A rope or tackle used in sailing to hoist the cathead of a ship; the mechanism for raising and lowering a ship's anchor cat.
Compound word from 'cat' (the ship's cathead, a beam extending from the ship's bow) and 'fall' (a rope or tackle used in hoisting). This is nautical terminology from the age of sail.
A 'catfall' has nothing to do with actual cats, but rather the wooden 'cat' beam on old sailing ships—ships had so many animal-named parts (cat, dog, fish tackle) that sailors basically named their whole ships like Noah's Ark!
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