Mechanical and Civil Engineering Seminar
Mechanical and Civil Engineering Seminar Series
Title: Two old machines and the attempts to analyze them: Roberval's weighing balance and Archimedes' screw pump
Abstract: This talk will describe attempts to understand the mechanical behavior of a weighing balance proposed by Roberval in 1690 and a screw pump that bears Archimedes' name but may or may not have been invented by him.
Originally, Roberval's balance was seen as a paradox because it appeared to violate the law of the lever. An analysis published in 1713 should have resolved the issue, but the merit of this paper was never recognized, and it has been long forgotten. Throughout the later years, many other analysists have succeeded in explaining the mechanics of Roberval's balance using a variety of methods, continuing into the early 1900s when various practical features of the balance were considered. These efforts make a nice example of the history of early structural analysis. However, the 1713 paper stands out as probably the first ever analysis of a complex structure by the free-body method, which is the foundation of modern structural analysis.
Regarding Archimedes screw, there are two questions to be answered: the torque required to turn it and the volume of water it can hold. The torque appears to have first been determined (by a surprisingly simple equation) in a paper written in 1705, which was never acknowledged. Remarkably, a method for accurate computation of the water volume was not developed until 2000, a reflection of the complicated nature of the geometry involved. Never, though, has an explanation of the mysterious simplicity of the torque equation been offered, until now in this talk. The explanation also leads to a very easy procedure for computing the water volume.
Bio: John Hall is Professor Emeritus of Civil Engineering at Caltech. He is a former Dean of Undergraduate Students and interim Vice President of Student Affairs. His academic interests include earthquake engineering, finite element analysis, water resources, and history of science and engineering (early 18th century). He is well known for his work on the earthquake behavior of tall buildings and concrete dams.
NOTE: At this time, in-person Mechanical and Civil Engineering Lectures are open to all Caltech students/staff/faculty/visitors.