English translation
Rechenanlage “Verograph” zur genauen, laufenden Distanzbestimmung — Früher elektrischer Analog-Rechner
Complete English translation of the original German-language document (28 pages).
Series: Historical Anti-Aircraft Fire-Control Computers
The “Verograph” Computing System for Precise, Continuous Range Determination
Early Electrical Analog Computer
Technical Development from approximately 1936
Overview
Before and at the beginning of the Second World War, the anti-aircraft fire-control computers of all nations still employed mechanical calculating mechanisms to compute the future intersection point between an aircraft and the trajectory of the defensive projectiles. From this intersection point, the required angles (azimuth, elevation) were transmitted to the anti-aircraft guns, together with the fuse running time to be set. These computers were then called “command devices” (German: “Kommandogeräte”; English: “gun directors”).
One exception from this period employed an entirely different technology: the Zurich firm CONTRAVES AG independently developed an interesting computing method to perform a wide variety of tasks with high precision using electrical “resistance networks.” Electronic amplifier tubes were not yet suitable; a few were used, but as few as possible. Their stability was too low and their failure rate too high. The technology described here was deployed in the Swiss Army several years before the development of the “conventional” analog computer by Helmut Hölzner (V2 guidance) and remained in operational service for approximately twenty years.
Chronological comparison:
On p. 25 of this work a mechanical partial computer from 1917 is shown (range determination). The first large mechanical anti-aircraft fire-control computer was the “Vickers Predictor” from England, reportedly operational from 1928. Germany employed certain auxiliary instruments during the First World War, and later two large mechanical command devices in 1936 and 1940, produced in quantities of thousands. Switzerland introduced the Hungarian Gamma-Juhász device in 1938 and subsequently developed it further domestically at Hasler / Bern.
First impressions of the resistance computers: How does such a thing compute — and where would one ever have heard of this in training??
[page 1: figure only — 16 resistors linking two inputs (front, upper/lower) with two outputs (rear, upper/lower); each symbolic resistor actually comprises approximately 100 individual resistors. From a Contraves patent; see further below.]
[figure: Resistance coils in abundance — in truly large numbers! Below, they are tapped by rotating selectors. Detail photograph from the “Stereomat,” in practical service since 1939 and proven in use. Image from the Federal Archives.]
[figure: In the “Stereomat” computer there are many such resistance selectors. On the upper surface of the device (approximately 1 m long, casing removed) there are more than a dozen. Mechanical gearing establishes the contacts to the individual resistors. Image: Federal Archives.]
Even in the mechanical computers there were numerous electric motors, electrical switches, relays, etc. Mechanical quantities already known (e.g., flight altitude, compass heading, horizontal and vertical speed, flight time, etc.) were frequently re-transmitted electrically onto new rotating shafts. The issue is one of force distribution: the operating personnel who follow the aircraft with the telescope cannot turn all the downstream gearing from a handwheel. Everything must run smoothly and precisely — large forces are not compatible with the sensitive friction-wheel drives (= integrators) used; otherwise slippage and inaccuracies result. The actual calculations within the command device, however, take place entirely by mechanical means.
The firm Contraves was founded in 1936 with the goal of making anti-aircraft defense more precise. The plan was a large and complex system called the “Oionoscope,” which was completed only with great difficulty, after enormous expenditure of time, and only as a single prototype. The two electrical computers “Stereomat” and “Verograph” had been intended as components of the Oionoscope system, but were brought forward in production — and in the end formed the genuinely functional products that could be sold in small quantities over a longer period.
In an earlier work by the same author, “Oionoscope with Stereomat and Verograph,” the basic ideas of these computers had already been presented. At that time, however, the computing technique with resistance networks still appeared enigmatic and incomprehensible to the author — it was like a heap of disordered mosaic fragments without proper coherence. Through the assistance of Walter Vollenweider, a proper introduction finally became possible; now the fundamental principles seem reasonably understandable. Details are still lacking, but one can form a picture of the achievement of Contraves AG at that time. A great debt of thanks is owed to Walter Vollenweider! The earlier work mentioned can be retrieved at www.wrd.ch, under “Führungssysteme” (fire-control systems), then “Anfänge bis 1964” (beginnings up to 1964), or at the Military Library at Guisanplatz, www.big.admin.ch (search under the author’s name).
The present work describes the Verograph in greater detail (task, geometry, functional diagram) and explains the computing technique with resistance networks. The Stereomat from the same period using the same technology is mentioned occasionally; its impressive computation diagram appears at the very end of this work (p. 24). The Stereomat calculates, on the basis of two photographs, the true three-dimensional distance between the burst cloud and the aircraft. The Oionoscope is not discussed further here; see the earlier work cited (Ref. 6).
[page 2: figure — A Verograph computing system of Contraves on the move. In front, two electrical generating sets with petrol engines; then two heavy theodolites with built-in resistance computers, as well as the central device. Not included here are four telemeters at which measurement accuracy is checked (training operations). The theodolites must be set up at precisely surveyed positions (distance 1–2 km). Four carrying poles on each allow the devices to be carried and set on the tripod by eight men. Image from Ref. 1, January 1942 or earlier.]
Author: André Masson
December 2018
Geometric Layout of the Stereomat and Verograph in the Field
Stereomat: Determines the aiming error at the moment the bursting charge flashes. The calculation is performed retrospectively, when the aircraft has long since passed.
Verograph: Continuously determines the range from the anti-aircraft emplacement to the aircraft.
The theodolites used operate in each of the two computers within a different geometric system, with different axes of rotation. The Stereomat theodolites are accurately surveyed in but require no long cable. The Verograph has a single long, “pupin-coil” cable that is built into the computing network, with provisions for alignment at the main device: both wire pairs are to behave as nearly identically as possible. The measurement baseline is 1 to 2 km. Images: Federal Archives.
Left: The theodolites of the Stereomat adjust their two measurement angles when tracking the aircraft in the normal, intuitive manner: azimuth and elevation, tracked by two men at each device. Each theodolite photographs or prints both angles at the moment the bursting charge flashes (photo sensor). The film strips must be brought to the Stereomat by bicycle. There, the film initially had to be developed; this step was later eliminated thanks to printed or punched strips. Several measured angles are dialed in at the computer on handwheels, and at the touch of a button all trigonometric calculations are complete — but of course the aircraft is long gone. A “comparator” was subsequently developed (a measuring magnifier with various reticles, December 1945) so that the relevant angles could be determined directly at the remote theodolite and transmitted by telephone; this also eliminated the bicycle ride, making evaluation still faster.
Right: The theodolites of the Verograph have entirely different axes. One coordinate rotates a telescope mount about the axis of the connection line to the other theodolite (alpha in the figure above, angle relative to the vertical, assuming the theodolites are at the same height); the second coordinate rotates the telescope within the oblique mount about an axis perpendicular to the rotation axis of the mount (gamma in the figure above). Alpha is used only for tracking the aircraft but does not enter the calculation. The calculation is based solely on the two gamma angles. At each theodolite, two men continuously track both angles, assisted by an (early!) automatic servo-follow control. The device performs the calculations immediately.
At the main device, the precise distance to the aircraft is readable in real time, or is continuously available for further use in the Oionoscope or in telemeter training.
The coordinate transformation into a rotated coordinate system described further below (see page 8) finds its application in the Stereomat: a hand switch can select whether the computed aiming error (deviation between target and burst point) is expressed in a coordinate system with horizontal and vertical axes in the firing plane (x, y, z, not oriented to north, center figure), or in an obliquely rotated coordinate system relative to the gun (shot too long, too high in elevation, azimuth too large, right figure):
[figure: Changeover switch on the Stereomat (possibly only in later versions): output selectable in (x y z) or in (u v w).]
[figure: Output of aiming error in (x y z). Left the aircraft, behind it F the drogue target. x lies in the direction of fire (azimuth).]
[figure: Output of burst-point deviation in (u v w), corresponding approximately to fuze setting, azimuth, and elevation angle.]
Classical Range Determination to the Aircraft
In anti-aircraft defense, knowledge of the precise range to the aircraft is of the first importance. The range yields the time of flight of the projectile, on which the lead point also depends (the direction in which one aims).
During the First and Second World Wars (before radar measurement), range was determined with optical instruments called “Telemeter” in Switzerland and “Entfernungsmesser” (rangefinder) in Germany. These are optical double-telescopes with a large measurement base. The angular difference between the optics at left and right is measured while the aircraft is continuously tracked. For anti-aircraft use, the typical base length was 3 m (Switzerland) or 4 m (Germany), and in some cases longer — on ships up to 15 m. The longer the base, the more accurately the range is determined, but the more unwieldy everything becomes at the high angular velocities involved when the aircraft is near, or during a change of position. The author of this work completed his anti-aircraft recruit school in 1965, at which time light telemeters with a 1.25 m base were still in service with the 20 mm and 34 mm anti-aircraft guns. The following illustrations show the earlier 3 m telemeters for the 7.5 cm guns:
[figure: Swiss telemeter on Baur tripod: three persons sit behind the device. Two operators look monocularly through one objective each and track the rotating tripod after the aircraft by handwheel, both horizontally and vertically. The third man looks with both eyes through the large base and determines the range. Previously a simpler, three-legged tripod was used, with all personnel standing. Federal Archives.]
[figure: Instead of the 7 cm eye-spacing, the range operator looks at the aircraft along a 3 m base. Various sun filters and calibration options. At the rear, the attached Contraves gearing for linearization — only with this gearing (1941 or 1942) can the range values be fed directly into the command device, with electrical follow-up indicators. Federal Archives.]
[figure: Before the linearization gearing: the range operator (standing behind the device, forehead pad) reaches his right hand over the tube to the bright, thick measuring roller and sets the correct range. A further man reads the range from the scale beside it and calls it across to the command device. 3 m telemeter on old tripod, Air Force–Anti-Aircraft Museum Dübendorf.]
Even before Switzerland received its first large telemeter for experimental purposes (1937; Born, p. 86; smaller infantry or artillery telemeters existed previously), F. Fischer (ETH professor from 1933) had clearly seen that the precision of range determination in this way would be insufficient. In 1936 he co-founded the firm Contraves AG with fellow students and attempted to develop precision instruments for anti-aircraft defense and to sell them to the Army. In particular, he sought to determine the range to the aircraft far more accurately, with a measurement base of 1 to 2 km — to this end he developed novel electrical computing devices with resistance networks, which are somewhat difficult to comprehend. Radio tubes were not yet stable enough for the precision hoped for — they were therefore avoided as much as possible. The prior assessment of F. Fischer is consistent with the recollections of the last surviving witnesses of the heavy 7.5 cm anti-aircraft artillery: range determination had invariably been the source of the greatest errors.
Principle of Range Determination with the Verograph
In essence, only the sine rule is employed to determine the range to the aircraft, though in a refined manner. Triangle measured: Theodolite 1 — Theodolite 2 — Aircraft. Both theodolites are continuously tracked to the aircraft by means of two handwheels that themselves incorporate servo-follow control: as long as the angular velocity of the aircraft remains constant, no further correction at the handwheel is required. The theodolites have special coordinate systems such that the tracked telescope directly yields the measured angle between the measurement baseline (distance to the other theodolite) and the aircraft. The second angle (the obliquity of the triangle with respect to the vertical) is continuously tracked by handwheel in order to follow the aircraft, but is not used in the calculation.
Sine rule: Two side lengths in a triangle are in the same ratio as the sine values of the opposite angles — this holds for any triangle. The length of the measurement base is known, as are two measured angles from which the third angle (opposite the base) follows. The triangle is determined; the required range to the aircraft can be calculated. However, several transformations are still needed:
First transformation: Through certain transformations and conversion to other angles (some outside the triangle), an alternative form of the sine rule results, which is more conveniently used here. Everything has been verified; there is no mystery and no difficulty:
[page 5: figure — Theodolites are at P1 and P2; the aircraft is at F. The triangle lies at an arbitrary inclination in space. The two angles γ1 and γ2 to the aircraft are measured from a plane (dashed) perpendicular to the connecting line between the two theodolites. These angles γ1 and γ2 enter the calculation; the second angle at each theodolite, by which the telescope is tracked to follow the aircraft, is the obliquity of the triangle with respect to the vertical and does not enter the calculation. The base b between the theodolites is known precisely (typically 1–2 km). The range r1 is sought. All variables change continuously as the aircraft flies on.]
The transformed sine rule with the angles depicted above now reads:
b/r1 = (tan γ2 − tan γ1) · cos γ1
- r1 = sought range
- b = measurement base
According to this calculation, the sought range r1 is determined in the Verograph — in principle. But not so in practice; it becomes somewhat more complicated. The tangent functions of the measured angles γ1 and γ2 become very large when the angles approach 90°, i.e., when the aircraft is near the connecting line between the two theodolites. The errors for given step sizes (see later, resistance step sizes) then become very large, meaning a very fine step size would have to be chosen throughout the entire sky, whereas this would really be sensible only in a few places.
In order to keep the errors comparable everywhere, regardless of where the aircraft is located, a second coordinate transformation is applied. The calculation does not use the actual angles γ1 and γ2, but rather transformed abstract values that are no longer linearly related to the actual angles. The actual formula from which the range can be determined then involves hyperbolic functions of the distorted angles and appears rather non-intuitive. The transformation from real angles to abstract computed values is accomplished by ensuring that the handwheels are no longer coupled directly to the telescope, but to a mechanical auxiliary construction with a follower against a curved template. Turning the handwheel by the same amount does not move the telescope by the same amount in all regions of the sky. Only the handwheel revolutions enter the calculation.
[figure: The handwheel (far right), used to keep the aircraft continuously in the crosshairs, no longer drives the telescope directly, but instead a mechanical auxiliary construction. The template (curved profile below) defines the relationship between the real angles and the abstract computed values. The rotations of the handwheel are evaluated, not the actual angles in the triangle. The telescope shows the actual angle γ, i.e., the handwheel is turned until the aircraft is directly in the crosshairs. The handwheel revolutions lead mechanically to the selection of the correct electrical resistors in the subsequent computing operations. Image: Ref. 1]
Since even one of the surviving Contraves block diagrams for the computing operations in the Verograph retains the principle of the more easily visualized real angles (see p. 13), the abstract variables and the resulting hyperbolic functions as actually used in the computer are initially set aside. The principle of the calculation can also be understood with the ordinary trigonometric functions.
This second coordinate transformation is intended to achieve the same computational accuracy everywhere in the sky — only when the aircraft lies within a cone of 15.5° around the axis connecting the two theodolites does the calculation fall outside the required accuracy range.
Some historical illustrations of the Verograph and its two theodolites:
[figure: The two theodolites look identical but calculate different quantities. Handwheels for tracking the aircraft. Rotation axis 1: axis of the round eyepiece upper right (the axis remains fixed); rotation tilts the upper section. Rotation axis 2 (currently vertical): rotates the dark telescope upper left through up to 180°. Handwheels / eyepieces do not rotate along during aircraft tracking.]
[figure: Central recording device. On the right, cables from four telemeters are connected (training operation), as well as the two theodolites and the electrical generating set. On the left, a display and paper strip with four range errors. Bottom rear: telephone handset. All 3 images: “Operating Instructions for Verograph No. 202, Type II CH,” October 1943. Air Force–Anti-Aircraft Museum Dübendorf.]
[figure: Early form of the recording device: The alignment (two parts of the equation, p. 6) is performed manually. The handwheel tentatively sets the sought range; when the equation is satisfied, the display instrument at top center reads zero. The alignment was later automated (diagram p. 13). Top right, very small: precise range to the aircraft, as a numerical value.]
[figure: Above the handwheel of the recording device is a closed housing for careful alignment of the long measurement cable. The cable has a “pupin box” every 150 m to compensate the cable capacitances. W. Vollenweider’s view: This makes no sense for a single frequency alone. These are more likely coils with noise-suppression functions than true Pupin coils (perhaps the correct terminology was lacking at the time; “Pupin” was a well-known name). Quotation from F. Fischer: “The box contains… in each wire pair a shunt conductance tuned for distortion-free performance of the cable” (Ref. 1, p. 14).]
Images above of the Verograph theodolite and recording device: from the Operating Instructions for Verograph No. 202 (Type II CH), Air Force–Anti-Aircraft Museum Dübendorf, 20.10.1943.
Computing Technique with Resistors: An Attempt at Reconstruction
The aim now is to understand, to a reasonable degree, the principle of the resistance networks. At no point in the correspondence between Contraves and the military authorities was anything mentioned about the fundamental procedure of the calculations; in the archives (Federal Archives, Air Force–Anti-Aircraft Museum at Dübendorf) nothing concerning the computing technique has been found. The picture conveyed here is based on numerous fragments and partial images, drawn primarily from Ref. 1, Ref. 2, Ref. 4, and from patent specifications found from Contraves. The patent specifications generally employ a very idiosyncratic language, but at least often contain fine figures from which something can be read off.
By way of introduction, to acclimatize — as an eye-catcher illustrating the approach (a well-documented but relatively unimportant example — not present in the Verograph; employed in the Stereomat, cf. p. 4, but not even mentioned in the computation diagram, cf. p. 24; in Ref. 2 the coordinate transformation is also shown in three dimensions, with 3 angles):
Example of a coordinate transformation by means of a resistance network (from Ref. 2, Stereomat)
The calculation uses four-terminal networks (four-poles), six-terminal networks (six-poles), eight-terminal networks (eight-poles), etc. — these are units having 4, 6, or 8 lead wires. Each (input or output) signal consists of two wires carrying, e.g., +3 V and −3 V respectively, symmetrically. If two quantities A and B are to be added, C = A + B, a “six-pole” is required. The reference level zero, earth, ground, never occurs. Calculation is performed with alternating voltage (in the Verograph: 75 Hz).
The following is the computing principle for a coordinate transformation. In the figure below, the following voltages are applied to or taken from the corners of the resistor cube (the voltages correspond to coordinates in meters):
- 1, 2 = input x 5, 6 = output x’
- 3, 4 = input y 7, 8 = output y’
All coordinates may be variable in time! x, y are the original coordinates; x’ and y’ are coordinates in the rotated system.
The following computation must be ensured by the resistors:
x’ = x cos φ − y sin φ y’ = x sin φ + y cos φ
φ will generally be variable in time. Each resistor is mechanically tracked to the variable angle φ by means of gearing.
[figure: This is merely the pure topology of the resistors. At the corners are “decouplers,” not shown here, for signal summation — see next figure. Each individual one of these “16” resistors consists of a complete set (approximately 100) of mechanically selectable resistors (in the coarse/fine range, many more). Image from Contraves Patent 201663 (1937/38), as are the following drawings.]
[figure: The decoupler six-pole (below) can branch (copy signal x to x1 and x2) but can also add, when two different voltages are applied at x1 and x2. The dashed resistors represent the input or output resistances of the following stages. The variable x “branches” into two paths. If x changes, both paths reflect the change. If a voltage applied at x1 changes, only output x is affected, not x2 (the paths x1 and x2 are “decoupled”; there is no back-coupling between them). All three resistors between terminals 1 and 2 are equal in value (evident from a single other Contraves drawing).]
The concrete circuit diagram of the eight-pole for the coordinate transformation given above, including the four decouplers at the corners, follows:
An eight-pole: This is the actual circuit for the coordinate transformation. The 4 × 4 resistors can be adjusted / selected by the symbolized “handwheels,” i.e., entirely mechanically (gearing, drives — manual operation is not required). The mechanical drives of the Stereomat are preserved as photographs in the Federal Archives; see directly below (not yet found for the Verograph). This circuit is possibly somewhat more general than just the coordinate transformation shown above (which has only a single angle), because four entirely independent angles can be set here. Cf. Ref. 6, page 10.
The transformers are related to the fact that apparently “independent” voltages can be added (as with several individual batteries). Everything is operated by alternating voltage (in the Verograph: 75 Hz). Input and output resistances must be carefully observed! Prof. Fischer repeatedly emphasizes that all input and output resistances throughout the entire circuit must be equal in value. Each individual resistor R1 to R4 consists of a complete set of very many resistors, addressable by a rotary selector.
- Decouplers at terminals 1,2 and at 3,4 (both inputs): function as splitters
- Decouplers at terminals 5,6 and at 7,8 (both outputs): function as summers
The following are representations by Walter Vollenweider (personal communication, e-mail of 21.5.2018) of how to visualize and verify the splitter and the summer. Everything can be followed in detail using Ohm’s Law alone. Note that there is no common electrical “null point,” i.e., the voltages lie asymmetrically.
Note: “Koppler” = “Entkoppler” (decoupler) — these terms mean the same thing.
In both cases, the diagram is drawn with the input on the left and the output on the right. In both summation and splitting, the output voltage is attenuated by a factor of ½, and the power by ¼; this is described as an attenuation of 6 dB. Constant and known attenuations are no problem for a computing system.
Circuit diagram, upper right: Measured with a voltmeter, one cannot see that the two voltages are “offset” (above zero and below zero respectively, where zero is the midpoint of the input). This is the reason why no reference to “zero,” “earth,” “common,” etc. is ever found in Prof. Fischer’s writings. Even in the summer, the output is asymmetric.
Important for the functioning of the entire computing system: In the addition, one input (terminals 3,4) has no influence whatsoever on the other input (terminals 5,6). If, for example, “3” and “15” are being summed, but the value for “3” were to shift slightly when “15” is replaced by, say, “20,” the addition would no longer be precise.
Apart from the decouplers and summers, the resistors in the networks are not constant, but are continuously tracked to the current state (position of the aircraft):
Numerical representation of the required trigonometric functions — for example, finding sin 31.4°:
It is not a special computing technique that allows the numerical provision of trigonometric functions, but rather a form of storage technique: every (partial) result that could ever occur has already been calculated beforehand and is permanently wired in with the appropriate resistors. Once the “calculation” runs, the currently appropriate resistors are selected at any moment by mechanical gear drives.
[figure: Two of the three drives that in the Stereomat translate the input angles into the selection of the appropriate resistors. Visible: 13 couplings to resistance selectors. The Stereomat does not calculate in real time; eight angles from two stereo photographs together with the baseline are entered retrospectively by hand.]
Resistance selectors:
>> Now we come to the key point! This is central! <<
The situation can be visualized as a Wheatstone bridge, but one that is not balanced to zero. Input: a specific operating voltage. Output: any value between plus and minus the input value. For 100 desired steps of the result, 100 specially detuned bridge circuits must be stored — or a single bridge with always-different component resistors. If significantly more than 100 steps are desired to increase accuracy, coarse/fine cascades are employed (see p. 14): for each coarse step (degree), a further hundred fine steps are nested within.
[figures a through d: Wheatstone bridge circuit, repeatedly redrawn. Symmetrical bridges have only two different resistance values: r3 = r2 (b., c.). d.: Between terminals 3 and 4 comes the subsequent circuit, with internal resistance R. It is important that between terminals 1 and 2 the crosspiece also has the same resistance R. This allows stages to be cascaded in series to any depth. d.: If the ratio of output voltage (3,4) to input voltage (1,2) is given as p, and the total resistances are always to be equal and the crosspiece must be symmetrical, then all resistors are fully determined: r1 = R(1−p)/(1+p) and r1 · r2 = R²]
[figure e: Two crosspieces in series yield as the overall transfer factor the product of the individual transfer factors. The overall input resistance is still R. From Ref. 1, p. 2]
Multiplication: Output voltage of a four-pole = input voltage times the selected reduction factor. Multiplication of a given voltage by three different factors = series connection of three different four-poles. Here, different values of the argument (e.g., different angles) are also possible for each individual factor.
Division: Multiplication by the previously computed reciprocal values. Page 23: a far more complex solution…
Multiplication or division in which the result assumes a larger voltage than the input: This is not possible with crosspieces — they can only reduce, i.e., produce smaller voltages.
In the Stereomat, tubes are installed at seven such points (division by the sine of an angle). In the Verograph this was presumably also necessary, because the hyperbolic sine (sinh u) can become greater than “one” (p. 21).
Addition / splitting: Two addition circuits are in use, both historically documented — but when one versus the other circuit is used remains somewhat unclear. Used in the reverse direction (input at the “sum” terminal), both circuits yield a splitting of the given value into two independent branches.
a) Addition with simple decoupler (= six-pole): See above, pages 8 and 9.
b) Addition with complete decoupler (= six-pole):
F. Fischer, in Ref. 1, p. 3: “In order to carry out the addition, we must turn to more complex bridge circuits” — see Fig. 6 directly below.
Under the following conditions, the 12 individual resistors are exactly determined; no freedom remains:
- all three crosspieces shall be symmetrical;
- when terminals 2,5 and 3,6 are terminated with R (input resistance of the following circuit), R shall also be measurable at terminals 1,4;
- this also cyclically permuted: … R shall also be measurable at terminals 2,5, and … R shall also be measurable at terminals 3,6;
- the voltage transfer factor between 1,4 and 2,5 shall be p12;
- the voltage transfer factor between 1,4 and 3,6 shall be p13;
- the voltage transfer factor between 2,5 and 3,6 shall be zero (these two branches cannot influence each other).
This more complex six-pole is also compared in the text with the differential gear frequently used in mechanical computing machines. With it, additions, subtractions, and signal splitting can be realized (the last is not used in mechanical computers — one simply takes off a second branch by gear). Cf. the differential in the automotive drivetrain.
In contrast to the mechanical gear, different weighting factors can conveniently be introduced here by the choice of resistors, between terminals “motor” (1–4) and “wheel 1” (2–5) or “motor” and “wheel 2” (3–6); or also in the addition path, i.e., from right to left: C = p·A + q·B.
Term “decoupler”: Voltage at terminals 2,5 does not influence the voltage at terminals 3,6. This is important for the entire computing scheme to function. In the Stereomat, this requirement is frequently emphasized!
Source: Ref. 1, pp. 3, 4.
Subtraction: Addition with the cables reversed for one of the variables.
Hypothesis, not explicitly found anywhere:
- For a 1:1 addition, the simple decoupler (see page 8) is used: C = A + B
- For a weighted addition, the complete decoupler is required: C = p·A + q·B
If the weights p and q must also be variable during the course of the calculation, all 12 resistors must be continuously adjusted (alternatively, p·A and q·B can each be multiplied separately and then added 1:1, which requires only 8 variable resistors).
Own measurements on the simple decoupler:
In a test circuit, the splitting of a signal into two branches and the addition of two voltages have been measured experimentally. Individual batteries independent of one another were used as voltage sources, together with a standard high-impedance voltmeter. All three resistors of the decoupler had the same value (resistors read off by hand), and the simulated input resistances of the subsequent circuits again had the same value — likewise at the signal injection point (here a series resistor would more properly represent the “output resistance,” but this affects neither the principle nor the measurement result).
Terminology: Since one can no longer speak of “input” or “output” because both are possible at every terminal, the terms “total” and “partial” are used here. In the diagram on page 8, Fig. 1: terminals 1, 2 = total voltage; terminals 3,4 and 5,6 = partial voltages.
Result of the measurements: The simple decoupler functions excellently!
- Only one voltage U connected at Total: Partial voltages at both locations = ½ U
- Only one voltage U connected at one Partial terminal: Total voltage = ½ U; Partial voltage at the other terminal = 0
- Two voltages connected at both Partial terminals: Total voltage = ½ (U1 + U2)
Functional Diagram of the Verograph
With the knowledge of the addition six-poles, it is now possible to follow how the Verograph determines the range to the aircraft. The equation from page 6 is shown here again. The tangent functions of the two measured angles are subtracted from one another, then multiplied by cos γ1. This is compared with (constant voltage) times b/r1, by forming the difference between both sides; this difference is motorized or adjusted manually by trial of the sought range, so as to keep it continuously minimized — i.e., as close to zero as possible at all times. (Here without the hyperbolic functions)
b/r1 = (tan γ2 − tan γ1) · cos γ1
- r1 = sought range
- b = measurement base
TV2 is the remote theodolite; TV1 is the one near the main device RV. The 75 Hz alternating voltage at TV2 is placed simultaneously on the long cable both directly and multiplied by the tangent of angle γ2. The telescope directed toward the aircraft adjusts the resistors in the R-network for tan γ2 continuously by mechanical selection with coarse/fine range, i.e., with high accuracy.
TV1 forms the value (“U · tan γ2” minus “U · tan γ1”) times “cos γ1” and feeds this value to the nearby main device, where it is compared and continuously equated with “U divided by range times base b.” The continuous alignment of the range is realized here with a motor (or possibly with a large alignment handwheel): instrument A is to show zero at all times. This is the “solving” of the trigonometric equation by continuous trial of the correct range.
[figure: Double lines = mechanical shafts with gear branches. Single lines = electrical variables (each with two wires). E = numerical value of the range.]
The derived range (horizontal shaft immediately above the letters RV) is recorded on paper and compared with the values from four separate telemeters: the four differences are continuously written on paper strips. In the Oionoscope, the range is used elsewhere via a rotating shaft.
Image from the Federal Archives, Oionoscope, November 1942, and from the Air Force–Anti-Aircraft Museum, Verograph, October 1943.
Whether the two six-poles for signal splitting (in TV2 and in RV) and the two six-poles for subtraction (in TV1 and in RV) are the simplified or the complete decoupler six-poles remains unknown for now. — The sign of the tangent difference can never reverse; if both observed angles are equal, the aircraft is infinitely far away.
In reality, the calculation does not use the ordinary trigonometric functions of the measured angles to the aircraft, as drawn in the diagram for easier comprehension, but hyperbolic functions of an auxiliary variable u that is not linear with respect to the measured angle γ (cf. pp. 6, 7). More on this in the appendix, from p. 18.
Increasing Accuracy through a Coarse/Fine Cascade
100 steps to cover the angular range from −75° to +75° was insufficiently accurate, and far more steps are not achievable with the resistance selector. One coarse step corresponds to approximately 1.5°, and this step is subdivided by 100 steps of a following fine stage, so that the smallest step corresponds to approximately 0.015° if everything were linear in angle.
[figure: Above/below the four coarse-step resistors (rows 1 to 4) are changeover switches for the selection of the fine rings. This allows the changeover to the next coarse step to occur at exactly the same moment as the reset of the fine chain.]
Left: Middle rows 1–4: Four variable resistors 1 to 4 form a crosspiece with adjustable coarse voltage, 100 steps over the entire angular range. Two outputs from the coarse stage: interconnected B-contacts.
Above/below the resistors, rows 5–8: No resistors, only slip rings for alternately switching across to the fine rings. Currently the four lower of the eight connections to the fine range are active.
A mechanical snap-action drive produces a stepped movement in the coarse range (standstill until the fine stage has gone around once).
Right: Four variable fine resistors, 100 steps (thus considerably more than drawn).
The cosine function is much flatter near 0° and much steeper near 80° — what is to be done there with fine steps that in the first case must be very small, and in the second much larger? What resistance values must be soldered in when the fine steps must assume entirely different values depending on where the aircraft is in the sky?
This works out, thanks to the addition theorem! What is needed is: cos(γg + γf), where
- γg = e.g., the 14th coarse step
- γf = e.g., the 42nd fine step
The identity is: cos(γg + γf) = cos γg · cos γf − sin γg · sin γf
This works out well: series connection = product. The figure above is, for example, the first half, cos(coarse) · cos(fine); then everything again with sin gives another diagram like the one above; together these yield the precise cosine function.
Per crosspiece (coarse or fine), there are 400 resistors each, making approximately 1000 in the diagram above (with some reserve in the fine stage, outside range, see below). This yields approximately 2000 resistors for cos(γg + γf) in total, per the addition theorem. Since three trigonometric functions in total must be provided (tan γ1, tan γ2, cos γ1) in the overall functional diagram, the total comes to approximately 6,000 precisely manufactured resistors for the trigonometric functions, plus “1/r” and “times b,” as well as the splitters/adders. The number of steps for the hyperbolic functions actually used is the same as estimated here. Hyperbolic addition theorems exist as well.
Still to be understood is the changeover when the fine steps are “full” and the next coarse step is engaged. Simultaneously with the changeover of the coarse step, the fine range must revert to its starting point. This must be made possible with the second brush set. This is not fully understood. And what purpose do the resistors or ring positions serve that evidently extend beyond the 100 steps?
Estimated Accuracy of the Verograph Measurement
The accuracy of range determination is constant in the reciprocal of the range for both the optical telemeter and the Verograph. F. Fischer estimates a typical error in (1/E) for the Verograph of approximately 0.2 · 10⁻⁶ m⁻¹. Converted back, this yields the following approximate accuracies of range determination for the Verograph at several typical ranges to the aircraft (for a 2 km base):
| Range to aircraft | Typical measurement error |
|---|---|
| 3 km | 2 m |
| 5 km | 5 m |
| 10 km | 20 m |
| 15 km | 45 m |
If these figures can actually be maintained, they are very fine, outstanding values for anti-aircraft use! The length of a “Flying Fortress” B-17 was 23 m, the wingspan 31 m. However: the telemeters with which the actual shooting is done are substantially less accurate than the Verograph.
Various additional notes:
-
Weight: One theodolite for the Verograph weighs 300 kg! The many resistors consist of wire coils; cf. image p. 1 (the image is of the Stereomat; the Verograph will look similar).
-
Survey: The accuracy of the survey of the two Verograph theodolite positions was to be 1 m or 0.5 m (over one to two kilometers). The Stereomat, Verograph, and also the Oionoscope were all likely intended for firing-range use rather than wartime field deployment. A rapid change of position is barely feasible (except possibly to prepared sites).
-
Sloping terrain: In the book “Fliegerabwehr” (Anti-Aircraft Defense) by Hermann Schild, on p. 36, a Verograph theodolite is shown whose main body does not sit horizontally on the base plate but is slightly tilted — caused by the difference in height between the positions of the two theodolites. There it can also be seen very clearly that the uppermost telescope section can really tilt all the way over (rotation angle around the eyepiece axis: 220°, i.e., the full upper hemisphere of 180°, plus 20° below horizontal on each side, according to a sketch in Ref. 1). This is the only known photograph in which this can be seen.
-
Automatic alignment: In the computation diagram of the Verograph (p. 13), the satisfaction of the main equation is achieved automatically by a motor: any deviation is amplified and the sought range is altered in the correct sense so that alignment is maintained as well as possible at all times. Optionally, alignment can be performed by a human using a handwheel, with or without an added velocity term. A switch (personal image 1549) shows the four modes of range alignment. It is common to all manual tracking operations (including the follow-up indicators at the command device) that a human can readily smooth and average jerky quantities. A human may possibly be superior to automatic solutions in this respect. — When built into the Oionoscope, however, the Verograph has no handwheel (one photograph preserved, personal image 1602). In an early overall diagram “Oionoscope D” (7.3.1940), the range tracking is also drawn as automated.
-
Manual computation work: In what manner the many partial resistors within the multi-terminal networks were practically computed is not known. There were of course no computers at the time. The achieved precision in the manufacture of the resistors likewise remains unknown. — Possibly the difficult-to-comprehend publication Ref. 3 by F. Fischer contains details on the mathematical tricks or simplifications that make the individual resistors easier to determine.
-
Amplifier tubes: Listed in the spare parts for the Verograph are four types of amplifier tubes (CF 50, CF 3, EL 3, EF 9, all Philips), as well as a rectifier tube EZ 4 (Philips) and an iron-hydrogen resistor for the secondary theodolite (Osram, 0.5 A, 18–54 V, used as a constant-current source). The purpose served by the amplifier tubes is not known in detail. Some were certainly used in the amplifier that motorized the range adjustment to keep the error continuously at zero. The term “tube voltmeter” has been encountered in this context, feeding the error to the “galvanometer.” The current for the motor will have required powerful tubes, since the range adjustment must occur quickly. Certainly, measures to prevent oscillation were incorporated. (These are only the tubes listed as spare parts — the total tube count remains unknown.)
-
Unique: From Ref. 5, p. 37, a Contraves retrospective written forty years later, in 1976: “I believe the Verograph was and remains the only electromechanical analog computing device in this accuracy class (i.e., with coarse/fine cascade) that was ever built. Only the very fast digital computers of the 1970s were able to handle a computing problem of this kind without delay.”
-
Evaluation of measurement errors — yet more intensive: Four telemeters could be continuously monitored by the Verograph for measurement accuracy — the errors are displayed and recorded on paper strips with a non-linear scale (so that both small and large errors remain easily readable). Subsequently, a separate “evaluation device” was built to evaluate the measurement errors of two telemeters still more intensively (instruction manual for the device: May 1945). The device generates the arithmetic and quadratic mean values of the measurement errors and displays them directly in arc seconds on two electrical pointer instruments each. Measurement: from “start,” the first readings follow after 17 seconds; measurement is possible for a maximum of 270 seconds. With this device, incorrectly calibrated telemeters and incorrectly measuring men can be distinguished.
[figure: Evaluation device for two selectable telemeters. Top: pointer instruments for a = linear mean value, b = quadratic mean value. Outer lower section: instantaneous measurement error, mechanical pointer, scale ±144° corresponds to angle error of ±360” and ±280” respectively for telemeters with 3 m and 1.25 m base.]
[figure: Rear of the evaluation device. Four tubes No. 2: rectifier tubes. Tube No. 4: iron-hydrogen resistor. No. 5: glow tube. 6, 7: fuses, 4 A and 10 A. The computing principle is not known. Images and manual for the evaluation device: Federal Archives, Dossier E5560C#1982/151#83*]
- Forgotten treasures: One complete Verograph system and one complete Stereomat system still exist today, each with two theodolites, packed in trailers that are fairly rusted and can no longer be opened (possibly never opened since their last use in the 1960s??). The locations have been the Technorama, AMP Burgdorf; today they are probably stored in Tavannes. It would be fine to accord these devices the honor they deserve and to finally display them properly in the Air Force–Anti-Aircraft Museum — where nothing at all is to be found (apart from the paper archives) of the early Contraves computers that faithfully performed their service for approximately twenty years. It would be wonderful if circuit diagrams were still to be found — but this seems unlikely given the field use of the devices. Instrument mechanics were hardly available; repairs went to Contraves.
[figure: From left to right: Stereomat computer, Stereomat primary and secondary theodolite, Verograph recording device. Photographed at AMP Burgdorf, A. Masson, February 2017. The long tubes above individual trailers carry the measurement bases of earlier muzzle-velocity (v0) measurement systems (mounted in front of the gun muzzles).]
Chronology of Both Resistance Computers, Stereomat and Verograph
Drawn mainly from Ref. 4: “Die ersten zehn Jahre der Contraves AG” (The First Ten Years of Contraves AG), Dr. H. Bründli and Dr. M. Lattmann, company journal; and from Ref. 5: “40 Jahre Contraves” (40 Years of Contraves), special issue of Contact (internal communications of Contraves AG, Zurich), 6/1976.
- 1936 (20 March): Founding of Contraves AG. Later also abbreviated CZ, Contraves Zurich.
- 1936 (5 August): First found patent application from Contraves: angle- and path-faithful motion transmission (delay with steel band, as used in the Oionoscope; also delay four-poles with L and C, various further delays).
- 1937 (17 August): Patent application submitted by Contraves: “For the continuous transformation of coordinates” by means of eight-poles (patent registered: 15 December 1938; patent published: 1 March 1939, CH Patent No. 201,663).
- 1938 (February): F. Fischer publishes theory on 2n-poles (Ref. 3) — very abstract, hard to comprehend, impractical.
- 1938: The Stereomat is placed in production order with Albiswerk.
- 1939: First Stereomat completed, delivered to the KTA (War Technical Department) and tested in practical operation at the Zuoz firing range (initially without the new theodolites; initially operated with the old Askania cine-theodolites). Satisfactory results.
- 1940: The KTA orders the first Verograph (development still in prototype state). Payment of Fr. 100,000 for the first Stereomat. Order for five further Stereomats.
- 1941: Five Stereomats delivered; one goes to the Army Ordnance Office of Germany, one possibly to Sweden (as a reserve for a later Swiss Oionoscope). First Verograph completed; it “worked at the first attempt.” Start of production of ten Verographs.
- 1941 (8 December): Demonstration of the Verograph to a commission from Germany (note in the Federal Archives).
- 1942: The first two Stereomat theodolites are handed over to the KTA. January: Publication on the Verograph, Ref. 1. “The Verograph has led to various foreign orders.”
- 1943: Start of delivery of the first Verograph series to the Swiss Army.
- 1944: Export of Stereomat theodolites to Sweden can still take place in time; thereafter blockades occur.
Subsequent Contraves developments up to before the Super-Fledermaus (often from Ref. 5, images with unfortunately only brief captions). Italics: Development within the Swiss Army using the English Radar Mark VII, unrelated to Contraves. In all countries, military budgets declined drastically after the end of the war.
- 1948: Development of a “Radar-Verograph for electrical range measurement of aircraft.”
- 1948: Fire-control device: 3 men sit on a tripod mount and track the aircraft — an approximately 2 m telemeter is rigidly mounted. Alongside: a single-axle trailer with the “computer for fire-control device.” Development order from Sweden.
- 1951: “Fire-control director 1951. For the first time with radar.” Image: tripod with rotating section, radar screen, and 1.25 m optical telemeter. Trust in the radar range is apparently still limited, or an approximate or faster range reading is sought. Three seats visible: possibly no automatic radar tracking yet, or during daytime manual tracking may also be more accurate.
- Various fire-control devices: FLG 54, with separate computer; FL Falcon 1954 (entirely different); FL 1955; FL BAT 56 (all possibly prototypes?). (BAT = German for bat / Fledermaus)
- 1950–57: Swiss Army trials with the English Radar Mark VII. In 1957, a few devices go to the troops. Conversion of several Kommandogerät Gamma command devices for mechanical input of radar values, with 3 new follow-up indicators: azimuth, elevation, range.
- 1958–60: Further Radar Mark VII purchased, 12 units in total.
- 1956: Development and construction of the “Fledermaus” (Bat) on a single-axle trailer, precursor of the globally successful Super-Fledermaus.
- 1962: Switzerland orders 78 Super-Fledermaus fire-control devices and 156 Contraves gun directors. (Wikipedia, possibly applicable later: 111 devices in service, plus 38 with MTI, Moving Target Indicator, for airfield anti-aircraft suppression of standing echoes [FlGt 69]. This was a great relief for the mountain airfields with their extreme terrain signals.)
- 1964: The first Swiss anti-aircraft regiment is converted to medium caliber and Super-Fledermaus (FlGt 63). The heavy 7.5 cm anti-aircraft artillery is retired. Command devices and large telemeters become obsolete. 71 older telemeters had already been withdrawn in 1959.
[figures: FL 1948, Swedish order; FL 1948, associated computer; FL 1951, radar + telemeter; FL 1951, associated computer; FL Falcon 1954; Fire-control device 1955; Fire-control device BAT 1956; Fledermaus 1956. All eight images above (1948–1956) from Ref. 5. Further images can be found online in Swedish military museums.]
Note on the fire-control device 1955: Tracking the aircraft manually by joystick (requiring a clear view of the sky) and operating the radar can barely be done by the same man: the brightness differences are too great. He is clearly not looking through an optic — this must be the radar display. With the Fledermaus, a tent mounted around the radar screen (not visible here) provides complete blackout of the surroundings.
Appendix: Numerical Values of the Required Resistors — Practical Feasibility of the System
>>> Now it really gets into the details… <<<
At this level of the individual resistors, no information whatsoever has been found — in no archive, no museum, in no document. Based on the sparse indications from Prof. Fischer, an attempt is made here to reconstruct how the individual resistors must have been calculated. Nothing has been verified!
On p. 11 (caption to the illustration of the crosspieces, Fig. d), the prescription is given for the resistance values that must be incorporated in a crosspiece so that the overall circuit yields the required transfer factor. In this appendix, the resistance values are computed numerically — to see whether any surprises arise, or whether everything remains realizable.
Conceptual Basis
If, while experimenting with the resistance recipe on p. 11, one had the feeling that something was not quite right, or if one becomes entangled in strange contradictions in the following tables: those suspicions are probably correct — but they are 80 years too late, too modern. Today one automatically assumes that an input is reasonably “stiff” and that the output of each stage can supply sufficient current. Before the advent of semiconductors and radio tubes, that was not yet the case. Everything that follows refers to a measuring bridge or crossbar network that is substantially detuned from its no-load condition by the loading of the subsequent circuit. This unavoidable detuning is already accounted for in the resistance recipe on p. 11.
Two situations are worked through in the following:
a) Normal geometry with the ordinary trigonometric functions sin, cos, tan — as the operating principle of the Verograph was described earlier (but not as the Verograph is actually built). Here the calculation works directly with the angle that the theodolite telescope continuously determines between the measurement baseline and the aircraft.
b) The angle to the aircraft is nonlinearly distorted before it is introduced into the calculations. The rotations of the handwheel on the theodolite enter the calculation, whereby one degree of telescope change near 0° requires fewer handwheel rotations than at a larger angle. (Angle 0°: the aircraft lies perpendicular to the line connecting the two theodolites, cf. p. 6.) With this artificially introduced distortion, a new equation must be solved — one involving the hyperbolic trigonometric functions sinh, cosh — and everything now becomes somewhat less intuitive.
a) Normal Geometry with the Ordinary Trigonometric Functions sin, cos, tan
The correct geometric reasoning has been presented earlier for the purpose of understanding the solution and calculation approach. However, the Verograph could not be realized in this way — as becomes apparent from the electrical resistances, some of which would be far too small or far too large. The following tables show the coarse range and fine range of the angles. The coarse range has approximately as many sub-steps (approx. 100) as realized in the Verograph, but the fine range would need to be subdivided more finely than shown here: 100 steps per coarse step.
According to Ref. 1, the exact calculation range of the theodolite angle runs from −75° to +75°. It is not clear whether the 150° combined on both sides were divided into 100 steps, or whether it was possible to merge the two symmetric halves so that 75° is divided into 100 steps, or whether the calculation was extended to 90° on both sides despite reduced accuracy. There are thus several possibilities for dividing the angles into 100 steps.
The following resistance tables are calculated with an arbitrarily assumed total resistance of the crossbar network of 1000 ohms. The values of the large and small resistances (each occurring twice in a crossbar network) and the differences from the preceding resistance are given. In a long chain, the differences are what is soldered in.
Result: The electrical resistances, especially in the fine range, cannot be manufactured so small and still precisely — this is impossible to realize!
[page 19: continued on next page]
Coarse Range: 0° to 90° (usable to 75°). Table divided similarly to the Verograph.
| Angle (degrees) | cos | R small (Ohm) | Diff (Ohm) | R large (Ohm) | Diff (Ohm) |
|---|---|---|---|---|---|
| 2 | 0.9994 | 0.30 | — | 3,282,139.70 | — |
| 4 | 0.9976 | 1.22 | 0.91 | 820,035.00 | 2,462,104.70 |
| 6 | 0.9945 | 2.75 | 1.53 | 364,089.78 | 455,945.22 |
| 8 | 0.9903 | 4.89 | 2.14 | 204,509.06 | 159,580.72 |
| 10 | 0.9848 | 7.65 | 2.76 | 130,646.10 | 73,862.96 |
| 12 | 0.9781 | 11.05 | 3.39 | 90,523.13 | 40,122.96 |
| 14 | 0.9703 | 15.08 | 4.03 | 66,330.38 | 24,192.75 |
| 16 | 0.9613 | 19.75 | 4.68 | 50,628.49 | 15,701.89 |
| 18 | 0.9511 | 25.09 | 5.33 | 39,863.46 | 10,765.03 |
| 20 | 0.9397 | 31.09 | 6.01 | 32,163.44 | 7,700.02 |
| 22 | 0.9272 | 37.78 | 6.69 | 26,466.44 | 5,697.00 |
| … | … | … | … | … | … |
| 38 | 0.7880 | 118.56 | 12.99 | 8,434.44 | 1,037.70 |
| 40 | 0.7660 | 132.47 | 13.91 | 7,548.63 | 885.81 |
| 42 | 0.7431 | 147.35 | 14.88 | 6,786.49 | 762.14 |
| 44 | 0.7193 | 163.24 | 15.89 | 6,126.05 | 660.43 |
| … | … | … | … | … | … |
| 56 | 0.5592 | 282.71 | 23.10 | 3,537.13 | 314.71 |
| 58 | 0.5299 | 307.26 | 24.54 | 3,254.59 | 282.54 |
| 60 | 0.5000 | 333.33 | 26.07 | 3,000.00 | 254.59 |
| 62 | 0.4695 | 361.03 | 27.70 | 2,769.83 | 230.17 |
| … | … | … | … | … | … |
| 74 | 0.2756 | 567.84 | 39.98 | 1,761.05 | 133.38 |
| 76 | 0.2419 | 610.41 | 42.56 | 1,638.25 | 122.80 |
| 78 | 0.2079 | 655.75 | 45.34 | 1,524.97 | 113.28 |
| 80 | 0.1736 | 704.09 | 48.34 | 1,420.28 | 104.69 |
| 82 | 0.1392 | 755.66 | 51.57 | 1,323.35 | 96.93 |
| 84 | 0.1045 | 810.73 | 55.07 | 1,233.46 | 89.89 |
| 86 | 0.0698 | 869.58 | 58.86 | 1,149.97 | 83.49 |
| 88 | 0.0349 | 932.55 | 62.97 | 1,072.32 | 77.65 |
| 90 | 0.0000 | 1,000.00 | 67.45 | 1,000.00 | 72.32 |
Fine Range: 0° to 2°. Both cosine and sine components are required (addition theorem).
In the Verograph, the fine steps are finer than shown here: if a coarse step is 1.5° (150° divided into 100 steps), then a fine step would be 0.015°, or three times finer than in the table below. The differences in R values then fall into the range of less than one milli-ohm — which will practically no longer be realizable. The gigaohm values do not sound particularly appealing either… Small and large resistances not only have to be manufactured, but also to sufficiently accurate values.
| Degrees | Cos | R small cos | R large cos | Sin | R small sin | R large sin |
|---|---|---|---|---|---|---|
| 0.05 | 1.000000 | 0.000190 | 5,252,489,493.28 | 0.000873 | 998.256 | 1,001.747 |
| 0.10 | 0.999998 | 0.000762 | 1,313,121,873.33 | 0.001745 | 996.515 | 1,003.497 |
| 0.15 | 0.999997 | 0.001713 | 583,609,351.12 | 0.002618 | 994.778 | 1,005.250 |
| 0.20 | 0.999994 | 0.003046 | 328,279,968.34 | 0.003491 | 993.043 | 1,007.006 |
| 0.25 | 0.999990 | 0.004760 | 210,098,939.73 | 0.004363 | 991.311 | 1,008.765 |
| 0.30 | 0.999986 | 0.006854 | 145,901,837.78 | 0.005236 | 989.583 | 1,010.527 |
| 0.35 | 0.999981 | 0.009329 | 107,193,010.07 | 0.006109 | 987.857 | 1,012.292 |
| 0.40 | 0.999976 | 0.012185 | 82,069,492.08 | 0.006981 | 986.134 | 1,014.061 |
| 0.45 | 0.999969 | 0.015421 | 64,844,890.87 | 0.007854 | 984.415 | 1,015.832 |
| 0.50 | 0.999962 | 0.019039 | 52,524,234.93 | 0.008727 | 982.698 | 1,017.607 |
| 0.55 | 0.999954 | 0.023037 | 43,408,342.92 | 0.009599 | 980.984 | 1,019.384 |
| 0.60 | 0.999945 | 0.027416 | 36,474,959.45 | 0.010472 | 979.273 | 1,021.165 |
| … | … | … | … | … | … | … |
| 1.50 | 0.999657 | 0.171367 | 5,835,433.52 | 0.026177 | 948.982 | 1,053.761 |
| 1.55 | 0.999634 | 0.182983 | 5,464,983.88 | 0.027049 | 947.326 | 1,055.603 |
| 1.60 | 0.999610 | 0.194980 | 5,128,718.27 | 0.027922 | 945.674 | 1,057.447 |
| 1.65 | 0.999585 | 0.207359 | 4,822,556.63 | 0.028794 | 944.024 | 1,059.295 |
| 1.70 | 0.999560 | 0.220118 | 4,543,009.96 | 0.029666 | 942.377 | 1,061.146 |
| 1.75 | 0.999534 | 0.233259 | 4,287,080.42 | 0.030539 | 940.733 | 1,063.001 |
| 1.80 | 0.999507 | 0.246781 | 4,052,180.70 | 0.031411 | 939.092 | 1,064.859 |
| 1.85 | 0.999479 | 0.260684 | 3,836,068.31 | 0.032283 | 937.453 | 1,066.720 |
| 1.90 | 0.999450 | 0.274968 | 3,636,791.91 | 0.033155 | 935.818 | 1,068.584 |
| 1.95 | 0.999421 | 0.289633 | 3,452,647.07 | 0.034027 | 934.185 | 1,070.452 |
| 2.00 | 0.999391 | 0.304679 | 3,282,139.70 | 0.034899 | 932.555 | 1,072.323 |
b) Solution with Distorted Angles and Hyperbolic Functions
The Verograph does not calculate with the true telescope angle, but with a distorted auxiliary variable u, which corresponds to the rotations of the handwheel when tracking the aircraft. Near 0°, fewer handwheel revolutions are needed per degree of telescope movement; at large angles, more are needed. The conversion from u to the telescope angle φ takes place purely mechanically, using a precision template curve (cf. p. 6). The template ensures that dφ/du is proportional to cos φ: at constant handwheel rotation on the theodolite, the telescope rotates strongly at φ = 0°, then progressively less, until at φ = 90° it would not move at all. The relationship between u (handwheel) and φ (telescope angle) is designed so that:
sin φ = tanh u or tan φ = sinh u
As a result of this transformation, the trigonometric equation that the Verograph solves (cf. p. 6) must be substantially modified; hyperbolic functions come into play. A comparison follows of the normal trigonometric curves sin/cos/tan (solid lines) with the hyperbolic functions (dashed):
[page 21: graph — sin (from −90° to +90°) and sinh, vertical scale −2 to +2]
[page 21: graph — cos (from −90° to +90°) and cosh, vertical scale 0 to 3]
[page 21: graph — tan (from −90° to +90°) and tanh, vertical scale −5 to +5]
The hyperbolic functions look substantially different from the trigonometric ones. How the three facts —
- the distortion of handwheel revolutions u relative to the measured angle (telescope to aircraft),
- the use of hyperbolic functions instead of trigonometric ones, and
- the fundamental equation to be solved (originally the law of sines) changes markedly with hyperbolic functions —
…fit precisely together and are to be understood remains rather nebulous to the author. Everything has been faithfully and rather incomprehendingly taken over from Ref. 1.
New Equation Which the Verograph Must Solve
(u₁, u₂ = handwheel rotation angles of the two theodolites; the value for sinh u₂ is transmitted via cable from the more distant theodolite)
b / r₁ = (sinh u₂ − sinh u₁) · (1 / cosh u₁)
Where b = measurement baseline, r₁ = sought distance.
Verograph: The two theodolites realize sinh from the rotation angles of the two handwheels — used to track the aircraft — through the resistance networks. However: sinh can in certain ranges become greater than one — but that cannot be achieved with pure resistance elements. One can only attenuate with resistors, never amplify. An electron tube is required here. One might envision it roughly as follows — nothing definitive has been found:
- Pre-calculate the sinh values over the entire measurement range (yielding, e.g., values in the range 0 to 3.42, corresponding to telescope angles from 0° to 74°, up to approximately the range limit or accuracy limit of 75°).
- On paper, divide all these values by a constant factor — here assumed to be 3.8 for example — yielding a new, reduced value range of 0 to 0.9.
- Calculate the required resistances in the crossbar network for the range 0…0.9, and solder in the resistance differences.
- At the end, the voltages obtained behind the coarse-fine resistance chain are amplified again by a factor of 3.8 using an electron tube.
This is a more demanding task for a tube than the digital representation of numbers in flip-flops, as in the later electronic computers ENIAC (1946) and ERMETH (1956). An incorrect amplification directly affects the result. In the Stereomat, tube test circuits are present, which — thanks to built-in test resistance networks — allow the tube amplification to be measured and corrected. This will also be the case in the Verograph.
If the constant factor (here, e.g., 3.8) is made somewhat larger than necessary, one avoids transfer factors near unity, thereby eliminating the impractical very large and very small partial resistances.
The input impedance of the amplifier stage with the electron tube must again correspond to the impedance of all other stages; possibly also its output impedance.
Resistance Table for sinh (Coarse Range)
Assumptions:
- 50 intervals for approximately 75 degrees: u (handwheel revolutions) increases linearly, the angle not quite.
- The telescope angles are shown for clarity in the first column, calculated from tanh (column 4); they are not used anywhere.
- sinh has been reduced by a factor of 3.8 so that no transfer factor of a crossbar network ever exceeds 1. This reduction factor must later be compensated using a radio tube.
| Telescope angle (°) | Interval No. | u (handwheel) | tanh(u) | sinh(u) | sinh reduced (÷3.8) | R small (falling) | R small diff | R large (rising) | R large diff |
|---|---|---|---|---|---|---|---|---|---|
| 0.0 | 0 | 0 | 0 | 0.000 | — | 1000 | — | 1000 | — |
| 2.3 | 1 | 0.04 | 0.04 | 0.04 | 0.011 | 979.16 | 20.84 | 1,021.28 | 21.28 |
| 4.6 | 2 | 0.08 | 0.08 | 0.08 | 0.021 | 958.72 | 20.44 | 1,043.06 | 21.78 |
| 6.9 | 3 | 0.12 | 0.12 | 0.12 | 0.032 | 938.63 | 20.09 | 1,065.38 | 22.32 |
| 9.1 | 4 | 0.16 | 0.16 | 0.16 | 0.042 | 918.86 | 19.77 | 1,088.30 | 22.93 |
| 11.4 | 5 | 0.20 | 0.20 | 0.20 | 0.053 | 899.37 | 19.50 | 1,111.89 | 23.59 |
| 13.6 | 6 | 0.24 | 0.24 | 0.24 | 0.064 | 880.11 | 19.25 | 1,136.22 | 24.32 |
| 15.8 | 7 | 0.28 | 0.27 | 0.28 | 0.075 | 861.07 | 19.04 | 1,161.35 | 25.13 |
| … | … | … | … | … | … | … | … | … | … |
| 32.5 | 15 | 0.60 | 0.54 | 0.64 | 0.168 | 713.00 | 18.31 | 1,402.52 | 35.12 |
| 34.4 | 16 | 0.64 | 0.56 | 0.68 | 0.180 | 694.69 | 18.31 | 1,439.49 | 36.97 |
| 36.3 | 17 | 0.68 | 0.59 | 0.73 | 0.193 | 676.36 | 18.33 | 1,478.50 | 39.01 |
| 38.1 | 18 | 0.72 | 0.62 | 0.78 | 0.206 | 658.00 | 18.36 | 1,519.76 | 41.26 |
| 39.9 | 19 | 0.76 | 0.64 | 0.84 | 0.220 | 639.59 | 18.41 | 1,563.50 | 43.74 |
| 41.6 | 20 | 0.80 | 0.66 | 0.89 | 0.234 | 621.12 | 18.47 | 1,609.99 | 46.48 |
| 43.3 | 21 | 0.84 | 0.69 | 0.94 | 0.248 | 602.59 | 18.54 | 1,659.51 | 49.52 |
| 44.9 | 22 | 0.88 | 0.71 | 1.00 | 0.263 | 583.97 | 18.61 | 1,712.40 | 52.90 |
| … | … | … | … | … | … | … | … | … | … |
| 67.2 | 40 | 1.60 | 0.92 | 2.38 | 0.625 | 230.66 | 20.51 | 4,335.46 | 354.00 |
| 68.0 | 41 | 1.64 | 0.93 | 2.48 | 0.653 | 210.08 | 20.58 | 4,760.17 | 424.71 |
| 68.9 | 42 | 1.68 | 0.93 | 2.59 | 0.681 | 189.43 | 20.64 | 5,278.87 | 518.70 |
| 69.7 | 43 | 1.72 | 0.94 | 2.70 | 0.711 | 168.74 | 20.69 | 5,926.29 | 647.42 |
| 70.5 | 44 | 1.76 | 0.94 | 2.82 | 0.742 | 148.00 | 20.74 | 6,756.66 | 830.37 |
| 71.2 | 45 | 1.80 | 0.95 | 2.94 | 0.774 | 127.23 | 20.77 | 7,859.61 | 1,102.95 |
| 72.0 | 46 | 1.84 | 0.95 | 3.07 | 0.808 | 106.44 | 20.79 | 9,394.73 | 1,535.12 |
| 72.6 | 47 | 1.88 | 0.95 | 3.20 | 0.842 | 85.64 | 20.80 | 11,676.33 | 2,281.60 |
| 73.3 | 48 | 1.92 | 0.96 | 3.34 | 0.878 | 64.85 | 20.80 | 15,420.92 | 3,744.59 |
| 74.0 | 49 | 1.96 | 0.96 | 3.48 | 0.916 | 44.07 | 20.78 | 22,693.31 | 7,272.39 |
| 74.6 | 50 | 2.00 | 0.96 | 3.63 | 0.954 | 23.31 | 20.75 | 42,895.22 | 20,201.91 |
The required resistances in the system with hyperbolic functions are far, far better — the resistance differences (i.e., the resistors to be soldered in) are wonderfully well-behaved. This can be realized without difficulty. Unfortunately this does not hold for the fine range. Here the values are still far too small… some approximations were evidently unavoidable.
The idea of “division by a constant factor on paper, with subsequent amplification by the same factor using a tube” probably applies more to the Stereomat, since in the Verograph the entire equation could be divided by a constant factor. But then what purpose do all the tubes serve?
Tube types in the Verograph: see p. 16.
Generation of 1/cosh u₁ via Coarse and Fine Resistance Networks
To conclude, it is shown how the expression “1/cosh u₁” was generated with coarse and fine ranges in the resistance networks (from Ref. 1). Understanding this remains demanding.
What exactly the quantities p (possibly rho) and s (possibly sigma) represent is not clear. In Ref. 4 these quantities are not even mentioned in the same presentation; in Ref. 1 there are remarks that are difficult to comprehend.
On the right side of the rotating shafts are the two coarse-range values u and the two fine-range values h (with a smaller range of rotation angle). Double line = mechanical rotating shaft in the theodolite, from the handwheel.
A “special octopole” (fixed, i.e., without variable resistors) cross-couples the signals through at the bottom and through at the top. The coupling between the two input signals on the left (1, 2) is zero, as is the coupling between the two signals on the right (3, 4). Each signal path has two wires, hence the octopole (eight-terminal network).
Fraktur script denotes hyperbolic functions.
Note that the transfer factor of each crossbar network applies with the same value in both directions.
The meanings of sigma and p are not understood. No electron tube is required. The earlier conjecture that a division is performed as multiplication by pre-calculated reciprocal values is thus not always valid — the situation here is clearly more complex.
Concluding Presentation: The Mathematical Program of the Stereomat
The Stereomat is based on the same computing technique as the Verograph, but was realized somewhat earlier. Its task: how far apart are the shell burst point and the aircraft at the moment of the flash? The shortest spatial distance between the projectile and the aircraft could in any case also be smaller — for example if the fuze running time was set too large or too small. The required angles are read from images of the two cine-theodolites (initially photographic film requiring chemical development, later punched or printed strips). The photograph is triggered by a photoelectric cell. The Stereomat calculates directly, i.e., without coarse-fine cascades. For more details see the paper on the Oionoscope: Ref. 6.
Division by cos, by cos², or by sin² in any case requires a tube with corresponding amplification. Double line = mechanical rotating shafts; all required angles measured at the theodolites are dialed in by hand at the bottom of the diagram, thereby selecting the electrical resistances. Single line = electrical signal. Upper right — output: difference between burst point and aircraft, total distance s or the three spatial components. Output on paper strip using servomotors. The symbol ”<” means: an electron tube must amplify here. Operational at the Zuoz firing range from 1939.
References
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F. Fischer: Ueber elektrische Rechengeräte hoher Genauigkeit, unter spezieller Berücksichtigung eines neuen Entfernungsmessers für die Flabartillerie (Verograph). Schweizer Archiv für angewandte Wissenschaft und Technik, 8th year, No. 1, Feb. 1942, pp. 1–15.
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F. Fischer: Ein neuartiges Rechengerät und einige Zusatzapparaturen. Schweizer Archiv für angewandte Wissenschaft und Technik, 5th year, No. 3, March 1939, pp. 74–84. Describes the Stereomat.
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F. Fischer: Beitrag zur Theorie des 2n-Poles, der als n-Klemmenpaar betrieben wird. Schweizer Archiv für angewandte Wissenschaft und Technik, 4th year, No. 2, Feb. 1938, pp. 29–42. Very mathematically and theoretically formulated.
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Dr. H. Brändli, Dr. M. Lattmann: “Die ersten zehn Jahre der Contraves AG.” Company journal, April 1977.
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40 Jahre Contraves. Special issue of Contact (internal newsletter of Contraves AG, Zurich), 6/1976.
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A. Masson: Oionoskop mit Stereomat und Verograph. July 2016. Available at www.wrd.ch or www.big.admin.ch.
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K. H. Grossmann: Der Stereomat, ein Rechengerät für die Fliegerabwehr. Schweizerische Bauzeitung, Vol. 113/114, Issue 15, 1939, pp. 178–181. Fairly mathematically formulated. Retrievable via retro.seals.ch. Contains material on the complete adder (cf. above p. 12). Fairly mathematically formulated.
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W. Peres: 25 Jahre Flak. Wehrtechnische Monatshefte, 44, July 1940, No. 7, pp. 156–161. (Available in the Guisan Library.) Describes computing devices from Germany used to determine the distance to an aircraft as precisely as possible using a long baseline of 2–3 km. Two solutions to this problem are presented in detail:
a) A device from 1917 (!) solves the problem in the same coordinate system as the Verograph as follows: The law of sines with its proportions is logarithmized — whereby products transform to sums and quotients to differences. The equation to be solved now reads: (e = distance, b = baseline, I, II = measured angles to the aircraft in the “roof plane”)
log e = log b + log sin II − log sin (II − I)
Sign convention for I: possibly the “direction” on the theodolite.
The two measured angles to the aircraft, after “remote-electrical transmission,” rotate two drums in each of which a precisely machined spiral groove has been milled: distance from the end of the drum = log sin (rotation angle). This value is sampled in the groove, and the values of “log sin” are added or subtracted mechanically. A third drum, rotated by hand, shifts a curve beneath the machine-controlled reading point and allows the distance to be read back from log e. Both of the following images are from Ref. 8. The image must be rotated 90° counterclockwise for the adjacent text to apply.
[page 25: figure only]
b) A “modern device” (published 1940) likewise adds or subtracts the logarithmic values using a tensioned band guided around shiftable rollers. This device is implemented in rectangular coordinates (horizontal distance / height), so the triangle in the map plane is first determined — after which the measured elevation angle log cos γ is added in the vertical triangle. The settings for the two azimuth angles and the elevation angle are made by hand using follower pointers. The distance is set by hand such that the take-up roller points to the mark. log e can be viewed as the sum / difference of the roller positions. The device has a certain elegance that cannot be denied.
The devices for distance determination using a long measurement baseline are called “Veithen devices” (a proper name, after a reserve lieutenant). In Germany the coordinate system of the 1917 device (and also of the Verograph) is called “Thetes coordinates” or “Tetes” (a proper name); in Switzerland they were designated “Thetis coordinates.” For a geometric representation of the situation, see p. 3 above. Only three years before this computing device, there was no Flak at all — only a BAK (Ballon-Abwehr-Kanone, balloon-defense gun). The long-baseline measurement method was employed in Germany between the wars to monitor the training of range-finders, in exactly the same way as later with the Contraves devices. For direct combat use the method is said to be unsuitable, for three reasons:
- Too slow for surprise attacks.
- “Lack of uniformity in target designation when several aircraft are simultaneously present in the sector, especially when formations, chains, echelons, or even larger aerial units appear.”
- Impossibility of use without time-consuming survey of the baseline.
Up to this point: all according to Ref. 8.
Regarding the solutions from Germany discussed above: the electrical errors arising in the long cable to the remote theodolite when ordinary follower pointers are used for angle transmission (alternating current, three 120°-coils align at the receiver the same as at the transmitter) would deserve more precise investigation. Prof. Fischer specifically wished to avoid this. Properly understanding his own cable compensation in the Verograph is demanding. Two “twelve-terminal networks” (twelve-poles) were used for the compensation of the cables (one long cable with two wire pairs, two short cables with three signals in total). These apparently make it possible to set the phase and voltage of all connections precisely.
Cable Compensation in the Verograph
The auxiliary theodolite (top) is connected to the recording device by a long cable (1–2 km). Both wire pairs, each drawn as a single line, are separately shielded. The main theodolite (bottom) stands directly next to the recording device and is connected by two cables with three signal paths.
Cable compensation is also accomplished using resistance networks. Two adjustable four-terminal networks each (symbolic handwheels) allow a small additive correction to be mixed into the main signal in the fixed twelve-pole network, until the phase and amplitude are correct for all signal paths. Possibly inductors and capacitors are also involved in the correction possibilities.
The function of the twelve-poles (6 inputs/outputs) consists, according to the notation, apparently in a threefold splitting of the signal followed by a threefold summation, probably with equal weighting 1:1:1.
Cf. the main schematic with better labeling: page 13.
Image from Ref. 1.
Publications and Military Secrecy
What may one publish openly that facilitates knowledge of current or even future military equipment — and this in times of political tension or in direct wartime?
The contemporary publications on the Flak computers are sparse, but occasionally there are passages in which discussion is surprisingly open — not only about the tasks, but also about the operating principles of the devices. A speculative interpretation: the devices had to be sold, and so contacts to potential buyers existed in any case. In the case of Contraves, during the Second World War there were business relationships with the German Wehrmacht, with Sweden, and with Italy, probably also with further countries. It is possible that secrecy (which was reportedly very strict at Hasler Bern, for example) was somewhat shared and not entirely consistent. A document from Hasler also attests to this: the newly developed command device for the 34 mm guns is shown in 1938, in an opened state, to German officers (Hermann Schild, Fliegerabwehr, p. 146, 1982).
Among the surprisingly open publications one would count (Ref. 1–3: having not understood them for several years, they now appear relatively detailed — for a country that would give anything to produce something like this):
| Reference | Subject | Organization | Date |
|---|---|---|---|
| Ref. 1–3 | Stereomat and Verograph | Contraves, Zurich | 1938–1942 |
| — | Sound triangulation in the listening device | — | — |
| — | Command devices / gun control | — | — |
| — | (Whether the Kuhlenkamp book was freely available is unknown) | Hasler, Bern | 1944 |
| — | (With the exception of the new KdoGt 40: not a word about it!) | Kuhlenkamp, Army Ordnance Office D | 1943 |
For more precise details see earlier papers.
The degree of military secrecy can also be inferred from the filing/publication dates of granted patents.
Biography of Fritz Fischer
Fritz Fischer was presumably the most creative mind of the early Contraves AG. Source: https://www.deutsche-biographie.de/sfz16222.html
- 1924: Doctorate at ETH as an electrical engineer.
- From 1926: Central Laboratory Berlin, Siemens & Halske; from 1928 in a management role there. Remote-control experiments for the target ship Zähringen and for a Ju-52. Servo-tracking controls for guns. Work on sound film and color film.
- From 1933: Returned to ETH for political reasons; professorship and establishment of the Institute for Technical Physics.
- From 1936: Work for Contraves; from 1939 work on the Eidophor (TV projection).
- Died 28 December 1947.
Earlier Works in This Series
This is the eleventh paper by the author on the mechanical computers of the anti-aircraft artillery. Earlier topics were:
| Paper | Subject | Date |
|---|---|---|
| First | SPERRY command device | Autumn 2014 |
| Second | GAMMA-JUHÁSZ-HASLER command device | 2014/15 |
| Third | Various anti-aircraft devices: range determination, control and training devices | — |
| Fourth | Computing with precisely shaped steel bodies | March 2016 |
| Fifth | Command device for the 34 mm gun (angular-velocity device) | May 2016 |
| Sixth | Early CONTRAVES devices: Oionoscope with Stereomat and Verograph | July 2016 |
| Seventh | Sound ranging: Elascop and Orthognom | Nov 2016 |
| Eighth | Curving-flight calculator | Jan 2017 |
| Ninth | Automated computers for shell trajectories | May 2017 |
| Tenth | Angular-velocity meter: aircraft measurement in World War I | Oct 2017 |
In addition there were four smaller papers:
- AMP Burgdorf, historical Flak devices on display (including Stereomat and Verograph)
- Workshop instruments from Gamma-Budapest (production / testing of the daily corrections on the Gamma command device)
- Versions of Gamma devices in Switzerland, telemeter, “gleanings”
- Operating manual for the Stereomat; comparison of the 1944/1946 editions; Contraves devices for Sweden.
The larger papers can be accessed at www.wrd.ch (under “Führungssysteme” → “Anfänge bis 1964”) or at the Military Library at Guisanplatz, www.big.admin.ch (search by author name).
André Masson, CH-4900 Langenthal.
December 2018