Getting Started in Celestial Navigation

[Captain Smollett]

Getting started with celestial navigation is not as difficult as many books and web sites might suggest.  In my opinion, the problem is the approach they use to teach the technique: too much theory and not enough "just do it."  Theory's great and all, and it is a fascinating field of study, but if all you really want to know is where to put the little dot (or set of dots) on your chart, well, knowing that you are solving the spherical triangle and using haversines, etc, does not really help all that much.

In other words, too much emphasis is placed on "ooh, look, here's some hard math that *I* can do...that makes me special."  On the other hand, no matter what method of celestial navigation you are using or what specific technique you use to reduce sights within that method, you will never be good at it (and get good fixes) if you cannot use the sextant properly, which means both precisely and accurately.

(1) To get good results (and not get discouraged and give it up too early), you HAVE to have a properly adjusted sextant.  This means the mirrors must be parallel in their fixed plane.  Instructions for adjusting the mirrors should have come with the unit, but if not, there's bound to be someone with your model online that has written how to do it.  Beyond that, there's always contacting the manufacturer.

You check this by sighting along a vertical object (like a pole or the mast of your boat) and making sure the two halves of the image line up horizontally - for example, the edge of a vertical pole should not "jump" as you move from one mirror to the other (by sweeping the sextant side-to-side slightly).  If the mirrors are not parallel, you cannot get good sights.

(2) The other sextant "adjustment" you HAVE to know is the Index Error (generally abbreviated IE).  Index Error is the sextant reading when the instrument is "nulled," which is the fancy way of saying that the images in both halves "line up" when you are looking through it.

In theory, when the sextant is set to 0*00' and you look through it, the object(s) you are looking at should all line up - horizontally because your mirrors are parallel and vertically because a 0*00', they are parallel in their movable plane as well.  In theory.

If you have to adjust the sextant to make the image line up, that's the Index Error.  It is usually possible to adjust out the Index Error, but it's not really necessary.  What is REQUIRED however, is that you know the Index Error, so you can add/subtract the "zero" correction to all your measurements.

It might be helpful to think of Index Error as being similar to the Variation correction used to convert between True North and Magnetic North to make sure the compass measurements are "correct."

You can check the Index Error on any stationary object, but it's best to use something that's at least a little bit distant; checking with the stern rail from the companionway is better than nothing, but something farther is better still.

(3) Crawling Before Walking: One of the difficulties with getting good with the sextant is knowing when you've gotten a good sight vs if you made a mistake.  In celnav, the objects you are sighting are always in motion - two sun sights taken just seconds apart will have different Hs (Height - Sextant) measurements, so you have no "instant feedback" by reproducing the measurement.

One trick is to practice, practice, practice on stationary objects like the height of buildings or radio towers or trees, etc, until you can measure the same object many times and get the same Hs every time (to within a minute or two of arc).  This means different days, also.

Reproducing your measurements is your PRECISION, but does not tell you that you are actually measuring the CORRECT angle.

(3a) If you do this fixed object practice sights on something that you know how far away it is and how tall it is, and you have a calculator with trig functions, you can calculate the Hs you SHOULD be getting with your measurements, Hc:

Hc = arctan ( object height / distance to object )

and both height and distance need to be in the same unit (feet, miles, whatever).  If your measured Hs (corrected for Index Error) and calculated Hc are the same, your measurements are ACCURATE (as well as precise, if you can reproduce them).  The goal obviously is to be both as accurate and precise as you can be.

(3b) Tip: With a mechanical device like a screw, you will get more accurate results if you always make the measurement by turning the screw in the same direction for the final bit.  Don't turn it back and forth trying to line up the images, you will forever be fighting the backlash in the screw mechanism (it may be small, but never zero).

I'll add more to this later, but this should be a good start.  The sextant is a valuable tool not only for celnav, but also for eyeball navigation in pilot waters (relative bearings between Aids, height of an Aid to get distance off, etc), so even if one never plans to shoot celestial sights for fixes, getting good with sextant measurements on fixed objects is good,useful practice.

[JWalker]

Grog for this!

thanks, I'm very interested in celnav but havent done anything about it yet.


I will though!
;D

[Captain Smollett]

Quick follow-up to point (3a):

That equation is only valid if you are willing to ignore the curvature of the earth.  This means the distance to the object must be small (a mile or two for a very tall object like a big tower).

[Bubba the Pirate]

Grog! The more I use the GPS on my Droid the less likely I am to take one with me on the boat. Or if I do it will be a secondary to the sextant.

[Captain Smollett]

Before going further with how-to tips, I thought some expectation tips might be in order.

Celestial Navigation is not GPS.   ;)  It's not a one-size, "navigate for me" technique that is useful, or needed, in all navigation scenarios.

For my own part, I divide my navigation requirements into at least two categories: pilotage and open water.  Celnav is really only useful for open water navigation (sorry if that seems like stating the obvious, but my big point follows in a moment).  If you can see Aids to Navigation (natural or artificial), you don't need celnav.

The problem is that we have become conditioned to 10 yard-ish accuracy of GPS...no matter what waters we are sailing.  I remain continually intrigued why so many boaters use GPS in pilot waters, when keeping an eye on Aids and the lay of the land is just as easy and a bit more foolproof, but that's another discussion.

As such, people hear "celnav gets you to within 4 miles or so if you are GOOD at it" and scoff.  And worse, when those first sights are taken and reduced, and off by 5-10 miles, it's all too easy for the celnav beginner to just give up.

My point is that if you NEED a more accurate fix than that, you should not be using celnav anyway.  It's not like we take sun sights in a harbor with the channel marked with Aids to Navigation...what would be the point?

On the other hand, on the open sea (or any open body of water), a fix within a 4 mile circle is actually pretty darn good...and in a pragmatic sense, good ENOUGH.  If you are near enough to some danger (a reef, a low lying lee shore, etc) that you don't fully trust such a fix...do you trust ANY fix besides the old EYEBALL "where am I?"

So, what can one realistically expect?

I've gotten a fix via successive sun sights that had an error of less than one mile when in a fixed location on land (using an artificial horizon).  A 4 mile circle is generally considered "as good as it gets" when on a pitching/rolling boat.

If you are plotting on a small or medium scale chart (for a passage), your pencil line width will be greater than that!  Like anything else, this tool should be used for the right job (planet scale navigation...not boat length level navigation) to get the best (and safest) results.

Next installments will be (in this order, unless someone requests otherwise):

(1) Land based practice with an artificial horizon

(2) A summary of what CelNav can tell you and the techniques used

(3) A survey of Sight Reduction Tools and Techniques

(4) Maybe some examples/practice problems (or links to web sites with such)?

[Marc]

I'm very much looking forward to the next installments Captain.  Marc

[Bubba the Pirate]

Keep it coming!  Can't wait. 

[Captain Smollett]

Above, I mentioned the importance at getting good at taking sights and that this, in turn, means getting reproducible measurements.  As a first step, we began by taking stationary sights on stationary objects.  This was for general practice and to build confidence.  The instant feedback of getting the same angle several times in a row reinforces very quickly that one is doing something right.

The next problem is to extend that to more realistic measurements with the sextant.  In this "installment," I introduce two complications, and both must be overcome to get good position fixes with celnav.  I emphasize, however, that one really should master the above "stationary" exercise; the confidence will help move forward.

The two complications we add to our practice are: (1) taking a sight on a moving object (like the sun) and (2) reproducibly recording the time of the sight.

The celestial bodies are always in motion relative to an observer on the earth's surface.  This might seem mighty small, but sun sights (for example) taken just a few minutes apart have easily measurable differences in Hs (Height, sextant).  Because of this motion, you will no longer get the same angle for successive measurements - and this is why you must be sure you are measuring "correctly."

The constant motion also means that you must know the time of the measurement in order to compare your measured "position" to your assumed position (the method of celnav we will continue to develop).  And when I say "know the time," it must be accurate to within a second or so - any error time will introduce significant errors in the calculation of the fix.

So, I suggest a series of sun sights be practiced, with both time of measurement and Hs recorded.

There are several techniques to getting the accurate time a sight was taken, but in all of them, an accurate time piece is required (accurate to the second).  One is to have a helper record the time the sextant user gets the sun to the horizon.  Another is to make many practice runs "timing" how long it takes you to get your eye from the sextant to the time piece so that those "lost seconds" can be subtracted from the actual time read.  One trick to help with this that some employ is to mount the time piece on the sextant itself.

For the purpose of this exercise, practicing taking a sight on a moving celestial body and accurately recording the time, don't worry about the horizon being used.  Since you are not (yet) comparing the Hs to any real geographically significant value, it does not matter if Hs is 'right' or not.  Just drop the sun to any convenient horizontal (and fixed) surface you have.

But, if you want to use an artificial horizon so that your Hs measurements CAN be used in later calculations, you can either buy one or make one (out of a pan of water).  The store bought one, while expensive, works VERY well since it completely shields the water from even the slightest wind.  This is critical, so if you make one, you will need to have similar shielding or it will be near impossible to use.

As a final note, don't forget that when using this type of reflective artificial horizon, the Hs measurements will be twice as large as what you'd get shooting a sight on the real horizon, so the Hs must be divided by 2.

[Captain Smollett]

It's been a while since I added to this, so my apologies!

The next item on the list was to be

(2) A summary of what CelNav can tell you and the techniques used

I had planned to cover a range of CelNav techniques, but have decided in the spirit of making the discussion "simpler" to forget going into lesser used methods and focus solely on what we are most likely to use.

The two most common CelNav contemporary position fixing techniques are "Noon Lat" and "Intersecting Lines of Position by the Intercept Method."  One can utilize other navigation tools such as "Running Fixes" in combination with these.

I want to focus on the Intersecting LOP's by Intercepts.  That's a mouthful, but what does it mean?

When we do ordinary pilotage navigation and we need to fix our position, one (very good) way to do so is to measure two Lines of Position and where they intersect is (to within our measurement and charting error) our position.  Two intersecting Lines of Position are the minimum required to fix position.

But, here's the kicker....recall that Lines of Position do not have to be STRAIGHT lines.  You can shoot a bearing to a lighthouse or a radio tower or some such and get a straight Line of Position to that object.  This is what most people think when they hear Line of Position.

You can also use one of many techniques to get "Distance Off" a pilotage object; in this case, we know the distance but not the bearing; that distance is the radius of a circle, and when we draw that circle on the chart (around the object), we know the boat is somewhere on that Line of Position.

Linear LOP's and Circular LOP's can be combined to obtain a fix from two LOP's.  ANY two LOP's can be used, even two circular LOP's.  In regular pilotage, we don't usually do it this way because bearings to objects are easier to measure so that linear LOP's are more common.

Understanding CelNav begins with thinking of circular LOP's.  That is essentially what we are measuring when we take a sight off a star, the sun, moon or planet.  Take two sights, and we have our two circular LOP's.

I said "essentially" because it is not quite that simple.  To understand the problem, we need to introduce the idea of "body location."  A celestial body's "location" is the position on the earth where the body appears directly overhead.  When we take a sight and compute a "distance," we are computing the distance between our position and the body's position.

This is the problem: that distance is usually huge.  When we do a distance measurement to a tv tower or a lighthouse or whatever that we can SEE from the boat, it's generally at most only a few miles away.  These circular LOPs are not very large circles.

But, circular LOP's from celestial measurements can be so large, over 1000 nm, that using the LOP directly to fix position is very error prone.

So, what can be done?  This is where the technique of "Intercepts" comes in.  In Celestial Navigation, an Intercept is simple a correction to a guessed position.  Conceptually, the procedure looks like:

• Guess your position
• Compute the sextant reading you would expect for the body if you were at your guessed position. (That is, compute a circular LOP using the distance from the body location to the guessed position).
• Use your measured sextant reading to compute the circular LOP
• Compare the LOP for the guessed position to the LOP for your real position and calculate how far you are from the guessed position

This method, while seemingly more complicated than simply measuring the LOP to a body, is far, far more accurate.

"Compute" in the above is what is referred to as "Sight Reduction" and there are several methods to doing this: tables, programmed calculators or direct calculation using equations.  Neither method is difficult to do in practice, but each has some details that must be understood to apply effectively.

Some Useful Terms:

Hs:  Height, sextant.  The actual sextant measurement with no corrections.

Ho: Height, observed.  The "observed" height (altitude angle) of the body after several corrections are applied to Hs.

Hc: Height, calculated.  The "observed" height you predict if your boat's position is the guessed position.

AP:  Assumed Position.  This is the correct term used for the guessed position.

Int:  Intercept, given a Hc - Ho or Ho - Hc, the distance you are away from the assumed position (** See Note Below).  In practice, the intercept for each sight gives you an LOP used to intersect with those from additional sights taken from "the same" position.  

Az:  Azimuth.  The angle with respect to Earth's North that the intercept should be drawn.  There are simple rules to follow to determine if the intercept should be drawn "toward" or "away" from the body....meaning, is the boat between the AP and the body's geographical location, or is the AP between the boat and the body's geographical location.

The calculations, or "Sight Reductions" are:

(1) Corrections to Hs to get Ho
(2) Converting the body's longitude to relative longitude from the AP
(3) Calculating Hc from the ephemeris data for the body
(4) Calculating Az
(5) Calculating Int from Ho and Hc

(**)  Note:

If one is going to do Celestial Navigation and you are NOT using a programmed calculator that does the conversions for you, it helps to think of distances in terms of angles.

For example, 1 minute of latitude =  1 nm

Hc and Ho are angles.  When you subtract them to get the intercept, the "distance you are from the assumed position" is computed as an angle.  Depending on how you do your charting, you may need to convert to "distance."