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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