As quoted in this article about analog[ue] computers as compared
to digital computers, "Add two and two. Coming from an analogue
computer, the answer would most likely be, 3.999 or 4.001." While
that is a true statement, there is one important feature that an
analog computer had over digital computers of the era: once initially
set up with a transfer function, outputs were nearly instantaneous
as the input was varied over a range of values, whereas a digital
computer could take quite a bit of time to crank through involved
mathematical equations. Performing tasks such as computing aircraft
flight paths and other sequential operations was the analog computer's
forte. If you needed to calculate exact values for atomic research
or cryptographic code cracking, that was and still is the domain
of digital computers.
See also
Mr. Math Analog Computer.
The Convair Analogue Computer
By R. D. Horwitz
Electronics Engineer
Engineering and Electronics Laboratories
Consolidated Vultee Aircraft Corp.
This milliondollar unit can be set up to obey the flight equations
of an airplane, computing motions of aircraft in flight.
Fig. 1. The "Convair" analoque computer in operation.
Two problem patchboard stations in normal operating position are
shown in onehalf section of the dual computer console. In the foreground
the engineer checks mobile recorder unit which draws graphs that
are the solutions to the problems on the computer. The resistance
and capacitance decade boxes are shown at top.
Today is the age of computers. A slide rule, an adding machine,
or even a man making a left turn onto a crowded highway is a computer.
Anything that involves the weighing of related factors and seeking
a solution of an unknown related to these factors can be considered
a computer. The concern of this article is with analogue computers
rather than digital computers.
One of the first questions asked when a visitor, not familiar
with computers, is shown the Convair computer is: "What is the difference
between an analogue and a digital computer?"
Analogue computers use continuously variable quantities such
as voltages or shaft rotations to represent numbers. Digital computers
use discrete quantities such as pulses to represent numbers and
compute by counting. One kind of analogue computer is an electrical
model of the mechanical system one wishes to study. Currents and
voltages in the computer correspond to forces and displacements
in the mechanical system. Convair's electronic analogue computer
is of a different type: it uses voltages and shaft rotations that
obey the same mathematical equations that govern the physical system
under study. This computer can be set up to obey the flight equations
of an airplane, computing the motions of the aircraft in flight.
"This is nice," says our visitor, "but let us get to something
simple. Add two and two." Coming from an analogue computer, the
answer would most likely be, 3.999 or 4.001. Such a computer is
not an exact device, but one that approximates correctness depending
on the accuracy of both the operator and the components in the computer.
"All right, then, what do you put in and where does it come out?"
asks the visitor. To answer this question, it is necessary to start
with the language of the computer.
The components of the computer have block diagrams that identify
their functions and serve as guideposts for the operator when he
sets up a problem. See Fig. 2. Fig. 2A is the symbol for an amplifier.
Usually the amplifier is shown with its input and feedback resistances
(Fig. 2B). It is the ratio of the values of these resistances that
determines the gain of the amplifier.
Since all voltages are referred to ground, the ground terminals
are usually not shown. The basic amplifier can do many things, (a)
It can add and when so doing is called a "summing amplifier" or
"summer," Fig. 2C. (b) It can perform integration, Fig. 2D, and
is called an "integrator." (c) With the aid of a potentiometer,
it can multiply by a constant (Fig. 2E). For this case the potentiometer
is adjusted so that it will divide any voltage such as x by 2. The
amplifier is adjusted for a gain of ten. (d) An amplifier in conjunction
with a servocontrolled motor, Fig. 2F, which drives the arm of
a potentiometer can multiply or divide. (e) For trigonometric functions,
the amplifier (Fig. 2G) controls a servodriven sinecosine potentiometer.
Fig. 2. Steps in setting up a problem for the
analoque computer to solve. See text for details on each individual
operation.
In each case, the amplifier is the heart of the computing element.
Other devices such as function generators for nonlinear equations,
limiters, relay amplifiers, and recorders are used where required
for a solution. The computer at Convair has many combinations of
these devices.
Now the visitor remarks, "These gadgets are all very fine. Let's
see you solve a problem with them."
That seems like a logical request so let us run through a simple
problem to see how the computer works.
Take a classical example, the spring supporting a weight. Fig.
2H. This problem requires some setup work before the computer can
be of use. First we must find an equation describing the problem.
X_{1} is the position of W hanging on the spring, k. X_{2}
is the condition when W is displaced by some force pulling the weight
down. The equation expressing this system is m(d^{2}x /
dt^{2}) = kx where x is the displacement of the weight
from its rest position X_{1}.
In order to set up the computer, the equation is rearranged to
read: (d^{2}x / dt^{2}) =  (k/m) (x). The desired
answers to this equation are the displacement, velocity, and acceleration
of the weight, W, at any time after the weight is released. The
computing elements (Fig 2I) needed for a solution are: two integrating
amplifiers (1), a potentiometer set at the ratio k/m (2), and an
inverting amplifier to change the algebraic sign (3).
Now we are ready to patch up the problem on the computer patchboard,
Fig. 2J. Assume, to start, that you have a voltage equal to d2x/dt2
on one end of a patch cord. This is plugged to the input of Integrator
1. The output of this integrator will be dx/dt. This value is patched
to Integrator 2 whose output will be x. Going back to the equation,
we note that d^{2}x / dt^{2} = (k/m) (x) so we patch
the output of Integrator 2 to a potentiometer set at the ratio of
k/m.
We still have to change the sign so the potentiometer is then
patched to the input of an inverting amplifier which changes the
sign. At the output of the inverter appears (k/m) (x), which is
equal to d^{2}x / dt^{2} which is the value we assumed
to be the input to Integrator 1 in the first place. So, we patch
the output of the inverter to this point.
We now have taken care of everything but setting the system into
operation. This requires that we duplicate in the computer the initial
conditions, i.e., the weight is motionless because it has not been
set into motion by releasing the force holding the weight in the
position where the displacement is x (the sign is negative because
the force is in a downward direction). To put this initial condition
into the computer, a charge corresponding to the initial output
voltage, x, must be placed on the feedback condenser of Integrator
2. There is no initial condition required at Integrator 1 because
the output of Integrator 1, which is the velocity, dx/dt, at the
start of the problem, is zero.
The control switch of the computer, which is in the "Reset" position,
is thrown to "Operate" which is analogous to releasing the weight.
The output voltage of Integrator 2 will rise and fall just as the
weight rises and falls.
These three answers can be obtained on a recorder or other measuring
device: The displacement of the weight, x; the velocity of the weight,
dx/dt; and the acceleration d^{2}x / dt^{2}, Fig.2J.
This problem is a very simple one to solve either by "longhand"
or with the computer. The value of the computer can be appreciated
if any of the parameters of the system are varied. The answers appear
instantly. Thus, it is possible to run a system from "one end to
the other" and be able to determine its capabilities at once.
Because of the comparatively lengthy setup time on the patchboards,
the Convair computer has removable patchboards. This allows the
operating station to be occupied only during actual computation.
While one operator is setting up a problem, another can be using
the machine. Fig. 1 shows the removable patchboard with a problem
patched in. It also shows portions of two operating stations. At
either side are the controls for each station. Answers may be read
on the eightchannel recorders in front as well as on the meter
on the control panel. Trunk lines between stations allow operators
to "borrow" equipment appearing on adjacent patchboards.
The milliondollar computer is housed in a temperature and humiditycontrolled
area to insure minimum variations caused by temperature fluctuations
or leakage due to atmospheric moisture. Many factors were considered
in the design and layout of the computer: (1) High stability over
long periods of time, (2) Isolation of critical elements. (3) Modern,
neat appearance. (4) Ease of operation and maintenance.
Needless to say, many problems had to be met and overcome in
the design and construction of the Convair computer facility. As
various portions are placed into service, new problems arise that
require solutions and new techniques are developed. With the completion
of the computer facility, Convair will have a versatile, accurate,
timesaving device that is rapidly becoming an indispensable tool
in the art of aircraft design and manufacture.
Posted June 19, 2015
