CelNav Three - Sight Reduction I

[HenryC]

CelNav Three  (Last Edit - 10/28/14)

Note:  There is a simple way to reduce sights with a pocket calculator which I describe in detail in this course.  But you should at least scan this material if you plan to do it that way.

Let's review the information we derived in the previous session, and which we're going to be using with the Pepperday Tables to reduce the sunline taken on 15 Jan 2015, at 14:03:04: UT.

GHA = 28d 26'.1
Dec = S 21d 06'.7
Alat = 26N
Alon = 80W
Ho = 20d 38'.7

Pepperday is a 9 page table of numbers used to look up what are called S and C values.  The rest of the booklet is made up of examples and instructions. I would suggest you make photocopies of the table itself, pages 11-19, and laminate them with clear plastic to protect them from moisture so you can keep them in your navigation kit.  On page 10 of the booklet is a copy of the sight reduction form, a guide that helps keep you and your figures organized as you go through the table as it does the calculating for you. 

These calculations are some pretty tricky spherical trigonometry done with haversines and logarithms, but you don't need to know that.  The table does all the number crunching, you just need to write down the intermediate values in the form and follow its instructions, step by step. I would suggest you make plenty of photocopies of the form on page 10 so you can practice.  Remember, practice is the key to this whole operation.  I haven't worked a sight in quite a while, and as I was preparing for this course I had to look up all sorts of stuff because if you don't do it every day, you forget.  I also made lots of mistakes while working. Anyway, the more you do it, the easier it gets and the less mistakes you make. Just like life.

I'm not going to show you how to use the table, Pepperday does a much better job of explaining it than I ever could.  Page 2 of the booklet tells you how to look up S and C values, and pages 3-7 explains how to use the table. There are examples of two sight reduction forms already filled out on page 4, so you have everything you need.  But I will walk you through the form while we reduce the sun line we took in CelNav Two, and I will give you some hints as we do the example so that it will
help you look up the S and C values and write down the numbers (it's easy to get confused when you get started).

But fear not, as you have probably figured out by now, I'm a big fan of Pepperday and  have great confidence in his method.  It is also so much more compact (and inexpensive) than all all the others and perfectly suited for yachtsmen. Another thing you will like about Pepperday, it rounds every angle off to the nearest minute of arc, so you don't have to worry about being super precise.  Pepperday also allows you to do the sextant corrections on the form if you prefer,  instead of through the Almanac the way we did it in CelNav Two.  It's not as super-accurate, but it's good enough for our purposes. After all, even under ideal conditions, you can only read a sextant to the nearest half-mile anyway. We'll do it that way.

Our "DR Lat" is 26dN and "DR Long" is 80dW.  The sun was roughly in the SE, so write down 135d in "Appr Az". Write these values in the upper left spaces so you won't forget them.

Our raw sextant reading, rounded off to the nearest minute, was 20d 31' at 14h 03m 04s. Write these values up in the boxes labeled "Sextant Altitude" and "Clock Time" in the upper right part of the form.  We have no clock error to worry about, so we're done there.  Finish up by writing down the clock time again in the box marked "GMT".

In the space marked "Ht. of Eye" write 6 meters (for our 20 feet, Mr Pepperday is an Aussie). Just remember a meter is a 39.4 inches, a little over a yard., so do the conversion in your head, it doesn't have to be that accurate.  Using the little box labeled "Ht Dip" as a guide, we make an entry of  -4.3 in "Dip Corr".  "Index corr" is - 1.5'. Look in the big box marked "Main corr" and you will see our raw sextant reading requires a correction of about +13'.6'. The sign is positive because we shot the lower limb of the sun.  Write +13'.6 in the little box labeled "Main corr" and add up all the corrections and write them in "Total alt corr" as +7'.8.  Rounding the corrections off to +8' we add to "Sextant Altitude" and write 20d 39' in the box labeled "corr obs alt".  You will note that is very close to the value we derived the long way from the Almanac. It only differs by 0'.3, a tiny angle the human eye can't see anyway. 

Shifting your attention to the left side of the form, ignore the "Star SHA" box, which is only for stars. In the space marked "GHA hours" write in the 14th hour (1/15/15) GHA for the sun from page 19 of the Almanac: 27d 40'.1. In the box beneath marked "Increm min/sec", enter the value we got from gray page iii in the Almanac: 0d 46'.0.  Add these two and round off, placing the result, 28d 26' in the box labeled "GHA".  Place the value we derived for the declination in the "dec" box, rounding off, 21d 07'. Circle the "S" to remind you it is a southerly declination. 

Write the assumed longitude in the little box marked "long", circling the "W-" because it is a west longitude.  This tells you to subtract the longitude from the GHA above it to get a value called the "LHA", or Local Hour Angle.  Write the result in the box labeled "LHA". The LHA is the westward distance in degrees from your meridian to the sun's meridian. If you subtract lon 80 from  GHA 28d 26' you get -51d 34', a negative number, and a negative LHA doesn't make sense, so add another 360 so it comes out as a reasonable LHA.  The little "360" written in the line reminds you to do this, so fill in the space marked "LHA" with 308d 26'.

The Pepperday form is now loaded with all the data it needs to calculate your Azimuth and Intercept.  I recommend at this point you take a break, have a cup, smoke one if you got one, and double-check your figures, because from here on in there is no turning back. In general, you will be working the form  to the right and down, and follow the arrows otherwise.  You will look up the S and C values as the instructions on page 2 of the table show you, and I will help out by guiding you through the process as best I can, and pointing out which page in the table you should be on so you don't get lost.

We'll do that in our next session, but there are a few comments I would like to make at this point.  As you can imagine, practice with the table is very important, and you have a wonderful online resource which can make that a lot easier for you.  The US Naval Observatory has a CelNav calculator at

http://aa.usno.navy.mil/data/docs/celnavtable.php

which will allow you to pick a location, date and time and generate a mini-almanac and sight reduction with all the information you need for practice.  It won't do you much good at sea, but it makes training a snap.  It is how I generated the data for this course, and how I can check my Almanac and sight reduction work.  (Sneaky, eh? Did you really think I drove to the beach and time traveled to next January to prepare this course?)

I just ran the calculator for the time and date I wanted, and it generated a GHA,  Dec, Fully Corrected Sextant Altitude and Azimuth (as well as the Refraction, SemiDiameter, and Parallax Corrections) for all the navigational bodies visible from my location.  Actually, I ran the program twice, once for my test problem coordinates, and once for my Assumed Position at 26N 80W, which is about 40 miles away.  This allowed me to set up the problem and check my Almanac and table calculations. Using this calculator to generate data for your own practice work will also teach you a lot about nomenclature and nautical astronomy.  While working the tables for practice, it is inevitable as a beginner you will make mistakes.  You will get the wrong answers, and have to work backwards to locate and correct them.  Don't resent this, welcome it. THIS is where  learning takes place.

There are other sight reduction methods available besides Pepperday, The one published with the Air Almanac is very popular with yachtsmen, and the usual method recommended in intro courses is easy to use (but relies on many big, bulky and expensive volumes). There is also a sight reduction table in the back of the Commercial Edition of the Almanac, but I tried it once and found it incomprehensible.  It took me all day to reduce a sight, I doubt if I would be able to use it in the real world.