USS Iowa BB-61 firing a 15 gun broadside 1984.
A 15 gun broadside is 9 - 16" guns and 6 - 5" guns firing.
The center of the muzzle blast is about 85 feet from the side of the ship. The visible part of the muzzle blast sphere is about 500 feet in diameter. As best we could calculate, the visible part of the sphere has a maximum width of about 600 feet when in full bloom. A single gun firing causes a depression in the ocean about 17 or 18 feet deep and about 600 feet wide in the ocean. The sphere is much larger in diameter than that but you only get to see a small portion of the bottom of the sphere in the ocean. This depression in the ocean from a single gun displaces about 11,000 tons of water.
When a 3 gun salvo is fired, the depression in the ocean is over 25 feet deep and the diameter of the sphere you get to see in the ocean is about 1,000 feet. A full broadside from the ship displaces about 100,000 tons of water, almost twice the weight of the ship. The displaced water pushes against the side of the ship and pushes it side-wise a bit.
It was interesting to me how the ship reacted to being pushed side-wise. How much the ship is pushed side-wise depends on the ship's speed. When doing shore bombardment the ship's speed is about 5 kts and the ship moves uniformly side-wise from bow to stern about 9 feet. At faster speeds the bow is held more firmly and the bow does not push side-wise. The bow wake, however, reduces the water pressure along the sides of the ship. The reduced pressure along the ships sides allows the rudders to more easily turn the ship by causing the fantail to move side-wise through the water thereby turning the ship.
The faster the ship is going, the lower the water pressure against the hull and the faster the ship will turn. The same is true of the muzzle blast and water pushing against the side of the ship. The fantail is pushed away from the direction of gun fire and the ship turns in the direction of the gun fire.
In the above picture the ship is traveling at about 10 or 12 kts. She is in a starboard turn of about 3 or 4 degrees towards the line of fire. If you will look at the ships wake you will see the line of the bow wake to starboard is some distance from the ship. The bow wake to port is against the side of the ship.
I used to love to watch this. When I could get away from my fire control duties I would go to the pilothouse and take the wheel. There you can watch the compass and see the ship turn when the guns are fired. I was always impressed by this then and I'm still impressed today. BB's, cruisers and DD's all move side-wise the same amount as described above. That is because the ships are all relative in weight, length, beam and size of armament, (size of guns).
The ship is 888 feet long and 108 feet wide
Turret emplacement data
16/1 224 feet from the bow. Trunnion height is 26.15 feet above the water line.
Gun trunnions are 132 inches forward of the turret center line.