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This article contains a brief summary of information found on the web regarding the application, design, and calculations of Archimedes screws.

Application

• The Archimedes screw was used as the original design for ship propellers.
• Wiki Info on Propellers
• Wikipedia also has lots of great posts about the use of the Archimedes screw in it's applications moving water for irrigation & drinking water - search for it.

• In the design of propellers, people found that the less turns the screw makes, the more efficient the screw is at pulling through the water.
• Watercraft tech posts from patentpending See especially the posts on Ericson's propeller from John Fitch used on early submarines and the post on the Turtle, a submarine used during the American Revolutionary War. I particularly like the Turtle (pictured), mostly because I had a dream one night about a submarine. When I woke up I sketched out something that looked very similar.

Design

• A makezine post about making an archimedes screw on the cheap using offset pieces of wooden planks mounted to a central shaft..

Formulas

• Finding the Inner Diameter given an outer diameter and the flight of a screw. The forum also provides tips on building test screws (such as making them out of cardboard). Although, the information is very badly written and a little hard to understand. Plus, the formula given isn't really very good (I don't think).
• Here is an article about a guy named Rorres who worked out the most geometrically efficient screw design.
• I found and attached Rorres' paper on creating the most efficient screw. The paper outlines optimal dimensions for the number of blades, ratio of inner to outer diameters, pitch ratios, and turning speeds.
• Somewhere in the world there are out of print copies of a book called 'Archimedean Screw Pump Handbook' by Nagel originally published in 1968.
• There is a general book on pumps called 'Handbook of pumps and pumping' By Brian Nesbitt available at google books. While there is very little information about Archimedes screws in particular, the book has information about a great number of pump designs.