The Electronic Calculator — A New Analog Computation Technique

This document translates the original French article “Une nouvelle technique de calcul analogique — Le calculateur électronique” published by CSF (Compagnie Générale de Télégraphie Sans Fil / Compagnie Française Thomson-Houston group). Language of original: French.

A New Analog Computation Technique

The Electronic Calculator

The constant progress of electronics has been enabling the realization of remarkable new devices for several years. Among these, the Grand Calculators — machines equivalent to large arithmetic machines — are well known. Less well known are the simpler analog calculators, whose role is to perform calculations starting from differential equations arising from physics problems: nuclear physics, ballistics, and so on.

The Atlantic and European government agencies, as well as our company, have been pushing for the development of electronic program calculators. The impetus of the French State and the Direction of Studies and Telecommunications (DET) has motivated CSF’s Research and Technology department, a French electronics company, to develop and manufacture analog calculators, an activity in which the French military is interested, along with other Atlantic countries and even neutral states.

The CSF Technique

What is the principal characteristic of CSF’s analog calculator? In a few words: the use of AC voltage transformations rather than DC, which gives the following advantages:

The three fundamental algebraic operations needed for solving any mathematical problem are:

Multiplication, by a constant k: this constitutes k × X = Y — that is, in circuit form: E₂ = k × E₁, where E₁ and E₂ are tensions.
Addition, which, from two numbers a and b, must form a + b.
Resolution of equations of type Y = f(X), which corresponds to E₂ = f(E₁).

These three operations are performed by CSF circuits in the following way:

Fig. 1: The multiplication circuit performs multiplication by a coefficient k of any number, by means of a transformer whose variable turn ratio (from 0 to 1) is achieved using a cylindrical condenser.
Fig. 2: The addition circuit performs addition of two numbers a and b by inductive addition (the secondary coils are wound in opposition so that the result is the sum of the tensions).
Fig. 3: The function circuit performs the resolution of the equation Y = f(X), using an inductance winding in the form of a curve; the cursor position corresponds to the function evaluated.

The Cylindrical Condenser (Variable Capacitor)

The circuit of Fig. 2 realizes the multiplication by a coefficient k of any number. The transformer used is cylindrical, composed of a rotor and a stator carrying distributed armatures. The curve traced by these armatures defines the function f(t) being entered.

The circuit of Fig. 4 performs the same multiplication but using a cylindrical condenser. This condenser is specially conceived to produce very low inertia (less than 10 gram-cm²) and a very large torque (greater than 1000 gram-cm). Its rotor is a bell shape of about 30 millimeters in diameter, and its total weight is less than 10 grams.

This motor, associated with the CSF calculator circuits, allows the solution of systems of implicit equations in several variables without the addition of any correction circuit. For example, in ballistics problems (DCA — anti-aircraft artillery), the elements of the trajectory (inclination and range) as well as the target coordinates can be defined.

Some Examples of Calculators

Coordinate Transformation

Assume one tracks at every instant the polar coordinates (distance D and angle θ) of a moving point, and one wants to imagine it from a fixed reference point as Cartesian coordinates X and Y. The calculator solves the equations governing this transformation:

ΔX = D sin G cos α
ΔY = D sin G sin α

The servomechanisms feed back the results continuously, converting the form of the data to the required outputs.

Derivation of a Function with Respect to Time

If one imagines a point moving as a function and wishes to find:

the calculation of function X;
the calculation of speed V;
a correction block to allow the computer to seek the point by itself.

One notes that at the entrance of block No. 2 one finds two derivatives which are continuously calculable; the sign of the correction quantities X and Y is obtained automatically.

Integration of a Function with Respect to Time

In the calculator of Fig. 5, the position of a moving point is retrieved at every instant; one wishes to know its position X continuously as a function of time. The speed V is represented directly by the output.

If V is known as a function of time, the calculator integrates continuously as follows: at each instant the speed V is fed in (equivalent to an input); the computer itself delivers continuously the result position.

This apparatus turns out to be even more elegant; the speed U is represented by the output as follows:

CR × V = −U

It is thus easy to integrate: X = U/Dt

Applications in Several Variables (Multiple Variables)

The CSF circuits permit treating problems with several simultaneously variable functions, Fig. 2. The calculator uses four simultaneously operating circuits like the above Fig. 2. The servomotor used is cylindrical, composed of a rotor and a stator carrying armatures. The curve traced by these armatures defines the function f(t) entered.

Thanks to these properties it is possible:

To realize long calculation chains involving no more than one amplifier, meaning to perform calculations with a precision independent of tube variations.
To obtain a precision better than 1/1000 by making the stability of each calculator circuit’s transformation ratio.

Fig. 4 shows how the four circuits simultaneously operating as in Fig. 2 are mounted. The servomotor used is cylindrical, composed of a rotor and a stator carrying distributed armatures. The curve traced by these armatures defines the function f(t) being entered.

In the CSF calculators, data and results are in general represented by the angular position of mechanical shafts. The shafts corresponding to the results are driven by servomotors by means of error voltages (servomotors) commanded by the electric tensions (error voltages) that go to zero when the problem is solved.

The servo motor is therefore an indispensable auxiliary part of every analog calculator. CSF designed its own; its type is a two-phase motor and it is specially designed to have a very low inertia (less than 10 gram-cm²) and a very large torque (greater than 1000 gram-cm). Its rotor is a bell shape of about 30 mm in diameter, weighing less than 10 grams.

This motor, combined with CSF calculator circuits, makes it possible — without adding any correction circuit — to solve systems of implicit equations in several variables. For example, in ballistics (DCA problems), one can determine the trajectory elements (inclination and range) as well as the target coordinates.

Application to Fire Control for Anti-Aircraft Artillery (DCA)

The Need for a Fire-Control Calculator

Since an aircraft constitutes a mobile target, it is evident that the firing of an anti-aircraft gun must aim the projectile not at the aircraft’s present position but at the point where the aircraft will be at the moment the projectile reaches it. Fig. 8 illustrates the problem of fire for two DCA weapons.

The point F, called “aim point” — the future position of the aircraft — is set at time T (called “firing time”) at a distance D from the battery. For example, the firing solution requires: waiting until the aircraft is at altitude h = 3,000 m and at a range of 3,000 m from the battery; the time to reach the burst point is estimated at 4 seconds; the aircraft travels at approximately 300 m/s. Calculation must therefore be performed with a precision on the order of 1:1,000.

One will understand that such a task cannot be solved by calculation alone. It is absolutely necessary to use a fast, accurate, and continuously operating calculator. The CSF calculator addresses this need in the following way:

The Role of the DCA Calculator

Fig. 10 illustrates schematically what a modern DCA installation looks like. It consists of:

The tracking radar (radar de tir)
The calculator (calculateur)
The junction box (boite de jonction)
The guns (pièces)
The generator (génératrice)

The figure shows schematically the articulation of tactics of a DCA installation comprising:

The tracking radar
The firing calculator
The battery of four guns

After the intervention of DCA, based on data from operations performed by the DCA calculator:

The stability, precision, and ease of the procedures provided by the computation serve the construction of calculators of various types. In the military domain, the CSF company is especially attached to realizing the following:

Possibilities of Use of the Calculators

The stability, precision, and ease of the procedures provided by the computation are applied to the construction of calculators of various types. In the military domain, the CSF company has particularly committed to realizing, with the same principles, multiple adaptations to the various requirements of use:

Anti-aircraft fire-control calculators always include the following equipment for fire control: a target tracking radar, a fire-control calculator, a range-finder corrector, and fire-control devices. These devices can replace one type of gun, calibrate different guns, and extract various ballistic tables.

Anti-aircraft defense calculators, of which a detailed system diagram is given in Fig. 10, can be produced to control various different systems. This diagram shows schematically the tactical articulation of a modern DCA installation.

Fire-direction calculators for telecontrolled systems, designed to guide the elements of fire towards the moving target — a guided weapon system, the output is continuously calculated.

Interception calculators, whose aim is to guide aircraft from the departure of the crews toward the target, using continuously calculated formation data while keeping the aircraft in continuous formation.

Pages 34–44 of the source publication. The article is illustrated with photographs of CSF analog computer hardware, including the cylindrical variable capacitor, the servo motor assembly, the MF (medium frequency) boards, and a DCA installation schematic.