09 June 2009

Differential analyzer

The invention: An electromechanical device capable of solving differential equations. The people behind the invention: Vannevar Bush (1890-1974), an American electrical engineer Harold L. Hazen (1901-1980), an American electrical engineer Electrical Engineering Problems Become More Complex AfterWorldWar I, electrical engineers encountered increasingly difficult differential equations as they worked on vacuum-tube circuitry, telephone lines, and, particularly, long-distance power transmission lines. These calculations were lengthy and tedious. Two of the many steps required to solve them were to draw a graph manually and then to determine the area under the curve (essentially, accomplishing the mathematical procedure called integration). In 1925, Vannevar Bush, a faculty member in the Electrical Engineering Department at the Massachusetts Institute of Technology (MIT), suggested that one of his graduate students devise a machine to determine the area under the curve. They first considered a mechanical device but later decided to seek an electrical solution. Realizing that a watt-hour meter such as that used to measure electricity in most homes was very similar to the device they needed, Bush and his student refined the meter and linked it to a pen that automatically recorded the curve. They called this machine the Product Integraph, and MIT students began using it immediately. In 1927, Harold L. Hazen, another MIT faculty member, modified it in order to solve the more complex second-order differential equations (it originally solved only firstorder equations). The Differential Analyzer The original Product Integraph had solved problems electrically, and Hazen’s modification had added a mechanical integrator. Although the revised Product Integraph was useful in solving the types of problems mentioned above, Bush thought the machine could be improved by making it an entirely mechanical integrator, rather than a hybrid electrical and mechanical device. In late 1928, Bush received funding from MIT to develop an entirely mechanical integrator, and he completed the resulting Differential Analyzer in 1930. This machine consisted of numerous interconnected shafts on a long, tablelike framework, with drawing boards flanking one side and six wheel-and-disk integrators on the other. Some of the drawing boards were configured to allow an operator to trace a curve with a pen that was linked to the Analyzer, thus providing input to the machine. The other drawing boards were configured to receive output from the Analyzer via a pen that drew a curve on paper fastened to the drawing board. The wheel-and-disk integrator, which Hazen had first used in the revised Product Integraph, was the key to the operation of the Differential Analyzer. The rotational speed of the horizontal disk was the input to the integrator, and it represented one of the variables in the equation. The smaller wheel rolled on the top surface of the disk, and its speed, which was different from that of the disk, represented the integrator’s output. The distance from the wheel to the center of the disk could be changed to accommodate the equation being solved, and the resulting geometry caused the two shafts to turn so that the output was the integral of the input. The integrators were linked mechanically to other devices that could add, subtract, multiply, and divide. Thus, the Differential Analyzer could solve complex equations involving many different mathematical operations. Because all the linkages and calculating devices were mechanical, the Differential Analyzer actually acted out each calculation. Computers of this type, which create an analogy to the physical world, are called analog computers. The Differential Analyzer fulfilled Bush’s expectations, and students and researchers found it very useful. Although each different problem required Bush’s team to set up a new series of mechanical linkages, the researchers using the calculations viewed this as a minor inconvenience. Students at MIT used the Differential Analyzer in research for doctoral dissertations, master’s theses, and bachelor’s theses. Other researchers worked on a wide range of problems with the Differential Analyzer, mostly in electrical engineering, but also in atomic physics, astrophysics, and seismology. An English researcher, Douglas Hartree, visited Bush’s laboratory in 1933 to learn about the Differential Analyzer and to use it in his own work on the atomic field of mercury. When he returned to England, he built several analyzers based on his knowledge of MIT’s machine. The U.S. Army also built a copy in order to carry out the complex calculations required to create artillery firing tables (which specified the proper barrel angle to achieve the desired range). Other analyzers were built by industry and universities around the world. Impact As successful as the Differential Analyzer had been, Bush wanted to make another, better analyzer that would be more precise, more convenient to use, and more mathematically flexible. In 1932, Bush began seeking money for his new machine, but because of the Depression it was not until 1936 that he received adequate funding for the Rockefeller Analyzer, as it came to be known. Bush left MIT in 1938, but work on the Rockefeller Analyzer continued. It was first demonstrated in 1941, and by 1942, it was being used in the war effort to calculate firing tables and design radar antenna profiles. At the end of the war, it was the most important computer in existence. All the analyzers, which were mechanical computers, faced serious limitations in speed because of the momentum of the machinery, and in precision because of slippage and wear. The digital computers that were being developed after World War II (even at MIT) were faster, more precise, and capable of executing more powerful operations because they were electrical computers. As a result, during the 1950’s, they eclipsed differential analyzers such as those built by Bush. Descendants of the Differential Analyzer remained in use as late as the 1990’s, but they played only a minor role.

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