US3063047A - Firing point locator system - Google Patents

Description

Nov. 6, 1962 F. G.

STEELE 3,063,047

FIRING POINT LOCATOR SYSTEM Filed Jan. 25, 1957 6 Sheets-Sheet l Nov. 6, 1962 F. G. STEELE 3,063,047

FIRING POINT LOCATOR SYSTEM Filed Jan. 23, 1957 6 Sheets-Sheet 2 E 2;/ aff/7% l Nov. 6, 1962 F, G. STEELE 3,063,047

FIRING POINT LOCATOR SYSTEM Filed Jan. 25, 1957 6 Sheets-Sheet 3 4,00/ /402 fJ/Y/a/ar l n l 40/ 412, l /4f4 Nov. 6, 1962 F. G. STEELE FIRING POINT LOCATOR SYSTEM Filed Jan. 25, 1957 6 Sheets-Sheet 4 Wwe u Nora c'zaczw/.f 2074/704/ Nov. 6, 1962 F. G. STEELE FIRING POINT LOCATOR SYSTEM Filed Jan. 25, 195'? 6 Sheets-Sheet 5 6 Sheets-Sheet 6 F. G. STEELE FIRING POINT LOCATOR SYSTEM Nov. 6, 1962 Filed Jan. 23, 1957 United rates Patent @nace il a 3,063,647 FIRING POINT LCATOR SYSTEM Floyd G. Steele, La Jolla, Calif., assigner to Digital Control Systems, Inc., La Jona, Calif. Filed Jan. 23, 1957, Ser. No. 635,9l6 28 Claims. (Cl. 343-7) This invention relates to a ring point locator system for determining the tiring point of a projectile, and more particularly to a tiring point locator system which utilizes a digital computer for determining the position and veloc` ity of a projectile at a point on its trajectory, and which is thereafter operable -to iteratively extrapolate the trajectory equations of the projectile to determine the firing point thereof.

`It has long been recognized that the effectiveness of artillery and mortar re would be sharply reduced if there was some manner to accurately and rapidly locate the tiring point of the projectiles tired thereby. Following the development of accurate tracking radars which are capable of tracking a projectile through at least a portion of its trajectory, various attempts have been made to construct firing point locators by utilizing the data produced -by ythe radar during its tracking mode to simulate the earlier portion of the trajectory and thereby indicate the projectiles firing point.

One of the first firing point locator systems suggested in the prior art included a plotting board which was utilized to plot the trajectory of a projectile while it was being tracked, after which the operator manually extrapolated the curve backward to indicate lthe projectiles ring point. The principal disadvantage of this system is that it is subject to human error and produces results which are grossly inaccurate when compared with the degree of accuracy necessary to reasonably insure subsequent destruction of the enemy weapon by friendly lire.

In still other prior art firing point locator systems analog computing elements have been utilized which are responsive to the intelligence data produced by the radar for predicting the location of the firing point by extrapolating simplified equations which roughly dene the ballistics of the projectile. One example of this type of prior art system is disclosed in U.S. Patent 2,761,129, issued August 28, 1956, to E. G. Hills for Apparatus for Locating a Missile Projecting Device, wherein a trigonometric solution of a missiles trajectory in a polar coordinate system is utilized to present the approximate tiring point location on an associated plotting board, the solution of the trajectory equations being accomplished through the addition of analog signals representative of position and the time rate of change of position.

Although analog systems which operate in the foregoing or similar manner have been constructed and tested, their utility is inherently restricted by several important factors. Firstly, the accuracy provided lby these systems is frequently inferior to that provided by the manual plotting method described previously owing to the fact that the error contributed by each analog element in the system, when compounded with the errors contributed by the other elements, produces an intolerable system error. In addition, the systems are extremely complex, bulky and expensive, and great care must be exercised in adjusting the various analog elements to provide even a slight degree of accuracy and reliability.

The present invention, on the other hand, overcomes the above and other disadvantages of the prior art ring point locator systems by providing a system in which a digital computer is utilized to determine first the position and velocity of a projectile at a point on its trajectory, and which is thereafter operable to iteratively extrapolate the trajectory equations of the projectile to determine the tiring point thereof. In accordance with the basic con- 3,063,47 Patented Nov. 6, i962 cept of the present invention, the tiring point locator system herein disclosed comprises a radar operable to track a projectile through at least a portion of its trajectory to produce output signals representative of the instantaneous coordinate position of the projectile along each of the coordinates of a three dimensional coordinate system in space, an analog-to-digital converter for converting the radar output signals to electrical signals digitally representative of the position and time rate of change of position of the projectile at substantially the midpoint of a sampled portion of the projectiles trajectory, and an electronic digital computer operative to extrapolate the trajectory equations of the projectile utilizing as initial conditions the known position and Velocity of the projectile at a point on its trajectory.

More specifically, in the preferred embodiment of the invention herein disclosed the analog-to-digital converter functions to generate three difunction signal trains corresponding to the X, Y and H coordinates of an orthogonal coordinate system and representative of the instantaneous position of the projectile as it is being tracked, each train including a predetermined number of sequential difunction signals. These signals are then applied to associated binary accumulators which function to determine the average coordinate position of the projectile during the interval through which the signals are generated, and which also function to determine the coordinate velocities of the projectile by dilferencing the average positions of the projectile during the lirst and second halves of the interval.

In order to most clearly comprehend the invention it should be here pointed out that the term difunction signal train refers to a train of signals each having a fixed period and having either a high level representing a irst quantity or a low level representing a second quantity, the average values of the quantities represented by the signals occurring over a given interval corresponding to the average value of the physical quantity represented by the train during the given interval. For example, if it is assumed that the first and second quantities represented by the -signals in a train are the maximum range of the system along the corresponding coordinate axis expressed positively and negatively, respectively, then the average value of the signals occurring over a given interval represents the average coordinate position of the projectile during the interval. the average position of the projectile along each coordinate may be determined by actuating an associated binary accumulator to increase its count in one direction in response to each high level signal in the train and in the opposite direction in response to each low level signal, the binary number stored in the accumulator at the end of the operation corresponding to the coordinate position of the projectile at the midpoint of the sampled portion ofv ing the signals in one group and sequentially applying the inverted signals and the remaining uninverted signals to an associated accumulator. The resultant binary number in the accomulator is then representative of the difference between the average position of the projectile during the rst half of the sampled portion of its trajectory and the average position during the second half of the sampled portion of its trajectory, or in other Words, the time rate of change of the projectiles position at the midpoint of the sampled portion of the trajectory. Y

In accordance with the invention the coordinate positions and velocities derived in the foregoing manner are entered as the initial conditions in a plurality of digital integrators which are interconnected to selectively extrap- In accordance with the invention, therefore, i

olate the trajectory equations for the projectile, either forward or backward in time, to produce output signals representative of the changes in the projectiles coordinate positions as the extrapolation process is carried out. These signals are then combined with the initial position signals which are in turn utilized to actuate three digital servos which are operative to drive three respectively associated mechanical counters to present a visual indication of the coordinates of the point of the projectiles trajectory to which the trajectory equations have been extrapolated.

Among the novel features of the present invention there is also disclosed a bidirection digital position servo operable to drive a positionable element to a position corresponding to the coordinate position of a point on a projectiles trajectory in a three dimensional coordinate system in space. Still another novel feature of the invention herein disclosed is the utilization in the associated digital servos of a bidirectional quantizer which senses incremental rotational changes in the position of a shaft by sensing changes in the inductive reactances presented by a pair of ferromagnetic core inductors positioned adjacent the periphery of a toothed ferromagnetic disk which rotates in accordance with shaft rotation. A further novel feature of the quantizer is the detection of incremental changes in the shaft position by generating tirst and second bilevel signal trains one of which leads the other by 90 when the shaft is rotated at a fixed rate in one direction and which lags the other by 90 when the shaft is rotated at a fixed rate in the opposite direction, a change in the level of the first train signifying an incremental change in rotational position while the polarity of the change is indicated by the level of the second train when the first train is changing levels.

It is, therefore, an object of the invention to provide a tiring point locator system which functions to determine first the position and velocity of a projectile at a point on its trajectory and which is thereafter operable to interatively extrapolate the trajectory equations of the projectile to determine the firing point thereof.

Another object of the invention is to provide a tiring point locator system which utilizes a digital computer to incrementally extrapolate the trajectory equations of a projectile either forward or backward in time to either` verify the projectiles impact point or ascertain its tiring point.

A further object of the invention is to provide a tiring point locator system which utilizes a plurality of digital integrators interconnected in accordance with the trajectory equations of a projectile to extrapolate the trajectory backward in time to determine the projectiles tiring point, the digital integrators utilizing as initial conditions the known coordinate positions of the midpoint of a sampled portion of the projectiles trajectory.

Still another object of theinvention is to provide a system for digitally determiningthe coordinates of the midpoint of a sampled portion of the trajectory of a projectile moving in a three dimensionalY coordinate system.

Anadditional object of the invention is to provide a system for determining-the coordinates of the midpoint of aV sampled portion of the path traveled by an object'moving in space by generating a plurality of difunction signal trains representative of the instantaneous positionV of the object along a correspondingv plurality of coordinates in a rectangular coordinate system, and accumulating the individual difunction signals in the trains tovproduce electricalA signals representativey ofl the average coordinatev positions of the object during the interval it was traversing the sampled portion of its path'in space.

It is another object Vof the invention to provide a system for digitally determining the coordinate velocities of a projectile moving in an orthogonal coordinate system in space at the midpoint ofv a sampled portion of the projectiles trajectory.

It is also an object of the invention to provide a system for determining the velocity of an object moving in an orthogonal coordinate system in space at the midpoint of a sampled portion of the objects trajectory by generating a plurality of difunction signal trains each including N signals and representative of the instantaneous position of the object along a corresponding plurality of coordinates which dene the coordinate system, and accumulating the signals in each train to present signals representative of the numerical difference between the summation of the iirst N/ 2 signals in each train and the summation of the last N/Z signals in each train.

Still a further object of the invention is to provide an input conversion apparatus for rotating a shaft to a position corresponding to the average value of an applied analog signal over a predetermined period by generating a difunction signal train including N difunction signals during the period, each signal having either a first value representing a predetermined maximum value of the analog signal or a second value representing a predetermined minimum value of the analog signal, the average value of the N signals being proportional to the analog signal over the period, and rotating the shaft through an incremental rotational angle proportional to the maximum or minimum value over N in response to each rst or second valued difunction signal, respectively.

Another object of the invention is to provide a bidirectional digital position servo operable to drive a positionable element to a position corresponding to the coordinate position of a point on a projectiles trajectory in a three dimensional coordinate system in space.

A further object of the invention is to provide a bidirectional digital quantizer which senses incremental rotational changes in the position of a shaft by sensing changes in the inductive reactances presented by a pair of ferromagnetic core inductors positioned adjacent the periphery of a toothed ferromagnetic disk which rotates in accordance with shaft rotation.

Still another object of the invention is to provide a bidirectional digital quantizer for detecting incremental changes in the rotational position of a shaft by producing first and second bilevel signal trains one of which leads the other by when the shaft is rotated at a fixed rate in one -direction and which lags the other by 90 when the shaft is rotated at a tixed rate in the opposite direction, a change in the level of the tirst train signifying an incrementaly rotational change, while the level of the second train at the same instant signifies the sense of the change.

The novel features which are believed to be characteristic of the invention, both as to its organization and method of operation, together with further -objects and `advantages thereof, will be better understood from the following description considered in connection with the accompanying drawings in which several embodiments of the invention are illustrated by way of example. It is to be expressly understood, however, that the-drawings are for the purpose of illustration and description only, and are not intended as a deinition of the limits of the invention.

FIG. l is a block `diagram of a tiring point locator system, in accordance with the invention;

FIG. 2 is a graph illustratingthe manner in which the firing point locator system yof the invention determines the-coordinates and coordinate velocities of a projectile at a point in the projectiles trajectory;

FG. 3 is a block diagram, partly in schematic form, of a digital projectilev tracking computer, in accordance with the invention, which has been employedin the system of FlG. l;

FIG. 4 is a schematic diagram of a quantizer, in accordance with the invention, which may be utilized in the digital servos in the computer of FIG 3;

`lEGS. 5a and 5b are waveforms of signals appearing at various points in the circuit of FIG. 4;

FGS. 6a and 6b are waveforms of the output signals produced by the circuit of FIG. 4 illustrating the manner in which the quantizers of the invention convey output intelligence;

FIG. 7 is a 'detailed block diagram, partly in schematic form, illustrating the principal physical components of the computer shown in FIG. 3;

FIG. 8 is a word diagram illustrating the manner in which intelligence is stored and processed in the computer of FIG. 7; and

FIG. 9 is a schematic diagram illustrating the manner in which the logical gating circuits lare mechanized within the computer of FIG. 7 to perform logical and arithmetic functions.

Referring now to the drawings, wherein like or corresponding parts are now designated Iby the same reference characters throughout the several views, there is shown in FIG. 1 a ring point locator system, in accordance with the invention, which includes a projectile tracking computer 10 operative in conjunction with a tracking radar 12 and a plurality of signal converters 14 Ifor determining either the liring point FP or impact point IP of a projectile shown at A2. Before describing the manner in which the projectile tracking computer of the invention performs its computational function, consideration will be given first to the coordinates in which the system is operative and the manner in which tracking of the projectile is accomplished.

More specifically, in setting up the system shown in FIG. 1, tracking radar 12 is placed at a rselected point on the topography and thereafter serves as the origin of an orthogonal coordinate system x, y, h in which the computer operates, the computed coordinates of the projectiles tiring point or impact being displayed by the computer in a plurality of registers X, Y and H. As will be described in more detail hereinafter, by merely presetting registers, X, Y and H to numbers representing the map coordinates of the tracking radar location, the ydisplay in the output registers after a projectile tracking operation may be utilized to present the actual map coordinates of the tiring point or impact point.

In the operation of the system, radar 12 is normally operative in a scanning mode during which time the radar is utilized to scan for projectiles which have been fired. When a projectile is detected, the operation of the radar is changed, either manually or automatically, to a tracking -mode in which the radar locks on and tracks the projectile through at least a portion of its trajectory; at the start of the tracking mode the radar also transmits directly to the computer an electrical start signal FR indicating that the computer should initiate a routine termed Fit, which will be described in detail hereinafter.

In addition to the aforementioned start signal, the radar also makes available to converter 14 three analog signals EX, EY and EH whose voltages are respectively representative of the instantaneous position of the projectile being tracked in the coordinate system x, y, h. It will be recognized, of course, that in a conventional radar the target position is presented basically in terms of range, elevation angle and azimuth angle. However, since there are numerous techniques available for resolving this information into an orthogonal coordinate system, further description of the structure of radar 10 is considered unnecessary. v

As yset forth hereinbefore, the projectile tracking computer of the invention is basically a digital device which receives its input intelligence information in the form of bilevel signal trains which represent the input intelligence digitally. Although the computer of the invention may be readily adapted for operation upon a number of different forms of digital input signal trains without departing from the invention, it will be assumed hereinafter that the computer receives its input information in the form of three difunction input signal trains EX, EY, EH which are produced by converter 14 in response to the analog i signals EX, EY and EH, respectively.

One form of structure which is available for converting an applied analog signal to a corresponding difunction signal train is disclosed in co-pending U.S. patent application Serial No. 540,699, filed October 17, 1955, by Siegfried Hansen, for Analog-to-Difunction Converters, now U.S. Patent No. 2,885,662. Still another structure which represents an improved version of the foregoing device is disclosed in copending U.S. patent application Serial No. 592,963, filed June 21, 1956, for Apparatus for Analog-to-Difunetion Conversion, by Daniel L. Curtis, now U.S. Patent No. 2,885,663. In mechanizing converter 14, of course, either a single time-shared converter or three separate converters may be employed for operating on the three input signals EX, EY and EH to generate the three output difunction signals IDX, EY and QH, respectively. It should also be noted from FIG. 1 that converter 14 also receives signals TPH, TPX and TPY` from computer 161; these signals, as will be described in detail hereinbelow, are timing pulse signals each of which divides time into what will hereinafter be termed difunction signal intervals, the timing signals being applied to converter 14 so that each of the difunction signal trains x, lZiY and IDH is synchronized with the computer to present one difunction output signal during each operational cycle of the computer as hereinafter described.

Before continuing with the general description of operation of the projectile tracking computer of the invention, the manner in which input intelligence is conveyed by a difunction signal should rst be discussed in more detail. It will be recalled that a difunction signal train may be defined as a series of bivalued signals, each signal having either a first value or a second value, the average of the signals in the train representing the average value of the quantity being conveyed. Thus, for example, if the difunction signals represent either a plus or a minus one, the average value of the train over a given interval is obtained by adding the number of plus ones, subtracting the number of minus ones, and dividing the difference by the total number of signals occurring within the interval.

Consequently, a difunction train wherein the pattern +1, +1, +1, -1 is cyclically repetitive represents whereas a train wherein the cally repetitive represents If now the analog signal EH representing height, for example, has a voltage range from -E to +E representing the height range from -20,000 feet to |20,000 feet, then a difunction pattern of +1, +1, +1, -1 represents +10,000 feet with respect to the radar, while a difunction repetitive pattern of +1, 1, -l represents a -1/3 of the range in the negative direction, or +6,667 feet with respect to the radar.

Returning now to the description of FIG. 1, when the projectile tracking computer receives signal FR indicating that the radar is tracking a projectile, and that consequently difunction signals 123x, EY and EH are available for sampling, appropriate gate circuits are opened within the computer to receive a predetermined number of difunction signals in each of the input trains. More specifically, if it is assumed that the particular embodiment of the invention here shown starts accepting difunction signals when the projectile is at point A1 in FIG. l, it Will accept precisely 4096 difunction signals in each of the input trains, at the end of which time the projectile is at a point A2 in its trajectory, and the computer will accept no further input information. With this information the computer'is then operative, `as described hereinafter, to compute the coordinates X0, Y0 and Ho of the midpoint 7 M by averaging the difunction on signals received, and to selectively extrapolate either forward or backward along the projectiles trajectory to compute the coordinates of either the firing point FP or the impact point IP.

It should be noted that although the firing and impact points are shown in FIG. l to lie in plane XY, in practice the elevation of these points will depend upon the terrain; consequently, when the computer extrapolates forward or backward, the location of the impact and firing points is determined by referring to a topographical map of the area, the impact and firing points being given by the X, Y and H register readings when these readings coincide with a corresponding set of values defining actual points on the associated map.

The X and Y registers preferably represent their respective coordinates in meters owing to the fact that topographic maps customarily are plotted in meters. In particular, in the specific embodiment of the invention to be shown and described each -j-l difunction signal in difunction trains X and DY preferably has a physical significauce of +21/2 meters and each -1 difunction a physical significance of -21/2 meters. Consequently, the X and Y coordinates have a range of i4096 2V2 or i10,240 meters, the X coordinate for example, having a value of 10,240 meters if all 4096 difunction signals received are at their low level, and a value of +10,240 meters if all 4096 difunction signals are at their high levels.

In a similar manner, the individual difunction signals in height difunction train EH are preferably scaled to have a significance of -}5 feet or -5 feet, depending upon whether the signal is high or low, respectively. Thus the maximum height capable of being represented by difunction input train EH is 4096 5 or 20,480 feet, the use of feet being preferred because topographical maps show elevation in feet.

Before setting forth in greater detail the structure and detailed operation of the invention, consideration will be given to the mathematical concepts involved in the operation of the computer and the equations which are mechanized therein.

MATHEMATICAL ANALYSIS velocity H. Thus the height coordinate may be written The vertical velocity term H may be expressed as the sum of the projectiles vertical velocity VH at the known point and the sum of the incremental changes in velocity during the previously mentioned interval, this latter term being the integral with` respect to time of the vertical acceleration H. Consequently, the vertical velocity may be written as:

H=VH+jiidf (2) The vertical accelerating forces operating on the projectile in space are the acceleration of gravity g, and atmospheric drag. While gravity is independent of velocity, drag is a function of velocity and may be expressed, within the projectile speeds of interest, as the product of a constant KH and the velocity. Thus the vertical acceleration of the projectile may be expressed as:

=tg+1 nf1i 3) Substituting Equation 3 in Equation 2 then gives:

H=vaftgdf+KHHdo 4) a Y In a similar manner, the X and Y coordinates of the projectile at any instant may be found from the equations:

X=X0+firdr (5) and where X0 and Y0 are the coordinates of a known point on the trajectory of the projectile and X and Y represent the velocity vectors of the projectile along the X and Y coordinate axis.

Although the velocity vectors X and Y are of course independent of gravity, they are effected by atmospheric drag. Accordingly the velocity vectors may be expressed x: VX-fKXXdf (7) and i/:VY-jKYidf (s) where KX and KY again represent constant drag factors,

and VX and VY are the velocities at the known point on the trajectory.

Referring once more to FIG. 1, it will be recalled that the computer of the invention is operative to compute the `average values of the difunction signals transmitted to the computer during the interval in which the projectile moves from point A1 to point A2, and that these average values when multiplied times the full scale range correspond to the coordinates X0, Y0 and H0 of the midpoint M of the tracking interval. In addition, as will be described hereinbelow with respect to FIG. 2, the intelligence information conveyed to the computer through the difunction signal trains may be utilized to determine the velocities VX, VY and VH of the projectile at the midpoint M. It will be recognized, therefore, that since the acceleration of gravity g and the drag factors are constants, the computer of the invention has all of the information necessary to extrapolate Equations l, 5 and 6 backward to find the coordinates of firing point FP, or to extrapolate the equations forward to determine the coordinates of impact point IP.

Consider new the manner in which the difunction signals transmitted to the computer during the tracking interval A1 to A2 may be employed for computing the velocities VH, VX and VY of midpoint M. With reference now to FIG. 2, there is shown a plot of the trajectory in the plane of the trajectory for illustrating the manner in which the height coordinate H0 of the midpoint M is produced, and the manner in which the vertical or height velocity VH is determined.

It will be noted first that the trajectory does not have a uniform slope, but instead follows a roughly parabolic curve at it moves from point A1 to point A2 through the interval T during which time, as aforesaid, the computer receives 4096 difunction signals in the train 15H. Recall now that the average value of a difunction signal train multiplied by the full scale range corresponds to the average value of the variable position which the train represents. Accordingly, it will be recognized that the height represented by the average of the train is that of the point ldesignated HAVE in FIG. 2, and not the actual height of the midpoint M above the XY plane of the radar. It may be shown, however, that the difference between the computer height HAVE and the actual height of midpoint M is ATZ as indicated in the drawing, where A is equal to one-half the acceleration of gravity, or approximately 16 feet per second, and T equals the duration of the tracking interval.

ggg, gnupg!! is a constant, it follows, thereis also a constant which represents a constant error in height of the computed midpoint, the height error being, for example, approximately 80 feet for a computer embodiment each of whose 4096 iterations is precisely 2 milliseconds in duration.

It should be pointed out at this time that a correction for this error in height is made when the computer is first set up for operation at a particular point, and that the error is thenceforth completely compensated. More specically, when the X, Y and H registers shown in the computer of FIG. 1 are adjusted to the yradar coordinates during system set up, the H register is set to a value corresponding to the actual height of the radar above sea level, plus eighty feet. Thereafter, it follows from the above description, the height coordinate H of point M can be obtained by merely averaging input difunction train MH between the times t1 and t5 in FIG. 2, the function being expressable by the following equation:

t5 is Max rangeXZlH 20,480Z1ZlH t,

n it HO- T 4096 523MB feet (9) Continuing now with the description of FIG. 2, the vertical velocity component VH is obtained by determining the first difference between the average height of the projectile during the interval t1 to t3 and the interval t3 to t5. More particularly, the 4096 difunction signals generated in the interval T may be separated into two groups of signals each including 2048 difunction signals, the first group representing the average height of the projectile between times l1 and t3, and the second group representing the average height of the projectile in the interval between points z3 and t5.

Again, as in the valuation of the height of midpoint M hereinabove, the average values represented by the two groups of difunction signals do not represent the true altitudes of midpoints P1 and P2 in the two signal intervals, but are smaller than'the true altitudes by the error signal e which may be shown to be equal to V HAT AT t5 #a MaX range XZEH-l-e] rangeXZlZH-l-e] t3 t2 AT AT tu AT feet per difunction interval l 1) This last equation Will be recognized as stating that the B et vertical velocity VH at the midpoint M may be obtained by summing the tirst 2048 difunction signals in difunction train lZlH, subtracting the result from the sum of the second group of 2048 difunction signals in train DH, and dividing the diierence by the incremental time AT which in turn represents 2048 difunction signal intervals.

Through a similar analysis, the position coordinates X0 and Y0 of midpoint M, and the associated midpoint velocities VX and VY may be shown to be derivable by operating upon the input difunction signal trains EX and lZly in accordance with the following equations:

t5 l5 Max rangeZ MX 10,2402JZ5X t1 ti is f5 VX: AT

meters per difunetion interval A T meters per dif unetion interval It should be noted that the derivation of these equations is simplilied by the fact that there is no gravity force to be considered. It also will be recognized by those familiar with digital computational techniques that Equations 9 through 15 indicate that the initial conditionsV required to solve Equations 1 and 4 through 8 may be derived by simple accumulation processes performed upon the difunction signal trains received by the projectile tracking computer of the invention during the tracking operation.

:Consideration Will now be given to the general manner in which the computer operates, including the technique utilized for deriving the requisite initial conditions from the difunction signal trains, and the general manner in which the computer then functions to solve the trajectory equations.

GENERAL DESCRPTON OF COMPUTER OPERATION Table I Routine Function Clear Set-up subroutine..

Clear computer in preparation for computation. Set X, Y and H registers to radar coordinates. Derive from difunction signal trains the initial clzgnditions expressed in Equations 9 through Extrap o1 ate Forward Solve trajectory equations for impact point. BackwardA Solve trajectory equations for tiring point. Prepares computer for Fit Routine on the next tracking operation.

The general operation of the computer in carrying out the foregoing routines will be described with reference to FIG. 3 which is a block diagram of the computer.

Referring now to FIG. 3, the computer includes three computing sections 300, 302 and 304 which are ern` ployed in conjunction with three respectively associated digital servos 306, 308 and 310 for performing the computational functions of the computer during the Fit and Extrapolate routines, the entry of the difunction signal trains 15H, IDX and EY during the Fit routine being controlled by a combined timing and gating circuit 312. As shown in FIG. 3, timing and gating circuit 312 includes a timing signal generator 314 which generates the standard timing pulse signal Tp referred to previously hereinabove, each signal marking olf one difunction signal interval at the input converters.

The timing and gating circuit also includes a pair of counters 316 and 318 which are actuable by start pulse FR received from the radar to respectively count off 4096 difunction signal intervals and 2048 difunction signal intervals. In operation, counter 316 is used to generate a signal representing the duration of the Fit subroutine, this signal being utilized to control the transmission of precisely 4096 difunction signals in the difunction trains 10H, 10X and lZlY to the computing sections 300, 302 and 304. The 2048 counter 318, on the other hand, is utilized for separating the first group of 2048 difunction signals in each of the input trains from the second group, to thereby enable the derivation of the velocity vectors defined by Equations 1l, 14 and 15.

In addition to the gating circuit 312 also includes an extrapolate control circuit generally designated 332 which is employed to initiate the extrapolate routine of the computer and to selectively signal extrapolation in either the forward direction to determine the projectiles impact point, or in o the reverse or backward direction to determine the projectiles firing point. As will be described below in more detail, the direction of extrapolation is determined by controlling the mathematical operations performed by the computing elements within computing sections 300, 302 and 304.

Referring once more to FIG. 3 each of digital servos 308 and 310 is similar structurally to height servo 306, which will now be described in detail. Basically the servo is similar to the digital servo shown and described in copending U.S. patent application Serial No. 525,148, led on July 29, 1955 for Bidirectional Digital Rate Servo System, by the present inventor, now U.S. Patent No. 2,829,323. As shown in FIG. 3 the servo includes: a reversible motor 334 which is selectively energizable from a source 336 of direct-current potential under the control of a motor relay circuit 338; a digital quantizer 340 which is operative in conjunction with a pair of pick-off heads 342 and 34.4 for generating an output signal train which indicates incremental rotational movements of a toothed disc 346 attached to the shaft of motor 334; an accumulator register 347 for receiving and accumulating the quantizer output signals; and feedback means, including a switch 348, a low pass lter 350 and a buffer amplifier 352, for controlling the direction of energization of motor 334 in accordance with the value of the signals stored in register 347.

In addition to the foregoing elements, the height servo 306 also includes a mechanical shaft revolution counter 353 which presents a visual indication of the rotational position of the shaft of motor 334, a control switch 354 which is utilized for initially setting into the mechanical counter the height coordinate of the radar, and a variable resistor 356 which is utilized for controlling the response of the servo. It should also be noted from FIG. 3 that the digital servo has an alternate feedback circuit through switch 348 and a servo register 358 which constitutes part of computing section 300 to be described hereinafter, the output train from quantizer 340 being applied to the input circuit of servo register 358 through an adder circuit 360.

Accumulator register 347 and servo register 358 are both basically electronic digital accumulators, or more speciically, binary count-up count-down counters, each foregoing elements, timing and a counter having a predetermined number of binary bit places and being responsive to an applied train of bivalued signals for increasing the count stored therein by one digit each time a signal representing one value is received, and for decreasing by one digit the count stored therein each time a signal of the opposite Value is received. In the operation of the servo, the most signicant digit of the binary number stored in one of the registers 347 and 358 is employed to control the energization of motor 334, servo register 358 being utilized when switch 348 is in its normal position, which represents the compute operation, whereas accumulator 347 is utilized to control the motor energization when switch 348 is in its reset position.

Considering the operation of the accumulator and servo register with more particularity, assume that in the null condition accumulator 347 is normally cleared or in other words, contains all zeros, and that switch 348 is in the reset position. Assume also that a Ibinary one in the most significant digit, when presented as a low level signal and passed by tilter 350, energizes relay 338 to drive motor 334 in a clockwise direction, while a binary zero in the most significant digit, when presented as a' high level signal and filtered, energizes relay 338 to drive the motor in the counter-clockwise direction. If then an incremental unit of clockwise or counter-clockwise rotation of the motor shaft causes the quantizer to put out either a -l or a +1 representing signal, respectively, it will be seen that the servo register oscillates back and forth between a binary number in which all digits are zeroes and a binary number in which all digits are ones. Accordingly, mechanical counter 353 will present a stabilized output display in which the least significant digit oscillates in amplitude in accordance with the scaled significance of the quantizer output signals.

Assume now, however, that a relatively large binary number is placed in accumulator 347, the only limitation imposed being that the most significant digit of the number is zero if the number is positive or one if the number is negative. When this is done the servo motor will be energized to drive the mechanical counter in the appropriate direction until the quantizer feedback to the accumulator causes the number to be reduced so that the most significant digit changes from zero to plus one, or vice versa. Thereafter the servo register will oscillate for a short period and finally stabilize in its null condition as described hereinafter. It should be noted here that variable resistor 356 in the motor supply voltage permits the servo motor to operate at full energizing torque until the null point is passed, after which it enables rapid damping of any oscillations which might occur.

At the conclusion -of the servo operation, therefore, the count presented by the mechanical counter has been changed by the magnitude of the binary number which was stored in the servo register and in a sense corresponding to the sign of the number; accordingly the mechanical counter has been servoed digitally in accordance with the binary number which was entered in the accumulator. The manner in which the servo operates in conjunction with the remainder of the computer will be described hereinbelow after a brief discussion of the structure of computing sections 300, 302 and 304.

Referring once more to FIG. 3, computing sections 300, 302 and 304 are shown to include program sequencing gating networks 362, 363 and 364, respectively, and a plurality of digital integrators which are interconnected therewith. Although the gating networks are shown in FIG. 3 as three separate entities, it should be pointed out that in the detailed embodiment of the invention to be described hereinafter a single gating network is timeshared by all three computing sections.

With reference now to computing section 300 in particular, the computational processes are performed by servo register 358 and three digital integrators 365, 366 and 367, respectively. Register 358, which will herein- 13 after be termed the H servo register, is utilized to control the operation of the associated height servo 366 as previously described.

With respect to the structure of digital integrators 365, 366 and 367, a complete and rigorous discussion of their basic functioning, from both electronic and mathematical standpoints, is set forth in detail in copending U.S. patent applications, Serial No. 388,780, filed October 28, 1953, for Electronic Digital Differential Analyzer, and Serial No. 564,683, filed February 10, 1956, for Electronic Digital Dierential Analyzer, both by the `same inventor. As illustrated by integrator 365, a digital integrator comprises two registers termed the integrand register and overflow register, here designated 368 and 370, which are operative to store digital information in the form of signals representing binary t numbers, and a transfer network interconnecting the two registers. In addition the integrator includes an output circuit for presenting a train of bivalued signals representing the integral generated, a-nd a pair of input circuits one of which is coupled to register 368 for receiving a train of bivalued signals representing the integrand or the quantity to be operated upon, while the other input circuit is employed for applying to the transfer network a train of bivalued signals representing the operand.

In operation, integra-nd register 368 is operable as an accumulator for summing the signals in the applied signal train, while register 370 is utilized as an overflow register into which the binary number in register 368 is cyclically either added or subtracted once each signal interval, the particular operation performed depending upon the value of the operand signal received during the interval. The overllow digits resulting from each of the additive transfers to the upper register 370 are then eX- tracted during successive intervals to produce the output train representative of the integral.

To more succinctly point out the operation of an integrator, consider the application to register 368 of a difunction integrand signal [IH representing the time rate of change of velocity, and the application to the transfer network of an operand signal di representing time. It is apparent that register 368, operating as an accumulator, will produce a binary number representing the vertical velocity FI by summing the signals in the train dH. It may be shown, then, that the output train generated by the integrator represents the function Illdt, as indicated in the drawing.

It should be noted from FIG. 3 that integrators 366 and 367 in computing section 300 do not include input circuits for receiving an integrand signal train, but instead have constants stored in their lower registers, the height drag factor KH being stored in integrator 366 whereas integrator 367 stores the acceleration constant g. Thus these two integrators operate in essence as constant multipliers, their output signal trains representing the product-s of the operand times the constants stored in their lower registers. It should be noted, however, that the projectile tracking computer of the invention operates in real time, and that the operand signal dt applied to integrator 367 represents either a -l-l or 1, depending upon whether the computer is extrapolating forward in time or backward in time.

Consider now the operation of the computer in carrying out in sequence the routines set forth in Table I above. The computer Clear routine is carried out when the radar is first set up at the desired map coordinates, and is utilized to clear accumulator 347, servo'register 358, the upper and lower registers in integrator 365, and the upper register in integrators 366 and 367 so that their contents represent zero, the mechanism for accomplishing this routine not being shown in FIG. 3. It will be appreciated of course tha-t a similar routine is carried out simultaneously in computing sections 362 and 304. It should also be noted that those integrator registers carry- 14 ing constants, such as the lower registers in integrators 365 and 367, remain unaffected by the Clear routine.

In addition to clearing the computer, the Clear routine also permits a set-up subroutine to be carried out to enter into the mechanical counters the coordinates of the radar. More specilically, during the Clear routine switch 354 is switched from its servo position, as shown in FIG. 3, to either the Up or Down position, to thereby energize motor 334 to rotate counter 353 to present the corresponding map coordinate of the radar. This operation is carried out for each of the three coordinates, it being remembered that the height visually displayed by the H counter should be set to a quantity equal to the true altitude of the radar plus the previously discussed constant of feet. It should also be noted tha-t variable resistor 356 may be utilized to control the motor speed, and that while the set-up subroutine is being carried out, energy is removed from the motor relay 338 in each of the digital servos.

After the Clear routine has been completed, the servo register in each of the computer sections is coupled to its associated digital servo and a start signal is awaited from the associated radar indicating that a tracking operation has commenced and to initiate the Fit routine. In this routine, the receipt of the Start signal FR, as shown in FIG. 3, opens a gate 372 in timing and gating circuit 312 to initiate the counting operations within counters 316 and 318, counter 316 in turn functioning to open a gate 374 in program sequencing circuit 362 to thereby pass to servo register 358 the next 4096 difunction signals in input train IDH.

During the period of the first 2048 difunction intervals in the sampling interval, 4096 counter 316 functions to open a gate 376 in the program sequencing circuit to thereby accumulate the irst group of 2048 difunction signals in register 368 of integrator 365 to present a number representing the average position of the projectile during the iirst half of the counting interval. At thel conclusion of this period 2G48 counter 318 functions to close gate 376 and to open an inverting gate 378 to thereby apply to register 368 the second group of 2048 signals in the difunction train IDH, these signals being inverted or complemented. In this manner, the linal number standing in H register 368 represents the summation of the iirst 2048 signals minus the summation of the second group of 2048 signals. In other words, the final number in the register represents a solution to Equation 1l and is the value of the vertical velocity VH of the midpoint of the projectiles sampled trajectory.

It should be apparent that the number standing in servo register 358, if digital servo 306 was not permitted to operate, would represent the height coordinate H0 of the projectile at the midpoint in its sampled trajectory, or in other words a solution to Equation 9. As a practical matter, however, as soon as servo register 358 starts to accumulate signals in the difunction input signal train, digital servo 306 is unbalanced and motor 338 starts -driving counter 353 in a restoring direction, the output signals from quantizer 340 being applied to adder 360, along with the signals from gate 374, so that the servo register maintains accurate position follow-up of counter 353.

At the conclusion of the Fit routine, gates 378 and 376 in program sequencing current 362 are `both closed and, consequently, no further difunctio-n input signals are accepted. It should -be pointed out that as a rule digital servo 306 will not yet have reached its null positions, and will therefore continue to drive mechanical counter 353 in a restoring direction. It should be recognized however, that if the servo is permitted to drive to its null position, then the count visually displayed by counter 353 will represent the altitude of the midpoint M in FIG. 2. A-fter the operator of the computer has received a signal indicating that the Fit routine has been terminated, he

may energize extrapolation circuit 332 to cause the computing sections to extrapolate the trajectory equations either backward to evaluate the ring point or forward to evaluate the impact point.

`Consider now the manner in which the various integrators are interconnected to solve the trajectory equations. It should be noted rst that if the trajectory equaions are to lbe extrapolated forward intime, a signal dt representing a continuous train of plus one difunction signals is applied to the transfer networks of integrators 355 and 367 so that the contents of the associated lower register are added to the contents of the upper register once per iteration. Conversely, if the equations are to be extrapolated backward, a signal dt representing a continuous train of minus one difunction signals is applied to the transfer networks of these integrators so that the contents of the lower register are subtracted from the contents of the upper register once per computational iteration.

Turning then to the elements of computing section 3%, if it is assumed that the number stored in H register 368 represents the vertical velocity then the output train presented by integrator 365 represents the quantity dt. if this output train is applied to the transfer network of integrator 366 to control its additive transfers, it will be recognized that the output train from this integrator will be KHdt, since the constant drag factor KH is stored in the lower register. In a similar manner, the output train from integrator 367 may be shown to be gdt .since the gravity acceleration constant g is stored in its lower register. By combining the output trains from integrators 366 and 367 in an adding network 378, a resultant sum signal train is produced representative of the quantity (KHIIdt-l-gdt) as indicated in the drawing, or stated differently, is representative of the velocity derivative al as may be vertified by differentiating Equation 4 `set forth above.

The resultant sum train is then passed by gate 380, which is opened' during the extrapolate routine, to the register of integrator 365 which accumulates the signals in the train dl to modify the original velocity vector VH stored therein during the Fit routine. Accordingly it will be recognized that integrators 365, 366 and 367 provide an iterative solution of trajectory Equation 4.

The output train Hdt from integrator 365 is `also applied to servo register 358 through a gate 382, which is opened during the extrapolate routine, and through adder 360. It will be appreciated that the quantity Hdt corresponds to the height derivative dH, as may be verified by differentiating Equation 1, the servo register `functioning to accumulate the difunction signals in the input train and to further energize the digital servo system in accordance with the summation of the received signals.

Before completing the generalized description of operation of the projectile tracking computer of the invention, it should rst be pointed out that during the Fit and Extrapolate routines identical processes are carried out substantially simultaneously in X and Y computing sections 302 and 304 and their associated digital servos. More specically, it will be recalled that program sequencing circuit 362 of H computing section 300 is actually a gating matrix which is time-shared with computing sections 302 and 304, the sequencing circuit first being utilized to yperform a single iteration for vertical velocity and height, then Jror X velocity and X coordinate, then for Y velocity and Y coordinate, and then back to vertical velocity and height.

With respect to the computational elements employed in computing sections 392 and 394, each includes a servo register yand two integrators which `function in the same manner as servo register 358 and integrators 36S and 366 in computing section 3h0, the only distinction being that computing `sections 362 and 3h41 have no equivalent to integrator 3o7 in computing, section 399 since the acceleration of gravity is not a' function of the X and Y coordinates of trajectory. r`he servo registers are designated 384 and 336, respectively, while the X coordinate velocity and acceleration integrators are designated 383 and 390 and the Y coordinate velocity and acceleration integrators are designated 3% and 394;. Thus, in the Extrapolate routine the output trains from the acceleration integrators in the X and Y computing sections are merely reapplied to the integrand registers of the associated velocity integrators to thereby solve Equations 7 and 8, respectively, while the output trains of the velocity integrators `are applied to the associated servo registers in their associated computer section to provide a solution to differential Equations 5 and 6, respectively.

Continuing now with the description of the Extrapolate routine, all three computing sections are operable in synchronism to selectively extrapolate either forward or backward by successive iterations. Although not disclosed in detail in FIG. 3, the specific embodiment of the invention to be shown and described in detail hereinbelow provides controls for either continuous extrapolation in the desired direction, extrapolation in groups of ve iterations, or extrapolation by utilizing only a single iteration at a time. Inasmuch as thedigital servos are operative continuously throughout both the Fit and Extrapolate routines, the choice of the extrapolate control to be employed is determined by how close the position coordinates visually displayed in the mechanical counters of the digital servos approach the coordinates of a point on the associated terrain map.

For example, assume that the coordinates displayed on the counters at the conclusion of the Fit routine are those of a point high in the projectiles trajectory, and that it is desired to evaluate the projectiles firing point. The cornputer is then placed in continuous extrapolation in the backward direction until the servo counters indicate that the map coordinates of a point on the terrain are being approached. The continuous extrapolation is then stopped to permit the digit `servos to null, after which the livesrtep or single-step extrapolation switches are selectively energized in the appropriate direction until the coordinates presented in the mechanical counters are identical with the map coordinates of a point on the terrain. These coordinates then represent the firing point. By applying a similar technique of extrapolation in the opposite direction, on the other hand, the impact point of the projectile may be ascertained.

Having obtained the desired information the computer must now be reset to prepare for a subsequent tracking operation on another projectile. In order to fully comprehend the manner in which the Reset routine is accomplished, it should first be understood that throughout the complete running of the Fit and Extrapolate routines, the signals generated by the quantizer in each of the digital servos are applied not only to the associated servo register of the computing section, but also to the associated accumulator register within each of the digital servos. Consequently when the projectiles impact or firing point has been determined, accumulator register 347 in digital servo 306, for example, contains a number whose magnitude and sign are representative of: the amplitude and sense of the numerical change of the count in counter 353 in going from the original coordinates of the radar to the coordinates of the firing point or impact point.

In carrying out the Reset routine, the servo loop in the digital servo is changed by switch 348 so that motor 333 is energized from accumulator 347, thereby driving the digital servo to a null whereat the accumulator is emptied and the height counter again presents a visual indication of the radar altitude. Meanwhile similar operations carried out concomitantly in digital servos 398 and 3l() return to their respectively associated output registers t the coordinates of the radar. In addition, the Reset routine is also employed to again clear the servo register and the integrators in each of the computing sections in the same manner as described previously for the Clear outine. The computer is then ready to again perform the Fit routine vof its computational operations whenever the radar again signals that a projectile is being tracked. It should be here pointed out that the diagrammatic view of the invention as shown in FIG. 3 illustrates the basic mode of operation of the projectile tracking computer, but does not necessarily show each element of the computer in its optimum form. For example, although switches are shown to be utilized for controlling the Reset operation, in practice the output of either the servo register or accumulator is selectively gated electronically to control the energization of the associated servomotor. In a similar manner, each of the accumulators, servo registers and integrators, shown as separate physical entities in FIG. 3 may be carried as Words in a magnetic drum recirculating memory, as will be described in detail hereinbelow. Y

DETAILED DESCRIPTION OF OPERATION In order to fully comprehend the operation of the specific embodiment of the invention described in detail hereinbelow, it is first essential to understand the operation of the quantizers in the individual digital servos, the type and nature of the signals produced thereby, and the intelligence information conveyed Iby these signals. With reference then to FIG. 4, there is shown a schematic ,diagram of a quantizer which may be utilized in height servo 306 for presenting output signals representative of changes in the rotational position of toothed disk 346 as detected by the previously described pick-olf heads 342 rand 344. f v

`As shown in FIG. 4, the quantizer includes an oscillator 400 which produces a sine wave `output signal which in turn is applied through a transformer 402 to a pair of series L-C circuits, one circuit including a capacitor 404 and the inductance of pick-off head 344 while the other circuit comprises a similar capacitor 406 and the in-V ductance of pick-off head 342. In addition, the quantizer includes a pair of detection circuits 468 and 410 respectively associated with pick-off heads 344 and 342, respectively, each Vdetection circuit in turn including a plurality of rectiliers and capacitors for producing a pair of complementary voltage level output signals representative of the position of its associated pick-olf relative to the teeth on ltoothed disk 346.

Both of pick- oli heads 342 and 344 are fixed relative to each other and are positioned adjacent the' outer periphery of toothed disk 346, each head comprising a horseshoe shaped ferromagnetic core which presents through its associated winding a variable inductance Whose magnitude is dependent upon whether a tooth of disk 346 is beneath the air gap in its core. More specifically, the inductance presented by each head is at a maximum when a tooth of disk 346 is adjacent its air gap, and is at a minimum when the air gap in its core is the space between adjacent teeth.

The value of the capacitor in each L-C circuit is seletced to provide an L-C series circuit resonant at the frequency of the applied signal when the inductance is at its maximum value. Consequently, when a tooth is adjacent the gap in a pick-olf head a relatively large alternating current signal is presented across the head, whereas a rela-tively small alternating current signal is presented across the head when the inductance of the head is at its minimum value.

As further illustrated in FIG. 4, each detection circuit is connected across its associated pick-oit head and includes two parallel paths to which the signal appearing across the head is applied by a pair of coupling capacitors 412 and 414, respectively, the parallel paths in detection circuit 403 functioning to produce a pair of complementary output signals AH and AYH representative of the relative position of head 344 with respect to the teeth of disk 346, while similar paths in circuit 414k function to produce a pair of complementary output signals BH and BH representative of the relative position of head 342. The left-hand path, as viewed in FIG. 4, includes a reference diode 416 having its anode connected to a -27 volt source, not shown, and its cathode connected to capacitor 412 and to the anode of a blocking diode 417, the other end of this diode being connected, in turn, to the cathode of a clamping diode 418, to one end of a pull down resistor 419, and to one terminal of an output capacitor 420. The other terminal of capacitor 420 is grounded while the second end of resistor 419 and the anode of diode 418 are connected respectively to a source of B- and to a source of -12 volts, either of which source is here shown.

The right-hand path in the detection circuit, in a similar manner, includes a reference diode 422 having its cathode connected to a +15 volt source, not shown, and its anode connected to capacitor 414 and to the cathode of a blocking `diode 423. The anode of diode 423 is then coupled to a B+ source, not shown, by a pull-up resistor 424, to the anode of a clamping diode 425 whose cathode is connected to ground, and to one terminal of an output capacitor 426 whose other terminal is grounded.

t In the absence of an applied alternating current signal, the voltage across capacitor 42@ is normally `l2 volts since the pull-down resistor renders diode 418 conductive, whereas the voltage across capacitor 426 is at ground potential owing to the fact that diode 425 is rendered conductive from the B+ source through resistor 424. It also folows, therefore, that the junction of diodes 416' and 427 is floating midway between l2 volts and `27 volts owing to the fact that diodes 416 and 417 are both backbiased, while the junction of diodes 422 and 423 is floating midway between ground and +15 volts since these two diodes are back-biased.

With reference n-ow to FIGS. 5a and 5b, there are shown the waveforms appearing at various points in the detection circuit as toothed disk 346 is rotated from its position as shown, relative to head 344, to a position Where one of the teeth is adjacent the gap in head 344. As shown rby the left-hand portion of the waveforms in FIGS. 5a and 5b, when the head is adjacent a space in the disk a relatively small alternating current signal is applied to the junction of diodes 416 and 417 and to the junction of diodes 422 and 423 as shown `by waveforms 416a and 422a, the peak-to-peak amplitude of the signal 'being less than l5 volts so that all four of these diodes remain back-biased. Accordingly, the output signals AH and AH across capacitors 423 and 426 are at -12 volts and ground potential, respectively.

Assuming then that disk 346 rotates so that a tooth is adjacent pick-oft head 344, a signal of relatively large Iamplitude is impressed across the junctions of diodes 416 and 417 and of diodes 422 and 423 as illustrated Iby waveforms 416g and 422:1, the signal causing diode 417 to conduct as the signal raises the junction of diodes 416 and 417 above l2 volts and causing diode 423 to conduct when its negative going portion falls below ground potential. Consequently diodes 418 and 425 become backbiased, and the voltage across capacitors 420 and 426 tends to follow the signals passed by diodes 417 and 423.

As shown by the waveforms AH and AH, respectively, when the signal thereafter goes through regions of negative slope and positive slope, respectively, the voltage across capacitors 420 and 426 does not follow the waveforms 416a and 422g, but instead provides a form of envelope detection analogous to the detection of the modulating signal in an amplitude modulated carrier signal. This result is produced by the fact that diodes 418 and 42S remain back-biased while the input signal is large, and that diodes 417 and 423 are frontebiased `only when charge is being added to the capacitors and are back-biased as soon as the alternating current signal goes below the voltage on the associated output capacitor. Consequently capacitors 420 and 426 have only a high impedance discharge path during those portions of the input signal cycle 'when they are not being charged from the input signal.

The structure and function of detection circuit 410 are identical to the structure and function of circuit 408 described hereinabove, circuit 410 -being operable to produce a pair of complementary output signals BH and BH representative of the position of pick-olf head 342 relative to disk 346. For purposes of discussion hereinbelow, a high level or ground potential in signal AH or BH will be termed a one-representing signal, while a -12 volt or low level voltage will be termed a zero-representing signal. Conversely, complementary signals AH and B'H present a one-representing signal as a low level voltage and a zero-representing signal as a high level voltage.

Consider next then the manner in which the quantizer, including its two detection circuits, indicates a change in the rotational position of toothed disk 346. With reference once more to FIG. 4, if each tooth on disk 346 and an adjacent space are considered to be one cycle or one increment of rotation, then pick-off heads 342 and 344 are 90 out of phase with respect to each other. Referring then to FIGS. 6a and 6b, there are shown the waveforms of signals AH and BH as they appear when disk 346 is rotated at a constant speed, the waveforms of FIG. 6a representing clockwise rotation of disk 346 while the waveforms of FIG. 6b represent counterclockwise r0- tation `of the disk. It will be seen that waveform BH leads waveform AH by 90 when the disk is rotating in a clockwise direction, and lags waveform AH by 90 when the disk is rotating in a counterclockwise direction.

Assume now that one complete revolution of disk 346 actuates the mechanical counter to produce a change of 100 feet in the altitude visually displayed in the counter. Assume also that the maximum 4rate of rotation of the toothed disk is one-twentieth of a revolution per difunction interval, or in other words, is of l8 per iteration of the computer. It follows then that the maximum rate f change of the altitude presented by the counter is 5 feet per difunction interval.

It will be apparent from the description set forth below, however, that for a five-toothed disk such as is utilized in the height servo, the quantizer is only capable of distinguishing between ten foot increments of altitude, inasmuch as the quantizer can respond only to such movement Vof the disk as will produce a change in the output signals AH and BH, as previously described with regard to FIGS. 5a and 5b. Thus at the end of a difunction interval the quantizer output signals presented may be identical to those presented at the end of the previous interval, and will therefore indicate that no change has taken place in the counter-reading. On the other hand, if the quantizer signals are different from those presented at the end of the previous difunction interval, then a change of either plus ten feet or minus ten feet is indicated.

In the operation of the quantizer a change in the signal AH at the end of successive difunction intervals is utilized to indicate that the reading has changed by either plus ten feet or minus ten feet, whereas if the AH signal remains at the same level as before a zero change is indicated. The BH signal, on the other hand, is utilized to indicate whether 4a change in altitude of ten feet is positive or negative, since as pointed out previously, the signal BH either leads or lags the signal AH 4depending upon whether the rotation of the counter is 4clockwise or counterclockwise, respectively.

More specifically, it will be noted from FIG. 6a that the disk is -rotating in a clockwise direction if signal AH goes from its one-representing value or high level to its zero-representing value or low level and signal BH is at its zero-representing value or low level, whereas FIG. 6b

illustrates that a high level for signal BH when signal AH changes from its high level to its low level indicates an increment of rotation inthe counterclockwise direction. In a similar manner these figures illustrate that a change in signal AH from its low level to its high level represents an increment of clockwise rotation when signal BH is at its Ihigh level, and an increment of counterclockwise .rotation when signal BH is at its low voltage level. All of the foregoing conditions and their operation significance are correlated by the following table, Table II.

Table II Possible Prior Present Present Change in H conditions An An Bn 0 0 0 0 No change. O 0 1 D0. 0 1 0 -10 feet. 0 1 1 +10 feet. 1 0 0 Do. 1 0 1 -10 feet. 1 1 0 0 No. change 1 1 1 D0.

It will be recognized from the foregoing table that it is necessary to store signal AH at the end of each difunction signal interval so that it may be compared with the signal AH as it is presented at the conclusion of the following interval to determine if there has been a change in its voltage level. As will be disclosed in more detail hereinbelow, the storage of signal AH is accomplished in the detailed computer to be hereinafter described by magnetizing a predetermined spot or cell in a recirculating magnetic memory in accordance with the level of the signal.

The structure and operation of the quantizers in the X and Y digital servos are substantially identical with that of the height servo described hereinabove, the only material distinction being that these quantizers operate in conjunction with toothed disks which have ten teeth in lieu of five as in the height servo. More specifically, it will be recalled that the difunction altitude or height is represented by a difunction train wherein each signal represents i5 feet, whereas the height quantizer produces output signals representing either zero or 110 feet, thereby setting up a 2:1 scale factor between the signals. Assume now that one turn of the X and Y mechanical counters represents meters instead of 100 feet, andthat the 2:1 scale factor between quantizer output signals and difunction input signals is to be maintained in order to simplify the computers circuitry as described hereinafter. Inasmuch as each signal in the input difunction trains I/)X and EY has a significance of 121/2 meters as discussed previously, it follows therefore that the quantizers in the X and Y servos must produce signals representing zero or i5 meters. Accordingly it will be recognized that ten teeth must be provided in the disks utilized in the X and Y servos to provide the 20 detectable transitions in rotational position which are required to detect an incremental change of 5 meters in the rotation of a shaft where a complete revolution of the shaft signifies 100 meters.

The manner in which the X and Y quantizers present their output signals is identical with that previously discussed for the height servo, the X quantizer generating output signals AX, AX, BX and B'X while the Y quantizer generates output signals AY, AY, BY and BY. Thus Table II, set forth hereinabove, is equally applicable to the X and Y quantizers with the exception that changes in the X and Y coordinates presented by the associated counters are represented by changes of t5 meters instead of feet.

With reference now to FIG. 7 there is shown in more detail the computational elements employed in a specific projectile tracking computer which has been constructed in accordance with the teachings of the-present invention. As shown in FIG. 7 the computer includes a front panel 700 on which are mounted the various computer controls and the mechanical counters for displaying the results of the computation, a recirculating memory system including a magnetic drum unit generally designated 702 for storing applied electrical signals as magnetic cells on a magnetizable medium, a plurality of liip-ops or bistable storage elements which are designated by alphabetical characters, and a logical gating matrix 704 which is operable under the control of the various flip-flops for transferring intelligence information between the panel controls and magnetic drum unit 702, and for performing electrically the computational processes carried out within the computer.

In the particular embodiment of the invention shown in FIG. 7, magnetic drum unit 702 comprises a rotatable drum 706 having a magnetizable periphery, a synchronous motor 708 energizable from a fixed frequency source 710 for rotating the drum at a constant speed, and a plurality of magnetic transducers some of which are utilized for writing applied electrical signals as magnetized cells on the drum periphery and others of which are employed for reading the magnetization of cells on the drum periphery to present electrical output signals representative of the magnetization. The utilization of synchronous motor '708 and fixed frequency source 7l0 is dictated by the fact that the computer must perform its Fit routine in real time, and must therefore rotate drum 706 through a predetermined angle during each difunction interval. It should be noted, however, that it is not essential to employ a synchronous motor, since au induction motor energized from a servo having precision follow-up may also be utilized to provide synchronous memory operation.

As indicated in FIG. 7 by the dotted lines on the periphery of drum 706, the drum surface is divided into tive channels or tracks designated C1, P1, P2, L1 and L2, each of which has one or more magnetic transducers permanently associated therewith. More specifically, channel C1 is a clock or timing signal channel on which a predetermined number of alternately polarized magnetic cells are permanently recorded, the magnetic pattern on this track being employed to energize an associated reading transducer 7ll2 which in turn is coupled to a clock pulse generator 714 which produces a continuous train of high frequency pulses for synchronizing the operation of the computer through gating matrix 704. In a similar manner channels P1 and P2 are also utilized to store permanent predetermined patterns of magnetic cells; these two channels will be termed the first and second marking channels and are operable in conjunction with a pair of respectively asociated reading transducers 716 and 718 and a pair of reading amplifiers 719 and 720 for energizing a pair of channel reading flip-flops P1 and P2 in accordance with lthe magnetization of channels P1 and P2. Thus each of flip-flops P1 and P2 presents at its output terminals a pair of complementary signal trains which are cyclically repetitive with each drum revolution and whose sequential signals correspond to the magnetization of the successive cells on their associated tracks. As will become more apparent from the description of FIG. 8 hereinbelow, channel P1 is utilized both alone and in conjunction with channel P2 to separate or distinguish diferent pieces of intelligence information stored in channels L1 and L2. Channel P2, on the other hand, is also utilized to ystore signals representing the constant acceleration factor g and the drag constants K11, KX and KY required to solve the trajectory equations previously described.

As shown in FIG. 7, channels L1 and L2 are different from the permanently recorded channels described hereinabove in that they each operate in conjunction with a pair of magnetic transducers. More particularly, chan-k nels L1 and L2 are recirculating registers utilized to store serially the results of the computational processes carried out within the computer, and are operable in conjunction with a pair of Writing transducers 721 and 722 and a pair of reading transducers '723 and 724, respectively, the Writing transducers being energized from a pair of Writing flip-flops M1 and M2 through a pair of respectively associated writing amplifiers 725 and 726. The reading transducers, in turn, are employed to energize a pair of channel reading flip-flops L1 and L2 through a respectively associated pair of reading amplifiers 727 and 728.

ln the operation of the computer intelligence information is stored on the surface of drum 706 in a serial fashion and in the form of binary bits, that is, as either a binary one or a binary zero. Stated differently, each track may be considered as an endless chain of magnetic cells each of which may be magnetized in one sense to represent a binary one or in the opposite sense to represent a. binary zero, each cell having a circumferential length about the drum equal to the length of each recorded clock pulse in channel C1. Accordingly, the reading amplifiers and their associated output flip-flops present a different binary information bit for each successive clock pulse interval, while the writing amplifiers and flip-flops M1 and M2 function to sequentially record in channels L1 and L2 a separate and distinct binary information bit during each successive clock pulse interval.

Consider now the relative positions of writing transducers 721 and 722 with respect to reading transducers 723 and 724. As Will be disclosed in more detail hereinbelow, the computer performs one complete computational iteration by operating on the H, X and Y coordinates serially or in sequence during the interval required to present in read flip-flops L1 and L2 the binary bits previously stored'in iiip-liops M1 and M2. Accordingly, the recirculating time of the L1 and L2 channels is precisely one difunction time interval since it will be recalled that during the Fit routine one difunction input signal is received bythe computer during each computational iteration.

Owing to the fact that permanent marking channels P1 and P2 are continuous around the drum while channels L1 and L2 are relatively short recirculating registers, it will also be recognized that the length of the drum periphery must be an integral multiple of the length of the recirculating registers so that the marks in the marking channels always occur concomitantly with predetermined intelligence bits in the recirculating registers. In the particular embodiment Vof the invention here shown and described, the periphery of drum 706 is precisely five times the length of the recirculating registers; the reason for choosing a one to five ratio, as will be discussed more thoroughly hereinbelow, is to permit extrapolation of the :trajectory equations in groups of tive iterations at a time, or in other Words, to permit the computer to extrapolate through one entire drum revolution.

Consider now the rotational speed of drum 706 in a practical embodiment of the invention, and the number of clock pulses stored around the drum. It will be recalled from the description of FIGS. l and 2 that the duration of each difunction signal interval is 2 milliseconds; accordingly, one revolution of the drum then consumes ten milliseconds, since there are five difunction intervals per revolution. It follows, therefore, that the drum speed is 6,000 r.p.m., which may be obtained for example, by driving an eight pole synchronous motor from a 400 cycle per second source.

With respect to the number of clock pulses recorded around the drum periphery, it will be apparent from the description of FIG. 8 set forth hereinafter that there are 133 bit spaces in each of the recirculating channels for spaans? performing the requisite computational functions. Consequently 4the drum has 5 l33==665 clock pulses recorded around its periphery. It should be noted here, incidentally, that the reading and writing heads on the recirculating channels are separated by a distance equal to the length of 131 magnetizable cells, rather than 133, owing to the fact that read ilip-ilops L1 and L2 and write Hip-flops M1 and M2 provide a memory for two of the binary bits in each of these channels.

With reference once more to FIG. 7, control panel 700 includes a plurality of switches for controlling the operation of the computer, some of these switches having been described previously with respect to FIG. 3. For example, switch 348 in FIG. 3 is also shown on control panel 700 and is designated the routine control switch, this switch having three switching points designated Clear, Reset and Compute. When the switch is set to the Clear position, a high level signal is presented to logical gating matrix on the conductor designated C@ and a low level signal on conductor @E to indicat that the Clear routine is being carried out, while low and high level signals are presented on conductors and @3, respectively, to indicate that the Reset routine is not being carried out. Conversely, when switch 348 is set to its Reset position high level signals are presented on' conductors and (KV) and low level signals on conductors( R' land@ to indicate that the Reset routine is being carried out and not the Clear routine. On the other hand when switch 348 is in its Compute position,

low level signal-s are presented on both the and@ conductors while high level signals are presented on conductors and Gi) to indicate that neither the Clear nor Reset routine is being carried out. It should be here pointed out that when switch 348 is set to the Clear position, a biasing voltage is removed from certain ipflops in-the computer, as described' in more detail hereinbelow, to force these Hip-Hops to their zero-representing conduction states.

Continu-ing with the description of control panel 7%, when switch 348 is in its Compute position start signal FR `from 4the radar for initiating the Fit routine is passed on to a Fit control switch 730, this switch having three switch points designated Manual, Oft and Radar. When switch 736 is in the Radar position the FR signal from the radar actuates a relay, not shown, which transmits Ia high level signal to theV logical gating matrix over the conductor designated@ and a pulse signal over the conductor designated' (F-pulse); in addition the relay energizes the signal lamp 732 indicating that the Fit routine is taking place. On the other hand, if switch 730 is in the 01T position, the radar start signal FR merely energizes lamp 732, the computer operator thereby being notified that he can manually initiate the Fit routine by switching to the manual position, at which time a high level signal is presented over conductor It should be pointed out here that the conductor designated E is complementary to conductor in that a high level signal is presented on conductor E at all times except during the Fit routine when conductor presents a high level signal.

As shown in FIG. 7 the control panel also includes the counter set-up switch 354 previously described with respect to FIG. 3, and in addition a counter selector switch 734 which has three switch positions designated H, X and Y and which is utilized in conjunction with switch 354. More specifically, it will be recalled that in describing FIG. 3 hereinabove, it was assumed for illustrative purposes that switch 354 was associated with the height servo alone. In practice, however, a single switch is utilized in conjunction with counter selector switch 734 to selectively set-up the initial coordinates in each of H, X and Y counters while the Clear routine is being carried out; thus while routine control switch 34S is in the Clear position, counter selector switch is moved sequentially to its H position, then to its X position, and tinally to its Y position, ineachof which positions switch 354 is selectively moved to-either its up position or down position to change the coordinates visually presented by the correspondingly designated mechanical counter.

It should be noted here that the computer also includes a single speed control knob 736 which corresponds to the variable resistor designated 356 in the height servo of FIG. 3, the speed control being utilized to control the speed of all of the servomotors when switch 354 is in its servo position, and being utilized to energize the single servo motor designated by the setting of counter selector switch 734 during the clear routine when switch 354 is switched to its up or down position.

In addition to the foregoing control elements, panel 730 also includes three diterent extrapolate control switches respectively designated 740, 742 and 744 for providing either continuous extrapolation of the trajectory equations after the conclusion of the Fit routine, extrapolation by tive iterations or steps, or extrapolation by a single iteration or step. As shown in the drawing, each switch has a normal position from which it can be moved to either the left or right to extrapolate the trajectory equations backward or forward, respectively.

Consider next the signals transmitted to logical gating matrix 704 by the extrapolate control switches. When all three switches are in their normal positions, low level signals are transmitted to the matrix on the conductors designated (Back), (Forward), (1 cycle-down),

(5 cycle-down), and (continuous down), while high level signals are transmitted to the matrix on the conductors designated l cycle-up), (5 cycle-up), and (continuous up). Upon actuation of any of the three switches from its normal position, a high level signal is presented on either conductor (Back) or the conductor (Forward), depending upon whether the switch is moved to the left to extrapolate backwards or to the right to extrapolate forward. In addition, the voltage states normally presented are reversed on the pair of conductors associated with the particular switch which has been actuated. For example, if the single-step switch 744 is moved to the left to extrapolate backwards by one iteration, high level signals are presented on conductors (Back) and on l cycle-down), whereas a low level signal is presented on conductor (1 cycle-up); the remaining conductors, on the other hand, remain at their normal voltage levels. During the Extrapolation routine, of course, conductor presents its aforementioned high level signal.

As indicated by the busses designated 746, 747 and 748 in FIG. 7, the three quantizer output signals from each of the digital servos previously described are also transmitted to logical gating matrix 764, while the matrix transmits three output signals OH, OX and OY back to the control panel. These latter three sginals represent the output signals from the computer and are utilized to control the direction of energization of the servomotors in the digital servos during the Fit, Extrapolate and Reset routines. In terms of the digital servo structure previously described with respect to FIG. 3, signal OH is applied to filter S in the height servo 306, while signals OX and OY are applied to similar filters in digital servos 3% and 31E), respectively.

Continuing now with the description of the basic elements of the specific projectile tracking computer shown in FG. 7, the computer as shown includes nineteen ipops or bistable storage elements which are operative in conjunction with memory unit 7t2, gating matrix 704, and the input control switches to provide temporary storage for intelligence information, to control the subcorrespondingly designated 25 lroutines carried out within the computer, to control the mathematical operations carried on within the computer, and to transfer intelligence information to and from the memory unit.

Before describing the functions performed by the individual ilip-flops, consideration will be given lirst to the designation of the input and output conductors of the various flip-flops shown in FIG. 7. Each flip-flop may comprise either vacuum tubes, transistors, magnetic cores, or any other elements suitable for providing bistable operation, and includes a pair of input conductors which are designated the S input conductor and Z input conductor, respectively, each conductor being further designated by an alphabetical postscript corresponding to the alphabetical designation of its associated flip-flop. In addition, each flip-flop includes a pair of output conductors one of which is designated by the same alphabetical ldesignation as the flip-flop from vwhich it is taken, while the other is designated by the prime of the alphabetical designation of the flip-flop. Thus, for example, flip-Hop K1 has both SK1 and ZKl input conductors and K1 and Kl output conductors.

In operation each flip-flop will be assumed to he responsive to the application of an input signal to its S input conductor for setting to a conduction state corresponding to the binary value one, and to the application of an input signal to its Z input conductor for setting to the opposite conduction state, which corresponds to the binary value zero. In addition it will be assumed that when a flip-flop is in its one-representing state the voltage presented on its correspondingly designated output conductor has a relatively high level value while the voltage presented on its prime output conductor has a relatively low level value. Conversely, when a flip-flop is in its zero-representing state, the voltage presented on its output conductor has a low level value whereas a high level voltage is presented on its prime output conductor. For example, when flip-flop K1 is in its one-representing state, high and low level signalsv are presented on output conductors K1 and Kl, respectively, whereas these voltage levels are reversed when flip-flop K1 is in its zero-representing conduction state.

Returning now to the description of FIG. 7, the flipops there shown may be classified in six groups according to the functions they perform, two of these groups having been discussed previously with regard to the description of memory unit 702. More specifically, flipops L1, L2, P1 and P2 may be termed the memory reading group and function as electrical windows for the correspondingly designated channels on drum 706 by sequentially presenting as output signal trains the magnetization of sequential cells in the memory, each flip-flop assuming its one-representing state when a binary one is read by its associated reading transducer and its zerorepresenting state when a binary zero is read. Flip-flops M1 and M2, on the other hand constitute a memory writing flip-flop group for recording information bits in channels L1 and L2.

The remaining four groups of flip-flops are bracketed in FIG. 7 and are termed counting group 750, program control group 752, temporary memory group 754, and computational group 756. The counting group designated 750 comprises four flip-flops C1, C2, C3 and C4 which are operable as a scale-of-ten binary counter for distinguishing between or separating the various intelligence words stored in channels L1, L2, P1 and P2, as will be illustrated more fully with respect to the description of FIG. 8 hereinbelow. Program control group 752, on the other hand, includes two flip-flops Q and R which function to provide signals to indicate whether a computational function is being carried out, and to prevent reactuating the computer falsely when a computational func- 26 tion has been carried out and the panel control switch which initiated the function has not yet been released.

The temporary memory flip-flop group including ipflops IH, IX and IY is utilized to store certain operational results produced during one pass of the recirculating memories so that these results may be utilized in the succeeding computational iteration. `More specifically, it will be recalled from FIG. 3 that during the extrapolate routine the output signal from integrator 365 is applied to integrator 366 to control its additive transfers, a similar operation being carried out in computing sections 302 and 304 as well. However, as will be shown in detail in FIG. 8, integrator 366 is operated upon in the serial recirculating memories before integrator 365 is operated upon; consequently flip-flop IH is utilized to store the output signal from integrator 365 until it can be utilized for operating on integrator 366 during the subsequent memory pass, while flip-flops IX and IY perform the identical function for the integrators in computing sections 302 and 304.

The functions performed by the computational flip-flop group 756 are relatively complex and will be more clearly understood from the detailed description set forth hereinafter. Briefly, however, this flip-flop group includes flip-flops S1, K1, S2 and K2 which are operable in conjunction with read flip-Hops L1 and L2 and write flipflops M1 and M2 for changing the magnitudes of the numbers stored in the various integrators and registers in accordance with the values of the input received, for making additive transfers between the integrator registers, and for controlling the operation of the 4096 counter and the 2048 counter described hereinabove. i

Finally, it should be noted that the three timing pulse signals TPH, TPX and TPY utilized for interrogating the difunction converters described in connection with FIG. l are transmitted to the associated analog-to-difunction converter from gating matrix 704, while the three input difunction signals from the converters are applied to the gating matrix. It will be noted that the three difunction trains are designated IZVH, lx and lZ'Y in FIG. 7; the reavson for utilizing the complementary difunction signals in this specific embodiment of the invention is that it simpliiies the solution of the difference Equations l1, 14 and 15 as will be described more fully below.

In order to comprehend more fully the detailed operation of the projectile tracking computer of the invention, the arrangement of intelligence information in the memory unit will now be described; it should be noted that in computed parlance the sequence and arrangement of intelligence in the memory is termed the word structure, and is utilized frequently to teach the sequence of operation of the computer.

With reference now to FIG. 8, there is shown in graphic form the word structure of the computer as it appears at the reading flip-flops during one difunction time interval, the sequence of appearance being from right to left. As shown in FIG. 8, there are 133 clock pulses (Cp) presented during one pass of the recirculating register, the 133 digit time intervals dened by these clock pulses being divided into ten Words of varying length and designated g through Y. For purposes of simplicity, the g word will henceforth be termed the gravity word, while the words designated H, X, and Y will be termed the acceleration words. In a similar manner the words designated H, X and Y will be termed the velocity words, whereas the words designated H, X and Y will be termed the position words.

It will be noted from the word diagram that each of the position words includes l5 binary information bits, each of the velocity words l2 binary information bits, and each of the acceleration words, including the gravity Word, 13 binary information bits. The selection of the number of bits used to represent each word is made in View of the accuracy required of the system, and the vnumber of iterations.

fact that the various integrators to be described hereinbelow mustbe scaled with respect to each other to permit proper communication between integrators and provide a resultant output signal scaled to actuate the servos described hereinabove.

With reference once more to FIG. 8 it Will be noted that marker channel P1 has a binary value of one recorded in the last digit place of each word for demarking the end of each word, and a binary value of one recorded in the rst digit place of each position word, the remainder of the digit places in the P1 marking channel having binary zeros recorded therein. These marks, as wil'l be seen from the description below, are utilized to change the operations performed by the various iiip-ops in carrying out the computers computational processes, and for sequencing the counting flip-flops -C1 through C4 in flip-flop group 750 in FIG. 7. In a similar manner, marker channel P2 also includes a binary one in the last digit place of each Word, and in addition, has a binary value of one recorded in the next to the last digit place of each velocity word. Ignoring for a moment the remaining digits stored in the acceleration words of channel P2, it wil'l be noted that the next to last digit place in each of the velocity words has a binary one recorded therein while the next to last digit place in each of the position words has a binary zero recorded therein.

Recall now that channels P1 and P2 extend around the entire memory drum, and are five time as long as the L1 and L2 recirculating channels, or in other words, the word structure of FIG. 8. In each of the P1 and P2 channels, therefore, the recording pattern shown in FIG. 8 is repeated precisely live times so that the proper marks are presented in channels P1 and P2 during each recirculation of channels L1 Vand L2. It will be recognized, however, that the computational processes carried out by the cornputer must be initiated at a predetermined instant in order Vfor the intelligence stored in the memory to be processed in the proper sequence and for the specified The marker bit utilized for initiating the computational processes is termed the origin mark, and is represented by a binary value of one permanently recorded in the next to last digit place of one of the ive Y position words which occur in a complete revolution of channel P2, the origin mark being indicated in FIG. 8 by the dotted line 800. It will be recognized, therefore, 4that once during each complete revolution of the memory drum, flop-flop P2 will present a onerepresenting signal which corresponds to the origin mark and signifies that the gravity word is about to be presented to be operated upon.

Consider now the remaining binary bits stored in the acceleration words of channel P2. It will be remembered from the description of FIG. 7 that the constants g, K11, KX and KY are essential for extrapolating the trajectory equations which are stored in the P2 channel. As shown in FIG. 8, the constant g is stored in the iirst twelve digit places of the gravity word sector of channel P2, While the constants KH, KX and KY are stored in the rst twelve digit places of the H, X and Y acceleration words, respectively, of channel P2. It will be recognized, there-fore, that marker channel P2 serves as the integrand registers for integrators 367, 366, 390 and 394 in FIG. 3. The values of the constants stored in these registers and their representation will be discussed more fully below.

As pointed out hereinbefore, lthe markers at the end of the various words in the P1 and P2 channels are utilized in conjunction with counter flip-ops C1 through C4 to distinguish between the different words. It will also be recalled that these flip-Hops operate as a scale-of-te'n counter for demarking the words, the output waveforms of hip-flops in performing their counter function being shown in FIG. 8 by the waveforms C1, C2, C2 and C4. The conduction states of the flip-flops for the various words are correlated by the following truth table.

Table fIII 'Counter dip-dop states Yord -Ci C2 Ca C4 Y 1 o o 1 Y v0 l 0 1 It will be noted from this table that the Y coordinate words Y, Y and Y are specified by the conduction states C'3C.1, the X coordinate words by the conduction states C2C4, the g word by C3C4, and the remainder of the H coordinate words 'by C3C.1. It will also be noted that within each group of words associated with each coordinate, the acceleration Words are identified by conduction states C1C'2, the velocity words by the conduction state C1, and the position words by the conduction state C2.

Consider next the intelligence information stored in channels L1 and L2. As shown in FIG.8 the computer has a single 4096 counter whose count is stored in the gravity word of channel L1 to control the duration of the Fit routine, and three 2048 counters whose counts are stored in the acceleration words of channel L1. It will be recalled that only a single 2048 counter was shown in FIG. 3 for controlling the inputs to the velocity registers. In practice, however, it has been found preferable to employ three separate 2048 counters located immediately preceding the three velocity words for controlling the velocity word inputs during the Fit routine, since it is then unnecessary to utilize an yadditional pop for holding throughout the three velocity words to indicate whether the first or second group of 2048 difunction input signals is being received. It is clear, of course, that each of these three countersoperate in an identical manner and store the same numerical count.

Continuing with the description of FIG. 8, channel L2 is utilized as a composite register channel which functions as the overow registers for al1 of the various integrators and also functions as the servo registers. More specically, the gravity word sector of channel L2 represents the overflow register of integrator 667 in FIG. 3,

while the acceleration words H, X `and Y represent the overow registers of integrators 366, 390 and 394 in FIG. 3. In a similar manner, the overflow registers of velocity integrators 365, 388 and 392 in FIG. 3 are represented by the velocity wordsII, X and Y in channel L2, while the position words H, X and Y function as servo registers 358, 384 and 386, respectively. The remaining words in channel L1 are also utilized in a manner analogous to the use of channel L2, the integrand registers of velocity integrators 365, 388 and 392 in FIG. 3 being represented by the H, X and Y words of lchannel L1, while the H, X and Y Words of the L1 channel function as the accumulator registers in the digital servos 306, 30S and 310, respectively.

Consider now the scaling of the various registers, or in other Words, the physical significance of a binary one stored in the various binary digit spaces of the servo registers, accumulators, and the integrator registers. It will be recalled lthat each +1 difunction signal in the input difunction train IDH has a scaled significance of +5 feet and each -1 difunction signal has a scaled sig-

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