplane glue, and is ugly as home-made sin. But for $60 it does everything a $600 Astra (which is used for some of these photos) or a $2,000 Tamaya sextant will do, and with a bit of extra effort (for celestial navigation) it will do the job just as well. If you aren’t planning to use a sextant regularly as part of your routine navigation (we all probably should, but most of us don’t) then there really is not a good reason to spend more than this. Also, for the purpose of this method of sextant piloting, the Davis Mark 3 is lighter and a bit simpler to use than the more expensive metal varieties. But any sextant at all will do fine for this method.
The only trick is that we are using the sextant turned on its side instead of being held vertically as we do for celestial navigation. And instead of shooting three visual bearings in any order we please, we must choose one object to be the middle bearing. In this example the Space Needle is the easy and obvious choice, but if your objects are spread closer to 120° apart from each other, your choice of a “middle” bearing may be more arbitrary, and that is fine.
Instead of measuring the bearings directly as we did with the hand-bearing compass, we use the sextant to measure the angle between the middle object and the one to the left of it, and the middle object and the one to the right of it. Unlike for celestial navigation, whole degrees are accurate enough for this purpose, we can politely ignore the vernier scales.
We measure the angle between the Space Needle and Smith Tower to be 34°, and then we measure the angle between the Space Needle and the middle TV tower on Queen Anne Hill to be 14°. Again, this geometry is not optimal; in a perfect world I would
want the objects to be about 120° apart from each other. But the geometry in this example is sufficient for a good fix.
We need one more specialized tool, and it is not used for celestial navigation or really much of anything besides what we’re using it for here. It runs about $40, which, coupled with the Davis Mark 3 sextant is $100 total—still less than the cost of a Garmin eTrex. This tool is a three-arm protractor. It has a fixed middle arm, and two moveable arms. The protractor is graduated from 0° to 360° in both directions from the fixed arm.
Once the two sextant angles have been taken, they are “dialed in” on the three-arm protractor. Once dialed in, I find that a small bit of transparent tape to hold the arms in place is really useful. So, with the Space Needle as the middle bearing, we move the right arm to 34° for Smith Tower, and the left arm to 14° for Queen Anne.
Once these angles are dialed in and taped down, simply align the center arm with the center object on the chart, and then slide the center arm down along this object until the other two objects are also under their respective arms. I recommend aligning the object with the largest angle first, in this case Smith Tower.
Once all three objects are under their arms, use the hole in the center of the protractor to mark your chart. This is your fix.
Note that even with rounding to the nearest degree the fix is within 50 meters of where I was actually standing. This technique was once used for land surveying; with a metal sextant and a metal three-arm protractor, the accuracy is literally limited only by the accuracy of the chart cartography.
There is one rare but important circumstance in which this will all fail, and that is when the you happen to be on the same circle as the one which is defined by the three objects you are shooting. This is easily remedied, as I have done here, by ensuring that the middle bearing is closer than the other two. But should you find yourself in this situation, the arms will line up anywhere on that circle. Simply continue down your track for another few minutes until you are no longer on that circle, and then resume taking bearings as you were previously.
Method 3: Hybrid fix using Hand-Bearing Compass and Three-Arm Protractor
So now we come back around to redeeming our hand-bearing compass. And we’re going to do so by throwing away magnetic variation and deviation entirely.
Simply take the raw compass bearings (Smith Tower 053°, Space Needle 019°, Queen Anne 005°), then subtract the right or left bearing from the center bearing. 53-19=34° angle between the Space Needle and Smith Tower, 19-5=14° angle between the Space Needle and Queen Anne. Exactly the same as we derived with the sextant, and plotted exactly the same way with the threearm protractor and you will have the same fix.
Practice with both of these techniques and see which works best for you in each circumstance. I use both my sextant and my hand-bearing compass for coastal chart navigation, and find that each has unique strengths. We will be using both of these tools quite a bit in various ways in future columns. We probably will not discuss the three-arm protractor again here; this is what it does, and it does it very well. Good watch!
The author takes a bearing by holding his sextant horizontally; vertical orientations are for celestial navigation.
Our fix is overly large and not from the point where we took our bearings; the error is due to magnetic deviation.
Shooting the 029° bearing of Seattle’s landmark Space Needle.
As we can, see this method gives us a much more useable fix.
Marking our fix with the 3 armed protractor.
Our 3- armed protractor with our sextant angles dialed in.