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.