CelNav Two - Using the Almanac

[HenryC]

CelNav Two (Edited 10/27/14)

OK. Enough theory and explanation.  Let's move on to an example. I live in Fort Lauderdale. Suppose I go out and shoot the lower limb of the sun on 15 January, 2015, at 14h 03m 04s UT.   I get a raw sextant reading of 20d 30'.8.  You will note I use tenths of a minute for the fraction,  no one uses "seconds of arc" any more. I make a mental note that the sun is bearing roughly SE, as you would expect for mid-morning, Local Time.

I tested my sextant by getting a reading on the horizon of 0d 01'.5, so I know I have an Index error of -1'.5. I also know my sextant is 20 feet above sea level, so my Dip correction is -4'.3 from the Dip correction table on the right-hand column of page A2 of the Almanac.  Applying both of these corrections to my reading I get an Apparent Altitude of 20d 25'.0.  I also have to make corrections for Refraction, Semidiameter and Parallax (the sun has a tiny Parallax correction, usually ignored by navigators, but on page A2 all these corrections are done for you simultaneously on the left hand column for the sun, under "Oct-Mar".  Just look down the App. Alt. column to the closest value to 20d 25'.0 and read off the total correction which is +13'.7.  Apply this value to your Apparent Altitude, and your corrected sextant altitude Ho = 20d 38'.7. This is the true and exact elevation above the horizon in degrees of the Sun as seen from my (unknown) location on 15 Jan 2015  at 9:03:04 Eastern Standard Time. 

Hs = 20d 30'.8  Sextant Height
             -  4'.3  Horizon Dip error (always negative)
             -  1'.5  Sextant Index Error
            +13'.7  Refraction+SemiDiameter+Parallax (from page A2)
------------------
Ho = 20d 38'.7 Observed Height


The Sun is used so often in navigation that the Almanac gives you pages A2 and A3 for Sun Corrections, along with other frequently used values for Dip, stars and planets. The Almanac folks also give you an extra tear-out copy of page A2 on stiff, yellow paper you can use as a bookmark. But you still have to do the Index and Dip corrections for yourself, because the Almanac has no way of knowing how high above sea level you are, or how far off your sextant is.

OK, we've provided the exact time, and the exact Ho.  So let's provide the other items the Sight Reduction Tables need to give us an LOP.  First, we need an Assumed Position (AP), a "seed" location to use as a start point of our calculations.  Fortunately, the Pepperday tables don't need a special location, any nearby spot will do, so I pick the intersection of two grid lines on my chart, a nice round even number, Lat + 26,  Lon - 80.  In navigation, N is +, W is -. I know this is a spot just offshore in the Atlantic near the Broward, Miami-Dade County border.  It's exact location relative to me does not matter, as long as I can easily locate it on the chart. I mark that spot on the chart with  a dot, and the letters "AP".

The only other information Mr Pepperday wants from us is the GP (the Geographical Position) of the Sun at the moment we observed it.  The sun (and every other celestial body) is always directly overhead of some spot on earth at any particular time.  But the celestial bodies and the earth are always in motion, so the GP of any body is constantly moving.  So. we have to look it up in the Almanac.  The GP of a body is not listed in Latitude and Longitude, it is in sky coordinates, Declination and Greenwich Hour Angle (Dec and GHA, for short).  Dec is the easy one, it is identical to Latitude, and is given in degrees N or S of the Equator.  A star above the earth's equator has a Dec = 0.  One directly over the S Pole has a Dec = - 90.  One over the N Pole has a Dec = + 90.

GHA is the angle, measured W from the Greenwich Meridian, from 0 to 360 degrees to the body.  So as the earth turns from W to E, the celestial bodies appear to move from E to W. For example, if you look up the sun in the Almanac tables,   it moves from E to W, that is, the GHA is constantly increasing as the earth rotates.  All bodies go through roughly 360 degrees of GHA every day as the earth spins, there is also some small amount of motion in Dec, due to its own, and the earth's, motion through space. 

So if you turn to page 19 on the 2015 Commercial Edition of the Almanac. look down the "Sun" Column at the time corresponding to Thur, 15 Jan, 2015 at 1400 UT, and you will see the Sun's GHA was 27d 40'.1 and its Dec was S 21d 06'.7.  An hour later, at 1500 UT, the sun is now at GHA 42d 39'.9, Dec S 21d 06'.2.  As you would expect, the sun moves through about 15 degrees of GHA and about half a minute of Dec in an hour of time, due to the earth's spin, and its orbit around the sun. But we need the GHA and Dec for the exact time between the even hours, 14h 03m 04s UT. You have to add the little bit that gets incremented during those 3m and 4s. This is tricky, so pay attention.

Write down the GHA and Dec on page 19 for 1400h , which are 27d 40'.1 and S 21d 06'.7, respectively.  Note also the little code "d"  of 0.4 at the very bottom of the "sun" column on that page. That little "d" code is a declination correction factor we'll need later on.

Now skip to the gray pages ("Increments and Corrections") in the back of the Almanac and find the table for 3 minutes, (in my copy it is on page iii).  Scroll down the "sun" column to 4 seconds and note the value there of 0d 46'.0 .  Add this to the GHA for the even 1400 h and the result is 27d 40'.1 + 0d 46'.0 = 28d 26'.1.  (Be careful how you carry in your additions, you're dealing with mixed degrees and decimals here).  The Dec changes very little, and that is what the little "d" code is for.

On that same 3m table on page iii, look up the "v or d" of 0.4 corresponding to a "corr-n" of 0'.0. This is the Dec correction for those 3m and 4s.  But do you add or subtract it? Look carefully at the Declinations for 1400 and 1500 hours we looked up on the 15 Jan page. Is it increasing or decreasing during that hour?  If it is increasing, we ADD the correction, decreasing we SUBTRACT it.  It is decreasing, but since in this case the Corr-n is 0.0, we do nothing at all and just go with a Dec of S 21d 06'.7.   What this means is that the Dec at that date and time is decreasing so gradually that we don't need to correct for those 3 min and 4 seconds.

So to summarize, we now have the following data, ready to feed into the Sight Reduction Table:

Greenwich Hour Angle GHA = 28d 26'.1
Declination                  Dec  = S 21d 06'.7
Assumed Latitude        Alat  = 26N
Assumed Longitude     Alon  = 80W
Observed Altitude          Ho  = 20d 38'.7

We know where on Earth the Sun is directly overhead at that date and time.  And we also know
where in the sky the Sun appears to us at that date and time.  If we could figure out where in the sky the Sun would appear if viewed from the Assumed Position (Lat +26d, Lon -80d) we could figure out how far away we are from the AP.

In our next session we will go into Pepperday and use those values to get an Azimuth and Intercept for an LOP.

The Sun's GHA has coded within it the exact time. After all, isn't the position of the sun in the sky how we define the time?

Don't despair.  If all this seems hopelessly tedious to you, just keep in mind you will be working from pre-printed forms which will guide you through every step of the way.  Also, as you work with this, you'll start seeing a lot of places where you can take shortcuts, cut corners, or otherwise skip lots of unnecessary work.  You know when teaching, you have to be thorough, but as you master any trade, you start learning the tricks and work-arounds, the kluges and fudges. 

To get a different perspective on all this, look over Explanation on page 254 of the 2015 Commercial Edition of the Almanac, particularly the sun example on page 256, ( 8. Examples).  You will see examples there for deriving GHA and Dec for Sun, Moon, Planets and stars.  The Sun is the easiest, but the others follow similar principles.