Bye, Bye, Birdie Part III Robert Reeder

Passage Maker - - Contents - By 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.

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