I realize now this long range gunnery debate is a "thing" for you after reading the thread "Long Range Gunnery" commencing at
http://www.kbismarck.org/forum/viewtopi ... =36&t=2637
After reading contributions from luminaries like Brad Fischer and Bill Jurens I take the latter's observations as a good guide:
My first guess would be to multiply the table figures by 0.5, i.e. to assume about 1% hits at 30000 yards for normal target angles.
100 shells for one hit- maybe.
and I note your own estimation was at odds:
He presents a graph at the end which would indicate to me that it wasn't unreasonable to expect good results from these guns at a range of 35,000 yds. My estimate from interpreting the final graph is about 7% hits on a battleship size target at that range from hot guns, which would make such an attempt worthwhile.
However such estimations are based on extrapolations from experimental data flawed by such points as:
Target speeds were, admittedly, often somewhat slower than might be experienced in combat, especially when towed targets were being used. Offset shoots enabled the target to travel at higher speeds, but somewhat restricted the course changes permitted due to safety issues.
In other words- unrealistic
. Wishing and wanting and hoping is one thing, but in real life the chances of hits are clearly diminishingly small.
Even the studies slew things to try and be encouraging.
A Naval War College study performed during World War II estimated that an Iowa Class (BB-61) battleship firing with top spot against a target the size of the German battleship Bismarck would be expected to achieve the following hit percentages.
Range Percentage hits against a broadside target Percentage hits against an end-on target Ratio
10,000 yards (9,144 m) 32.7 22.3 1.47:1
20,000 yards (18,288 m) 10.5 4.1 2.56:1
30,000 yards (27,432 m) 2.7 1.4 1.92:1
By choosing to consider an end-on target
the really difficult problem of estimating inclination accurately
neatly disappears. Battleships fighting each other would be on nearly parallel courses to unmask all batteries. 10 degree error in estimating inclination means that shell travelling for 70 seconds at a ship which has moved a kilometre is heading for the wrong place. A hit would be only a result of inaccuracy/dispersion. Luck.
Back in the real world when bombarding Japanese static land targets with an area much larger than a battleship:
TU 34.8.2's bombardment began at dawn on 15 July. The three battleships fired 860 16-inch (410 mm) shells at the city from a range of 28,000–32,000 yd (26,000–29,000 m). Aerial observation and spotting of damage was made difficult by hazy conditions, and only 170 shells landed within the grounds of the two plants.
All the best