Sight Reduction

There is a plethora of ways in which sights can be reduced:

  • Longhand with mathematical tables.
  • Short methods using tables.
  • Inspection tables.
  • Slide rules, including the Bygrave and the German MH1.
  • Electronic - calculator, phone app, spreadsheet or online calculator.

My aim is to describe some of these methods. I will assume that the reader understands basic concepts such as lines of position (LOPs), interecepts, latitude and longitude, the celestial sphere and hour angles. I will add a method when I have successfully used it.

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Cloudy Weather Johnson

In about 1875 AC Johnson RN published a slim book On Finding The Latitude and Longitude In Cloudy Weather, Etc. earning the author the nickname Cloudy Weather Johnson. The book went through many editions. The 1905 edition was the twenty-eighth.

With this volume the navigator could determine has latitude and longitude by the Double Chronometer method. The only other document required was the Nautical Almanac.

Cloudy double Chronometer The first stage is to take two time sights, about an hour or an hour and a half apart. Using assumed latitudes two longitudes are calculated. The volume contains log cosine, log secant and half log haversine tables which can be used.

The azimuths are determined using Johnson's Table I.

Cloudy Weather cover Table II is then entered to determinine corrections from which latitude and longitude can be found. Multiplication of several three digit numbers is required. Johnson describes how his Table I and Table II can be used to multiply and divide two numbers. I did not have any success with this and instead cheated and used a calculator.

The arithmetic could probably be done with long multiplication and long division. It is over 50 years since I was taught these techniques but can probably remember them - I wonder if later generations have been taught them? Extracting data from Table II requires double interpolation.


Worked Example
I took two time sights and worked one by Cloudy Weather and the other by Norie. With no apologies for my handwriting the worksheet below shows how I used On Finding The Latitude and Longitude In Cloudy Weather, Etc. to find my position from the computed time sights. I can confirm that GPS and Google Earth are correct (-;)

cloudy_reduction




HO 211 Ageton

For many years I had assumed that Short methods were so called because they were quicker and easier than long methods such as the cosine-haversine formula and Norie. Recently, when I tried HO 211 Ageton (first published in 1931), I discovered that Short refers to the size of the tables. Ageton is a slim volume (50 pages) vs Norie (600+ pages) but (in my opinion) the method is confusing. There is (again in my opinion) just as much work as cos-hav/Norie.

ageton instructions
ageton front cover

The instructions for Ageton occupy a full page. I had to make several attempts at drawing a flow chart before I understood the method and was able to work a sight.

ageton table


The following worked sight shows just how complicated the Ageton method is. I used my GPS position as my assumed position. The intercept of 0' is pure luck - usually my intercepts are < 1'.

Ageton sight




Classic Ageton

In 2015 Greg Rudzinski, a member of the Navlist forum, produced a modified Ageton table in which the A and B values are framed by sin and cos values. Greg's table can be used to solve the spherical triangle by the classic sin formula, hence the name of the table.

classic ageton table

In the Ageton table A = log cosecant and B = log secant (both multiplied by 100,000) so the modified table can be used to solve the classic spherical triangle

sin h = Sin L Sin d + cos L cos d cos t

by substituting log cosecant for log sine and log secant for log cosine. There are two rules defining signs.

I have re-worked the previous sight with the Classic Ageton method. You will note that all that is needed is a knowledge of the sin formula - unlike the full page of instructions for the Ageton method:

Ageton classic sight reduction

The Sight Reduction form needs to be tidied up. I note that Rule 2 is not visible.

Still to be discussed are the large errors in Ageton in some situations and the lack of interpolation.




Last Updated: Tuesday 9th August 2016

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