15,000 yards was considered close range and a hit was considered probable with the first salvo.
20,000 yards was considered medium range with a 15%-20% probability of a hit with the first salvo.
25,000 yards was considered long range with a 1%-2% probability of a a hit with the first salvo.
These were hits against a ship.
Haven't come up with any information yet on the normal ranges the gun line fired from.
I assume the bombarding ships would want to be out of the range of enemy shore artillery. 15,000 yards sounds out of range for most land based artillery.
Just information to mull over when thinking about the effects of heavy surf on NOBA.?
I would approach these number with some caution but certainly the closer the ships were to the shore the higher the probability of early hits being achieved. Nothing like the hundreds of rounds being expended in naval battles at 20,000+ yards against manoeuvering ships at 30 knots mind. Having well-trained shore parties also had a major impact on naval gun fire support.
Quantity has a quality of its own,.... as they say.
As an example I would point to the Salerno landings and the trouble the landings ran into as the Germans piled up six panzer (Herman Goering, 16th and 26th) and panzer grenadier (3rd, 15th and 29th) divisions in the first few days after the landings. American light cruisers such as
Savannah,
Boise and
Philadelphia each mounted 15 x 6" guns, which meant a full broadside carried more weight than an entire battalion of 155mm medium artillery. Combined with other US and British 6" cruisers mounting 12 guns, the 8" cruisers and (later) the battleships
Warspite and
Valiant the naval guns broke up repeated attacks against the three (later four) British (46th, 56th) and American (36th reinforced by 45th) infantry divisions and their supporting tanks.
Destroyers came within 3000 yards of the shore line in order to send their salvos inland and the cruisers were operating between 5,000 and 10,000 yards of the shoreline but came closer inshore in order to lay bombardments down on German tank and artillery concentrations as much as 8000-9000 yards or more inland. Once ranged in it generally took only a few broadside salvos from the cruisers and battleships to destroy or drive off their targets.
The unit diary from the 16th Panzer divisions notes during the height of the German counterattacks that,
"Whenever German units attacked on the 14th September, such heavy fire from the sea and air struck them that they were only able to gain local successes...."
Between 13th and 14th Sept
Philadelphia fired 921 rounds of 6" shells and was relieved by
Boise. Boise then picked up the action firing more than 600 rounds at eighteen targets just that afternoon and evening. While that works out at an average of about 34 rounds per target, one target was a concentration of some 20 German tanks that was "obliterated" by 84 rounds from her guns.
The previous day
Boise came close inshore and used used 36 rounds to silence a German heavy battery up in the mountains above the beachhead.
On the 16th of Sept, after further failed attacks, Vietinghoff (German 10th Army commnder) conceded,
"The attacks,... were unable to reach their objectives owing to fire from naval guns and low-flying aircraft, ... in order to evade the effective shelling from warships, I authorised the disengagement on the coastal front."
The allies did have troubles of course. Where shore parties were absent the German attacks caused serious damage and even had Mark Clark considering evacuating the American beachhead (we have a number of ASL scenarios covering the Salerno battles but w/o the naval guns).
Rinse and repeat at Anzio with lessons learned. At Anzio the naval guns were even more effective than at Salerno.
[I like to keep this information handy for when some folks talk about 'panzers on the beaches' in Normandy being decisive.
Meh,... not so much.]