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Archimedes' screw is the orgin of the modern propellor.
http://lisahistory.net/hist106/pw/articles/Archimedes.pdf -
The history of the Screw Propellor
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Without this first invention most boats would still use sails so it is a key part of the development of the propellor, however it is still some time before it is first seen.
https://academic.oup.com/icc/article-abstract/13/2/419/644433 -
John Fitch built the first steamboat in the United States. This is a paddle boat known as Fulton's Clemont, but it is a step toward the screw propellor because it is a steam boat https://cybercemetery.unt.edu/archive/oilspill/20130312030756/http://www.sam.usace.army.mil/Portals/46/docs/recreation/OP-CO/montgomery/pdfs/5thand6th/ahistoryofsteamboats.pdf
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The SS. Archimedes was the first ship propelled by a propeller and steam. https://www.nature.com/articles/143487a0
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USS Princeton was the first U.S. steam powered screw ship however, it did not reach much success and eventually exploded and killed the secretaary of state and the secretary of the Navy. https://monitor.noaa.gov/150th/ericsson.html
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The SS Great Britain broke records in speed by crossing the Atlantic ocean in 14 days https://dawlishchronicles.com/2018/09/04/ss-archimedes-arrival-of-the-screw-propeller-1839/
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First successful steam powered ship in the U.S. The Monitor was used in the civil war. It was a steam powered Iron clad that used the screw propellor. https://www.history.navy.mil/content/history/museums/nmusn/explore/photography/ships-us/ships-usn-m/uss-monitor-ironclad.html
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The discovery of the Cavitation phenomenon led to a major breakthrough into the screw propellor http://caltechconf.library.caltech.edu/85/1/cav2001_sessionB9.001a.pdf
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A patent of a screw propellor is depicted using the Cavitation phenomenon. This propellor design is strating to resemble the Modern day propellor https://patentimages.storage.googleapis.com/b9/fe/51/88f7bb399ea540/US1518501.pdf
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The discovery of the Cavitation Tunnel is a discovery used to help the caviation phenomenon. This will lead to the modern day propellor