Multiple flight course second order missile programmer

Feb. 16, 1965 ι. h. schroader etal 3,169,727

MULTIPLE FLIGHT COURSE SECOND ORDER MISSILE PROGRAMMER

Filed June 25, 1960

Sheets-Sheet 1 a

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BY §

INVENTORS

Irvin H. Schroader Melvin E. Hosea Leo C. Miller st ,e .5 &lt; * s

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COMPUTER SECTION

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ATTORNEYS

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Feb. 16, 1965 i. _H. schroader etal 3,169,727

MULTIPLE FLIGHT COURSE SECOND ORDER MISSILE PROGRAMMER

Filed June 23, 1960 _{7 2}

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Feb. 16, 1965 i. _H. schroader etal 3,169,727

MULTIPLE FLIGHT COURSE SECOND ORDER MISSILE PROGRAMMER

Filed June 23, 1960 7 Sheets-Sheet 3

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Feb. 16, 1965 i. h. schroader etal 3,169,727

MULTIPLE FLIGHT COURSE SECOND ORDER MISSILE PROGRAMMER

Filed June 23. 1960 7 Sheets-Sheet 4

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Feb. 16, 1965 i. h. schroader etal 3,169,727

MULTIPLE FLIGHT COURSE SECOND ORDER MISSILE PROGRAMMER

Filed June 23, 1960 7 Sheets-Sheet 5

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Feb. 16, 1965

MULTIPLE

3,169,727

MISSILE PROGRAMMER

1. H. SCHROADER ETAL

FLIGHT COURSE SECOND ORDER

Filed June 23, 1960

Sheets-Sheet 6

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Feb. 16, 1965 i. h. schroader etal 3,169,727

MULTIPLE FLIGHT COURSE SECOND ORDER MISSILE PROGRAMMER

Filed June 23, 1960 7 Sheets-Sheet 7

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United States Patent Office „ , „^{3169 727} _ Patented Feb. 16. 1965

3,169,727

MULTIPLE FLIGHT COURSE SECOND ORDER MISSILE PROGRAMMER

Irvin H. Schroader, Simpsonville, and Melvin E. Hosea and Leo C. Miller, Silver Spring, Md., assignors to the ^δUnited States of America as represented by the Secretary of the NavyFiled June 23, 1960, Ser. No. 38,408 18 Claims. (CJ. 244—14) ' , . . 10

The present invention relates generally to improvements in missile guidance systems and the like and more particularly to a new and improved missile guidance system for beam-riding missiles wherein a single guidance system is adapted for quick changeover from one mid- 15 course missile guidance program to any one of a plurality of . other such programs in accordance with missile requirements and target considerations, all such guidance programs being so suited to their specified conditions of operation as to minimize missile fuel consumption, insure 20 maximum missile range, and provide continual variation of the guidance system sensitivity of the missile in accordance with maximum target kill probability.

In the field of missile guidance system development, it has been the general practice to employ ground comput- 25 ing devices in conjunction with cooperating guidance transmitters to guide various beam-riding missiles to their targets. Although such devices have generally served their purpose, they have not proved entirely satisfactory under all conditions of service and operation for the 30 reason that considerable difficulty has been experienced in minimizing the deleterious effects of noisy radar input data upon both the computer and resulting programmed missile trajectory, with subsequent effects upon missile fuel consumption, missile range, and probability of col- 35 lision of the missile with the target. Hence, , those concerned with the development of missile guidance systems have long recognized the need for a guidance system capable of such wide adaptability as to enable rapid and precise' changeover from one type of mid-course missile 40 guidance program to some other mid-course program, which might be made dependent upon any desired set of input parameters such as range, angle, or a combination thereof, and which would simultaneously avoid all of the foregoing difficulties commonly encountered by such sys- ⁴⁵terns.

An additional critical problem confronting those who devise such missile guidance systems has been the almost universal quest for a versatile programming system capable not only of acting upon any desired combination ⁵⁰of input parameters but of manipulating such data in accordance with basic master programming equations to effect proper approach of the position coordinates of the missile to those of the target in a manner which would assure maximum missile range, minimum missile fuel ⁵⁵consumption, and greatest probability of target kill. The present invention fulfills all of these needs.

The general purpose of this invention, therefore, is to provide a multiple flight course missile programmer which embraces substantially all of the advantages of ⁶θ previously employed missile guidance systems and yet possesses none of the aforedescribed disadvantages. To attain the latter, the instant invention contemplates, among other things, provision of a multiple flight trajectory missile programming system capable of guiding ⁶⁵beam-riding missiles along prescribed trajectories most suited to considerations of missile performance characteristics and target threat, and which will perform in a manner insuring maximum efficiency through the smoothing of input radar data, in the computing stages of the ⁷⁰programmer itself, thereby minimizing the effects of noisy output information upon missile servos. The latter smoothing effect upon output information to the guidance transmitters is continued until the missile is within close striking range of the target and serves to minimize drag on the missile caused by wing vibration and subsequent high resistance to air flow while the missile is in flight.

The missile guidance system of the instant invention further contemplates the provision of a novel second order programmer computing section which acts upon input data so as to cause the elevation and azimuth of the guidance transmitter to approach the elevation and azimuth of the target, before target intercept, in accordance with a prescribed second order generalized system equation, the constants of the latter equation and the input data to said computing section being chosen to suit the characteristics of the missile being fired and the desired flight course program to be followed. In this manner, the novel missile programmer of the instant invention provides a computing section for realizing a plurality of varied flight trajectories which may be made angle dependent, range dependent or dependent upon any other desired set of input parameters. The latter novel and inventive computing section is thus extremely well adapted to the fulfillment of all necessary guidance requirements.

Accordingly, an object of the present invention is the provision of a new and improved missile guidance system.

. Another object is to provide a new and improved missile guidance system capable of quick changeover from one mid-course guidance program to another.

A further object of the instant invention is the provision of a novel missile guidance system capable of quick changeover from one mid-course guidance program to another and which may be made dependent upon any desired set of input parameters.

Still another object resides in the provision of a new and improved missile programmer which minimizes missile fuel consumption, increases missile range, and insures maximum probability of target kill.

. Yet another object of the instant invention is the provision of a new and improved missile programming device capable of causing missile position data to approach target position data in a preferred manner to effect maximum efficiency and probability of target kill with minimum drag upon the missile during flight.

A still further object of the persent invention resides in the provision of a new and improved missile guidance system which prevents “banging” due to noisy guidance information data and consequent damage to missile wing flaps and missile servos.

Another object of the persent invention is to provide a novel multiple flight course missile programmer assuring guidance flight trajectories with increased fuel economy and improved accuracy.

A still further object of the present invention is to provide a new and improved missile guidance system capable of variable guidance sensitivity during mid-course missile guidance and wide adaptability to a great variety of programmed flight trajectories.

It is a still further object of the instant invention to provide a new and improved missile guidance system of such versatility as to be adaptable to missiles which are totally beam-riding, namely those which ride the guidance beam from guidance initiation to the point of actual target collision, and also to missiles which are only partially beam-riding, in that they ride. the guidance beam only until they approach the vicinity of the target.

Other objects and many of the attendant advantages of this invention will be readily appreciated as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings, wherein:

FIG. 1 is a schematic representation by block diagram

3,169,727 ό

of a complete missile guidance and control system constructed in accordance with the instant invention;

FIG. 2 is illustrative of a missile riding a guidance beam to a designated target and defines some of the symbolism to be used for various parameters subsequently set forth in the specification;

FIG. 3 illustrates the axes of motion for a typical three coordinate tracking radar system utilized in conjunction, with one embodiment of the instant invention;

FIG. 4 illustrates geometrically the conversion of three coordinate information from the tracking radar system shown in FIG. 3 to equivalent two coordinate information form;

FIG. 5 is a schematic representation by block diagram of a complete missile flight course programming computer in accordance with the instant invention;

FIGS. 6 and 6α illustrate typical circuit embodiments of a complete missile programming computer in accordance with the present invention, including both the input and output data sections;

FIG. Ί illustrates a novel second order missile programmer computing circuit in accordance with the instant invention;

FIG. 8 illustrates a servo system arrangement typical of those utilized in conjunction with the missile guidance system of the instant invention;

FIGS. 9 and 10 are illustrative of programmed missile flight trajectories obtainble in accordance with one embodiment of the instant invention; and

FIG. 11 is a graph illustrating the manner in which guidance sensitivity may be varied in accordance with one embodiment of the present invention.

The multiple flight course second order missile programmer of the instant invention comprises basically a new and improved electronic analog computer in combination with a series of servo systems and working with necessary input and output radar systems, including the power, cabling and switching necessary to implement the latter. The resulting system is thereby rendered capable of accepting radar data in synchro form and, through the use of follow-up servo systems, of converting this data to D.C. signal form for utilization by the electronic analog programming computer section to provide the required missile flight program in accordance with prescribed trajectory equations to be hereinafter more fully described. Furthermore, the system, as disclosed in the illustrated embodiments, is also capable of converting the computed flight program, in both azimuth and elevation, from the conventional D.C. signal output information form emanating from the computer into synchro data form which may then be conveyed to the guidance transmitter radars to command the latter into proper position. The guidance system concept of the instant invention may also be readily presented, among its many practical embodiments, in such a manner as to facilitate interchange or cross-connection of its components, servos and computing amplifiers to provide a great variety of different trajectory flight programs depending upon specific operational and performance characteristics of the missile to be fired and various target considerations. Such a system may also be utilized to provide a substantial variety of post intercept programs. In practice, the flexibility of these units is even further enhanced through the wide use, wherever possible, of multiple patch panels, the latter being classified in accordance with functions handled, such as synchro data, D.C. functions, etc.

Typical desired firing and flight trajectory conditions for modern guided missiles are that the missile be fired at a relatively high launcher elevation angle, that the missile ascend as rapidly as possible to a high altitude, that the missile cruise as long as possible at this high altitude for maximum ramjet efficiency and yet maintain a suitable compromise with the missile’s target intercepting ability, and that, as the missile approaches the vicinity of the target, the missile be caused to intercept the target in a maneuver within the acceleration capabilities of the missile to produce either a target hit or a near miss and thereby destroy the target.

The instant invention contemplates the manipulation of various input data in accordance with generalized system equations, the constants of which are chosen in accordance with missile characteristics and target considerations to bring the missile to its target in the prescribed manner. A computing system, in accordance with the present invention, for accomplishing the latter will perform the same series of functional operations upon any and all input data irrespective of whatever parameters such input data may represent. Therefore, a great variety of flight programs are made possible for any given missile through the programming system of the instant invention merely by varying the nature of the input data and constants for the generalized system equation manipulations in the programming computer section.

By way of example, two types of programmed trajectories within the scope of the instant invention will be described. The two sample flight programs illustrated will be designated type “A” and type “B.” The type “A” program is specifically designed for use with missiles which are “pure” beam or totally beam-riding, that is missiles which ride guidance beams all the way to their respective targets, whereas the type “B” program is primarily adapted for use with a partially beam-riding missile which rides a guidance beam only to within close proximity of the target and thereafter “homes in” on the target by means of guidance devices which may be wholly within the missile itself and independent of any ground control.

Referring now to the drawings, which illustrate one embodiment of the instant invention, there is shown in FIG. 1 a schematic representation by block diagram of a complete missile guidance system which, in accordance with the instant invention, is capable of switching from a first mid-course guidance program such as type “A,” to a second mid-course guidance program such as type “S,” the characteristics of the latter guidance programs to be subsequently more fully described.

FIG. 1 shows a search radar 20, incorporating a separate height finder 21, which sends out a radar search beam 13 to a target 12 and in turn receives a reflected signal 14 from the target. Many types of search radar instrumentation are suitable for utilization in carrying out the latter function, including search radars having built in height finders or those which incorporate such units separately. The output of the search radar 2® and height finder 21 consists of information relating to rough values of target azimuth and range and an even rougher value of target elevation. The latter output data is then conveyed as input information to a tracking radar 22, which may take a great variety of forms but which vzill be here illustrated as incorporating a three-coordinate system utilizing train, traverse, and elevation axes, the actions of each of which will be hereinafter more fully described.

The target azimuth, target range and target elevation information from the search radar 2® and height finder 21 enables the operator of the tracking radar 22 to either actually “lock on” the target 12 or to throw the tracking radar into “search” operation, which is essentially a scan raster of plus or minus a discrete number of degrees about a position which is believed by the operator of the tracking radar 22 to be the approximate target position as indicated by the rough information received from the search radar system. Other modes of radar systems feeding the tracking radar 22 might include such systems as the Air Force “SAGE” type concentrated network of defense radars to provide input data to the tracking radar system.

The tracking radar 22 transmits its own radar beam 15 to the target 12 and receives a reflection 16 therefrom. The output data from the tracking radar 22 consists of target elevation, target train, target traverse, and slant range from the tracking radar 22 to the target 12. The

3,169,727 latter output information from tracking radar 22 is derived for further use through synchro devices physically located at the tracking radar unit itself. Shaft rotations about the various axes of the tracking radar 22 are converted by means of such synchro devices to synchro signals, three- 5 wire lines being conventionally embodied for each synchro, to provide outputs from each synchro which are directly proportional to the number of degrees of radar shaft rotation from an established zero reference position. _]0

The synchro output data from the tracking radar 22 is in turn fed to a computer section 23 of the instant invention. The latter tracking radar data is first directed to the input converter servo section 24 of the computer 23 wherein the synchro input information is converted by jg means of servomechanism devices to electrical signals in the form of D.C. voltages proportional to the original radar shaft rotations from which the input synchro signals were derived. Such D.C. voltage signal form is required for use by the programmer section 25 of the com- ₂₀puter 23. The programmer section 25 utilizes the latter D.C. voltage outputs of the input converter servos as electrical voltage inputs to a computing section which manipulates such input voltages on the basis of prescribed generalized trajectory equations, and produces D.C. output ₂₅voltages which are then fed to an output converter servo section 26.

The output converter servo section 26 of computer 23 reconverts the D.C. output voltage signals from the programmer section 25 to synchro signal output form for 30 transmission to and utilization by the guidance radar transmitters denoted generally as 27 in FIG. 1 of the drawings. The latter guidance radar transmitters 27 can be physically located near the tracking and search radars 22 and 20, respectively, or at least within a few hundred feet of the 35 tracking radar to prevent the introduction of severe parallax errors; the distance to the search radar not being as critical.

The guidance radar 27 transmits a radar signal 17 to the missile 19, but only in a single direction, that is, guid- 40 ance radar 27 receives absolutely no reflected signal from the missile. The major distinction between the guidance radar 27 and the tracking radars are that the guidance radar is commanded into position by the output elevation and azimuth signals from the ground computer section 23. In the illustrated embodiment, however, the guidance radar transmitter does track in range on the type “A” program. In contrast to the operation of tracking radar 22, the tracking accomplished by the guidance radar is not carried out by receiving a signal from the missile constituting a reflection of an original signal generated in the guidance radar itself. On the contrary, missiles utilizing the type “A” program trajectory carry a beacon 28 incorporated into the missile and which is triggered by the guidance beam 17 from the guidance radar 27 to gen- -erate a beacon signal 18 of its own. The latter beacon signal 18 is directed from the missile 19 to the guidance radar 27, the time of delay of the arrival of the beacon signal at the guidance radar being a measure of the slant range to the missile.

_ For the type “B” program, which is designed for utilization solely by missiles which incorporate separate homing systems, the program flight trajectory is not dependent upon input information to the computer section 23 relating to the difference between target slant range and missile __ slant range, and hence, the guidance radar 27 is not required to track in range for such a program.

For the type “A” program, therefore, the missile slant range information received by the guidance transmitter 27 is fed back into the tracking radar 22 to enable the ₇θ latter unit to direct an output to the computer section 23 which is the difference between slant range to the target and slant range to the missile, whereas for the type “B” program, with “homing,” there is no tracking in range by the guidance radar 27 nor any feedback of such informa- 75 tion from the guidance radar 27 to the tracking radar 22, and, therefore, in the latter instance, the output of the tracking radar is simply slant range to the target.

Missiles utilizing the multiple flight course programmer of the instant envention must, of necessity, be beam riders. Such a missile is captured by the radar beam 17 emanating from the guidance transmitter 27 so that the missile 19 is caused to follow the beam as the beam moves in accordance with the programmed flight trajectory equation Servomechanism devices within the missile 19 itself steer the missile in accordance with the transmited guidance signals so that the missile is caused to always remain within the guidance beam after capture, provided the guidance beam moves in such a manner that the missile capabilities of linear velocity and lateral acceleration are not exceeded.

In actual operation, before launching, the operator elects in accordance with the nature of the missile to be fired, either the type “A” or type “B” program trajectory. The operator then proceeds to flip various switches in the guidance radar, e.g., for tracking in missile range or not, and simultaneously operates switches in the programmer section 25 of the computer 23 to select proper constants and input data channels for the chosen program.

Synchro data form is utilized for accurate transmission of data between the input radar system 22 and the computer section 24 as well as between the computer section 26 and the output guidance radar transmitters 27. Such synchro output is utilized primarily because of the required maintenance of transmission precision, namely minimal line losses, over long distances, particularly those in excess of 100 feet. Another reason for using synchros is to enable a system of multiple speeding facilitating transmission of data utilizing two synchro inputs. In one embodiment of the latter arrangement, a pair of synchros may be provided with one synchro turning at a 1:1 speed ratio and the second rotating at a 36:1 speed ratio such that the first synchro turns a full revolution for 360 degrees while the second turns one revolution for every 10 degrees of rotation. Such a dual speeding arangement enables finer precision of reading angles.

. As outlined above, several instances arise in the missile programming apparatus of the instant invention wherein a shaft rotation or a voltage must be converted into some other information form. The most common device utilized for accomplishing such conversions is the “servo.”

Referring to FIG. 8 of the drawings, a “servo,” for purposes of the present discussion, is considered to be a unit comprising an input converter device 30, a servo amplifying device 31, and a servo motor 32 incorporating a follow-up feedback system 33 to the input converter 30. In general terms, the output voltage θ_ο introduced by the follow-up system 33 into the converter 30 is substracted from the input command voltage 0_r to the input converter 30 to produce an error signal e which, upon amplification by the servo amplifier 31, causes the shaft of the servo motor 32 and incorporated follow-up system 33 to rotate in such a direction as to reduce the error voltage e to zero, thereby establishing a null position of the servo motor shaft. The resulting equilibrium shaft position of the servo motor 32 is thus directly proportional to the command voltage ¢,. The latter shaft position can be used as such, or converted to a proportional voltage, either A.C. or D.C., by means of an electrical output converter 34 generally consisting of a suitable potentiometer arrangement, as will be further illustrated in connection with the programming computer circuitry to be hereinafter more fully described. The purpose therefore of a position servo is to cause an output member, such as the shaft of servo motor 32, to follow the position of a possibly remote input shaft or member.

. Briefly, synchro devices suitable for use with the device of the instant invention essentially comprise trans3,169,727 formers having single rotatable windings. Synchro transmitters, synchro differentials and synchro control transformes are of interest in connection with the instant invention.

A typical synchro transmitter will have a rotor winding, excited by some A.C. voltage reference, which may be 115 volts or the like, and which is continuously rotatable through 360°. Three stator windings are electrically spaced at 120° intervals in the outer shell of such a transmitter with a single side of each of the stator windings in common. As a result, the voltage induced in each stator windings is a unique function of the rotor position of the. transmitter. These three voltages may be transmitted by means of a conventional three-wire synchro transmission system over distances of considerable magnitude without deterioration in accuracy, since it is principally required only that relative balance be maintained, that is that the ratios of the various stator voltages to each other be maintained constant, there being no requirement that the absolute magnitude of the latter voltages be also maintained constant. Therefore, since each of the three synchro transmission lines will have the same loss characteristics, relative losses will be cancelled.

The three synchro leads from the stators of the synchro transmitter are terminated at the corresponding three stators of a control transformer in the input converter servo section 24 of the computer 23, the latter control transformer being similar in structure to that of the synchro transmitter, although electrically some minor differences obtain. The rotor winding of the control transformer will have a voltage induced in it until it has been rotated to exactly the same relative position as the rotor of the synchro transmitter. Over a considerable angular displacement, an error voltage proportional to the angular misalignment between the rotor of the control transformer and the rotor of the synchro transmitter will be produced, so that the control transformer thereby serves as a differential device for producing an error voltage which may be then directed to a servo amplifier such as amplifier 31 shown in FIG. 8 of the drawings.

On occasion, in the device of the instant invention, it is necessary to obtain in synchro form a quantity representing the addition of two shaft rotations. The latter may be accomplished by means of a synchro differential inserted between the synchro transmitter and the synchro control transformer. The three output leads from such a synchro differential will carry voltages which will be the same as those that would be produced by the synchro transmitter if the rotor shaft angle of the synchro transmitter were increased by the angular rotation given the synchro differential.

The error voltage derived from the control transformers must receive voltage and power amplification before a servo motor, such as the motor 32 shown shown in FIG. 8, can be successfully operated from it. In the vicinity of a null or zero error rotor position the output from a typical control transformer, as used in the illustrated embodiments of the instant invention, is of the order of one volt per degree of error. A good synchro servo should be capable of acting on an error as small as 0.01°, represented by an error signal output voltage of 10 millivolts, and yet still turn out three volts to the servo motor. Therefore the servo amplifier utilized with such a control transformer must have a voltage gain of approximately 300, and should be capable of supplying about 5 watts of power where a large rotor error signal calls for high velocity slew to a new position. The servo motor driven by the output of the servo amplifier in turn drives the control transformer via the follow-up system 33 and through appropriate gearing so that a null position of the control transformer rotor is finally realized.

The essential functions of the synchro servo system, as described above, is to serve as a data receiver and converter for distant radars or guidance transmitters such as those shown in FIG. 1 of the drawings. In such instances, the servo motor of the synchro servo device drives one or more precision wire-wound potentiometers which serve to convert the rotor shaft position of the input converter or control transformer into an accurately proportioned voltage. In some cases, auxiliary devices, such as ball and disc integrators, trigonometric functiontapered potentiometers or A.C. resolvers are also driven as may be required for desired conversions in any specific situation. In any case, the output conversion voltages so derived may be then passed into¹ the computer section for further manipulation in accordance with prescribed equations.

Since the accuracy of the typical single synchro is generally only eight minutes of arc, then, as previously set forth, the single speed synchro servo device shown in FIG. 8 of the drawings and described above may prove insufficiently accurate for many purposes. In actual practice, therefore, two synchro transmitters and two synchro control transformers are used in a one and 36 speed combination. Thus, the error voltage is derived from a control transformer making one revolution per 10° of the incoming data. If the servo falls into error greater than 2°, a two-speed mixer is utilized to switch control to the one-speed control transformer to prevent the settling on a false null every ten degrees. In such dual speed data systems, an ambiguous zero is found to exist at those values of the transmitted variable which require an even number of rotations of the high-speed synchro and an integral number of half revolutions of the low-speed synchro. The problem of this ambiguous zero can be solved by inserting in series with the error voltage from the one-speed synchro control transformer what is commonly referred to in the art as a “stickoff” voltage. The purpose of the latter stickoff voltage is to displace the false zero of the one-speed system so that there is enough voltage from the one-speed system to drive the servo motor away from what was the ambiguous zero. Such a method of utilizing a stickoff voltage in a dual-speed synchro system is well known in the art, and the equations for the required stickoff voltage needed with any particular dual-speed synchro data system are to be found in the M.I.T. “Radiation Laboratory Series,” vol. 25, “Theory of Servomechanisms,” pages 85-88.

For internal data transmission, analog voltages within the computer section of the missile programmer of the instant invention may be carried by means of cables over reasonable distances, providing proper precautions are taken to provide adequate shielding and thereby avoid or minimize ground current loops.

FIG. 3 of the drawings depicts in diagrammatic form the arrangement of the various axes of a three-coordinate tracking radar system 22 such as that utilized in the complete guidance system shown in FIG. 1. The three-axis system illustrated in FIG. 3 includes a train or azimuth axis 31 which is perpendicular to the horizontal or ground reference plane and an elevation axis 32 parallel to the ground reference plane. Rotation about the elevation axis 32, therefore, is always in a plane which is perpendicular to the ground plane. A traverse axis 33 is also provided in the system 22, the traverse axis 33 being permanently affixed to the elevation axis 32 so that the traverse axis pivots with the latter in the vertical plane. Thus, rotation about the traverse axis 33 will always lie in a plane intermediate the ground reference plane and a vertical plane. Although it would be possible to align the tracking radar unit 22 to any position merely by rotation about the train and elevation axes alone, the traverse axis 33 is included to enhance the versatility of such tracking radar units by increasing their ability to track rapidly moving targets which may pass directly overhead. Normally, once the elevation and train axes, 32 and 31, respectively, have been rotated to specific positions to enable tracking of a point following a trajectory in a transverse plane, that is, one intermediate the vertical

3,169,727 and horizotnal planes, it would be necessary to simultaneously continue rotation of both the train and elevation axes if the system 22 were to successfully follow the motion of the target while it remained in such a transverse plane. However, where a traverse axis such as 33 is employed, the train and elevation axes 31 and 32 need be utilized merely for initial alignment of the radar 22 with the target. Thereafter, as long as the target is constrained to motion in the same transverse plane, the radar 22 can follow the target simply by sweeping about the single traverse axis 33. Such radar system arrangements have found extremely wide use on shipboard where enemy planes may frequently come in low and fast directly overhead, causing extreme difficulty where accurate tracking necessitates radar rotation about more than a single axis.

The use of the three-axis radar system- 22 described above, though vastly improving tracking capabilities for rapidly moving targets, does however introduce some complications insofar as the simplification of input information to the programming computer is concerned. It is desirable, therefore, to reduce the target position data emanating from the tracking radar 22 from a threecoordinate system to a two-coordinate system before introduction to the computer section 2S.

Elevation angle e_s is unaffected by the existence of a traverse axis. However, rotation about the traverse axis 33 does produce a reflected change in the horizontal or train plane. FIG. 4 of the drawings illustrates the conversion of traverse angle readings into the ground or train plane. It will be evident from FIG. 4 that the traverse angle reading θ_τν can be reflected into the train plane simply by dividing the traverse angle by the cosine of the angle of elevation 0_E or, in other words, multiplying the traverse angle θ_Τν by the secant of the angle of elevation. The latter condition may be expressed as follows:

sec (1) where rf_T=Azimuth of target in degrees

T_N=Train angle of target in degrees Tv=Traverse angle of target in degrees E_T=EIevation angle of target in degrees

Reference is now made to FIG. 2 of the drawings to depict and explain the symbols used for the various parameters set out in the description hereinafter to follow. FIG. 2 shows a target 12 and a missile 19 in flight to the target and guided by a guidance beam from the guidance radar transmitter 27.

The following symbolism is utilized.

In the time symbolizing system, subscript letters are used to indicate the start of a specific operation as follows:

F=Firing

G=Guidance program initiation (capture of missile by guidance beam)

P=Present time

I=Intercept of target by missile

The system of indicating angles and ranges employs subscripts in a slightly different manner. Basically, the first subscript indicates the equipment or place which is under consideration. The second subscript indicates the time which is pertinent. However, for simplicity, the time symbol subscript P (present time) is omitted where no confusion would result. Therefore, the necessary symbols for the ensuing discussion are set out below:

rf_GP=A_G=Azimuth of guidance transmitter at present time

A_GG=Azimuth of guidance transmitter at guidance initiation

A_Tp=A_T=Azimuth of target at present time

E_GP=E_G=Elevation of guidance transmitter at present time

E_GG=Elevation of guidance transmitter at guidance ini5 tiation

E_TP=S_T—Elevation of target at present time

D_Tp=D_T=Slant range to target at present time

Z&gt;MP=D_M=Slant range to missile at present time

Di=Target slant range rate == Missile slant range rate

IG;=Program constant, elevation /A=Program constant, azimuth w_n=Gain sensitivity factor for second order missile programmer computing circuit

Tpi=Time from present to intercept e₀=Output. data from second order computing circuit e₍=fnput data to second order computing circuit . de_o^eE=(^o—^ei) For elevation computing circuits ^eA=(^eo—^ei) For azimuth computing circuits c—A constant