It seems that both sides built ships referred to as rams. I assume they were designed to ram other ships. So was ramming still practical during the Civil War? What would be the number of ships successfully rammed? Some of the ironclad Civil War rams were kind of slow and would not a ship need to have a fair speed to be used as a ram?
This question can best be addressed in context, so I'll need to go back a little ways...
Ramming was the principal (and almost the only) means of inflicting severe damage to other vessels in the era of oared warships such as galleys or triremes. Some of the larger Roman warships could carry some "artillery" in the form of ballistae or catapults, but rate of fire was slow and ammunition was quite limited. Naval victories were effected by boarding actions, by archery to reduce the other crew (and therefore the vessel's mobility), and ramming. The main idea was to destroy the other ship's power of movement by killing oarsmen and shaving off oars with the ram-- once incapacitated, the victim could be taken by boarding or finished off by ramming the hull.
(A notable exception was the sort of flamethrower developed by the Byzantine navy in the Middle Ages, usually referred to as "Greek Fire," but this was a closely-guarded secret that did not see general use in other navies-- and in fact, there is still some uncertainty and debate about exactly how it was done.)
The advent of gunpowder and large sailing vessels revolutionized naval warfare. Sailing warships mounted banks of guns on the broadsides rather than banks of oars, and the amount of destruction that could be dealt over a distance constantly increased with the technology. Oared warships were still used, but increasingly in specialized situations, and they were nearly always quite small (such as the galleys employed in the Revolutionary War at Valcour Island).
Early on, the damage was really still aimed at the crew or the sails rather than the vessel. Well-built wooden ships can take a surprising amount of punishment and stay afloat, apart from the threat of fire. As naval artillery improved, the tactics changed-- but killing crew and disabling movement (by shooting away masts and rigging) were still the main methods of winning victories. But in the early 1800s, the technology changed again with the advent of steam power and improved weaponry, such as rifling and especially explosive shells. This made rapid and devastating damage to the structure of the ship itself increasingly possible, and led directly to the introduction of armor plate to restore the former relative invulnerability of the vessel.
Ramming (with intent to cause structural damage) was quite impractical in the height of the age of sail, but when steam allowed freedom of maneuver apart from the wind, there were many who thought that this made ramming once again practical (such as Charles Ellet, who took direct inspiration from the ancient triremes). There was a brief interlude when this was true, but ramming was usually only successful when the target already had its mobility constrained, such as the becalmed USS
Cumberland at Hampton Roads, or on the Western rivers where maneuver was necessarily limited by the river itself. The American Civil War occurred during this interlude; but even then the window of effectiveness of ramming closed rapidly with constantly-improving artillery and buoyancy improvements like truly watertight compartmentalization from construction in iron rather than wood. Within a few years, opposing warships wouldn't be able to get close enough to ram; the solution to
that was the "automobile" torpedo. And so the naval technological arms race rapidly left ramming behind.*
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*With exceptions. It was not unknown for destroyers to ram submarines to sink them in the World Wars, but this happened only sporadically.