# Патент USA US2404011

код для вставкиGR Z 9 4 04 9 O 1 l Y _ W y .Y July 15, 1946' v.. , , “www""MMW” - , w. T. WHITE 5 y 2,404,011 PREDI GTI ON APPARATUS Filed June 2l, 1943 ' ÍNVENTOR MALTE@ Z- /l//WTE « BY ' :7 MÃÉRNE . . y’ 't I» L* ‘A Patented July 16, 1946 2,404,011 UNITED sTATEs PATENT oFFicE 2,404,011 PREDICTION APPARATUS Walter T. White, Hempstead, N. Y., assigner to Sperry Gyroscope Company, Inc., a corpora tion of New York Application June 21, 1943, Serial No. 491,637` 5 Claims. (Cl. 2535-615) 1 2 This invention relates generally to the art of terms of two angular coordinates and one dis tance or range coordinate, such as by an optical gun ñre control and, more particularly, to novel prediction apparatus which combines the sim sight and rangeñnder. The two angular coordi nates ‘are usually elevation and azimuth, and since these are identically treated, at least inso plicity of previously known approximate predic tion solutions with the accuracy of previously known true prediction solutions. One object of the invention is to provide sim ple and accurate prediction apparatus for gun far as the prediction problem is concerned, a gen eral angular coordinate (6) will hereinafter be referred to. The prediction component of the whole nre control solution involves determining the prediction angle (A0) by which the guns must be offset from the line of sight to the target in order to compensate for the motion of the target ñre control. Another object of the invention is to provide prediction apparatus which is comparable in slm plicity to an “angular rate by time” system but having a greater accuracy. Still another object of the invention is to pro during the projectile time of flight (tp). The simplest and most approximate type of vide a prediction system comparable in simplicity 15 prediction solution is commonly known as the to an “angular rate by time” system but having “angular rate multiplied by time” solution. This an accuracy comparable to more complicated sys tems such as those based on Taylor’s series. solution finds its greatest application in inter aircraft and short range anti-aircraft fire control An object of the invention is to provide pre systems wherein a certain amount of accuracy in diction apparatus which takes account not only 20 the solution may be sacrificed for simplicity of of the angular rate of change of a target coordi equipment and rapidity in the solution. nate, but also the time rate of change of that In such “angular rate by time” prediction sys rate during the time of night of the projectile, tems, data corresponding to the angular coordi A further object of the invention is to provide nate (0) is continuously supplied to the predic an “angular rate by time” prediction system 25 tion apparatus from the sight. This angular co wherein the angular rate is corrected by a factor ordinate data is diñerentiated to obtain data cor proportional to the time rate of change of the angular rate and also to the average value of the time of flight likely to be encountered in responding to the time rate of change of the an gular coordinate, hereafter referred to as the practice. angular rate 30 ‘ A still further object of the invention is to pro dt vide simple prediction apparatus which takes into This angular rate data is then multiplied by the account the acceleration of the target position projectile time of flight (tp), and the resulting coordinate during the projectile time of flight. Other objects and advantages will become ap 35 product is taken as the required prediction angle (A0). Thus the solution is based on the following` parent from the specification, taken in connec approximation for the prediction angle: tion with the accompanying drawing wherein the invention is embodied in concrete form. In the drawing: Fig. 1 is a schematic diagram of mechanical 40 Referring now to Fig. 3, the solid line 3 repre apparatus embodying the principles of the inven sents a portion of a typical curve which might be tion; - Fig. 2 is a wiring diagram of the analogous electrical apparatus embodying the principles of obtained by plotting the angular rate (if) 45 dt _ the invention; and Fig. 3 is a graph useful in explaining the theory as a function of time (t) for a particular target. of the prediction solution employed in the in Point I indicates the angular rate at the time vention. (To) at which the projectile leaves the gun, and Similar characters of reference are used in point 2 the angular rate at the time (Tp) at which all of the above iigures to indicate correspond 50 the projectile strikes the target. ing parts. Arrows are used to indicate the di In the simple “angular rate by time” solution rection of flow of information or control influ the assumption is made that the angular rate is ences. constant during the time of flight (tp). In other In all known nre control systems the position words it is assumed that curve 3 follows the dot of the target in space is continuously located in 55 ted line 4 from the time (To) to the time (Tp). 2,404,011 3 4 In practice this assumption is rarely, if ever, valid Referring to Fig. 3, such a solution is equivalent to assuming that the average value of the angu lar rate is at point 6 on dotted line 5 which value may be obtained by taking the angular rate at the time (To) and adding thereto the product of one-half the time of ilight (tp) and the time rate of change of the angular rate at the time (To). since in order to create such a condition the tar get would have to fly at a constant speed in a circle having the sight as its center. The solu tion for the prediction angle (A0), is in error then because no account has been taken of the change of the angular rate during the time of night. In other words, it is assumed that the angular acceleration is constant during the time of flight and that curve 3 therefore travels along the dot ted line 5 which is tangent to curve 3 at point I. In order to obtain an accurate solution for the prediction angle (A0), such as is required for long range antiaircraft ñre control systems, it has been proposed to make no assumptions at all concern Obviously, such an assumption is more valid than ing the motion- of the target, but to compute the true prediction angle (A0) based upon the true the assumption of a constant angular rate, and a more accurate solution for the prediction angle will be obtained than in an “angular rate by time” system. However, even this solution is more or less complicated since it is necessary to mode of motion of the target in accordance with the following expression based on Taylor’s series: obtain the iirst and second derivatives, the first and second powers of time of night, and to per form two multiplications. In the present invention, it is proposed to ob tain an approximate value for the average angu Correlating the above equation with Fig. 3, it will lar rate by adding to the angular rate at time (To) a correction proportional to the angular ac ing the true average value of the angular rate celeration ' during the time of night, and multiplying this average angular rate by the time of flight in or der to obtain the true prediction angle (A0). However, in order to accomplish such a solution Thus, the expression for the prediction angle it is necessary to take not only the iirst deriva 30 (A0) as solved for in the present apparatus may tive be written: v be seen that such a solution amounts to obtain di) d0 dt of the angular coordinate (0), but also the sec ond derivative (n dit) 35 dt2 and the third derivative and so on. than that of a simple “angular rate by time” solu tion, and will approach the accuracy obtained by taking the first two terms of Taylor’s series. However, by making K equal to 1/2tp (average) one multiplication by time of ñight is eliminated in the prediction apparatus. Accordingly by the because of the necessity of solving for the higher derivatives, the higher powers of time of flight, and the respective product terms of the series. In the above described system based on Taylor scribed may be considered as an approximation product d0 ne) is used and all subsequent products are considered negligible. A better approximation for the prediction angle (A6) than that obtained in an “angular rate by time” system could be realized by using thev ñrst two terms of Taylor’s series, the approxi mation then being: The value of K is chosen so as to be equal to one-half of the average values of al1 the time of flight likely to be encountered, that is K=1/2tp (average). In many applications the time of flight varies within rather small limits and there approximation to 1/21§p. Accordingly, the solution involve considerable complication of equipment V based upon Taylor series in which only the first d20 for the prediction angle will be more accurate lthen be multiplied by the corresponding powers of the time of night, and the respective result ing products must be added together to obtain `the prediction angle (A0). Such a prediction sys vtem, although it would provide a very accurate solution for the prediction angle, would take a long time to accomplish the solution, and would prediction angle (A6). Accordingly the process can be stopped whenever the desired degree of accuracy has been attained. Indeed, the simple “angular rate multiplied by time” system ñrst de d0 40 fore the predetermined value of K may be a good d t3 These respective derivatives must series, the successive terms of the series intro duce successively smaller components of the true d20 M_ dt+Kdt2>tVd `t"+Kdt2`t” present invention a certain degree of accuracy is obtained with the minimum complication, and in cases where just this degree of accuracy is required the apparatus of the present invention may be found very useful. Referring now to Fig. 1 wherein mechanical 55 apparatus for solving for the prediction angle (A0) based upon the above analysis is shown, data corresponding to the angular rate dt is received as a. proportional rotation of input shaft I0 from other portions of the ñre control system (not shown). Shaft I0 is connected to actuate one input member of a differential II, the output member of which is connected to ac tuate the ball carriage I2 of a variable speed device I3, as by rack I4 and pinion I5. The vari able speed device is shown as the usual disc ball carriage, and cylinder type wherein a constant speed motor I6 drives a disc I'I., which in turn drives a cylinder I8 through the interconnecting ball carriage I2 at a rate proportional to the speed of the motor I6 and to the displacement of the ball carriage I2 from its central position with respect to disc I1. Cylinder I8 is connected by shaft I9 to drive the second input member of OIL-rinvii 2,404,011 '6 diñ'erential II which operates t'o displace the .and will therefore be displaced by an amount proportional to the prediction angle (A9) in ac cordance with the above derived equation: pinion I5 an amount proportional to the differ ence in the displacements of shafts II) and I9. As it well known, this arrangement of varia ble speed device I3 and differential I I operates to attain a condition of equilibrium at which the rates of rotation of shafts I0 and I9 are equal. A@ = d20 t, In the apparatus of Fig. 1 the value of K may be made equal to one-half the average time of night, as is required, by choosing the proper When this condition has been reached, the dis placement of ball carriage I2 is proportional to the time rate of change of the angular displace d0 10 speed of motor I6 and proper values of the vari ous gear ratios involved. Referring now to Fig. 2, wherein an electrical ment of shaft III, and is therefore proportional to the acceleration or second derivative embodiment of the invention is shown, it is4 as sumed that a direct voltage signal correspond dt2 15 ing in polarity and magnitude to the angular rate of the angular coordinate (0). This can be seen by a consideration of the fact that should shafts I0 and I9 not be rotating at the same rate, the has been generated in other portions of the fire third member of differential I I will be additionally displaced, causing a corresponding displacement 20 control system and is applied across input leads 30, 3D’. »These input leads are respectively con of ball carriage I2 in such a direction as to in nected to the grids 32, 32’ 0f electron tubes 33, crease or decrease the angular rate of shaft I 9 33'. yA plate supplyvoltage, indicated as a bat until it does equal that of shaft Ill. Since the tery 34, is connected at its negative end, which rate of rotation of shaft I9 is proportional to the displacement of `ball carriage I2 because of 26 may be grounded, as shown, to cathodes 35, 35’ and at its positive end to the plates 36, 36' the nature of operation of variable speed device di@ through equal resistors 31, 31'. A grid bias volt I3, the displacement of ball carriage I2 may be age is provided, indicated as battery 39, having taken as proportional to the time rate of change of the angular displacement of shaft Il), and its positive side Aconnected to cathodes 35, 35’ therefore proportional to the time rate of change 30 and its negative side connected to grids 32, 32' giif) <3) dt2 of the angular rate dt ,through equal resistors 38, 38’. The electric circuit so far described is simply an amplifying circuit adapted to produce across the opposing terminals of the series circuit con 35 sisting of resistors 31, 31' a voltage of the op This second derivative, appearing as a propor tional displacement of ball carriage I2, is intro posite polarity to that appearing across input leadsBII, 30', and having a proportional but great er magnitude. If it is assumed that zero signal voltage is received across leads 30, 3U', it will put member of differential 20, as by rack 2I and 40 be apparent that equal plate currents flow in tubes 33, 33’ and thence through resistors 31, 31' pinion 22. A second input member of differen in opposite directions. Accordingly, the total tial 20 is displaced by an amount proportional voltage across the series circuit consisting of these to the angular rate duced as a proportional displacement of one in two resistors would be zero. However, should an input voltage signal be received of a polarity such that lead 30 is positive with respect to lead by being directly actuated from shaft III thr‘ough 3U', the grid of tube 33 will be rendered more shafts 23, 24, and 25, and the associated gearing. positive and the grid of tube 33’ will be rendered Differential 20 operates to angularly displace its less positive than their quiescent values. Ac output shaft 26 by an amount proportional to 50 cordingly, more current will flow through resistor the sum of the angular displacements of its two 31 than through resistor 31’, and the potential of input shafts. Accordingly, output shaft 26 is the upper terminal of resistor 31 will become angularly displaced by an amount proportional to more negative than the potential 0f the lower the quantity terminal of resistor 31'. A resulting voltage will d0 d20 55 thus be produced across the opposing terminals dt of resistors 31, 31' havinga polarity opposite to that of the input voltage signal received across The angular displacement of shaft 26 is in leads 30, 30', and an amplified magnitude. In troduced into a mechanical multiplier unit 21, the same manner, should an input signal be re into which there is also introduced the time of ceived having opposite polarity to that just as flight (tp) as an angular displacement of shaft sumed such that lead 3U’ is positive with respect 28 from other portions of the ñre control system. to lead 30, an opposite polarity voltage would The multiplier unit 21 may be of the type dis be produced across resistors 31, 31’ such that closed in U. S. Patent No. 2,194,477 for a Multiply ing machine, issued in the names of W. L. Max 65 the lower terminal of resistor 31’ is negative with respect to the upper terminal of resistor 31 by a son and P. J. McLaren, dated March 26, 1940. proportional amount. 'I'hus the voltage across As disclosed in that patent, the multiplier unit is adapted to produce an angular displacement resistors 31, 31', corresponding to the input volt of an output shaft equal to the product of the age across leads 30, 30', is proportional in mag angular displacements of two input shafts. Ac nitude and opposite in polarity to the magnitude cordingly, output shaft 29 will be displaced by 70 an amount equal to the product of the time of flight (tp) and the quantity and sense of the angular rate ‘ Q dt This voltage is lapplied across a series network consisting of condenser 4I) and resistor 4I con “www ‘2,404,011 7 nected in parallel, resistor 42, lresistor 42', and comes more and more accurate, the greater the value of y, provided the condenser 40' and resistor 4|’ connected in parallel. Neglecting `for the moment the `eiïect of condensers 40, 4D', it will be apparent that re sistors 4l, 4l', 42, 42’ comprise a simple voltage 5 divider network so that a voltage Will be devel Raw” and the accuracy is quite satisfactory for lire control applications. This voltage is then applied to the grids of elec tron tubes 43, 43’ which, in conjunction with their oped across the opposite terminals of resistors 42, 42', proportional in magnitude to that across re sistors 31, 31', and therefore also proportional in magnitude to the angular rate 10 associated circuit elements, form an amplifying circuit having exactly the same operation as the QQ> amplifying circuit described with respect to elec tron tubes 33, 33’. ThisI latter amplifying circuit therefore operates to produce an output voltage 40' upon the current through the resistors 42, 42' across terminals 44, 44’ having a polarity oppo it will be seen that an additional component of site to that across resistors 42, 42', and having an amplified magnitude. There is thus produced current will flow through these resistors When ever the voltage across resistors 31, 31' is chang across the output terminals 44, 44’ of this am plifying circuit a voltage having an amplitude ing. If condenser 40, 40’ and resistors 42, 42' are chosen such that the time constant of their series 20 proportional to and polarity corresponding to circuit is small, this added component of current the magnitude and sense of the quantity will be proportional in magnitude to the time d0 d20 rate of change of the voltage across resistors 31, 31’ and will therefore be pl‘OpOrtional in magní This voltage is then applied across the termi tude to the second time derivative 25 nals of the linearly wound resistor 45 of poten dt Considering now the elïect of condensers 40, @23) tiometer unit 46 which has a movable contact arm diz of the angular coordinate (a) . 41 actuated in accordance with time of flight Accordingly, the (tp) received as a proportional rotation of shaft total voltage across the grids of tubes 43 and 43' 48 from other portions of the fire control sys 30 tem. The final voltage generated across output is proportional in magnitude to the quantity leads 49, 49’ will be proportional to the voltage d0 d20 impressed upon the -resistor 45 and also propor tional to the angular displacement of shaft 48. The values of resistors 4I, 4|', 42, 42" and con Therefore, the voltage across output leads 49, 49' densers 40, 40’ in this case also are chosen so 35 will loe proportional in a magnitude and will cor that K will have a value equal to one-half the respond in polarityßto the magnitude and sense average time of ñight. These values can be de of the quantity termined in any suitable manner. For example, d0 d20 the relation between the input (e) to tubes 36_ and 36' and the voltage before grids of tubes 43 40 and 43' (Eg) can be .chosen to be and will therefore correspond to the prediction at Kir) et+ Km» angle (A6) . where p is the differential operator 45 It will be apparent that should the received sig nal corresponding to the angular rate i v dt be represented -by the amplitude and phase of an p. is the amplification factor of each of tubes 36 alternating voltage rather than the magnitude and 36', and the resistances R, and the condens 50 and polarity of a direct voltage, as has been as \ ers C are identified by subscripts corresponding to the reference characters used in Fig. 2. Substitution of i dt gg dt . l Eg=llRî-î gi'i'Rlzolod-tg] R d0 d20 NOW _B_n R42 can be adjusted to equal a; so that d0 d20 E,= îl-¿JfRtCtä-z] Then, if We let K =R42C40, d0 and differentiating circuits could be substituted for those shown in Fig- 2 to produce an alter nating .current output signal corresponding to the 55 prediction angle (A0). Although the invention has been described as applied to a ñre control system wherein the pre for 11 and for e gives sumed, suitable alternating current amplifying d20 Eg= gi-l- K W diction is accomplished in terms of spherical co ordinates, it will be apparent that a linear coordi 80 nate (rc) of the target’s position could as well be substituted for the angular coordinate (0) with equally advantageous results in computing a lin ear prediction (Ax). Since many changes could be made in the above 65 construction and many apparently widely differ ent embodiments of this invention could be made without departing from the scope thereof, it is intended that al1 matter contained in the above description or shown in the accompanying draw 70 ing shall be interpreted as illustrative and not in a limiting sense. What is claimed is: l. In a lire control system, wherein a measure of the time rate of change of a coordinate of the The first of the above equations for Eg results from some simplifying approximations. It be-- 75 target position is received as the magnitude of a OlLH “D i l 2,404,011 9 10 ñrst variable voltage, and a measure of the pro jectile time of ilight is received as an angular vdisplacement of a shaft, prediction apparatus comprising an electrical network receiving said ñrst voltage and consisting of a iirst resistor con nected in series with a parallel arrangement of a second resistor and a condenser, a potentiometer unit having a linearly wound resistive winding connected to receive the voltage across said first resistor, and a rotating contact arm cooperating age angular rate as a multiplicand whereby a with the potentiometer winding actuated from said shaft. 2. A ñre control system `having an apparatus for computing close approximations of predic tion angles, comprising means controlled accord ing to the variable angular rate of a target, other means for further controlling said means to add to said angular rate a linear correction to obtain an approximate value for the average angular rate of the target, said correction being the prod uct of a derivative of said angular rate and a constant, a multiplying device for multiplying by a time of flight value, means for actuating said multiplying device in accordance with 'said approximate average angular rate whereby a product is obtained from the multiplying device product is obtained from the multiplying device which is closely proportional to the required pre diction angle. 4. A fire control system having means for com puting prediction angles, comprising an ampli fier, an input circuit therefor energized by a volt age proportional to the angular rate of the target, circuit means in the amplifier for computing a correction voltage and adding said correction voltage to the angular rate voltage to obtain a ‘ voltage approximately proportional to the aver age angular rate of the target, said correction voltage being a ñrst derivative of the angular rate multiplied by a constant equal to one-half of an average time of flight value, multiplying means connected to the output of the amplifier adapted to multiply the average angular rate voltage by a time of ilight factor whereby a voltage is pro duced at the output of the multiplying means proportional to the required prediction angle. 5. A fire control system having means for com puting prediction angles, comprising an ampli fier, an input circuit therefor energized by a voltage proportional to the angular rate of the tion angle. 3. A fire control system having an apparatus target, circuit means in the amplifier comprising a resistor and condenser network for producing a voltage proportional in magnitude to the ñrst derivative of the angular rate of the target multi for computing close approximations of predic plied by a constant, the network components tion angles, comprising means controlled accord ing to the variable angular rate of a target, other means for further controlling said means to add to said rate a correction to obtain an approximate being so chosen that the constant is equal to one half of the average time of ñight, means in the network for adding this voltage to an amplified which closely approximates the required predic value for the average angular rate of the target, said correction being the product of a derivative of said angular rate and a constant, said constant being equal to one half of the average time of flight of the projectile, a multiplying device, means for operating said device with a time of ñight value as a multiplier and said value of aver voltage proportional to the input voltage to pro duce a voltage proportional to the approximate average angular rate of the target, and means for multiplying the average angular rate voltage by a factor proportional to time of ñight in order to obtain a voltage proportional to the required prediction angle. WALTER T. WHITE.

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