Weeks after I asked the ballistic math questions, I got this email:
Was intrigued by your trig problem.
Herewith my answers:
1) take distance and bearings at regular intervals, say 20 seconds apart. (take bearing and ten seconds later take distance, repeat for 1 minute. Using change of bearing and distance, plot 1 minute of travel; use of graph paper expedites solution for speed and direction. Alternately, use similar triangles and trig functions to calculate.
2) from cannon bearing 18.33 degrees at 7.74 km.
3) after 1 minute of travel, the cannon should be laid to 23.00 degrees at 7.50km.
4) 1 MOA at 7500 meters is a bit over 2 meters dispersion. If one assumes that both horizontal
And vertical dispersion are the same, which is NOT usually the case with arty, then the area inside the impact zone is about 4 square meters. Given the projected area of the ship, a hit ought to be a certainty.
Regards, Historian
4 is tricky because you didn’t give the measure for your dispersion value. Is it extreme spread or standard deviation? Also at most extended ranges windage and range estimation are the big errors, not ballistic dispersion. Dispersion is generally circular, but only perpendicular to the projectile trajectory, not in the ground or target plane.
Jeff, you are right. If the SD is 1 moa, then 3 SDs is 3 MOA, or about 6 meters. Even if one assumes that this is a radius, not a width, the impact area is 96.8% likely to be within a radius of 6 meters. The implication of this is that rifles, and cannon, are far more accurate than the distance measurement and direction determining techniques used until recently. IOW, the problem with arty is figuring out exactly how far away, in what direction, and which way and how fast the target is moving. And in fact, that is the hard part of long range rifle shooting, too.
An M114 155mm howitzer shell would be in the air for 13 seconds to hit something at 7500 meters. Depending on where on the earth it was fired from there would be a measurable and probably accuracy reducing effect from the coriolis effect due to the earth turning under the shell.
Just sayin.