US2660371A - Gun directing system - Google Patents

Description

NOV- 24, 1953 D. J. CAMPBELL x-:T AL 2,660,371

GUN DIRECTING SYSTEM Filed Aug. 2s, 1945 '7 sheets-sheet 1 Nov. 24, 1953 Filed Aug. 28, 1945 D. J. CAMPBELL ETAL GUN DIRECTING SYSTEM 7 Sheets-sheet 2 HMPL /F/ER NOW 24, 1953 D. J. CAMPBELL ETAL 2,660,371

Y GUN DIRECTING SYSTEM Filed Aug. 28, 1943 '7 Sheets-Sheet 3 TT NEY D. J. CAMPBELL ET AL GUN DIRECTING SYSTEM 7 Sheets-Sheet 4 NOV- 24, 1953 D. J. CAMPBELL ET AL .2,660,371

GUN DIRECTING SYSTEM ATTORNEY NOV- 24, 1953 D. J. CAMPBELL ET AL 2,660,371

GUN DIRECTING SYSTEM Filed Aug. 28, 1945 7 Sheets-Sheet 6 ATTO RN EY Nov. 24, 1953 D. J. CAMPBELL ET A1. 2,660,371

GUN DIRECTING SYSTEM Filed Aug. 28, 1943 7 Sheets-Sheet 7 INVENTORS DAJ. CAMPBELL S. P. MCC/95E, JE.

H HABE/s, ../E.

Patented Nov. 24, 1953 UNITED lSTATE OFFICE GUN DIRECTING SYSTEM Application August 28, 1943, Serial N o. 500,349

18 Claims.

This invention relates generally to the art of gun nre control, and more particularly to means for and methods of continuously directing gun lire so as to effect hits against rapidly moving targets, such as airplanes. Although primarily ntended as an anti-aircraft director, the apparatus of the present invention Will obviously function equally Well to solve the more simple fire control problems, such as directing 'lre against surface craft, stationary targets, and so forth. An identical fire control director is disclosed in copending application Serial No. 500,348 for Gun Directing System, led August 2S, 1943, in the names of Arthur A. Hauser, Edward J. Nagy, Gilford E. White, and Herbert Harris, Jr.

Prior gun directors, such as those described in U. S. Patent No. 2,065,303 entitled Apparatus for the Control of Gun Fire, issued December 22', 1936, in the names of W. Chafee, et al., and in copending U. S. application, Serial No. 470,685, how Patent No. 2,492,355, for Gun Directing System, led December 30, 1942, in the names of D. J. Campbell and W. G. Wing, include predicting apparatus which is based upon the assumption that the target flies at a constant speed in a constant direction during the projectile time of flight. While this assumption is very often valid, for example, during the bombing run of a bomber aircraft, it is obviously desirable to be able to nre effectively at targets ying in a I' curved path, The present director includes apparatus for continuously indicating the actual course the target is nying. From this course indication it is possible to tell whether the straight line night assumption is or is not valid. AuXiliary predicting apparatus is provided in the present director, which may be rendered eiective when the course indicator indicates that the target is flying in a curved path, and which then operates to introduce a correction to compensate for the targets deviation from straight line night.

The present invention also comprehends novel regenerative tracking apparatus which may be used in conjunction with either the radio automatic or optical manual tracking systems providedA This regenerative tracking apparatus operates to automatically take over the task of tracking the target as soon as accurate tracking has once been established by either of the other f tracking systems. The regenerative tracking apthat of compensating for changes in vtarget course or speed.

. An improved predicting circuit for solving for the future position of a target ying 'a straight line course is provided. This circuit is similar to that employed for a similar purpose in copending application, Serial No. 470,686, but improved means are provided for controlling the sensitivity of the circuit during operation. The linear target rates computed in this predicting circuit are compensated in a novel manner to take into account the eil-ect of Wind upon the projectile.

Novel and improved ballistic apparatus is also disclosed for computing the coordinates of the shell-burst position which correspond to Vthe values of angle of train, quadrant elevation, and time of flight represented by three corresponding shaft displacements in the director. The ballistic apparatus is claimed in the above-mentioned .copending application S. N. 500,348. A novel mechanical multiplying unit having a linear output characteristic is provided for performing certain of the multiplications required in the ballistic apparatus. However, any suitable linkage multiplying device may be used for this purpose.

An important feature of the invention is the provision of means ior converting the rectangular coordinate error signals, representing the resp'ecik tive differences between the rectangular coordinates of the computed future position of the target and the corresponding rectangular coordinates of the shell-burst position, into corresponding error signals representing the amounts the quadrant elevation, angle of train and time of night shafts are in error. These signals are then used directly to actuate the servos controlling' the position of these shafts, thereby providing a proportionate type of control having a high degree of accuracy and very little tendency to hunt.

In prior gun directors a correction for fuZe' dead time was computed upon the assumption that the rate of change of fuze data is constant during the dead time interval. In the present invention, the fact that under ordinary circumstances the fuse data will vary in a substantially parabolic fashion with respect to time is recognized, and a iuze dead time correction is computed on that basis.

Accordingly, the principal object of the present invention is to provide improved apparatusv and methods for directing gun fire against a target.

' Another object of the invention is to provide` predicting apparatus adapted to compute the true future position of a target flying in a circular path.

Still another o ject is to provide a novel smoothing and differentiating circuit especially adapted to have its dynamic characteristics changed during operation.

A further object of the invention is to provide regenerative tracking means for a gun director.

A still further object is to provide an indication of the direction of flight of a target.

An object of the invention is to provide novel and improved ballistic mechanism for use in a gun director. r

Another object is to provide an error conversion mechanism for converting errors in rectangular coordinates to corresponding errors in quadrant elevation, angle of train and time of night.

Still another object of the invention is to provide improved apparatus for correcting fuze data for fuze dead time.

A further object is to provide a mechanical calculator adapted to produce an output displacement equal to the product of its two input displacements.

Other objects and advantages will become apparent from the specicaton, taken in connection with the accompanying drawings, wherein the invention is embodied in concrete form.

In the drawings,

Fig. 1 is a schematic diagram of the whole gun directingk apparatus of the present invention;

Fig. 2 is a schematic and wiring diagram of the regenerative tracking mechanism of Fig. 1;

Fig. 3 is a schematic drawing illustrating an alternate method of adapting the regenerative tracking mechanism of Fig. 2 to a gun director;

Fig. 4 is a schematic drawing of the rectilinear converters of Fig. 1;

j Fig. 5 is a detailed drawing of the smoothing, diierentiating, and predicting circuit of Fig. 1;

Fig. 6 is a chart giving the dynamic characteristics of the smoothing, differentiating and predicting circuit of Fig. 5, and illustrating the method of varying the dynamic characteristics during operation of the circuit;

Fig. '7 is a more detailed schematic representation of the wind corrector of Fig. 1;

- Fig. 8 is a diagram useful in explaining the i theory of operation of the curvilinear predictor of Fig. 1;

Fig. 9 is a schematic and wiring diagram of the curvilinear predictor of Fig. 1;

Fig. 10 is a modified form of Fig. 9;

Fig. llis a more detailed schematic drawing of the primaryV ballistic corrector of Fig. 1;

Fig. 12 is a more detailed schematic drawing of the secondary ballistic corrector of Fig. 1; Y Fig. 13 is a drawing of a'mechanical multiplier;

Fig. 14 is a schematic drawing of an alternate form of secondary ballistic corrector; Fig. 15 is a schematic and wiring diagram of the diierence indicator and converter of Fig. 1; Fig. 16 is a detailed schematic drawing of the fuze corrector of Fig. 1.

I Similar characters of reference are used in all of the above gures to indicate corresponding parts. Arrows are employed to indicate the direction of now of information or control innuences.

Throughout the director of the present inventlon data is represented and transmitted by mechanical displacements, and direct and alternat" ing potentials. It will be understood, where not stated, that a mechanical displacement so'employed is proportional in magnitude to the magnitude of the quantity represented thereby, and corresponds in direction to the algebraic sign of the quantity represented. Similarly the magnitude of the direct or alternating potential is proportional to the magnitude of the quantity represented thereby, and the polarity or phase of the potential corresponds to the sign of the quantity.

In 1 there is shown a schematic diagram of the whole gun directing system of the present invention, the ultimate purpose of which is to electrically transmit angle of train (A. T.) quadrant elevation (Q. E.) and fuze setting (F) data to the guns, as an output leads l, Z and 3, respectively. For the sake of clarity in the description, and simplicity in the explanation, the apparatus of Fig. 1 may be considered to accomplish its purpose in the following three distinct and more or less independent steps:

1. Range finding and tracking apparatus is employed to obtain continuous spherical coordinate data representative of the present position of the target, that is, present azimuth (Ao), present elevation (En) and present slant range (De), obtained as proportional angular displacements of present position shafts, 4, 5 and 6, respectively.

2. This present position spherical coordinate data is converted to corresponding present po- Sition rectangular coordinate data (n, yn, and zo). This present position data is then differentiated to yobtain present position rectangular coordinate rate data (in, yo, and au) and this rate data is then multiplied by the projectile time of night (tp) in suitable prediction apparatus to obtain the rectangular coordinates (mp. 21p, and 2p) of the predicted, or future, position of the target, that is, the point in space at which the target will be located at a time (tp) later. This predicted position data is obtained as proportional angular displacements of future position shafts l', 8 and 9, respectively.

3. This predicted position data is employed in suitable ballistic mechanism to obtain angle of train (A. T.) ,and quadrant elevation (Q. E.) data for positioning the guns, fuze (F) data for cutting the projectile and time of night (tp) data for use in the prediction apparatus. The angle of train, quadrant elevation, fuze, and time of night data are obtained as proportional angular displacements of shafts Ii), Il, l2 and i3, respectively.

The rst problem, namely that of angularly displacing shafts d, 5 and 6, respectively, in proportion to present azimuth (Ao), present elevation (E0) and present slant range (Dn) will now be considered. In tracking the target in order to obtain azimuth and elevation data two modes of operation are provided: 1. radio automatic, and 2. optical manual. The desired one of these modes of operation may be selected by suitably positioning selector switches il! and lli which, it will be understood, are simultaneously operated as a unit. In both radio and optical modes of operation range data is automatically supplied from the radio sighting apparatus.

When switches l 4, ifi are in their optical position an azimuth and an elevation operator actuate handwheels l5, l5', respectively, until the line of sight dened by the telescope it is directed toward the target. Two eyepieces i1, il" are provided on telescope i6, one for each operator.

through which they can see the ltarget and thus determine whether the telescope has been properly oriented.

Handwheel I5 actuates a vshaft I8 which in'turn drives a permanent magnet generator I9, vand also drives the rotating contact arm 'of a linearly Wound potentiometer 2i, the opposite terminals of which are connected to a suitable constant source of direct voltage, indicated as `battery 22, and the intermediate terminal of Which is connected to ground, as shown. Accordingly, there will be provided on lead 23, which is electrically connected to contact arm 2li, a direct voltage proportional in magnitude and corresponding in polarity to the angular displacement of handwheel I5 from a datum position. This voltage signal is placed in series with the output voltage of generator I9 which last voltage, as is well known, will be proportional in magnitude, and will correspond in polarity, to the rate at which handit/heel I5 is being displaced. Accordingly, the voltage appearing on lead 24 will be the algebraic sum of two component voltages, one proportional to the displacement of handwheel I 5 and the other proportional to the rate of said displacement.

The voltage on lead 24 is transmitted through switch I4 and .is then added to, by being placed in series with, the voltage appearing on output lead ,25 of the regenerative tracking mechanism 28. For the present it will be assumed that the regenerative tracking mechanism is not operating A(switch 2'! is in the off position), and that therefore no additional voltage is added from the regenerative tracking mechanism. Accordingly,

the voltage on lead 28 is identical with that on lead 2li.

'The voltage on lead 28 is introduced into the azimuth servo 29 which may be of any suitable type of Servo unit adapted to produce an angular displacement of its output shaft at a rate proportional in magnitude and corresponding in direction to the magnitude and polarity of its input signal. Output shaft 38 actuates the present azimuth shaft 4 through gearing 3|.

Rotated by shaft 4 is a worm 32 engaging the large azimuth gear 33 which is fixedly mounted in .the director support. Thus, 'the existence of a voltage signal on lead 28 will cause worm 32, shaft and all of the rest of the director apparatus to walk around fixed gear 33 at a rate proportional to the voltage on lead 23. Accordingly, 'since the `azimuth operator has control of the voltage on lead 2S through his handwheel l5, he has complete control over the azimuth position of the director, and he may therefore continuously maintain telescope I5 directed at the target in azimuth. When this has been accomplished the angular displacement of shaft 4 is proportional to the present target azimuth angle (Ao). Present azimuth data is then introduced into the rectilinear converter 34 as the displacement of shaft 4.

The purpose of the generator i9 is to provide what is commonly termed aided tracking in order to facilitate the operators task of maintaining vtelescope IS directed toward the target. If generator I9 were not provided, it will be apparent that pure rate tracking would be obtained since the director and telescope i6 would then rotate at a rate proportional to the displacement of handwheel I5. By providing the generator, however, this rate is increased or decreased by an increment proportional to the rate of handwheel displacement. The time integral of the increment kwill be proportional to the time integral of the rate of displacement of the handwheel. The displacement of the director due to this increment will therefore be proportional to the displacement of the handwheel. Thus, it is seen that if the generator alone were employed without the potentiometer ZI, pure displacemen tracking would be obtained wherein the actual displacement of the director would be proportional to the actual displacement of the hand- Wheel. By employing both the generator and the potentiometer aided tracking is obtained wherein the director is displaced simultaneously at a rate and by an amount proportional to the olisplacement of the handwheel.

'The apparatus provided for manually tracking the target in elevation is identical with that just described for the azimuth control. Corresponding portions of the tracking apparatus for elevation and azimuth have been given identical reference numbers but are primed in the Vcase of the elevation control equipment.

In the case of elevation control, however, the present elevation shaft 5, driven from the elevation servo 29', rotates the line of sight defined by telescope 'I6 in a vertical plane through gearing 35, shaft 36, gearing 31, shaft 33 and gearing 39. Shaft 38 is connected to the radio scanner 4B of the radio sighting system to simultaneously rotate the line of sight thereof in elevation.

As in the case of the azimuth control, the elevation operator has complete control, through his handwheel I5', of the voltage appearing on lead 28', and therefore has complete control of the position of shaft 5 and of the orientation in elevation of the line of sight defined by the telescope I6 and the radio sighting system. Present elevation (En) is also introduced into the rectilinear converter 34 as a proportional rotation of present elevation shaft 5.

For radio automatic tracking, which is initiated by placing switches I4, I4 in their radio position, there is provided a radio sighting system which is preferably of the ultra high frequency pulse type described in copending U. S. application Serial No. 441,188, for Radio Gun Control vSystem, filed April 30, 1942, in the names of C. G. Holschuh et al., now Patent No. 2,617,982. As more completely described in that application, a radio transmitter 4I includes means for generating short periodic pulses of ultra high frequency radio energy. These pulses of radio energy are transmitted to a radio scanner 40 through a suitable transmission channel for high frequency energy, such as a wave guide, indicated schematically as lead v42.

Rotatably mounted on the radio scanner is a parabolic reflector d3, which is adapted to transmit into space in a fan-shaped beam along its axis 44 the pulses of electromagnetic energy received by scanner 40. Radio scanner 40 includes a motor adapted to 'rotate reflector 43 about a spin axis 45. As shown, the axis 44 of the parabolic re'ector is slightly offset from spin axis 45 so that, as a 'result of its rotation, a conical portion of lspace is irradiated with short pulses of electromagnetic energy. The rate of rotation of reflector 43 about spin axis Alili may be of the order of 200 times less than the pulse `repetition rate, so that all portions of the conical angle of space are irradiated.

Also included within the radio scanner 4,0 and rotated 'by the previously mentioned motor .is `a two-phase generator which generates two phase displaced voltages and transmits these voltages, as on lead 46, tothe radio receiver 41 to provide a time reference of the rotation of reector As more fully explained in the above-mentioned copending application, should a target lie within the conical portion of space irradiated by reflector 43, a portion ofv the electromagnetic energy striking the target will be reflected back to the reector 43 and received in the form of pulses corresponding to the transmitted pulses but delayed in time by an amount proportional to the distance to the target. These reflected pulses of electromagnetic energy are schematically indicated as being transmitted to the radio receiver 4l, as by lead 46, along with the time reference voltages. Should the target be lying along the spin axis 45, which is the line of sight dened by the radio system, it will be apparent that all the reflected pulses will be of the same intensity. On the other hand, if the target should not lie along spin axis 45, the intensity of the reilected pulses will vary substantially sinusoidally as the parabola 43 rotates, the maximum intensity occurring at the time that axis 44 most nearly coincides with the target orientation.

The radio receiver 4l includes detecting means for isolating a sinusoidal voltage corresponding to the substantially sinusoidal variation in intensity of the reilected pulses. Also included within radio receiver 4l are two phase sensitive ampliers, one for azimuth and one for elevation. 'i

By comparing the phase and magnitude of the isolated sinusoidal voltage with one of the time reference voltages in the azimuth phase sensitive detector, there is produced upon output lead 48 a direct voltage corresponding in magnitude and polarity to the azimuth component of the angular deviation between the target orientation and spin axis 45. Similarly, by comparing the phase and magnitude of the isolated sinusoidal voltage with the other time reference voltage in the elevation phase sensitive detector, there is produced upon output lead d8 a direct voltage corresponding in magnitude and polarity to the elevation component of the angular deviation between the target orientation and spin axis 45. rThese voltages, appearing on leads 48 and 43', can thus be thought of as azimuth and elevation error voltages, respectively, and as providing an electrical indication of the angular error between the line of sight defined by the radio sighting system (spin axis 45) and the target orientation.

As shown, in the radio positions of switches I4, i4 these error voltages are introduced into the azimuth and elevation servos 29, 29' to thereby cause rotations or" the present azimuth shaft 4 and the present elevation shaft 5. Rotations of these shafts in turn cause the line of sight defined by the radio system to be moved in azimuth and elevation in a direction such as to align Aitself with the target orientation and thereby reduce the error voltage signals appearing on leads 48, 48 to zero. In this manner the line of sight 45 of the radio sighting system is continuously and automatically maintained coincident with the target orientation, and present azimuth and present elevation data are continuously introduced into rectilinear converter 3d as proportional angular displacements of shafts Il and 5.

It will be understood that telescope ES and radio scanner it are mounted on the director such that the lines of sight defined by each are at all times coincident.

Slant range (De) data is automatically and continuously obtained by the radio sighting system in both the radio and optical positions of switches I4, I4. For this purpose a delay network 49 is provided which receives on lead 50, from the radio transmitter 4l, voltage pulses corresponding in time phase to that of the transmitted radio pulses. Delay network 49 operates to delay these voltage pulses by a time proportional to the angular displacement of slant range shaft l, which is received on shaft 5l. The resulting delayed pulses are then transmitted to a time comparator 52 as on lead 53. Also received by the time comparator are voltage pulses corresponding in time phase to that of the reilected pulses, as on lead 54. The time comparator is adapted to make a time comparison between the phase of the reflected pulses received on lead 54 and the delayed transmitted pulses received on lead 53. If these pulses should be absolutely in phase, then the transmitted pulses received on lead 55 must have been delayed by an amount exactly proportional to the range of vthe target. Accordingly, when this condition is met, the angular position of shaft 6 represents the true present slant range to the target.

If the reflected pulses received on lead 54 by the time comparator should not be in phase with the delayed transmitted pulses received on lead 53, the time comparator is adapted to produce on. output lead 55 a direct voltage corresponding in magnitude and polarity to the diierence in phase existing between these two pulses. This output voltage on lead 55, which may be considered as a range error signal, is placed in series with the output voltage appearing on lead 56 from the regenerative tracking mechanism 26, and is then introduced into the slant range servo 53 as on lead 5l, as in the case of elevation and azimuth control. It will be assumed for the time being that the regenerative tracking mechanism 26 contributes no additional voltage on lead 56, and that therefore the voltage received by the slant range servo on lead 5l' is the same as that appearing on lead 55.

This voltage input to the slant range servo 58 causes the servo to rotate its output shaft 59 at a rate proportional to the input signal. Shaft 52 actuates the present slant range shaft 6 through gearing '60 in such a direction as to cause shaft 5i to increase or decrease the amount of delay introduced in the delay network 49 as required in order to make the delayed pulses appearing on lead 53 coincide in time phase with the reflected pulses appearing on lead 54. As previously pointed out, when this condition of coincidence in time phase with respect to the voltages appearing on leads 53 and 54 has been obtained, the angular displacement of shaft 6 is proportional to the slant range to the target. This slant range data, appearing on shaft 6, is then also introduced into the rectilinear converter 34.

Because of the intrinsic diierence between the rectangular coordinate system and the spherical coordinate system, if the target is flying at a constant speed in a constant direction, the linear target rates will remain constant, whereas, the spherical coordinate rates will be constantly changing. Also, the three component linear target rates (ao, yo, and en) are suicient to definitely deine the target course and speed, whereas, in order to denitely denne target course and speed in spherical coordinates, not only is it necessary to know the rates of change (Ao, En and Do) of the spherical coordinates, but

also the spherical coordinates (Au, En, and Du) themselves must be known. It follows that if the target course and speed are known in terms of the rectangular coordinate rates (iro, lo and o) and the present position of the target is known in terms of the spherical coordinates (Ao, Eo and D), then the spherical coordinate rates (o, n and Do), are definitely dened and can be determined by simple trigonometry. The relationship works out as follows:

where R0 represents the present horizontal target range, and R0 represents the present horizontal target range rate. Rn, which is equal to Do cos En and R0, which is equal to Do cos Eo, are introduced into the formulae, in order to simplify the actual mechanical solution of the equations, as will later be apparent.

v As will be further described in detail with respect to Fig. 5, these component target rates (in, yo and so) are computed in the diflerentiating, smoothing and predicting circuit 6l and are produced as proportional angular displacements of output shafts 62, 63, and 64, respectively. Shafts 62, 63 land 64 actuate shafts 65, 66 and 61 through bevel gearing to introduce these component target rates into the regenerative tracking mechanism 26. The spherical coordinates Ao, Eo and Do of the present target position are also introduced into the regenerative tracking mechanism from shafts d, 5, and 6 by way of shafts 68 69 and l0, respectively. Present horizontal range (Ro), which is equal to Dn cos Eo, is computed in rectilinear converter 34 and is transmitted to the regenerative tracking mechanism as a proportional angular displacement of shafts Il and 12.

Having received Au, Eo, Do, Ro, :130, y'o and o as input data, the regenerative tracking mecha,- nism, as will be described in detail hereinafter, is adapted to solve Equations 1 to 4 and, when switch 2l is in the on position, to produce on output leads 25, 25 and 56 voltage signals which are proportional 'to the instantaneous spherical coordinate target rates n, n and Do respectively. These output voltage vsignals are placed in series with the error voltages received from the radio automatic or optical manual tracking apparatus, and the resulting voltage is applied as the input signal to the azimuth, elevation and slant range servos to rotate the present position azimuth, elevation, and slant range shafts at proportional rates.

Thus, if it be assumed that the target is flying in a constant direction at a constant speed, and that the target is being correctly tracked at the director so that the spherical coordinate present position data and the computed rectangular coordinate rate data fed to the regenerative tracking mechanism are all correct, then the spherical coordinate rate voltage signals, which the 'regenerative tracking mechanism computes `on leads 25, 25 and 56, will be `of the proper :inagnitude in themselves to cause the director to properly track the target thereafter. Thus, once regenerative tracking has been established, no voltage signal need be supplied by the radio or optical tracking mechanism, as long as the target maintains a constant course and speed. Should the target change its course or speed, the voltage signals supplied to the servos from the regenerative tracking mechanism will no longer be such as to cause the director to properly track the target, and the radio or optical tracking apparatus will then have to supply compensating component voltage signals to the servos in order to reestablish correct tracking. When correct tracking has thus been established, the regenerative tracking mechanism will again take over and supply the proper signals to the servos provided the target maintains its new course and speed.

In the above discussion it was pointed out that correct tracking had to be once initially established before the regenerative tracking mechanism could compute the proper voltage signals to continue the correct tracking. In initially getting on the target, it will be seen that no matter how erroneous are the voltage signals that are initially produced by the regenerative tracking mechanism, the radio automatic or manual optical tracking apparatus can completely override these erroneous signals, and can initially get on the target and establish correct tracking by providing error voltage signals which, when added to the erroneous voltage signals from the regenerative tracking mechanism, produce the resultant servo voltage signals which will produce whatever tracking rates are necessary. Thus, the radio automatic or optical manual tracking system, depending upon the position of switches M, I4', are always in complete control regardless of the regenerative tracking mechanism.

Accordingly, during the process of getting .on the target, the regenerative tracking mechanism and either the radio or optical tracking systems each supply one component of the servo signals. As the tracking process continues, that component supplied by the regenerative mechanism gradually approaches the correct value and that component supplied by the radio or optical system is gradually reduced, until nally the former component reaches the correct value and the latter component is lzero. As previously stated, the regenerative tracking mechanism will continue thereafter to automatically maintain correct tracking without fur-ther lsignals from the radio or optical systems as long as the target lmaintains a constant course and speed.

One lembodiment of -suitableregenerative tracking mechanism for solving Equations l to 4 is shown in Fig. 2. As there shown, input shafts 65, 66 and 6l', the angular displacements of which represent the rectangular coordinate rates at, y, respectively, actuate rotor windings '13, M and T5 of rotary transformers E26, 76 and l'l. Each of these rotary transformers have their lstator windings ?8, 'i9 and 8c supp-lied from 'a constant source of alternating voltage. The rotor windings are each shown at right angles to their respective stator windings, 'in which position zero voltage will be'induced in these rotor windings. This -zero voltage position of the rotor windings corresponds to the zero displacement positions of shafts-"65, 66 and 61. As is ywell known, as the rotor windings are rotated from their zero signal position, a Voltage will be induced therein propor-tionalto the sine of the angle through which they have been rotated. For ysmall angles of rotation from the zero position, the induced voltage will be substantially proportional Lto the angle itself.v The 11 proportionality factor between the angular disiplacements of shafts 55, 88 and 6? and the com ponent target rates represented thereby is made by design such that the rotor windings are only krotated through small angles for the maximum .target rates likely to be encountered. AccorduXes produced by these two windings are at right angles with respect to each other. These magnetic nuxes are superimposed upon each other in rotary transformer 82 and will each induce a component voltage in rotor windings 8d and 85. Rotor windings 8d and 35, which are also in spaced quadrature, are actuated in accordance with present azimuth (Ae) from input shaft 65.

The component voltage induced in rotor winding 85 as a result of the voltage across stator winding 83 will be proportional to the voltage across stator winding 83 and the cosine of the angle through which the rotor winding has been displaced. equal to the quantity 'Jo cos An. The component voltage induced in winding Sii from stator winding 8| will be proportional to the quantity :to sin Au. Stator winding 8l is Wound on rotary transformer 82 such that this induced voltage will be of the opposite phase. Accordingly, the total resultant voltage induced in winding 85 will be proportional to the quantity lo cos Au-:iro sin A0 This resultant voltage is placed across the re sistive winding 88 of a potentiometer unit 8l', the

Amovable contact arm 88 of which is actuated in accordance with present horizontal range (Re) from input shaft i2. Winding 86 is wound such i that the resistance from one terminal to the point of contact with movable arm 28 varies inversely with the angular displacement of the contact arm. Thus, the output voltage existing between contact arm 88 and one terminal of winding 88 willA be proportional to the voltage applied to the terminals of winding 8E and inversely proportional to the angular rotation of shaft 12. This output voltage, which is applied across the primary winding 89 of transformer 90, will therefore be proportional to the quantity which quantity will be seen to be equal to the `desired target azimuth rate (A) in accordance with Equation 1.

By similar reasoning, it will be apparent that the voltage induced in rotor winding 84 will be Aproportional to the quantity :isn cos A04-:170 sin Au,

4and is energized in accordance with vertical rate (n) from winding l5 of rotary transformer Ti.

Rotary transformer 93 has two rotor windings This component will therefore be 'be employed. essentially comprise two vacuum tubes connected and 96 also'mounted at right angles with respect to each other and both positioned in accordance with present elevation (Eo) from input shaft 59. Accordingly, there will be induced in rotor winding 98 a voltage'proportional to the quantity Rn cos Eo-i-o sin E0, which quantity is equal to target slant rangeY rate (Do) as shown in Equation 3. This slant range rate voltage signal is employed to energize the primary winding 91 of a transformer 98.

Rotor winding 95 of rotary transformer 93 wil have induced therein a voltageV proportional to the quantity zo cosvEo-Ro sin Eo, and this voltage is placed across the opposite terminals of the resistive winding 99 of potentiometer unit |00. Winding 99 is wound so as to have an inverse relationship of resistance with respect to angular position similarly to winding 86 of potentiometer 87. A movable contact arm |0| of potentiometer unit |00 is angularly displaced in accordance with target slant range (Dn) from input shaft 10. Ac-

cordingly, there will be produced between contact arm i0| and one terminal of winding 99 a voltage proportional to the quantity Zn() COS Ely-R0 SIl E0 Vwhich quantity is equal to the target elevation rate (En) as sho-wn in Equation 2. This target elevation rate voltage is employed to energize prilmary winding |82 of a transformer |03.

'alternating voltages corresponding in magnitude Vand phase to the quantity represented thereby.

In order to transform these alternating voltage signals into direct voltage signals having a magnitude and polarity corresponding to the quanti- -Jties represented thereby, any suitable type of phasesensitive rectifiers |04, |65 and |08 may These phase-sensitive rectiers so as to have their respective plate currents flow in opposite directions through a suitable resistive load, across the terminals of which the desired `direct voltage output is obtained on output leads l of each of these tubes, batteries H0, |i| and H2 are provided, the grounded positive terminals of which are connected to the cathodes of the tubes. Switches i3, i4 and l5 are schematically indi- A cated as being simultaneously operated from the on-off switch El. In the on position of these v switches, a connection is made from a midpoint of each of the windings |07, |08 and |09 through lresistors |23, |2d and |25, respectively, to the point on the batteries H0, ||I and ||2, respectively, which will provide a proper operating bias l.voltage for the tubes.

In the off position of these switches, however, the midpoint of windings |07, Hit and |09 are connected to the negative Aterminal of batteries H0, and H2, respectively, to provide a bias voltage for the tubes of a magnitude beyond the cut-oi value, to thereby prevent the tubes from operating. The midpoints :of windings |01, |03 and |09 are connected to 13 ground through condensers H6, H1 and ||8, respectively.

Accordingly, when switch 27 is in its on position, there will be produced in output leads 56, 25 and 25 direct voltages corresponding to slant range rate, elevation rate, and azimuth rate, as desired. On the other hand, when switch 2l is in its olf position, zero voltages will be produced across these leads since the rectiers are then rendered inoperative. The effect of con- 'densers H6, lll, and H8 and resistors |23, |24 and |25 will be to prevent the bias voltage on the grid of the tubes from going from its operating value to a value beyond cut-'off immediately as the switch is changed from an on to an ofi position, and vice versa. Thus, as switch 2`| is changed from an o to an on position, the 'direct voltage on output leads 56, 25 and 25 will only gradually build up to their proper values corresponding to the voltages across windings Sil, |02 and 86 of transformers S8, |03 and S0.

In the previous description of the operation of the `regenerative tracking mechanism, it was assumed that the regenerative tracking unit was Iin operation during the process of getting on the target and establishing proper tracking. Another mode of operation is to initiate correct tracking originally with the regenerative track- 1n'g mechanism not operating, that is, with switch 21 in the olf position. In such a case,

the automatic radio or manual optical tracking systems alone would be employed to initially establish correct tracking. With correct tracking established, the proper vangular rate voltages `will be produced across primary windings 9T, f

|02 and 89, but these voltages would be ineffective vin producing voltages across output leads 55, 25 and 25, since switch 21 would be in its off position. Now when switch 21 is placed in its on position, the proper spherical coordinate rate voltage signals for the servos will build up in leads 56, 25' an-d 25, but because of the previously explained operation of condensers IES, and ||8 and resistors |23, |20 and |25 these voltages -will build up gradually, giving the manual operator or the radio apparatus time to gradually diminish the rate voltages supplied by them'to zero. In this way the regenerative tracking mechanism can take over without any interruption in the proper tracking of the target.

By employing regenerative tracking mechanism as described, more accurate tracking is obtained both in radio automatic and in optical manual operation. In optical manual operation, for in` stance, it will be clear that the azimuth and lof the regenerative tracking' mechanism are even Vmore pronounced. Thus, if we assume that the target is flying a course such that the present .position .shafts must be continuously operated by their respective Servos, for example, as straight line course, it will be seen that error signals Imust'be continuously supplied to the servos from the radio sightingsystem in order to cause the present position shafts to move at all. But the radio sighting system can only supply error voltages when an actual error exists between the line of sight dened by the radio system and the actual target orientation. Accordingly, were the radio sighting system alone to be employed for tracking a moving target, perfect tracking could never be accomplished, since there would always have to be some error in order to actuate the servos. Of course, this error can be made very small by having a very high amplification factor in the servos. By employing the regenerative tracking system in conjunction with the radio sighting system, however, it is possible to completely eliminate these errors during the times that the target is flying a constant course and speed. In such a case, the regenerative tracking system is supplying all of the kvoltage required by the servos in order to properly track the target, and the radio sighting system is supplying zero error voltages, which means that no errors exist between the line of sight defined by the radio sighting system and the actual target orientation.

The regenerative tracking mechanism 26 may be employed to advantage in conjunction with an entirely dierent type of tracking systems than that shown in Fig. 1, and previously described. One example of an entirely different type of tracking system employing regenerative tracking mechanism 26 is illustrated `in `Fig. 3, wherein only control in elevation is shown, the

azimuth and slant range controls being identicalthereto. In Fig. 3 Ythe regenerative ytracking mechanism is shown operating only in conjunction with manual tracking, no provision being made for radio automatic tracking.

As shown in Fig. 3, the same regenerative tracking mechanism 26 vhaving the same ,inputs and outputs as shown in Fig. 2, and previously described, is employed. In this case, however, the servo voltage signals are wholly supplied from the output voltage leads 56, 25 and v25 'of 'the regenerative tracking mechanism. Thus, lead 25' is connected directly to the elevation vservo 29. 'I'he elevation servo 29 actuates the present elevation shaft 5 through intermediate `shafting 5 and differential H9. The other input member of differential H9 is actuated from shaft which in turn is controlled by the elevation operator through the elevation handwheel l5'. As before, the servo unit is of the type such that output shaft 5 is driven at a rate proportional 0 the magnitude of the vsignal received on .lead

It will be seen that present position lshaft :5, which controls the tracking telescope in levation, has two components of control, one .component being provided by the elevation handwheel operator and the other component being provided by the elevation servo as controlledby the regenerative tracking mechanism 2B. VThus, regardless of the voltage signals existing at any particular time on lead 25 and the corresponding rate of rotation of shaft 5', the actual position of shaft 5 and of the tracking telescope completely under the control of the operator. rIhe operator therefore displaces his handwheel 5', and the tracking telescope, as required 'in order to initially Aestablish Vcorrect tracking. When correct tracking has been established,'the regenerative tracking mechanism .26 will cause shaft 5 to rotate at the .rate Vrequired morder to maintain correct tracking. Thus, the -acomponent of control which the elevation handwheel operator must introduce in order to maintain` correct tracking will have been reduced to zero, and thereafter the elevation handwheel operator will only have to compensate for changes intarget course and speed.

- All of the apparatusthus far kdescribed has for its purpose the positioning of shafts l, k and 6 in accordance with the present position of the target in azimuth, elevation and slant range, respectively. This spherical coordinate present position data is received by the rectilinear converter 34 which transforms this spherical coordinate data into corresponding present position rectangular coordinate data (xu, yo and so), which is produced kas proportional angular displacements of output shafts 1M, |42 and |43, respectively. As a necessary step in this computation,

present horizontal range (Re) is obtained, and

thisappearsas ai proportional rotation of output shaft 'il The rectilinear converter 34, which is shown in Fig. 4, consists essentiallyof two types of computing components, (1) multiplying units and (2)` sine and cosine units, both of which are deadbeat mechanical calculators. units are preferably of the type described in U. S. Patent No. 2,194,477, for Multiplying Machines,

The multiplying` cosAo and sin Ao and transmits the former to the multiplyingunit |53, as on shaft iet, and transmits the latter to multiplyingk unit it, as on shaft |57. Multiplyn ing unit |53, having received cos Aofrom the sine `and cosine unit 55 and Ro from the torque amplifier |56, produces as a proportional rotation of its output shaft mi the east-West coordinate (am) of the present position of the target, which is the product Ro cos Ao; Zeroazimuth is taken as the position or east direction, and the positive azimuth direction isy taken as counterclockwise.

Similarly, multiplying unit |54, having received sin Au from the sine :and cosine unitk and Re from the torque amplifier itt, produces *as a proportional rotation ofits output shaft issued March 26, k1940, in the names of W. L.

Maxson and P. J. McLaren. fr described in that patent, such a multiplying unit is adapted to produce a rotation of its output shaft instantaneously equal to the product of the rotations of its two input shafts. Y

The principal elementof the above-mentioned Patent No. 2,194,477 is a spiral gear having teethk mounted thereon in such a path that a follower gear incontact with these teeth is rotated by an amount proportional to the square of the amount of rotation of the spiral gear. The sine and cosine units may consist of two such spiral gears, the path traced out by the teeth of each of which is modified such that in one case the rotation of the driven follower gear is proportional to the sine of the rotation of the spiral gear, and in the other case the rotation of the driven follower gear is proportional to the cosine of the rotation of the spiral gear. The Maxson sine and cosine unit is a well-known device of this character.

Referring again to Fig. 4, present elevation (Eo) data is supplied to the sine and cosine unit |44 from input shaft 5. The sine and cosine unit |44 calculates sin Eo and cos Eo, and transmits sin Eo to the multiplying unit |45, as by shaft M6, and transmits cos En to the multiplying unit le?, as by shaft |48. Multiplying unit |45, having also received slant range (Do) from input shaft ii, produces as a proportional rotation of its output shaft |43 the vertical component (et) of the present target position, which is the product Du sin Eo. Similarly, the horizontal component (Ro) of slant range (Do), which is the product of Do received from shaft 8 and cos En received on shaft les, is obtained in multiplying unit |137, and is transmitted to a dead-beat torque amplifier 53 by shaft |5I. rEhe torque amplifier Eet may be of any suitable type adapted to produce as on output shaft |52 a torque amplified signal (Re) which is identical to the input signal (Ro) on shaft |5| but for its greater torque. The wellknown torque amplifying device consisting of contacts, a capacitance motor and a Lancaster damper may, for example, be used for this purpose.

v|112 the north-southcoordinate (ya) of the presn ent position of the target, which is the product Ro Sin A0.

There are thus produced on output shafts IM, and |533 of rectilinear converter 34 angular displacements proportionalk to the zr, y, and e components of the present position of the target, referred to the director as the origin of the coordinate system. Inorder to convert this present position data into corresponding rectangular coordinate data having the guns as the origin of the kcoordinate system, three parallax knobs |6|,

|52, and i are provided kwhich may be respectively displaced in accordance with the linear distance from` the guns to the director in the eastwest (m) direction, north-south (y) direction, and vertical (c) directions, respectively. The displacements of knobs im, |62 and |63 are additively combined in differentials |64, |55 and |66 with the displacements of shafts Uil, |42, and let, respectively, to thereby produce upon shafts |67, iet, and |59, respectively, angular displacements proportional to the fr, y, and e components of the present position of the target, with the origin of the rectangular system taken at the guns.

It will be understood that knobs |6I, |82 and |63 have associated therewith a'relatively movable dial and index so that the operator may know when he has set in the proper parallax. Such a dial and index will be understood to be associated with all other knobs provided on the director for setting in data.

The present position rectangular coordinate data, now represented as proportional rotations of shafts itl, |68 and |69, are introduced into differentiating, smoothing and predicting circuit El. Time of flight (tp) data is also introduced into the predicting circuit 6| as a proportional rotation of input shaft |70 which is actuated from time of flight shaft I3 through shaft and the interconnecting gearing. As previously noted, it is the function of predicting circuit 6| to differentiate the rectangular coordinate input data to thereby obtain the component target rates in rectangular coordinates, which are produced as angular displacements of output shafts E2, 63, and fi. These rates are then multiplied by the time of iiight in order to obtain the rectangular coordinates of prediction, that is, the distance the target moves during theV projectile time of asada-'71.

Hight. The rectangular coordinates of prediction are then additively combined with the rectangular coordinates of the present position of the target to obtain the rectangular coordinates of the predicted future position ofthe target (Ip, yp' and ep) which are then produced ascorresponding angular displacements of output shafts |22, H3. and till, respectively.

Also introduced into the predicting Ycircuit. 9|' are v/indrate. corrections (AJ'JWI and Ay'w). These corrections arev obtained from Wind corrector l' 5: and are transmitted to predicting circuit 6| as proportional rotations ofv shafts |19, l?? and-|18, |119, respectively. These v'vind correction rates are additively combined with the rand y componentrates before these rates areI multiplied by time of' flight to obtain prediction, in. order toA compensate for the effect of Windco'n theproh. jectile after` it lea-ves the gun. A sensitivity adjustment knob |80.- isv also provided whereby the dynamic characteristics of differentiating, smoothing and predicting circuit may be varied.

Fig. 5 there is shown that portion of the differentiating, smoothing, and predicting circuit which operates on the n: component. As i's-there shown, the :ro present position input shaft l-.B'loperates into a differentiating circuit consisting essentially ofv variablel speed drives |8| and |92. and` their associated: shafts and differentials. This smoothing and differentiating circuit operates toproduce upon shaft |33 anA angular rotation proportional to a smoothed version of thev :z: component of the presentpositionl of the target, the unsmoothed version. ofv which is represented by the angular: displacement. of. input shaft |91. Also, the smoothingl and differentiating circuit operates to' produce uporrshaft l-Sii an angular displacement proportional to a smoothed version of the component target rate (in) in the :c direction.` Shaft |81@ is connected to. output shaft 52' which shaft is thereby displaced in accordance with the :c component of target rate (d20).

This component target rate (dsc) is additively operates to obtain the product (zito, tp) of thecomponent target rate received on shaft |85 and the time of flight received on shaft |10, and this product, representing the :c component of prediction, is producedV as an angular displacement of shaft |38. TheYa-ngular displacement of shaft i88- is then combined in dierential- |58- W-ith theangular displacement of shaft |83 to thereby produce an angular displacement of output shaft |-.'|-2 proportional toy the sum of the a: component of` present position and the :c component of prediction,-. and therefore proportional to the r cornponent of the future position of the target (rrp). The y and 2 components of the future position (ypand ep) are obtained as proportional rotations of output shafts H3 and lill., respectively, in predicting circuity 6ft, by apparatus identical with that shown in Fig. 5 for obtaining the. x component. of the future position of the target, exceptY that no wind rate correction is introduced in obtaining the e` component.

It was4 previously stated that the tvvo variablespeedv drives |81- and |82 operate onthe-:ro--sjg-g nal,- received as a proportional rotation of inputv shaft |61, to produce, as a proportional rotation' of Shaft |83, a smoothed signal iny the;

the' ball-'carriage |9| of. variable speed .device |852.

throughi rack. and pinion arrangement |92 and other suitable interconnecting gearing. Asv is,

well' known, ball carriage |9|.transmits the. mo-r tionof the. disc |93, which will, for the' present, be.- assumed to -be driven at a constant speed, to

the: cylinder |94 in such a way that the rate of rotation of cylinder |94 is proportional to the displacement of ball carriage |9| from the-cene' ter of' disc I 93.

The angular displacement of cylinder |94- isY connected, as by shaft |95, into' a second differ-A ential- |96, the other linput vof which is suppliedfrom shaft through interconnecting shaft |91. The output of differential 96,- which is the alge-- braio sum of its two inputs, actuatesthe shaftZ |98, which' in turn displaces the ball carriage |99 of the second variable speed device |81 throughrack and pinionzgearing 200. Ball carriage; |99 of variable speedqdevice |8| Variably transmitsthe rotation of the .disc 20|, which is. driven by the constant speedm'otor 202, to the cylinder 203.

The cylinderA is connectedv as by shaft 204 to ac-v tuate one input. member of a differential 205.

The other input member of the. differential 205.--

s actuated in accordance; with. the` displacement of cylinder |9l|-y of variable speed device |82 through shafting- |95-, |84 and 20S; The output member of differential- 205, which vis. thus actu-A ated-in accordance with the algebraic sum-ofthe displacements ofshafts .20d and 206, yis connected to output shaft 202,. which in turn actuates-V the.

smoothed present position shaft |83, which then' supplies thev subtractive input to equating vdifferential |89.

In considering theyoperation of the smoothing. and differentiating circuit, it will first be as,- sumedthat the-variable speed devicel |82 and the differential |96 are omitted so that shaft |98.- is-r directly actuated from shaft |90. The circuit vvould thenconstitute t'he ordinary differentiat-L mg circuit which, as is well known, would reach a conditionof equilibrium-When the ball carriage |99 had assumed such a position that the ang-ular rate of rotation of shaft |83 was equal tothe angular rate 4of' rotation ofthe input (mu) shaft |61'. At equilibriumthe angularpo'sition ofshaft |98 Would represent the time derivative (it) smoothed to' a certain extent. Shaft |83'Y would be actuated' inv accordance with xo, also smoothed toacertain eX-tent, but it/vvould lagV (ambyi an*- amountproportional to` thedisplacement of" ball carriage |991 from itscentralposition, so that-it could not be: employed asY asource of! smoothedv presentpositionzdat'a.

By incorporating the, additionalvarableaspeed i device |82 in the circuit, the lag` is automatically removed-from shaft |83.- so that its angular position-1 is an accurate, smoothed indication. of the'- (zo) present position data. Also a much more eectively smoothed time derivative (it) is obtained as a proportional rotation of the (zito) shaft |84.

With the variable speed device |82 incorporated in the circuit it will be seen that the circuit can no longer reach equilibrium when the rate of rotation of shaft |83 rst equals that of shaft |61,

because at this time shaft |90, and consequently ball carriage |9| of variable speed device |82, will be displaced an amount proportional to the previously mentioned angular displacement lag of shaft |03 with respect to shaft |61. Therefore, at this time the cylinder |94 is still rotating, and will continue to act through differential |96 to rotate shaft |98 and thereby further displace ball carriage |99 of variable speed device |8|, with the result that the rate of rotation of shaft |83 will begin to exceed that of shaft |61.

The output shaft |90 of equating differential |89 will then begin to rotate in a direction opposite to its original rotation so as to drive the ball carriage |9| back to its position of zero displacement. Therefore, it is seen that in the diierentiating circuit of the present invention, equilibrium can only be reached when the rate of rotation of shaft |83 is equal to that of shaft |61 and when there is no angular displacement lag between the two shafts, that is, when shaft |90 and ball carriage |9| have returned to their zero displacement positions.

Since one condition for equilibrium in the present circuit is that there be no angular displacement lag of shaft |83 with respect to the (mo) input shaft |61, it is apparent that the angular displacement of the (xo) shaft |83 is proportional to a smoothed value of aco.

Also, since the rate of rotation of shafts |83 and |61 are equal at equilibrium, that is, when ball carriage |99 is stationary, the angular displacement of shaft |98 is proportional to a smoothed version of the time derivative (rico) as in the ordinary differentiating circuit which does not incorporate the variable speed device |82. At equilibrium, however, it was seen that shaft |90, which provides one input to diiferential |96, had returned to a position of zero displacement so that the total angular displacement of shaft |98 must have been produced from shaft |95 which is the other input to differential |96. Therefore, the angular displacement of shafts |95 and |84 is also proportional to the smoothed time derivative (sto) Furthermore, since shaft |95 does not respond to changes in the rate of rotation of input shaft |61, that is, to changes in the time derivative (rito), as quickly as does shaft |98, the time derivative (cto) which is obtained as a proportional rotation of shaft |84 is more effectively smoothed than the time derivative which would appear as a proportional rotation of shaft |98 in the ordinary differentiating circuit employing only one variable speed device.

The smoothing, differentiating and predicting circuit shown in Fig. 5 is identical to that employed in previously mentioned copending application Serial No. 470,686 with the sole exception that the loop consisting of shaft 206 and differential 205 have been added in the present circuit. As explained in that application, the differential equation for the prior circuit without this loop may be obtained and from a mathematical analysis of this differential equation the curves shown in Fig. 6 giving the dynamic characteris- 2G tics of the circuit without the additional loop may be plotted.

The dynamic characteristics of interest are:

1) The settling time, which may be defined as the time after which all response errors are negligible (less than an arbitrary value), and

2) The amplitude ratio, which may be defined as the ratio of the amplitude of sinusoidal perturbations existing on the predicted position output data to the amplitude of the sinusoidal perturbations superimposed upon the present position input data.

The settling time curves are based on a constant rate of change (it) of the :c coordinate of the present position of the target equal to 150 yards per second, a constant time of flight equal to' 20 seconds, and a negligibile response error in future position (atp) defined as an error less than 15 yards. The amplitude ratio curves are based on a constant perturbation frequency of cycles per second and a constant time of flight equal to 20 seconds. The values of settling time and amplitude ratio are as indicated on the various curves. As shown, the circuit may have underdamped or overdamped response characteristics depending on Whether values of circuit constant K1 and K2 are chosen so as to define an operating point above or below the line 208, each point on which represents critically damped operation. Line 209 is the locus of all points having underdamped operation in which the rst overshoot peak is equal to '75 yards.

The curves of Fig. 6 then indicate the various settling times and amplitude ratios for the prediction circuit of said copending application, that is the prediction circuit of the present application with the loop consisting of shaft 206 and differential 205 eliminated, for various values of circuit constants K1 and K2. The circuit constants K1 and K2 are the proportionality factors for the variable speed devices of the prior circuit f which devices would correspond to variable speed devices |8| and |82, respectively, of the present circuit. Numerically, K1 would be equal to the ratio of an increment in the angular displacement of shaft |98 to the resulting increment in the angular velocity of cylinder 203, and K2 would be equal to the ratio of an increment in the angular displacement of shaft to the corresponding increment in the angular velocity of cylinder |94, assuming in both cases that the additional loop of the present circuit is not present.

Thus, as more fully explained in the aforesaid copending application Serial No. 470,686, any particular values of K1 and K2 correspond to the point on the chart of Fig. 6 at which the circuit will operate. Accordingly, it was possible to pick out that point of operation on the' chart having the desired dynamic characteristics, i. e., settling time and amplitude ratio, and to operate at that point by designing the circuit to have the numerical values of K1 and K2 indicated on the chart.

In the circuit of the present invention, Wherein the additional loop consisting of shaft 206 and differential 205 are included, the same method of design holds true. However, in this case a new constant Ka is introduced, which is the proportionality factor of the new loop, that is, the proportionality factor relating the displacement of shaft |84 to the amount of that displacement which is introduced into differential 205 to be added te the displacement of shaft 204. n Win be apparent that Ka is dependent upon the gear ratios chosen in designing the additional loop. Also, the numerical values of the variable speed drive proportionality factors in the old and new circuits will have to be diierent in order for the circuits to have the same dynamic characteristics. These variable speed proportionality factors for the new circuit containing the additional loop will be designated K1 for variable speed drive |8| and Kz for variable speed drive |82. The values of Kr and Kz required in order to operate at any particular point on the chart will depend upon the value of Ka chosen for the new loop. In fact the prior circuit can be thought of as a specific case of the new circuit, wherein Ks is chosen as zero, that is, the new loop is non-existent. Thus, in that specific case the values of Ki and K'z come out equal to K1 and K2, respectively. For values of K's other than Zero, dif-y ferent values of K1 and Kz will be required in order to operate at the same point.

Thus, the present circuit will have three circuit constants K'1, K'z and Ka the values of which determine the point of operation on the chart of Fig. 6, and therefore determine the dynamic characteristics of the circuit. The values of K1 and K'z required in order to operate at a particular point will be dependent upon the value of K3 chosen. If it is desired to operate at a particu- *navire-emma',

The circuit of the present invention can then be designed to have these values of K1, K2 and Ks.

As more fully explained in copending application Serial No. 470,686, it is desirable to alter the dynamic characteristics of the circuit during the Solution of the prediction problem so as to obtain a low settling time during the time of response to a change in present position input rate, and a low amplitude ratio, that is, good smoothing characteristics, thereafter. In the circuit of the prior application means were provided to alter the speed of the disc |93 during operation to thereby alter K2. In this way the point of operation could be changed from some point such as point 2 I0, having a fast response to some other point, such as point 2H, having a slower response and better smoothing characteristics.

It will be noted that in the prior circuit, as K2 changes, the point of operation must move along the dash line 2| 3 in a direction parallel to the K2 axis. This represents a disadvantageous limitation to the circuit of the prior application since complete freedom in choosing both the initial and final operating points is not permitted. For instance, it is desirable to be operating at underdarnped points both initially and nally, and this cannot be laccomplished with the prior circuit and still have any substantial change in dynamic characteristics since dash line `2|3 crosses into the underdamped region not far from initial point 2H). l

The addition of the new loop in the present circuit overcomes this undesired limitation Iand allows complete freedom of choice in picking the initial and final operating points. This comes about because of the existence of the additional circuit constant Ke. With K'a equal to zero, that is, in the prior circuit which has no additional loop, it has been stated that as K2 is varied the operating point travels along dash line 2| 3. However, in the new circuit, having a definite value of, K'a, as we Vary K2 the operating point will travel along some line such as 2M. This line may be called the sensitivity control curve for that value of Ks. As Ks approaches Zero, the control curve approaches dash line 2|3.. Thus, since the value of Ka determines the, direction of the control curve, it is possible to obtain Whatever control curve is desired, subject to the sole limitation that the control curve cannot havev a negative slope,

Accordingly, it is possible to, choose a desirable initial operating point, such as point 2m, and to choose a desirable final operating point, such as point 2 |2, the only limitation being that point 2 t2 may not be below point Since it is desired to maintain underdamped operation for both points, this condition is a desirable one anyway so that it really does not represent a limitation. Having chosen these two points it is then possible to choose a value of Ka such that the corresponding control curve passes through these two points.

Referring against to Fig. 5, the apparatus for varying the circuit constant K'z is controlled by a sensitivity control knob |89, the rotation of which proportionately displaces ball carriage 215 of a variable speed drive 2|5 through shaft 2|1, gearing 2m, shaft 2 9, and rack and pinion gearing 226. Disc 22| of variable speed device 2! 6 is driven from a constant speed motor 222. The cylinder 223 of variable speed device 216 actuates the disc |93 of variable speed device |82, the speed of which determines the circuit constant Kz. Thus, by operation of sensitivity control knob mi) it is possible to vary K2 as desired and to operate anywhere on control curve 2M oi Fig. 6 that is desired. If desired, a spring and detent arrangement could be provided assoeiated with control knob |86 so as to provide andndication to the operator of the particular settings oi' knob |86 corresponding to particular points of operation, such as points 2H), and2|2 of Fig. 6,

If desired a sensitivity control could be provided for each of the ze, y, and a prediction circuits. It is contemplated, however, that the same sensitivity control is to be used for all three. It is understood, therefore, that the rotation of the cylinder 223 of variable speed device 2|| is employed to actuate not only olisc |93 of variable speed device |82, but also the corresponding discs ofboth the y and a prediction apparatus.

Referring again to Fig. 1, it was previously stated that a wind corrector |15 produced, as proportional rotations of output shafts |16 and H8, wind rate corrections are, and Ayw, respectively, which corrections were added to the .r and y components of target rate in the predicting circuit l, respectively, in order to compensate for the effect of wind on the projectile. In order to compute these wind rate corrections, wind cor'- rector |15 has set into it on knob 24| the wind velocity in the east-west, or direction, and on knob 242 lthe wind velocity in the north-south, or y direction. The wind corrector |75 also receives quadrantY elevation (Q. E.) as a proportional rotation of input shaft 2&3. Input shaft 23 243 is actuated from shaft 244 which in turn is actuated from shaft 245, the angular displacement of which is identical with that of quadrant elevation shaft Time of flight (tp) is also set into the wind corrector on input shaft 245, which shaft is actuated from shaft 241, which in turn is actuated from shaft 248, the angular displacement of which is identical to that of the time of flight shaft |3. The Wind corrector then solves for the :c wind rate correction (Azw) as a product of the east-west wind velocity and a predetermined function of time of flight and quadrant elevation. Similarly, the y wind rate correction (Ayw) is solved for as the product of the north-south wind velocity and the same function of time of flight and quadrant elevation. Thus, the :c and y wind rate corrections, as solved for, may be expressed by the following formulas:

(7) Aiw=(E-W wind velocity) (Klip Q. E.-i-Kztpl-K3 Q. E.)

8) Ayw= Ns wind velocity) (Klip Q. EpjtzfztpJrKa Q. E.)

In previous gun directors, wherein the eect of wind on the projectile was compensated for by correcting the computed target rates, the eastwest and north-south Wind velocities themselves were employed as the wind rate corrections Azizw and Ayw, respectively. However, such a method of correcting for wind Velocity assumes that the actual displacement of the projectile due to the wind, will not be affected by the quadrant elevation of the guns, and that this displacement Will vary linearly with time of flight. Neither of these assumptions are valid, and for this reason the composite function of time of flight and quadrant elevation is introduced into the present wind corrector.

A detailed schematic drawing of the wind corrector is shown in Fig. 7. As is there shown, time of flight and quadrant elevation, received as proportional rotations of shafts 246 and 243, respectively, are introduced into a multiplying u nit 249 which may be of the type disclosed in the previously mentioned Maxson patent, but preferably is a simpler and lighter type, such as is disclosed in Fig. 13, and which Will be described in detail hereinafter.

The product (tp-QE.) appears Ias a proportional angular displacement of output shaft E) of multiplying unit 249. This product (tp-QE.) is introduced into a differential 25| through gearing 252 and shaft 253. Another differential 254 is provided, having one input member actuated proportionately to time of flight from shaft 246 through appropriate interconnecting shafts and gears, and a second input actuated in accordance with quadrant elevation from shaft 243 through suitable shafting and gearing. The output member of diierential 25d thus actuates shaft 255 in accordance with the sum of its two input quantities, one input being proportional to time of flight (Kztp) and the other being proportional to quadrant elevation (KgQE.) The sum (Kztp-l-KaQE.) is introduced into differential 25| through shaft 25B. The output of differential 25|, being proportional to the sum of its two inputs, may then be expressed by the quantity which appears as a proportional angular disgearing 260 and shaft 26|. The composite functions of time of flight and quadrant elevation is thus multiplied in multiplying unit 258 by the east-west wind velocity, which is received as a proportional rotation of input shaft 262, and the product representing the :v wind rate correction (Aw) is produced as an angular displacement of output shaft |16. Similarly, the same composite function of time of flight and quadrant elevation is multiplied in multiplying unit 259 by the northsouth wind velocity, received as a proportional angular displacement of input shaft 263, and the product representing the y wind rate correction (Af/w) is produced as an angular displacement of output shaft |18.

A simple and inexpensive linear multiplying unit which may be employed in ballistic mechanism, such as the Wind corrector |15 wherein the extreme accuracy of a Maxson multiplying unit is not required, is shown in Fig. 13. For concreteness in the application of this multiplying unit to a particular problem the two input shafts and one output shaft are given the reference numerals of multiplying unit 258 of the wind corrector shown in Fig. '1. Thus, a first input quantity (a) is introduced into the multiplying unit as a proportional rotation of input shaft 26|, and a second input quantity (b) is introduced as a proportional rotation of input shaft 262. Output shaft VEB is angularly displaced through the operation of the multiplying unit by an amount represented by the quantity (c), which quantity is equal to the product (ab) of the two input quantities. v

As shown, a lever member 264 is provided with a slot 265 extending the length thereof. Lever member 2M is adapted to rotate about a movable pivot 266 which engages slot 265. Pivot 266 is carried by an internally threaded movable nut 21 which engages the threaded portion 268 of input shaft 262. Thus, as input shaft 262 is angularly displaced, pivot 266 is moved longitudinally by a proportionate amount from a zero reference position, indicated as line 269. Thus, the position of pivot 266 to the left of reference line 269 may be represented by the quantity (b).

Input shaft 26|, the angular rotation of which is proportional to the quantity (a), is employed to actuate shaft 21| through gearing 212 having a gear ratio such that the angular rotation of shaft 21| represents the quantity (2a) This quantity is introduced into the subtracting differential 210, another input of which is actuated in accordance with the output quantity (c) from shaft 213. Thus, output shaft 214 of differential 216 is actuated in accordance with the quantity (2a-c). Shaft 214 actuates shaft 215 which in turn actuates a vertically movable member 216 through a rack and pinion arrangement 211. Thus, member 216 is moved with respect to a reference line 216 an amount proportional to the quantity (2a-c) Member 216 has Aa projection 219 thereon engaging slot 2t5 of lever member 264. Another vertically movable member 260 has a similar projection 28| thereon also engaging slot 265. Thus, it will be apparent, as member 216 is displaced, lever member 264 will be rotated about pivot member 266, thereby causing vertical displacement of member 280. The displacement of member 280 is proportional to the output quantity (c) and this vertical displacement is converted into a corresponding angular displacement of shaft 213 through rack and pinion arrangement 282.

Shaft 2HE is then employed to actuate output shaft |70 in accordance with the output quantity (c) which is equal to the product (ab).

Member i580 is arranged to move vertically along the reference line 269, and member 210 is arranged to move vertically along a reference line 283 which last reference line is displaced from referenze line by an amount egual to the quantity Thus, the distance of pivot 260 from reference line is equal to the quantity (2-17). The amount that pivot point 28| is displaced from reference line U3 as member 27B is moved is equal to the output quantity (c). Thus, it will be seen that from a consideration of the two symmetrical triangles formed by reference lines 283, 25S, 218 and slot 23%' the following relationship can be set up.

c Za-c Solving Equation 9 for the output quantity (c) we get the expression:

Thus, it is seen that the apparatus of Fig. 13 operates to produce an angular displacement of output shaft V56 which is equal to the product of the angular displacements of input shafts 26| Crab and 232. Obviously by employing rack and pinion gearing Where necessary, either of the inputs or the outputs could be represented in terms of a linear displacement rather than an angular displacement.

It will be recalled that the predicting circuit 6|y of Fig. 5 computes the prediction in any one coordinate by multiplying `the target rate in that coordinate by the projectile time of night. This computation of prediction is therefore based upon the assumption that the linear target rates are all constant during the time of night of the projectile. In other words, it is assumed that the target nies a constant course at a constant speed during the travel time of the projectile. Obviously, if the target is nying a curved course in a horizontal plane, as is the case when the pilot of the-target aircraftY has introduced rudder control, this assumption is not valid, and therefore the :c and y components of the futurer position of the target, produced as angular displacements of output shafts |12 and |13 of the predicting circuit 0 will not be correct.

-In order to provide corrections to the and y coordinates of the future position during curved night of the target, a curvilinear predictor 30| is provided having a course indicator 302 mounted thereon. Curvilinear predictor 30| receives the x and y component target rates (im) and (ilo) from shafts 5?. and 63 respectively, and also receives time of night data from shaft |10. Having received this data, the curvilinear predictor is adapted to .provide an indication on the course indicator 302 of the actual course of the target aircraft in the horizontal plane, i. e., it provides an indication of the direction of night of the target aircraft. If this course indication remains constant, the target must be'flying in a constant direction in the horizontal plane. Under these conditions the assumption upon which predicting circuit '5| computes the future position of the target will be valid. However, if a changing course is indicated on the course indicator 302, it will mean that the component target rates are not constant and that the predicting circuit is no longer computing the true future position of the target. Under these conditions an operator can position a switch 303 to its on position at which time the curvilinear predictor 30| operates to compute the necessary corrections (Arv and Ay) which must be applied to the x and y components of the future position in order to -compensate for the changing direction of flight of the target.

The curvilinear correction (Ax) is produced a's an angular displacement of output shaft 304 `of the curvilinear predictor.y Output shaft 304 actuates shaft 305 which is employed as one input to a differential 306, the other input of which is obtained from the a: coordinate future position shaft |72. The output member of differential member 306 actuates the true :c coordinate future position shaft 1. Similarly, output shaft 30! of curvilinear predictor 30| is actuated in accordance with the future position curvilinear correction (Ay). This correction is introduced as one input of the differential 308 through shaft 309 to be there added .to the displacement of shaft |13 to produce an output displacement on shaft 8 proportional to the true y coordinate of the future position of the target.

In Fig. 8 there is shown a geometrical representation useful in obtaining expressions yfor the curvilinear corrections Asc and Ay. In this .ngure point (O) represents the projection of the present position of the target on a horizontal plane defined by theand :y reference axes. Point (O) has the coordinates (xo, yo). It is assumed that the target is flying ata constant velocity (V) about point 3I0 at a constantv angular velocity (a). Thus, the target is flying in a circular pattern along the circular arc 3| l, and the instantaneous direction of the target is along tangent line 3|2 to arc 3H at point (O). This tangent line is shown as having an instantaneous direction at an angle with respect to the .1: reference axis.

During the projectile time of night (tp) the target will have traveled a distance (Vtp). Accordingly, the true future .position of the target will be at some point (P') having the coordinates (:cp and yp) point P being a distance Vtp along the arc from point O. The future position of the target computed by the differentiating, smoothing and predicting circuit 0|, however, would be at some point (P) having coordinates (xp and yp), point (P) being along the tangent line 3|2 at a distance Vfp from the point O. The distance PP represents the error between the future position computed by predicting circuit 6| and the true future position of the target Ax represents the x component of this-error, which must be computed by curvilinear predictor 30| and added to the :c component of the future position, as computed by predicting circuit 6|. Similarly, Ay represents the 111 component of the error which mllist be computed by the curvilinear predictor 30 lSince the target is assumed to be nying such as to have a constant angular velocity (a), the angle through which its direction of flight will have turned during the projectile time of night will 'be vequal to the product (afp). Therefore the angle 0 between linesdrawn from the point 30| to the point (O) land from the point 30| to the center of the chord connecting points (O) and (P') will be equal to l/gatp. From the geometry of the figure then it can be seen that the angle POP' is also equal to l/zatp. It can also be shown that the angle PPO may be taken yas a right angle to a fair degree of approximation. This approximation is particularly true when the rate of turn of the target is small.

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