More modern bubble sextants, A-10A; MA-2; MA-1; and Kollsman periscopic sextants take 120 shots (one shot every second for two minutes) for the automatic average, and entirely impossible number of sights for manual averaging. 120 shots should reduce the error of a 10 shot average by about two-thirds.
gl
--- On Mon, 3/11/13, Gary LaPook <garylapook@pacbell.net> wrote:
From: Gary LaPook <garylapook@pacbell.net>
Subject: [NavList] Re: Lean And Mean Bubble Sextant Sun Sight
To: garylapook@pacbell.net
Date: Monday, March 11, 2013, 9:20 PM
The size of the
total error is inversely proportional to the square root of number of sights taken to be averaged, the more sights, the greater the accuracy. The square root of 7 is 2.6 and the square root of 13 is 3.6 so the error of the 7 shot series should be about 1.4 times larger than a 13 shot series. (3.6/2.6)
If you are doing hand averaging then taking exactly 10 shots for averaging makes the averaging much easier and provides enough sights to get the error down to a usable level. From my website:
"Although you can take any number of shots, it makes it a lot easier to find the average if you take
exactly ten shots because it is much easier to divide the total of the readings by ten than by any
other number, just by moving the decimal point. Since we don’t normally deal with sexigesimal
numbers (base 60) we must use a special method to find the average of measurements taken in
degrees and minutes. To find the average you add up the minutes and degrees in separate
columns. Divide the sum of the degrees by the number of shots, simply moving the decimal point
if you have taken ten shots. You now have degrees and decimal degrees after the decimal point.
To convert the decimal degree part to minutes just remember that 0.1 degree is 6 minutes and
0.01 degree is 0.6 minutes. For example, say the total degrees of ten observations is 674 and the
total of the minutes is 162. Move the decimal point of 674 total giving you 67.4. then multiply
the “4" by 6 to convert to minutes making this part of the average 67̊ 24'. Next divide the sum
of the minutes, again just moving the decimal point if you have taken ten shots, and this gives
you 16.2' which you then add to the minutes found in the first step so the average then becomes
67̊ 24' plus 16.2' which equals 67̊ 40.2'. It takes about a minute and a half to average ten sextant
shots using this method. (If you were using a calculator you would have to convert all the
measurements to decimal degrees, add them up, divide by the number of shots and then convert
the result back to degrees and minutes format. It is easier doing it by hand. Noonan didn’t have a
calculator so he had no choice."
https://sites.google.com/site/fredienoonan/other-flight-navigation-information/recent-landfall-approach
Also see:
https://sites.google.com/site/fredienoonan/topics/accuracy-of-celestial-fixes
In particular,
https://b98f4441-a-62cb3a1a-s-sites.googlegroups.com/site/fredienoonan/resources/weems/weems-314-315.JPG?attachauth=ANoY7coiqSntB_DDBBgDWqh0h-fuPf3V7e9YwK5R1LeHLniEGALP69mq2AFDfI4E1dXeaYFXWVodg-NBpm4v7Y8etS2QmT9kTXAni0KSr0_IgMvd4wBq88uJrX8Q-4wALW2050fZ4RQP2-m7q5x3Sbz7OlWq5dVDleoQ6S0x3Cw_HBwY0kQefOI7i9RwZpU70zamTF6S_l5enXIFzyn9Mc7OuIjV8M6Rja7Zp4VhaW-Otu9S8cwFqjRfIhsTS0S-F7wsLIE_DZ5L&attredirects=0
https://b98f4441-a-62cb3a1a-s-sites.googlegroups.com/site/fredienoonan/resources/weems/weems-316.JPG?attachauth=ANoY7coGrnlaI7NlDTsSm258zELZKft7aAeY9Z4pwlufhNtUFODqNb3jeEfACJB1BEiFizaMpSVN_k0ZV0q0V2WcTiIXB4JG4l7PXHnBOdycXfsjgCeyYkHqij6HX-vWwBjIeThb9G95bHknwL2TmsZfM0Q2MkyHagXHPUdGGT2BKiFXuHXveWP5g5_M4B4Fh4IhgqNjRYfn2R5y7Gp6OYSbwza4bKUx7mbiPjV-D3j1ZJIM9mIw6Tk%3D&attredirects=0
gl
--- On Mon, 3/11/13, Paolo Borchetta <pb---com> wrote:
From: Paolo Borchetta <pb---com>
Subject: [NavList] Lean And Mean Bubble Sextant Sun Sight
To: garylapook---net
Date: Monday, March 11, 2013, 1:21 PM
Today I did a little experiment on finding the accuracy of a quick raw set of sun sights taken with my Link A-12 bubble octant to simulate actual in flight conditions when we might have to live with just keeping the sun and the bubble somewhere in the middle of the chamber without too much of a chance of perfect collimation.
I shot two sun lines at two hours distance from the same position marked with GPS, purposely it was a no frill, quick sight reduction, time of start of the session, time of end, averaged, same for the 12-13 or so sights for the first sun line and 6-7 for the second. Purposely I didn't apply any correction for T/P although today
was a bit hot.
Target was a very quick time of the manual sight reduction and a quick plotting.
Bottom line the cel. fix was 15 nmi from the GPS fix with bearing 119.7degT.
BAD or NOT? One thing I noticed is that the second LOP was a bit more off then the first (checking with the USNO data).
One initial observation that I can empirically make is that it appears that the more sights you take, the likely errors can offset each other, that could be the reason for the first LOP to be very precise as compared to the second.
However I'd like to hear some more opinion on the whole exercise.
Paolo
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