>There was no theory, ship's screws were designed by trial and error.
The early marine propeller designs consisted of an Archimedes-type screw with multiple full turns. During tests of one such design on a small boat in the Paddington Canal in London, half of the propeller broke off. The broken propeller (with only one turn) turned out to be able to propel the boat twice as fast. [0]
The inventor, Francis Smith, amended the patent to describe either a single-turn screw propeller or one with two screw threads each describing half a turn (essentially a two-bladed propeller).
The early marine propeller designs consisted of an Archimedes-type screw with multiple full turns. During tests of one such design on a small boat in the Paddington Canal in London, half of the propeller broke off. The broken propeller (with only one turn) turned out to be able to propel the boat twice as fast. [0]
The inventor, Francis Smith, amended the patent to describe either a single-turn screw propeller or one with two screw threads each describing half a turn (essentially a two-bladed propeller).
[0]https://www.bluebird-electric.net/boats_images/propellers-fr...