3min 15 sec

Pisces · 12-10-12, 12:35 PM

The 3 seconds difference from 13 minutes can be neglected for simplicity. It's only 0.4% off from exact (777.5 seconds, or 12m57s). Even 195 seconds (3m15s) is 0.3% from exact (194.4s) So, you give up the same amount of inaccuracy on your speed for either time-interval. This is not the reason why it is more accurate.

The idea behind taking the target motion over 4x 3m15s, instead of just 1x3m15s, is spreading the position error of the begin and endpoint over a longer time period.

Let's say your watchofficer on the bridge gives a target position report. He gives distances in steps of 100 meters, and a bearing in steps of degrees. A degree at maximum visual distance of 16km is 280 meters wide. So the beginpoint of the target motion is somewhere in such a 100m by 280m box on the map. If you are lucky it is smaller when the target is closer. But doing periscope observations is much more inaccurate anyway.

The target speed is a line connecting some point in the begin-box with the a point in the end-box, taken over the time period. There is a smallest distance connecting the inside borders of the boxes. But the speed can also be the largest distance, connecting the far edges of the boxes. The actual motion of the target is somewhere in between those lengths.

If the interval is really short (theoretical 1 second) then the position uncertainty totally envellops the target motion track. If the interval is much longer, then the position uncertainty is only a small fraction of the target motion. A 6 knot target moves 600 meters in 3m15s. Two 280m position uncertainty boxes spaced appart by 600m would suggest a speed of something between 3.2 and 8.8 knots. That's quite a range. Conclusion: 3m15s is useless considering position inaccuracy in the plots.

However, it moves 2.4 kilometer in 13 minutes. The uncertainty boxes are still of the same size, but are much further appart. Based on the uncertainty boxes, it could have a speed between 5,3 and 6.7 knots. Now you can be much more confident that it is actually moving with 6 knots! It could still be 5.5 knots, or 6.5 knots. But you certainly narrowed it down to something acceptable.

12-10-12, 12:35 PM	#8
Pisces Silent Hunter Join Date: Dec 2004 Location: AN9771 Posts: 4,904 Downloads: 304 Uploads: 0	The 3 seconds difference from 13 minutes can be neglected for simplicity. It's only 0.4% off from exact (777.5 seconds, or 12m57s). Even 195 seconds (3m15s) is 0.3% from exact (194.4s) So, you give up the same amount of inaccuracy on your speed for either time-interval. This is not the reason why it is more accurate. The idea behind taking the target motion over 4x 3m15s, instead of just 1x3m15s, is spreading the position error of the begin and endpoint over a longer time period. Let's say your watchofficer on the bridge gives a target position report. He gives distances in steps of 100 meters, and a bearing in steps of degrees. A degree at maximum visual distance of 16km is 280 meters wide. So the beginpoint of the target motion is somewhere in such a 100m by 280m box on the map. If you are lucky it is smaller when the target is closer. But doing periscope observations is much more inaccurate anyway. The target speed is a line connecting some point in the begin-box with the a point in the end-box, taken over the time period. There is a smallest distance connecting the inside borders of the boxes. But the speed can also be the largest distance, connecting the far edges of the boxes. The actual motion of the target is somewhere in between those lengths. If the interval is really short (theoretical 1 second) then the position uncertainty totally envellops the target motion track. If the interval is much longer, then the position uncertainty is only a small fraction of the target motion. A 6 knot target moves 600 meters in 3m15s. Two 280m position uncertainty boxes spaced appart by 600m would suggest a speed of something between 3.2 and 8.8 knots. That's quite a range. Conclusion: 3m15s is useless considering position inaccuracy in the plots. However, it moves 2.4 kilometer in 13 minutes. The uncertainty boxes are still of the same size, but are much further appart. Based on the uncertainty boxes, it could have a speed between 5,3 and 6.7 knots. Now you can be much more confident that it is actually moving with 6 knots! It could still be 5.5 knots, or 6.5 knots. But you certainly narrowed it down to something acceptable. Last edited by Pisces; 10-12-23 at 05:29 PM.