Analog computers and their applications

Simply, an analog computer is a computing device that has two
distinguishing characteristics:

- 1.
**Performs operations in a truly parallel manner.**Meaning it can perform many calculations all at the same time.

An analog computer works in parallel. This means it can carry out multiple tasks simultaneously. A digital computer, even though it may work considerably faster, can only perform one calculation at any one instant. The only way around this in a digital computer is parallel computing, where a single machine has multiple processors. Even then, programs must often be rewritten to take advantage of this.

- 2.
**And operates using continuous variables.**Meaning it uses numbers that that change not in steps, but change in a smooth continuous manner.

By contrast, a digital computer can only perform sequential (one at a time) operations, and operates on discrete (noncontinuous) numbers.

Electronic analog computers may seem to be "simple" or "like a toy computer",
in fact they are powerful tools that were used during the 1950s and 1960s to
design and test systems like ICBMs, supersonic aircraft and spacecraft. But the
analog computer can be used to model any physical system that can be described
by mathematical formulas, even more mundane ones from modeling the effects of
pollution on the fish population in a river to fine tuning the suspension on a
new car design. Analog computers will not only test a fixed design but also
allows variables to be quickly changed to test "what if" conditions. By scaling
time as an independent variable, physical processes that happen quickly can be
stretched out, and processes that happen over a long period can be shortened to
make the process easier to study. And it is very easy to study variables at any
point in the program while it is running to find faults in the program design.

Although the electronic analog machine is correctly termed a computer, it does
not perform its computations by numerical calculations as does the calculator or
the digital computer. The analog computer performs mathematical operations on
CONTINUOUS variables instead of counting with digits. Positive numbers are
represented by positive voltages and negative numbers are represented by
negative voltages, all scaled to the computer’s working range, usually -100
volts to +100 volts (vacuum tube) or -10 volts to +10 volts (transistorized),
Thus the analog computer does not subtract 20 inches from 45 inches to obtain 25
inches but, rather, it subtracts 4 volts from 9 volts to obtain 5 volts. This 5
volts the operator reads as 25 inches in accordance with his arbitrarily
specified "scale factor" of 1 volt equals (or is ANALOGOUS to) 5 inches.

The electronic analog computer is basically a set of building blocks, each able
to perform specific mathematical operations on direct current voltages and
capable of being easily interconnected one to another. Some of the basic
operations include addition, subtraction, multiplication, division, inversion,
and integration. By interconnecting these building blocks, mathematical
equations are modeled. BUT an analog computer is a true PARALLEL computer that
can solve one or one thousand equations at the same time. In fact, similar
analog computers can be easily connected together to increase their computing
power. When you think about the result of many equations being solved
simultaneously and becoming the input to other equations, and sometimes these
solutions are then fed back or looped back into the original equations with all
of the variables changing CONTINUOUSLY with time, then you can get a brief
glance into the incredible power of these computers. Output is usually a
voltmeter, oscilloscope, or plotter.

Many universities today like Massachusetts Institute of Technology, University
of Illinois, University of Notre Dame, and Purdue University offer classes or do
research using analog computers, because they realize that the last chapter of
the history of analog computers has not being written. It’s an ANALOG universe
and analog computers are a natural way to study and understand it.

An analog computer (spelled analogue in
British English) is a form of computer that uses the continuously-changeable
aspects of physical phenomena such as electrical,[1] mechanical, or hydraulic
quantities to model the problem being solved. In contrast, digital computers
represent varying quantities incrementally, as their numerical values change.

Mechanical analog computers were very important in gun fire control in World War
II and the Korean War; they were made in significant numbers. In particular,
development of transistors made electronic analog computers practical, and
before digital computers had developed sufficiently, they were commonly used in
science and industry.

Analog computers can have a very wide range of complexity. Slide rules and
nomographs are the simplest, while naval gun fire control computers and large
hybrid digital/analogue computers were among the most complicated. Digital
computers have a certain minimum (and relatively great) degree of complexity
that is far greater than that of the simpler analog computers. This complexity
is required to execute their stored programs, and in many instances for creating
output that is directly suited to human use.

Setting up an analog computer required scale factors to be chosen, along with
initial conditions – that is, starting values. Another essential was creating
the required network of interconnections between computing elements. Sometimes
it was necessary to re-think the structure of the problem so that the computer
would function satisfactorily. No variables could be allowed to exceed the
computer's limits, and differentiation was to be avoided, typically by
rearranging the "network" of interconnects, using integrators in a different
sense.

Running an electronic analog computer, assuming a satisfactory setup, started
with the computer held with some variables fixed at their initial values. Moving
a switch released the holds and permitted the problem to run. In some instances,
the computer could, after a certain running time interval, repeatedly return to
the initial-conditions state to reset the problem, and run it again.

The similarity between linear mechanical components, such as springs and
dashpots (viscous-fluid dampers), and electrical components, such as capacitors,
inductors, and resistors is striking in terms of mathematics. They can be
modeled using equations that are of essentially the same form.

However, the difference between these systems is what makes analog computing
useful. If one considers a simple mass-spring system, constructing the physical
system would require making or modifying the springs and masses. This would be
followed by attaching them to each other and an appropriate anchor, collecting
test equipment with the appropriate input range, and finally, taking
measurements. In more complicated cases, such as suspensions for racing cars,
experimental construction, modification, and testing is not so simple nor
inexpensive.

The electrical equivalent can be constructed with a few operational amplifiers
(Op amps) and some passive linear components; all measurements can be taken
directly with an oscilloscope. In the circuit, the (simulated) 'stiffness of the
spring', for instance, can be changed by adjusting a potentiometer. The
electrical system is an analogy to the physical system, hence the name, but it
is less expensive to construct, generally safer, and typically much easier to
modify.

As well, an electronic circuit can typically operate at higher frequencies than
the system being simulated. This allows the simulation to run faster than real
time (which could, in some instances, be hours, weeks, or longer). Experienced
users of electronic analog computers said that they offered a comparatively
intimate control and understanding of the problem, relative to digital
simulations.

The drawback of the mechanical-electrical analogy is that electronics are
limited by the range over which the variables may vary. This is called dynamic
range. They are also limited by noise levels. Floating-point digital
calculations have comparatively-huge dynamic range (Good modern handheld
scientific/engineering calculators have exponents of 500.)

These electric circuits can also easily perform a wide variety of simulations.
For example, voltage can simulate water pressure and electric current can
simulate rate of flow in terms of cubic metres per second. (In fact, given the
proper scale factors, all that is required would be a stable resistor, in that
case.) Given flow rate and accumulated volume of liquid, a simple integrator
provides the latter; both variables are voltages. In practice, current was
rarely used in electronic analog computers, because voltage is much easier to
work with.

Analog computers are especially well-suited to representing situations described
by differential equations. Occasionally, they were used when a differential
equation proved very difficult to solve by traditional means.

An electronic digital system uses two voltage levels to represent binary
numbers. In many cases, the binary numbers are simply codes that correspond, for
instance, to brightness of primary colors, or letters of the alphabet (or other
symbols). The manipulation of these binary numbers is how digital computers
work. The electronic analog computer, however, manipulates electrical voltages
that are proportional to the magnitudes of quantities in the problem being
solved.

Accuracy of an analog computer is limited by its computing elements as well as
quality of the internal power and electrical interconnections. The precision of
the analog computer readout was limited chiefly by the precision of the readout
equipment used, generally three or four significant figures. Precision of a
digital computer is limited by the word size; arbitrary-precision arithmetic,
while relatively slow, provides any practical degree of precision that might be
needed.

Related files

Handbook of Analog Computations