CelNav Six - Pocket Calculator Sight Reduction

[HenryC]

CelNav Six (Edited 10/28/14)

By now, you've probably figured out that celestial navigation by Sight Reduction Table is a very handy thing to know, but that maybe it is something that you may never want to have to NEED to know.  Can you imagine what it it must be like when you have to reduce a complex sight quickly and accurately because you're approaching a lee shore, or because you might miss your island destination and sail past it off the edge of the earth?  And imagine having to do this when you're cold, wet, seasick, haven't slept in 36 hours and you're being bounced around in a cramped and stuffy cabin and you're really, really scared.

Even under ideal conditions, there always seems to be something better to do aboard a yacht than spending time at the Nav Station (assuming you even have one).  Most of the time, if there is any other way to navigate, you will choose that over Mr Pepperday any time.  But there is a middle way, an intermediate strategy between GPS and reducing a celestial sight with pencil and paper.  There is nothing more confidence-building than having a Plan B. The answer is the pocket calculator. 

The calculator is how I normally do celestial, although I do enough table practice to keep my skills up so I always have it as a backup.  Pocket calculators today are absurdly inexpensive, very robust, and available with solar cell power, so you don't have to worry about batteries corroding or losing power.  For about $20 you can get one that fills the bill and is easy to read in dim light, and can be powered by a flashlight, if need be.  You can even afford a couple of extras as backups.

You can spend a fortune on a specialized CelNav calculator, or even program your own HP or TI to do the job (I used to), but I am starting to come to the conclusion that if relying on any calculator is a step away from total self-reliance, then relying on a specific calculator is ten steps away. Any calculator capable of doing trigonometric functions and capable of converting angular measure to decimal degrees and back with just one keystroke is fine.  For example: 10d 18'.5 is the same as 10.30833... degrees.  There is no need to go more than 5 decimal places.

Pepperday has a very nice section for using his book with a calculator, but for my taste, I want my Plan B to be very different from my Plan A so I don't tend to get the two mixed up with each other.  I prefer to use the formulas on page 279 of the Nautical Almanac (Section 6. of Sight Reduction Procedures, The calculated altitude and azimuth.).  There is a step by step example there too, and I will do our sunline here using that method as well.

Observational data,  from the sextant and the almanac: 

GHA = 28d 26'.1 = 28.43500d
Dec =  S21d 06'.7 = -21.11167d
Lat = 26N = 26.0d
Lon = 80W = -80.0d
Ho = 20d 38'.7

And from pg 279 of the NA
Step 1:

LHA = GHA + LON = -51.565d  = 308.435d (adding 360d to make it positive)

Step 2:

S = sin Dec = -0.36019

C = (cos Dec) x (cos LHA) = (0.93288) x (0.62163) = 0.57991

Hc = INVsin ( S x sin Lat + C x cos Lat)
Hc = INVsin ( -0.36019 x 0.43837 + 0.57991 x 0.89880)
Hc = INVsin ( -0.15790 + 0.52122)
Hc = INVsin (0.36332)
Hc = 21.3d = 21d 18'

Our computed altitude Hc is 21d 18'.
You will recall our observed altitude Ho was 20d 39'


Hc - Ho = 21d 18' - 20d 39' = 0d 39'

THE DIFFERENCE BETWEEN THIS Hc VALUE AND OUR Ho GIVES US AN INTERCEPT OF 39 MILES, ON THE SIDE OF THE ASSUMED POSITION AWAY FROM THE SUN'S GP. THE COMPUTED VALUE IS GREATER THAN THE OBSERVED, BY THE COMPUTED-GREATER-AWAY (CGA) RULE.

Step 3:

X = (S x cos Lat - C x sin Lat) / cos Hc
X = ( -0.36019 x 0.89880 -  0.57991 x 0.43837)/cos 21d 18'
X = (-0.32374 - 0.25422)/0.93170
X = (-0.57796)/0.93170
X = -0.62033

and we see X does not exceed the limits of 1 or -1

A = INVcos(X) =INVcos(-0.62033) = 128.3d

Step 4: Since LHA>180d then the Azimuth = A or about 128.3d

You will note these values for Azimuth and Intercept agree with the Pepperday sight reduction results.


Even if you decide learning Table Sight Reduction is not worth your trouble, you should definitely be able to do this calculator method as a backup for GPS if you should ever go blue water cruising.  If you have your Almanac aboard, you will have the instructions, and you can easily make up a form to guide you through it and log your intermediate results, and keep a few copies of it with your sextant or nautical almanac.  Since I suspect most of you will either never bother to master celestial,  or even if you do learn it,  eventually quit practicing and get rusty, this chapter may turn out to be be the most important one in this course.