Precise Compass Correction

[HenryC]

Please forgive me if I have previously published this article here.  I did a search for it and couldn't find it, but its possible I did publish it under another name. At any rate, I hope you find it useful.


MERIDIAN COMPASS CORRECTION WITH THE NAUTICAL ALMANAC

by Henry Cordova

Even in today's world of push-button navigation, the prudent mariner still relies on the magnetic compass. This is certainly the case while at the helm, although even an error of a few degrees here would probably go unnoticed .  A fix every few hours, or offshore, every few days, is all you really need to get you where you're going.  But what about your bearing compass?  Here precision is everything, whether you are taking anchor bearings or piloting along a dangerous coast.   Besides, a good hand-held bearing shooter is usually the only backup we may have aboard for the main steering compass.

Fortunately, extremely high quality hand-helds are now available at reasonable prices, but occasionally, they too must be calibrated if for no other reason than peace of mind.  The same can be said for flux-gate devices.  Even my trusty Mini 2000 failed me just the other day; after a long period of inactivity and storage the card seized up and would not turn.  I eventually broke it loose by tapping and shaking until the rose broke free and spun on its pivot.  Still, it now has an intermittent tendency to stick and jam, and it rotates sluggishly.  I can never trust that compass again, it must be replaced even if it should resume normal function in the future.  When my new hockey puck shows up in the mail, I will calibrate it using the only foolproof method, the stars.

Compass adjustment is best left to professionals, but every seaman should be familiar with some basic testing techniques.  Most weekend sailors are perfectly capable of determining if their compasses are off, but in an unfamiliar harbor, or at sea, the procedure should be a bit more formal and requires some drill.  The way to determine if  your compass is pointing in the right direction is to compare it with a fixed reference mark of precisely known azimuth.  Astronomical objects  fit the bill and they are always available, anywhere, anytime.  Astronomical compass checks require four things, the sky must be clear, you must know your position, you must know the time, and you must have a Nautical Almanac.  The fundamental procedure is to do a sight reduction for the celestial body using your known location as an assumed position and deriving the azimuth for that time and comparing it with your simultaneous bearing on the body.  If you are already confused, you are probably not alone, we have all let our navigational skills get rusty lately, but fear not.  There are shortcuts, and under some circumstances, the procedure can be considerably simplified.  For starters, we can eliminate the sight reduction step altogether by selecting a time when the body has a known azimuth, either due north or south. 

When an object is either due north or south of us it is said to be on the meridian,  the imaginary line that runs from horizon to horizon from north to south,  passing directly through the zenith overhead.  As the earth turns, every celestial body crosses your meridian from east to west.   Objects near the celestial poles (those places in the sky which are directly over the earth's north and south poles) appear to rotate about the poles.  For example, the north star,  Polaris,  (not directly at the pole but about a degree away) describes a little circle about the pole of a diameter roughly equivalent to three full moons.  Consequently, Polaris and other circumpolar stars never set, they cross the meridian twice during a twenty-four hour period. The same situation occurs for southern hemisphere observers, although they see stars revolving about the south celestial pole, instead.  Unfortunately for our friends down under,  there is no bright star comparable to Polaris near the south celestial pole.


Compass Check by Polaris

For northern hemisphere sailors, Polaris can be used for a rough compass check whenever it is visible since it is never more than about two thirds of a degree away from the meridian.  Its meridian distance varies from 359.3d to 0.7d, being exactly zero twice a day.  By the way, even the most astronomically challenged sailor can easily find Polaris by looking  north.  It's distance from the horizon is roughly equal to the latitude.  For example, a Florida sailor would look about 30d above the northern horizon and the star in that general area brighter than all it's nearby companions is Polaris.   Incidentally, Polaris, although brighter than it's neighbors, is only a second magnitude star, it is not extremely bright, and in any other region of the sky would not be particularly noticeable.  Every sailor should practice this until it is mastered;  not being able to find Polaris in an emergency is simply not acceptable.

For more accurate work with Polaris, you must have a Nautical Almanac and a timepiece.  The Almanac has tables near the back (labeled  "POLARIS  (POLE STAR) TABLES" ) which allow the navigator to determine exact latitude and azimuth.  We are only interested in the latter, so we restrict our attention to the bottom of the page, labeled "AZIMUTH" .  You will note that the horizontal rows of the azimuth table are labeled by latitude zones, five to ten degrees apart, and that azimuths don't vary much from zone to zone, that is, the azimuth is very insensitive to latitude and it is not needed very accurately.  The vertical columns, however, (labled  "LHA ARIES" across the top of the page ) are critical and the azimuth numbers are more sensitive to this value.  The Local Hour Angle of Aries is the angular distance from your longitude to Aries (an invisible point on the celestial equator astronomers use as the origin of their coordinate system), measured to the west.  LHA Aries combines time and space information but don't panic, all you need to know is how to derive this number, not what it means.  The following procedure at first may strike you as cumbersome, but once you work with it for a while and come to understand it you will  realize that, like everything else in the Almanac, this is the way it has to be done.  These guys know what they are doing.

Equation 1:     LHA Aries = GHA of Aries + Longitude        
                                     Longitude is a negative number when west of Greenwich.
                                     Greenwich Hour Angle (GHA) of Aries is taken for the date's Greenwich Mean
                                     Time, GMT, also called  Universal Time, UT;  Almanac left hand daily pages. 
                                     If  LHA Aries  is negative, or exceeds 360d, add or subtract 360d so it falls                                               
                                     between 0d and 360d.

Let's work an example while all this is still fresh in our minds...

It is  10:00PM EDT 4 July, 2003 and we are in Fort Lauderdale, Fl  (Lat approx +26d, Lon approx  -80d, (nearest degree accuracy  is good enough for our purposes).  Fort Lauderdale is in Time Zone -5R, see "Standard Times" in the Almanac. Note conversion to GMT has allowed for daylight savings time correction and change of date.

10:00PM EDT = 2200 EDT = 2100 EST = 0200 GMT,  5 July. 

It is possible to interpolate times between even hours by using the "Increments and Corrections" or "Gray Pages" in the Almanac;  but why bother, make it easy on yourself and do the observation at an even hour.  I like to keep a watch set to GMT so I can check my work, but you can also get GMT from your shortwave, telephone, or GPS.

In the Almanac daily pages for 5 July, the GHA of Aries at 0200 GMT is 312d 39.6m
and using Equation 1:

LHA Aries = 312d 39.6m + (- 80d) = 232d 39.6m

Entering the Polaris/azimuth table at column LHA Aries =  230__ 239 and row Lat =  20  the resulting azimuth is 0.2d.  Subtracting what your compass actually read from what it should have read gives you your total compass error. For example, if the compass reading had been 6.5d, then

Equation 2.
Computed - Observed = Correction
0.2d - 6.5d = -6.3d

Knowing this error gives you the means of establishing the correction to be added to your compass readings to give a true bearing.  You will need to correct every reading by adding a negative 6.3d, or subtracting 6.3d.

Going through this procedure several times will show it to be quite straightforward, in fact you will be able to do it in your head, without paper and pencil.  And once you get the hang of it, you will learn to round off for speed.   In practice, it is difficult to read any compass, even on a motionless platform, to a precision higher than 0.5d.   Looking at some of the nearby entries in the table it should be clear why neither time nor position need be known to high precision in order to use this method successfully.  And remember:  total compass error is composed of both its deviation and the local magnetic variation shared by all compasses in your area. 

Incidentally, an alert reader may have noticed that even though Polaris will never stray further than 0.7d from the north celestial pole, at some high latitudes the azimuth is given in the tables as being 1.7d away from true north.  How can this be?  I shall leave that, as they say, as an exercise for the student...


Compass Check by Noon Sun   

The sun is on the meridian at noon, and either due north or south of us depending on whether it, and the observer,  is north or south of the equator.  Actually, the sun bears due north or south at Local Apparent Noon (LAN),  that is how the term "noon" is defined.  But we measure time as mean time, not apparent time, and noon for the sun may differ from the noon on our clocks.  There are astronomical reasons for this, the sun's motion across the sky varies in speed throughout the year due to the shape of the earth's orbit but we can't build clocks that do this; so we rely on an imaginary average or "mean" sun for our timekeeping.   The trouble is that we must make our observations on the real one.  Fortunately, the Nautical Almanac can help us here.  Printed at the lower right hand corner of each right hand daily page is the GMT of meridian passage (LAN) to the nearest minute for the real sun for the days on that page.  For example, on 3, 4, and 5 July of 2003 the sun will hit high noon at 1204, 1204 and 1205, respectively.  An inspection of the solar meridian passage times for other dates will show that the sun can be either early or late for its noontime appointment by as much as a quarter of an hour.  This difference between LAN and 1200 Local Mean Time  (LMT)  is called the "equation of time", and is also listed to the nearest second in the Almanac, but we don't need this high an accuracy for our purposes; time of meridian passage will do.

To further complicate this, although  the Almanac gives us the GMT of LAN at Greenwich, we must determine it for our longitude.  We are fortunate that the time of meridian passage varies from day to day slowly enough that simply picking the date nearest our own is accurate enough.  You'll never be more than a minute off, so we can ignore this.  However, the longitude shift is another matter.   Also, we need to go out and do our observation at some time we can determine from our local clocks, and we are a long way from Greenwich.  The reasoning goes something like this.

We want to check our compass at LAN, when the sun is crossing the meridian.  According to the Almanac, this will be LMT 1204, so that is good enough for Ft. Lauderdale in our example.  An observer near the international date line would be far enough from Greenwich that he might want to pick the time for 5 July, but an error of even a minute is insignificant for our purposes, it amounts to a quarter of a degree, so let us ignore that situation.  We need to know the mean time in Greenwich when it's local noon in Lauderdale, so we use the following:

Equation 3
GMT = LMT - Longitude    

And remember W longitudes are negative, and that we must convert -80d to time units using the "Conversion of Arc to Time" page in the back of the Almanac:  -80d = -(5h 20m).  Substituting in equation 3:

GMT = 1204 - (- 05h 20m)  = 1724   

At 1724 GMT, you will be experiencing LAN in Fort Lauderdale.  If you don't keep GMT, this is 1224 Eastern Standard Time, (EST), or 1324  Eastern Daylight Time (EDT).  It is a good idea to start observations a few minutes early and continue them for a few minutes after the predicted times;   especially for the observer in our example: the sun is almost directly overhead in Ft. Lauderdale in July and taking a bearing is going to be awkward.  Using shadows from vertical objects helps.

Determining compass error is done as before, using equation 2.  The computed azimuth in our example is always 180d for North American residents since they live north of the Tropics.


Follow-up

The exercises above can be repeated using other bodies and to extraordinary precision, if required.  Many other similar calculations over and above traditional celestial navigation can also be performed with the data so compactly stored in this remarkable book, once you learn to use it.  It is also self-contained, containing complete instructions for its own use.  The Nautical Almanac is perfect evidence of what a well-managed government bureaucracy can do, we are getting our tax dollars' worth!  You will  find that after studying  it you will become a better all-around seaman because it puts you in touch directly with the natural Universe we sail, something no keypad and display can do.  The Nautical Almanac provides a wealth of  information of value to navigators, astronomers, geographers and surveyors.  In spite of its medieval Arabic terminology, it is far from being a relic of a bygone low-tech era,  it represents centuries of accumulated scientific and mathematical progress, and is itself produced with the most up-to-date methods.  Today it is also available in a variety of digital formats.  Don't leave home without it.



Acronym Glossary

LAT  - Local Apparent Time      (Your time, according to the real sun)
LMT - Local Mean Time             (Your time according to the mean or average sun)
LAN  - Local Apparent Noon    (When the real sun crosses your meridian)
GMT - Greenwich Mean Time    (LMT in Greenwich, England.  Also called Universal Time, UT)
GHA - Greenwich Hour Angle   (Angular distance from the Greenwich meridian, west to a celestial body)
LHA - Local Hour Angle            (Angular distance from your meridian, west to a celestial body) 
EST - Eastern Standard Time     (The LMT of the central longitude of the Ft Lauderdale time zone)
EDT - Eastern Daylight Time     (Ft. Lauderdale's Daylight Savings Time, EST + 1 hour)   

[HenryC]

It has been pointed out to me I did actually post this here previously, but that I removed it because of potential copyright issues.  However, it seems highly unlikely I will ever publish this anywhere, so I am putting it in again for your use.  The ubiquity of GPS is even making use of the magnetic compass obsolete and "old fashioned" (at least, among power boaters).