Fig. 9. Increasing turning force;
winch, or torque amplifier.
By 1930, Dr. Bush and his group had finished the first differential analyzer. It was entirely mechanical, having no electrical parts except the motors. It was so successful that a number of engineering schools and manufacturing businesses have since then built other machines of the Bush type. Each time, some improvements were made in accuracy and capacity for solving problems. But, if you changed from one problem to another on this type of machine, you had to do a lot of work with screwdrivers and wrenches. You had to undo old mechanical connections between shafts and set up new ones. Accordingly, in 1935, the men at MIT started designing a second differential analyzer. In this one you could make all the connections electrically.
MIT finished its second differential analyzer in 1942, but the fact was not published during World War II, for the machine was put to work on important military problems. In fact, a rumor spread and was never denied that the machine was a white elephant and would not work. The machine was officially announced in October 1945. It was the most advanced and efficient differential analyzer ever built. We shall talk chiefly about it for the rest of this chapter. A good technical description of this machine is in a paper, “A New Type of Differential Analyzer,” by Vannevar Bush and Samuel H. Caldwell, published in the Journal of the Franklin Institute for October 1945.
GENERAL ORGANIZATION OF
MIT DIFFERENTIAL ANALYZER NO. 2
A differential analyzer is basically made up of shafts that turn. When we set up the machine to solve a differential equation, we assign one shaft in the machine to each quantity referred to in the equation. It is the job of that shaft to keep track of that quantity. The total amount of turning of that shaft at any time while the problem is running measures the size of that quantity at that time. If the quantity decreases, the shaft turns in the opposite direction. For example, if we have speed, time, and distance in a differential equation, we label one shaft “speed,” another shaft “time,” and another shaft “distance.” If we wish, we may assign 10 turns of the “time” shaft to mean “one second,” 2 turns of the “distance” shaft to mean “one foot,” and 4 turns of the “speed” shaft to mean “one foot per second.” These are called scale factors. We could, however, use any other convenient units that we wished.
By just looking at a shaft or a wheel, we can tell what part of a full turn it has made—a half, or a quarter, or some other part—but we cannot tell by looking how many full turns it has made. In the machine, therefore, there are mechanisms that record not only full turns but also tenths of turns. These are called counters. We can connect a counter to any shaft. When we want to know some quantity that a shaft and counter are keeping track of, we read the counting mechanism.
The second differential analyzer, which MIT finished in 1942, went a step further than any previous one. In this machine, a varying number can be expressed either (1) mechanically as the amount of turning of a shaft, or (2) electrically as the amount of two voltages in a pair of wires. The MIT men did this by means of a mechanism called an angle-indicator.
Angle indicators have essentially three parts: a transmitter, a receiver, and switches. The transmitter ([Fig. 10]) can sense the exact amount that a shaft has turned and give out a voltage in each of two wires which tells exactly how much the shaft has turned ([Fig. 11]). The receiving device ([Fig. 12]), which has a motor, can take in the voltages in the two wires and drive a second shaft, making it turn in step with the first shaft. By means of the switchboard ([Fig. 13]), the two wires from the transmitter of any angle-indicator can lead anywhere in the machine and be connected to the receiver of any other angle indicator.
Fig. 10. Scheme of angle-indicator transmitter.