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Whle mowing the lawns this afternoon I noticed that the sun was visible more often than it was hidden by cloud. I checked a phone app and at my location the sun would be on the prime vertical at 1716 NZDST (-13). I looked at my watch and it was 1645. Clearly a double altitude sight was in order.

I took three pairs of sights. Unfortunately about 10 min before the sun was due west the sun disappeared behind a cloud. The cloud cover was such that I decided to put my sextant away. Then I noticed a blunder in the first pair of sights so I was left with two pairs of sights.

When I analysed the sights I discovered that the approximate formula cos lat = a/15/t is so sensitive to errors in time as to make it  useless. It is possible that I have made an arithmetical error but I found that a four second error in three minutes gives an change in lat of nearly 1 °. It is many many years since I studied differential calculus so I doubt I could work out d lat/d t for the above formula.

Here is what I did:

I observed the sun in an AH. I noted the times when the bottom and top limbs touched and then when the top and bottom limbs touched. That is a change of two diameters but I am using an AH so the actual change is one diameter or 32.4'.

To check the accuracy of the sights I worked the first sight of each pair as an intercept and then as a time sight (with gps lat). I then used the formula cos lat = a/15/t to determine the lat by double altitudes. The intercept was worked with the cos formula, a calculator and the ABC tables. The time sight was worked by calculator.

Base data

GPS  position  S41° 06.5'  E175° 05.2'

Zone -13  (NZDST)

Zone date 2016/12/5  (what is preferred time format for this forum?)

Sight 1

Ho  39°  39.4'

Time 1  165504

Time 2 165754

Intercept  0.2' A

Az  N 85.7 W

Long by Chron 175 5.0'

 

Sight 2

Ho  38°  35.9'

Time 1  170037

Time 2  170331

Intercept  0.7' A

Azimuth  N 86.5 W

Long by Chron  175° 6.1'

Double Altitudes

The change in altitude is 32.4 * 60 arc seconds

The time interval is 170 secs for the first pair and 174 sec for the second pair.

These numbers give 40° 19' and 41° 51' for the lat. What I find interesting is not the error in lat but just how sensitive lat is to the time interval.

Have I made a blunder?