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new sun sight - pabrides - 01-16-2021

GMT jan 15 2021, 06 23 56, Ho 41 33.5

My fix is exactly 10 nm SE along LOP 3. 

I took 3 AH sightings and averaged them.  Learning to average hexadecimal was a bit tricky, but I found that making the hours of time or sextant altitude equal helps.

For example: 
83 10.7  =  82 70.7 - adding 1 degree to min.
82 33.7  =  82 33.7
82 05.0  =  82 05.0

So 82 is the obvious average for degrees and what remains is to average the minutes:  109.4 ÷ 3 = 36.5

Averaging time was a bit more difficult :

06 22 30  =  06 22   30
06 24 12  =  06 22 132  - adding 2 min to seconds
06 25 26  =  06 22 206   - adding 3 min to seconds
 so,  368 ÷ 3 = 122.7.  Move 120 seconds back to minutes with a remainder of 2.7 seconds:  06 24 03. (My watch was 7 sec fast so actual time is on the first post line above)

Of course one could change each shot to a decimal value, add together, divide by 3, then change back to the hexadecimal,  but that takes a calculater and lots of button pushing, given your calculator has a button to do this.

I'd be interested to learn how you swabbies average shots.  I tried 4 or 5 different ways to average shots all resulting in different values.  The way I've shown works best for me and put my LOP right on my position.  See LOP 3 on the worksheet.

The arithmetic mean works great if the shots are spaced near equally: (a+b+c)÷3= mean average. Simple.
But if shots are delayed due to clouds or such a better solution might be the geometric mean: a×b×c =d then take the cubed root of d. If you have 5 shots then multiply and take the 5th root... etc. If a data set has flyers that skew the average -such as in the set 2.4, 2.3, 2.6, 2.1, 2.2, 2.4, 2.3, 7.5, 5.2 - You can see that the 7.5 and 5.2 will skew the average of two somethings out of proportion. The geometric method helps reduce the skew to something more reasonable.

2.4+2.3+2.6...+5.2=29.0, 29.0÷9=3.22
2.4×2.3×2.6...×5.2= 14, 274.4, 9th root of 14, 274.4 = 2.89

Without the big numbers - 2.4+2.3+2.6+2.1+2.2+2.4+2.3 = 16.3, 16.3÷7=2.33
_________________________ - 2.4×2.3×2.6×2.1×2.2×2.4×2.3 = 366, 7th root of 366 = 2.32



Cheers