Missile booster cutoff control system
United States Patent Fitzgerald et al.  
 l l MISSILE BOOSTER CUTOFF CONTROL SYSTEM [75] Inventors: Robert T. Fitzgerald, Clyde D.  
 Hardin, both of Rockville; Solomon Levine, Silver Spring. all of Md.  
 [73] Assignee: The United States of America as represented by the Secretary of the Army, Washington, DC.  
 [22} Filed: Aug. 1, I962 [2]] Appl. No.: 215,482  
 [52] US. Cl. 244/3.l4; 343/7 ED; 343/9 [51 Int. Cl. F42b l5/00 [58] Field of Search 244/14; l02/49 S, 50; 343/6, 7, 9  
 (56] References Cited UNITED STATES PATENTS 2.979.284 4/l96l Genden et al. .t 244/14 3.0081168 ll/l96l Darlington i t r r t. 343/7 3.()7U,0l4 l2/l962 Gose v. Nil/49 S 3.153.520 Iii/I964 Morris 244/14 Primary Examiner-Verlin R. Pendegrass Attorney, Agent. or Firm-Nathan Edelberg; Robert P. Gibson; Saul Elbaum b. antenna means connected to said microwave signal generator means for radiating said high-frequency output signal in the direction of the missile and for receiving signals from the missile;  
  means connected to said microwave signal generator means and to said antenna and responsive to said high-frequency output signal and to the received signals for producing a variable frequency output signal which is indicative of the rate of change of phase between said high-frequency output signal and the received signals, the change in phase being caused by the velocity of the missile; d. pulse generating means connected to said means for producing a variable frequency output signal for generating a first series of pulses which correspond to first alternate zero crossings of said variable frequency output signal and for generating a second series of pulses which correspond to second alternate zero crossings of said variable frequency output signal;  
  counting means connected to said pulse generating means for counting at a predetermined rate upon the occurrence of every pulse of said first series and for producing an output pulse when a predetermined count is achieved; comparator switch means connected to said pulse generating means and to said counting means for producing an output coincidence signal when said output pulse of said counting means coincides with a pulse of said second series. said output coincidence signal representing the instant when the missile achieves cutoff velocity; and  
  means connected to said comparator switch means and responsive to said output coincidence signal for terminating the powered flight of the missile.  
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 MULTIVIBRATOR OFF PULSE IIIIIIIIIIIIII BISTABLE I I I I I I I I I I I I FATENTES 81975 SI&#39;EE? t 0F 5 60 SUPERREGENERATIVE COMMAND 323;? REPEATER DETECTOR CONTROL I 54 {53 {57.  
 CIRCULATOR SWITCH {51 55 98 MIXER OSCILLATOR 131 QUENCH 16 couNTmG RATE AND COMMAND Fly. 6 AMPLIFIER CRCUITS TO COMMAND GENERATOR 91 113 m 1/ r us COMPARATOR GATE SAWTOOTH WAVE 109 GENERATOR SUBTRACTOR AND olvmER Fig. 9  
  D.A.C. COUNTER DOPPLER CYCLE /96 COUNTER 99 a2 COMPARATOR f PULSE swrrcH GENERATOR /NVNTOR$; PaaERT 7. F/TZ @EPHLD QLYDE 3, Hmwuv oLoMaN LEVINE .By. %-A;, a. 740 3:40-11;  
 MISSILE BOOSTER CUTOFF CONTROL SYSTEM The invention described herein may be manufactured and used by or for the Government of the United States of America for governmental purposes without the payment to us of any royalty theron.  
  This invention relates to the field of missile control, and more particularly to means for controlling missile booster cutoff.  
  One of the problems associated with short-range ballistic missiles is the recognition of the time when the optimum terminal missile velocity for a given range has been obtained. With present techniques, which are based on the assumption that the acceleration characteristics of the missile are known and uniform, this time is determined and set into the missile before launch. This imposes stringent controls on fuel characteristics and requires expensive, expendable timing mechanisms. Range accuracy is limited by deviations of individual missiles from the desired acceleration characteristics.  
  Therefore, it is one object of this invention to reduce the stringent control on fuel characteristics previously required.  
  A further object of this invention is to eliminate the need for expendable, expensive timing mechanism.  
  Still another object of this invention is to replace the preflight estimates of missile velocity based on average acceleration-time patterns.  
  Yet another object of this invention is to allow for inflight corrections for the deviation of individual missiles from these patterns.  
  A still further object of this invention is to permit missile booster cutoff at the instant of optimum missile velocity and distance from launch.  
  These and other objects are achieved by providing, within an intermediate range missile launching system, means for continously monitoring the missile velocity and distance from the launching point, for determining from these values the proper instant of booster power cutoff, and for effecting cutoff at the proper instant.  
  These and other objects of this invention will become more clearly understood from the following detailed description taken in connection with the accompanying drawings wherein:  
  FIG. 1 is a pictorial representation of possible trajectories of missiles controlled according to prior art techniques.  
  FIG. 2 is a vector diagram of acceleration forces acting on a missile during its powered flight.  
  FIG. 3 is a pictorial representation of possible trajectories of missiles controlled according to one embodiment of this invention.  
  FIGS. 4a and 4b are pictorial representations of possible trajectories of missiles controlled according to a second embodiment of this invention.  
  FIG. 5 is a block diagram of one embodiment of a system according to the present invention.  
  FIG. 6 is a block diagram of the preset counting circuit of FIG. 5.  
  FIGS. 7a-e consists of graphs of several voltages appearing in the circuit of FIG. 5.  
  FIG. 8 a block diagram of a second embodiment of this invention.  
  FIG. 9 is a block diagram of an addition to the circuits of FIGS. 5 or 8.  
  FIGS. l0a-d consist of graphs of voltages appearing in the circuit of FIG. 9.  
  FIG. 11 is a circuit diagram of one portion of the circuit of FIG. 9.  
  The principle object of ballistic missile flight is the placing of the missile payload on its target with as high a degree of accuracy as possible. In order to accomplish this object, it is necessary that the flight of the missile during its powered portion conform closely to preset values of acceleration and flight angle. In the past, it has been the practice to relay on the missile booster to produce a planned magnitude of acceleration, and to control the cutoff of the booster engine by means of a preset timing device. This timing device might comprise an accurately measured quantity of fuel which will be exhausted after a fixed time interval, or a mechanical clock timer which is mounted within the missile and which functions to cut off the missile booster after a fixed time interval. Such a system functions well when the booster produces the prescribed acceleration. However, when the acceleration produced by the booster deviates from this amount the missile velocity will be either too high or too low at the instant of booster cutoff. Furthermore, when the acceleration is too high the missile will be more distant from the launch point than planned at the instant of power cutoff, and when the acceleration of the booster is too low, the missile will be nearer to the launch point at the instant of cutoff.  
  The effect in prior art systems of such deviations in acceleration on missile range accuracy is shown in FIG. I for firing angles of less than 45 wherein the curve 10 represents the trajectory of a missile which is launched from the point 14 and which undergoes powered flight until reaching the cutoff point 12. The missile then follows a ballistic flight path until impacting on the target 19. If the acceleration of the missile referred to in connection with FIG. 1 is above the preset value, then the missile will follow a higher trajectory such as that represented by the line 11. As will be explained in connection with FIG. 2, the higher acceleration, when combined vectorially with the constant acceleration due to gravity, produces a slightly higher trajectory during the powered flight interval 14-16. Because the missile is being accelerated at a higher rate during its powered flight, the distance 14-16 between launch and cutoff will be greater than the distance 14-15. A missile having such higher acceleration will travel along the trajectory 11 and impact at the point 20, some distance beyond the target 19. Conversely when a missile has a lower acceleration during its powered flight it will reach the point 17 at the cutoff time and follow the lower trajectory 12, impacting at the point 21, which is some distance short of the target 19.  
  The present invention contemplates overcoming the range errors caused by slight variations in the acceleration characteristic of the missile booster. According to the simplest form of this invention, the desired correction is achieved by cutting off the missile booster power at the desired booster velocity, rather than after a fixed powered flight time. In another embodiment of this invention corrections are also made for the difference between the actual booster cutoff distance from the launch site and the predicted booster cutoff distance.  
  Before discussing the principles of the present invention, it will be well examine the changes in missile flight angle caused by varying values of acceleration during the powered flight stage. FIG. 2 represents a series of vector diagrams of the resultant acceleration of a missile during this stage. The vector shows the direction of the component of missile acceleration caused by the booster. The vector 3 represents the acceleration imparted to the missile by the force of gravity. The portion of the vector 20 having a length of a represents the magnitude of the acceleration caused by the booster when performing exactly as predicted. The vector addition of this vector with 3 produces the resultant 10&#39;. When the missile booster acceleration is slightly higher than expected, as shown by the vector length a it combines with the gravity vector to produce the resultant acceleration 11&#39;, and when the acceleration of the missile is slightly lower, as shown by the length a it combines to produce the resultant 12&#39;. In practice the acceleration caused by the missile booster might be of the order of 12 times the acceleration of gravity, but in FIG. 2 the acceleration is shown to be much smaller as compared to gravity so that the small changes in the resultant direction of the acceleration vector can be more clearly illustrated. Actually, when the acceleration is of the order of 12 times that of gravity, and when the acceleration caused by the booster varies in magnitude by 10% above or below the predicted acceleration value, the change in the direction of the resultant vector varies by less than one-half of a degree. However, it may be seen from FIG. 2 that as the booster acceleration decreases, the direction of the acceleration approaches the horizontal.  
  It has been discovered that for launch angles of less than 45 if the booster cutoff is determined by a preset missile velocity rather that by a preset time, errors caused by varying booster accelerations are greatly minimized. The resulting missile range error under this system is illustrated in FIG. 3 wherein variations in booster flight angle caused by variations in acceleration are greatly exaggerated for purposes of illustration. In FIG. 3 the curve 10 represents the trajectory of a missile having proper booster acceleration during the propulsion stage 14-35. At the point the missile achieves the proper velocity and the booster is cut off by a command from the ground. The missile then continues along the trajectory 10 until impacting at the target 19. The curve 11 represents the trajectory of a missile having a higher-than-normal booster acceleration during the interval 14-36. Because of this higher acceleration, the missile achieves the proper velocity at a distance from the launch point 14 which is slightly less than the distance at cutoff for the missile following the trajectory 10. Upon reaching the proper velocity at the cutoff point 36, the missile following the trajectory 11 has traveled a shorter distance down range than had the missile following the trajectory 10 when it achieved cutoff, and the missile following the trajectory 11 is traveling at a slightly steeper angle. Since the booster having higher acceleration is cut off when it achieves the same velocity as the booster having normal acceleration. and the shorter distance traveled compensates for the steeper trajectory, the range errors caused by this higher acceleration are greatly minimized as shown in FIG. 3 wherein the missile following trajectory ll impacts at the point 20, which is relatively close to the target 19. Similarly, a missile having a lower acceleration rate, such as that traveling along trajectory 12, is cut off after having traveled further down range, has a lower trajectory, and impacts at the point 21 which is slightly beyond the target 19.  
  In a second embodiment of this invention it has been found that a more accurate compensation for booster acceleration errors can be achieved by varying the booster cutoff velocity to correct for deviation of the cutoff distance from its desired value. As has been noted previously, accelerations above the desired value result in the achievement of cutoff velocity at a point in space which is closer to the launch point than expected. Conversely, when the booster acceleration is lower than the expected value it achieves cutoff velocity at a distance which is further away from the launch point. The distance error is one major source of the range errors which occur in a system which only achieves the desired cutoff velocity, these errors being indicated by the points 20 and 21 of FIG. 3. A technique for modifying the basic velocity control system in order to correct for this error will be illustrated in connection with FIG. 4a and 4b. As has been noted previously, the variation in missile flight angle due to a variation of 10% booster acceleration is less than one-half of a degree. Such angular variations around 45 launch angles, introduce very little error into the missile flight, and will be ignored.  
  Referring now to FIG. 4a, there is shown a curve 10 representing the trajectory of a missile which is launched from the point 14 and which impacts on the target 19. This missile goes through a powered flight stage until reaching the point 35, at which point the booster is cut off. The range R of the missile consists of the component d,,, which represents the horizontal distance which the missile travels during its powered flight and the componenet d, which represents the horizontal distance which the missile travels during its ballistic, or unpowered, flight. For the purposes of this discussion it may be assumed that the missile travels in a straight line during its powered flight, so that the direction of travel of the missile is at an angle 6 with respect to the ground at both the launch point 14 and the booster cutoff point 35. The distance along the missile flight path between the launch point 14 and the point 35 is represented by d. Thus, the horizontal distance traveled by the missile during the powered flight may be represented by the relation:  
 d d cos 0.  
 Assuming now that the missile is flying in a vacuum, i. e., it encounters no air resistance, the distance traveled by the missile during the ballistic portion of its flight may be expressed by the equation:  
 d,= V (cos 6) X t,  
 where V equals the missile velocity at the cutoff point 35 and t, equals the time of ballistic flight. Therefore,  
 the total range R traversed by the missile may be expressed by the relation:  
 R =d cos 0+ V (cos 6) (t Turning now to FIG. 4b, there is shown a portion of the missile trajectory 10 on which are shown the cutoff point 35 for a missile having the predicted acceleration characteristic and the cutoff point 35&#39; for a missile having an acceleration which is of greater value than that predicted. These cutoff points are separated by a distance Ad. The velocity vectors V and V for the missiles at their respective cutoff points are also indicated, wherein the vector V represents the velocity of the missile having normal acceleration and the vector V represents the velocity of the missile having greater than normal acceleration. The vectors V,. and V,, represent vertical and horizontal components, respectively, of the velocity vector V and the components V, and V,, represent the corresponding components for the velocity vector V. It is proposed to correct for this difference Ad in cutoff distance by effecting a slight increase in the cutoff velocity of the missile having the higher acceleration. The cutoff distance from the launch point of the missile having a higher acceleration may be represented by d&#39;(not shown). The relation between the distance d and the distance d is therefore given by d d Ad.  
  The United States of America as represented by the Secretary of the Army, Washington, DC.  
 The velocity V may be represented by V&#39; V AV.  
 According to equation (3) the range R of the missile having higher acceleration may be expressed by the equation R d&#39;cos 6 V (cos 0):;  
 R (dA d) cos 6 (V+ A V) (cos 6) t,  
 setting R R yields the equation:  
  d cos 6+ V(cos6) t,= (d-A d) cos 6+ (V+A V) (cos r (8) Ad cos 6 AV (cos 6) t,  
 It is obvious that the small change in velocity A V is equal to the missile booster acceleration multiplied by an incremental change in missile powered flight time A t,,, in other words,  
 A V a (A t,,)  
 dividing both sides of equation (9) by cos 0 and substituting equation (10) into equation (9) yields the relation:  
 In actual practice it will be necessary to introduce a factor K into the right side of equation l 2). The value of K would be experimentally derived for a particular missile design and would take such factors into account as air resistance and change in direction of the booster acceleration vector caused by changes in the magnitude of acceleration. According to equation 12), if the acceleration of the missile is such as to bring the missile to its preset cutoff velocity at some point before or after the cutoff point 35 of a missile having normal acceleration, then the range error can be corrected by effecting a slight increase or decrease in that cutoff velocity. For example, assume that a missile reaches cutoff velocity at the point 35&#39; and that the distance A d from the preset cutoff point 35 is equal to feet, the booster has an acceleration of 500 feet per second, per second, and the time of flight for the missile after cutoff is 50 seconds. These values of flight time and acceleration are typical for tactical missiles. Substituting these values into equation 12) yields a value of A! of 4 milliseconds, during which time the missile travels a relatively short distance, of the order of 5 or 6 feet, so that Ad is not appreciably changed. By following a similar development, and by checking velocity before the nominal value is reached, one can arrive at a relation for negative At where the missile booster acceleration was initially below the desired value.  
  It should be noted that missile ballistic flight time and approximate booster acceleration are normally known to a fair degree of accuracy prior to the launching of the missile so that in controlling the missile in accordance with the present invention, only two parameters of the missiles flight need be known-velocity and distance from the launch point. Systems capable of obtaining this information and controlling the missile booster cutoff will now be described in connection with FIGS. 5 through 11. The preferred embodiment of the present invention is based on the doppler system in which, in the case where only velocity is controlled, doppler periods are measured to give velocity information, and in the case where both velocity and distance are controlled, doppler cycles are counted to give distance information and doppler periods are measured to give velocity information.  
  The following paragraphs will describe in detail a system shown in FIGS. 5, 6 and 7 for effecting booster cutoff when a predetermined missile velocity is reached.  
 Broadly, this system involves a ground station located at the missile launching site. The ground station includes an antenna 54 from which is radiated a microwave signal beamed at the missile. The missile carrier a receiving antenna 60. Part of the radiation from antenna 54 that impinges on the missile is reflected back to antenna 54. This returned signal is mixed with a local signal to produce a doppler signal. The period of the doppler signal is proportional to missile velocity. Circuitry at the ground station measures the period of the doppler signal. When this period attains the value corresponding to the desired missile velocity, amplitude modulation of a fixed frequency is applied to the microwave carrier beamed from antenna 54. Suitable circuitry aboard the missile detects, and is actuated by, this modulation and cuts off the boosterv Referring now to FIG. 5, there is shown a block dia gram of a system for effecting booster cutoff when the proper velocity is reached. An oscillator 51 generates on unmodulated CW signal. The signal produced must be of a high enough frequency to give the desired range resolution, a signal in the 1 gigacycle region yielding one doppler cycle for every 6 inches of target movement being sufficient resolution for the purposes of this invention. Depending upon the selected operating frequency, the oscillator may be of the well known magnetron, klystron or solid state type.  
  The output of the osciliator 51 is conducted to a switch 52 which functions to prevent the output power from the oscillator from being radiated before the missile is far enough away from the ground unit. This switch prevents damage which might be caused if excessively high rf energy were placed upon the various mixer-detector crystals in the units. Any diode switch which functions by having a bias voltage applied to it may serve as this switch. The biasing control could be operated by a timer which turned the switch on when the missile had reached the distance of approximately 50 feet from the launch site.  
  The output of the switch is fed to a circulator 53 which serves to distribute the energy between the antenna 54 and the balanced mixer 55. The circulator is a well known device which is commercially available; the device used herein being a Ratheon Model CXMZ. The balanced mixer 55 has one input fed from the circulator 53, which input represents the reflected signal received from the missile by the antenna 54. The other input to the mixer is received from a port ofthe circulator 53 which takes part of the transmitted energy and attenuates it in the order of 35 db. This serves as the local oscillator reference energy to the balanced mixer 55. The reference energy is combined with the received signal in the balanced mixer 55. The two signals within the balanced mixer combine to produce the doppler signal which is conducted to the doppler amplifier 56. The balanced mixer 55 may be of the magic T-type such as that shown in U.S. Pat. No. 2,943,192, issued to Fabian T. Liss on June 28, 1960. The doppler amplifier 56 may be of any well known type of class A, linear audio frequency amplifier, and serves to receive the doppler frequency signal from mixer 55 and to amplify that signal to a usable output level.  
  The output of the doppler amplifier is fed to a pulse generator 63, which may be of any well known type, and which serves to generate a pulse output whenever the output of the doppler amplifier passes through zero. Thus, the pulse generator will produce a positive pulse when the doppler signal crosses zero going in the position direction and a negative pulse when the doppler signal crosses zero going in the negative direction. The output of pulse generator 63 is fed to the input of a preset counter 61 (shown in FIG. 6 and described more fully below) which in response to each negative pulse from the generator 63, begins to count pulses from a clock 67. The preset counter 61 counts to a preselected value and, after reading that count, produces a signal pulse having fixed duration. The output pulse from the preset counter 61 is fed to one input of comparator 57, and the positive pulse output of the generator 63 is fed to a second input of the comparator 57. When the positive pulse from the pulse generator and the output pulse from the preset counter 61 coincide in time, a signal is produced at the output of comparator 57 and is recorded on a coincidence counter 65. When the coincidence counter 65 has counted the occurrence of a fixed number of such coincidences, it transmits an activating signal to command generator 58. The reason for using a coincidence counter 65 to detect several such coincidence events is to eliminate the possibility that a spurious signal from the comparator 57 might activate the command generator 58. The preset counter 61 is automatically reset by the pulse which it generates at the end of of its count, so that is is in a condition to receive the next negative output from the pulse generator 63 and to begin a new cound cycle. The command generator 58 is an oscillator which is used to control the diode of the switch 52, so that upon the activation of generator 58 by comparator 57, the output of oscillator 51 is amplitudemodulated at a fixed rate.  
  The signal radiated by antenna 54 is picked up by antenna 60 on the missile and is fed to a command detector 59 which is set to detect the frequency produced by command generator 58 and which functions to separate the booster from the missile upon activation of generator 58. The output of command detector 59 could also be used to merely turn off the power of the booster rather than to effect a complete mechanical separation. After cutoff is effected the ground unit remains an operative signal transmitting unit while the unit mounted on the missile remains an operative signal receiving unit so that after booster separation these two units could be utilized to transmit a command signal of any type to the missile guidance equipment.  
  A clock 67 provides a series of accurately timed pulses to the preset counter 61. The counter records these pulses after it has been rendered operative by means of a positive pulse from generator 63. The clock 67 may be nothing more than a stable oscillator having a very high frequency with respect to the doppler frequency. Both of these elements are well known in the art and need not be discussed in greater detail here. One embodiment which the counter 61 could take is shown in greater detail in FIG. 6.  
  Referring specifically to FIG. 6, counter 61 is shown to contain a bistable multivibrator adapted to be turned on by negative pulses from generator 63 through conductor 94, and to be turned of by a pulse produced by a counter 83 when it has achieved a preset count. An output signal on conductor 96 from multivibrator 85 serves to render a diode switch 84 conducting during the interval between a multivibrator on pulse and off pulse. While the switch 84 is conducting, the output pulses from clock 67 are conducted to counter 83. When the counter 83 reaches its preset count, it produces a pulse at terminal 95 which serves to turn the multivibrator 85 off, which in turn renders the diode switch 84 non-conducting so that no more pulses from clock 67 appear at counter 83 until another negative pulse from generator 63 serves to turn the circuit 61 on. The multivibrator 85 could be of the vacuum tube or transistor type and could be similar to that shown on page I29, FIG. -1 I of Pettit, Electronic Switching, Timing and Pulse Circuits (I959). The multivibrator 85 could also include suitable signal inverting circuits where necessary at the plate inputs. The preset counter 83 is a basic components in the digital art and could be of the form shown and described by Gossick in the Proceedings of the IRE, volume 7, number 37, page 813 (1949).  
  Having described in some detail the structure and general theory of operation of the circuit of FIG. 5, a more detailed description of the utilization of intelligence by the circuit will now be given with the aid of the diagrams of FIG. 7. As has already been noted, the mixer 55 of FIG. 5 receives a portion of the transmitted signal and the received signal reflected from the missile and produces an output which represents the difference between these two signals. This output contains a component which is proportional to the frequency difference between the two input signals and is known as the doppler signal. This signal has a frequency which is directly proportional to the velocity of the missile. Therefore, the number of the doppler cycles appearing at the output of mixer 55 during any time period represents the distance traveled by the missile, and the time interval of any doppler period or half-period represents the average missile speed during that interval. The doppler amplifier 56 is designed to amplify this doppler signal and to suppress the other components of the signal generated in mixer 59. The output wave form of amplitier 56 is shown in FIG. 7a. This output is applied to the input of pulse generator 63, which produces a pulse each time the output signal from the doppler amplifier 56 passes through zero. The generator 63 produces a positive pulse when the output of amplifier 56 passes through zero going positive and a negative pulse when the output is negative-going. A simple device to perform the function of pulse generator 63 could be constructed from a voltage amplitude clipper which is fed by doppler amplifier 56, the output of said clipper being connected to a differentiating circuit. By means of a pair of oppositely poled diodes connected to the output of the differentiator of generator 63 the negative output pulses from the differentiator are conducted by conductor 81 to the terminal 94 of preset counter 61, while the positive output pulses of the generator 63 are conducted to terminal 99 of the comparator 57. The signal appearing on line 81 is shown in FIG. 7b, while the signal appearing on conductor 82 is shown in FIGS. 70. The pulses on line 81 are conducted to one input of the multivibrator 85 and serve to activate the counter 83 in the manner previously described. When the counter 83 reaches its preset count, it generates an output pulse 95&#39; as shown in FIG. 7d. This pulse is conducted to the input 100 of comparator switch 57 and whenever a pulse at terminal 100 coincides in time with a pulse at terminal 99 an output pulse appears at terminal 96 of the comparator 57 and is counted by counter 65. Since the preset counting circuit 61 is driven by a stable oscillator 67, the time between initiation of a count of a negative pulse output from generator 63 and the production of a pulse is of fixed duration. This duration is preset to coincide with the period of the doppler signal when the missile is moving at the desired cutoff velocity. Further, since the time interval between a negative pulse output from the generator 63 and the succeeding positive pulse output therefrom is equal to this doppler half-cycle interval, the positive pulse inputs to terminal 99 of comparator switch 57 will only coincide with the pulse inputs 95&#39; at terminal of switch 57 at the time when the missile velocity is equal to the desired cutoff velocity. Hence the counter 65 will only receive pulses when this condition exists. Since the missile is accelerating during its powered flight phase, the frequency of the doppler signal will be continually increasing so that the time between negative pulses from generator 63 and succeeding positive pulses will be correspondingly decreasing. The effect of this time interval variation on the output of comparator switch 57 may be seen from an examination of FIGS. 7d and e. In FIG. 7d is shown the initiation of counts in the counting circuit 61 at the times t and The series of closely spaced pulses following these times represent the production of counts by the counter 83, but do not represent the frequency of those counts since it is so high that the indication of each individual count is not feasible on the scale of this diagram. A count reaches its predetermined value at a fixed time after its initiations and then generates an output pulse 95. The pulse 95&#39; is then fed to the input 100 of switch 57 while the positive pulse occuring at times such as t and t, are fed to the input 99 of switch 57. Since the doppler frequency is continously increasing as the missile accelerates, the positive pulse 99 occur at successively shorter intervals after their immediately preceding negative pulses 94&#39;. This means that, at first, the pulses 99&#39; will occur after the termination of the gating pulses 95&#39;, but that, as the missile accelerates, the pulses 99&#39; will begin to occur in coincidence with the pulses 95 The pulses 95 are of such duration that a least ID to 15 cycles of the doppler wave will produce pairs of pulses 94 and 99 at time intervals such that the pulses 99&#39; will coincide with the gating pulses. When these two pulses do coincide in time, a count is generated in counter 65 and when a fixed number of counts have been generated in counter 65, such as ID or 15 counts, the signal appearing on conductor 97 activates command generator 58. The generator 58 produces a sine wave which is at a lower frequency than that produced by oscillator 51, and the command generator output is conducted to the diode of switch 52. This signal serves to modulate the output of oscillator 51 at the frequency of the output of gener&#39; ator 58 and the resultant amplitude modulated signal is transmitted via antenna 54 and is received by missile antenna 60. The modulated signal appearing at antenna 60 is detected by a command detector 59 which is designed to be sensitive to signals of the frequency produced by the generator 58. The signal so detected by the circuit 59 is then employed in a well known manner to either separate the booster from the missile warhead or to turn off the booster engine.  
  A modification of the system of FIG. 5 is shown in FIG. 8 wherein a superregenerative oscillator, or repeater, is inserted between the antenna 60 and the command detector 59. This oscillator is well known in the art and is of the class of devices fully described in Whitehead, Supperregenerative Receivers I950). The  
 repeater 110 receives the transmitted signal from the ground unit and re-radiates it by means of antenna 60 to antenna 54 of the ground unit. The signal received by repeater 110 is subject to a modulation or quenching&#34; at a predetermined frequency, known as the quench frequency. The superrengenerative repeater 110 is essentially an oscillator which is energized by a series of short pulses occuring at the quench frequency. At the instant of energization, the oscillator output begins to build up exponentially until the instant of energizing signal cutoff at which time the oscillator output begins to decrease exponentially. The oscillator itself produces a radio frequency signal having a frequency which is very nearly equal to the frequency transmitted by the ground unit. The characteristics of the superregenerative repeater 110 are such that the phase of the oscillator frequency output is controlled by radio frequency signals received by the repeater 110 at the instant of energization. The result is that the repeater 110 produces a series of pulse modulated radio frequency signals. Each pulse consists of a wave train having an initial phase which is equal to the phase of the carrier as received by antenna 60 from antenna 54. The signal radiated by antenna 60 is then received by antenna 54. The signal received by antenna 54 has a carrier wave whose phase differs from the phase of the output of oscillator 51, the phase shift being due to the signal transit time from antenna 54 to antenna 60 and back. The signal received by antenna 54 is conducted to circulator 53 and then to mixer 55 where it is combined with the output of oscillator 51. The result of this mixing of the oscillator frequency signal and the pulse modulated superregenerative repeater frequency signal is a signal having three main components; a signal at twice the doppler frequency, a signal having a frequency equal to the superregenerative oscillator modulating frequency (the quench frequency) plus twice the doppler frequency, and a signal having a frequency equal to the quench frequency minus twice the doppler frequency. By using the last pair of frequencies rather than the doppler frequency, it is possible to amplify the information signal at the quench frequency which is much higher than the doppler frequency, and thus to avoid the problem of microphonics which exist at the doppler frequency and to utilize a narrow band amplifier. After amplification in the amplifier 76, the envelope of the resultant signal is detected by the amplifier S6 in the circuit 73 to produce a resultant signal having a maximum energy at a frequency of four times the doppler frequency. This signal furnishes the intelligence by which the counters and comparators determine the proper missile-motor separation time. At separation time, the command unit supplies a signal that modulates the amplitude of the signal transmitted by oscillator 51. This signal is detected by the superregenerative oscillator, then amplified and filtered by the command detector 59 and transmitted to the booster cutoff control 70 to execute the separation command.  
  The circuit of FIG. can be modified so as to provide correction for errors in missile distance traveled at the time when the missile achieves cutoff velocity. Such a modification is shown in FIG. 9 wherein the added circuitry serves to vary the time of missile booster cutoff so as to correct for such displacement errors. In FIG. 9 a doppler cycle counter 105 is connected to the output of generator 63 in such a manner as to receive and record the positive pulses produced by generator 63.  
 The output of counter 105 is connected to the input of a digital-to-analog converter 107 which produces a voltage which is directly proportional to the count appearing on counter 105. The output of converter 107 is connected to a subtracting and dividing circuit 109. The circuit 109 is preset to subtract the voltage output of converter 107 from a fixed voltage which is proportional to the predicted distance of the missile from the laucnh point of 5 milliseconds prior to booster cutoff. The circuit 109 also serves to divide the difference voltage by an amount which is proportional to the product of the predicted missile acceleration and time of flight in accordance with equation (12). The resultant output of circuit 109 is therefore proportional to the small change in time of powered flight (A t,,) necessary to correct for small distance errors at time of cutoff, as explained supra in connection FIG. 4b. Counter counts the comparisons produced by circuit 57 in the manner previously described, and is connected to a sawtooth wave generator 119 and a gate 111 in such a manner that when counter 65 achieves its predetermined count it activates the sawtooth wave generator and turns on the gate 111, thereby permitting the output of circuit 109 and generator 119 to be applied to comparator 113. When these two inputs to comparator 113 are equal, comparator 113 generates a signal which activates command generator 58.  
  In order to achieve the desired distance correction it is necessary that information regarding missile velocity be obtained a short time prior to cutoff. This is necessary since, as was explained supra, if the missile has traveled further than its predicted distance in reaching cutoff velocity (if acceleration is too low) then it is necessary to effect the cutoff prior to the predicted time. It has been found that by adjusting the count produced by circuit 61 of FIG. 5 so that an output is produced at terminal 96 of comparator 57 when the missile velocity corresponds to the desired velocity 5 milliseconds prior to cutoff, a sufficient time delay is produced to effect the desired correction. Keeping in mind that the counter 65 when used in the circuit of FIG. 9 is acti vated when the missile achieves this velocity rather than cutoff velocity, the operation of the circuit of FIG. 9 will be explained in connection with the diagrams of FIG. 10. At the instant when the counter 65 of FIG. 9 achieves its predetermined count it activates the sawtooth wave generator 119 and the gate 111. At this instant the output of circuit 109 produces a signal which is proportional, in both magnitude and polarity, to At, of equation 12). If the missile has traveled further than the predicted amount, the output of circuit 109 will be negative; conversely, if the missile has traveled a shorter distance than expected the output will be positive. When activated, the generator 119 will produce a linear sawtooth wave which begins at a preset positive value and passes through zero 5 milliseconds after initiation. The output voltage of generator 119 then continues increasing in a negative direction until at least 10 milliseconds after initiation. This voltage, shown in FIG. 10a, serves as one input to the comparator 113. FIG. 10b shows the relation between the voltage V representing the predicted distance of the missile from the launch point 5 milliseconds before the missile reaches cutoff velocity, the voltage V representing the actual distance of the missile at that instant for a booster which has produced a lower than normal acceleration, and the voltage V representing the distance at that instant for a booster which has produced a higher than normal acceleration. FIG. 100 represents the result of the subtraction process in circuit 109. Thus, V represents a positive volgate having a magnitude which is equal to the difference between the voltage V,, and the voltage V while the voltage V A is a negative voltage i&#39;epresenting the difference between the voltage V minus the voltage V When the missile achieves that velocity from which it will reach cutoff velocity in milliseconds, the counter 65 activates the wave generator 119 and the gate 111, impressing the output of the generator 119 and the circuit 109 on the comparator 113. The comparator 113 is of the type which adds the two input signals and generates an output on lead 97 when the sum becomes less than zero. Either the subtractor 109 or the comparator 113 might include a simple voltage divider circuit to transform the voltage V to a voltage representing Ar,,. A preset voltage divider is adequate for this purpose since both the value of acceleration a and time of flight I in equation 12) were considered to be constant. The result of the summation of the sawtooh voltage of FIG. 19a and the voltage corresponding to At, in comparator 113 is shown in FIG. d, for three different cases. Thus, curve 86 represents the sum of the saw tooth wave with a positive voltage, representing the situation when the missile is below its predicted distance, the curve 87 represents the sum for zero distance error and the curve 88 repre sents the sum of the sawtooth wave with a negative voltage, representing the situation when the missile is beyond its predicted distance. From observation of curve 86 it may be seen that when the missile is below its predicted position the cutoff will not be effected until some time after the preset 5 millisecond delay, thus permitting the missile to achieve a slightly higher velocity in order to correct for this deficiency in distance. Conversely when the missile has traveled too far during its powered flight stage the cutoff will be effected earlier than predicted, as is the case with the curve 88. When the voltage VM is 0, the missile distance exactly corresponds to the predicted distance and cutoff will be effected at the predetermined time, This condition is indicated in FIG. 10d by the curve 87.  
  FIG. 11 shows one suitable form which the comparator 113 might take. In this figure input terminal 12] receives the output waveform from generator 119, while the input terminal 128 receives a voltage which is proportional to the required change in time of powered flight A1,. A circuit 129 represents one form of voltage divider which might be used to convert the voltage representing the distance error to a voltage representing the incremental change in flight time. This voltage divider, or its equivalent, could be incorporated in the comparator 113, as shown in FIG. 11 or it could be incorporated in the circuit 109. The voltage applied at terminals 121 and 128 are conducted through equal resistors R, and R to terminal point 126 where their algebraic sum appears. So long as this sum is of positive polarity, all of the current appearing at terminal 126 will be conducted throught diode D and the voltage at terminal 126 will be maintained at a low value. As soon as the voltage on terminal 126 becomes less than zero, or negative, the diode D will cease to conduct and its effective resistance from terminal 126 to ground will increase sharply, thus causing an increased voltage to appear across this diode and a signal to be conducted along line 97. As has been previously discussed, the signal appearing on line 97 will activate the command generator 58 of FIG. 5 and cause the missile booster to be cut off.  
  The counter of FIG. 9 could be of exactly the same form as the counter 65. The converter 107 is well known in the art and could be of the type shown in Huskey and Korn, Computer Handbook, page 6-44 (1962). The subtractor circuit 109 is also basic component in the art and could consist of an inverter and adding amplifier, or an adding amplifier, or an adding amplifier, one input to which is fixed-amplitude negative voltage. The gate 111 could be of the type shown in Terman, Electronic and Radio Engineering, page 659 (I955). The sawtooth wave generator 1 19 could be any of the types shown in Terman, op. cit. supra, at pages 615-51.  
  It should be obvious that the circuit modification of FIG. 9 could easily be incorporated in the circuit of FIG. 8, so that a system could be constructed to correct for both velocity and distance errors while using a supperregenerative repeater in the missile unit.  
  It will be apparent that the embodiments shown are only exemplary and that various modifications can be made in construction and arrangement within the scope of the invention as defined in the appended claims.  
 We claim as our invention:  
  1. A missile propulsion control system which terminates the powered flight of a ballistic missile at the optimum time to cause the resulting trajectory of the missile to intercept a predetermined targer area comprising:  
 a. microwave signal generator means for generating a high-frequency output signal;  
 b. antenna means connected to said microwave signal generator means for radiating said high-frequency output sign] in the direction of the missile and for receiving signals from the missile;  
 0. means connected to said microwave signal generator means and to said antenna and responsive to said high-frequency output signal and to the received signals for producing a variable frequency output signal which is indicative of the rate of change of phase between said high-frequency output signal and the received signals, the change in phase being caused by the velocity of the missile;  
 d. pulse generating means connected to said means for producing a variable frequency output signal for generating a first series of pulses which correspond to first alternate zero crossings of said variable frequency output signal and for generating a second series of pulses which correspond to second alternate zero crossings of said variable frequency output signal;  
 e. counting means connected to said pulse generating means for counting at a predetermined rate upon the occurrence of every pulse of said first series and for producing an output pulse when a predetermined count is achieved;  
 f. comparator switch means connected to said pulse generating means and to said counting means for producing an output coincidence signal when said output pulse of said counting means coincides with a pulse of said second series, said output coincidence signal representing the instant when the missile achieves cutofi&#34; velocity; and  
 g. means connected to said comparator switch means and responsive to said output coincidence signal for terminating the powered flight of the missile.  
 2. A missile propulsion control system as recited in claim 1 further comprising:  
 a. second counting means connected to said pulse generating means for counting one of said series of pulses and for producing an output voltage signal which is directly proportional to the number of pulses counted, said output voltage signal thereby being proportional at every instant to the distance traversed by the missile;  
 b. computing means connected to said second counting means for producing a signal representing the change in powered flight time required at the instantaneous position of the missile assuming at every instant that the missile has achieved a predetermined cutoff velocity; and  
 c. means connected to said comparator switch means and to said computing means and responsive to said output coincidence signal and said signal representing the change in powered flight time for actuating said means for terminating the powered flight of the missile at a time equal to the sum of the time of occurrence of said output coincidence signal and the change in powered flight time as represented by the signal produced by said computing means.  
 3. A system as recited in claim 2 wherein said computing means comprises:  
 a. subtracting means connected to said second counting means for subtracting the output voltage of said second counting means from a fixed voltage which is proportional to the predicted distance of the missile from the launch site at a predetermined period of time just prior to the instant when the missile achieves cutoff velocity and for producing an output difference voltage; and  
 b. dividing means connected to said subtracting means for dividing said difference voltage by a voltage which is proportional to the product of the predicted missile acceleration and time of flight and for producing an output quotient voltage, said quotient voltage being said second indication.  
 4. A system as recited in claim 3 werein said means for actuating said means for terminating the powered flight of the missile comprises:  
 a. sawtooth wave generating means and connected to said comparator switch means for producing an output voltage which varies as a linear function of time when said comparator switch means produces said output;  
 b. comparing means connected to said sawtooth wave generating means and to said dividing means and controlled by said comparator switch means for producing a comparison signal when the output voltage from said sawtooth wave generating means and said quotient voltage are equal said means for terminating the powered flight of the missile being connected to said comparing means and responsive to said comparison signal;  
 . command generator means stationed at the launch site and connected to said third comparing means for modulating the transmitted microwave signal at a command frequency at the instant when said third indication is produced; and  
 d. command detecting means mounted on the missile for detecting the modulated signal and for terminating the powered flight of the missile on detection of the modulated signal.  
  5. A missile propulsion control system as recited in claim 4 wherein said means for terminating powered flight comprises:  
 a. command generator means connected to said comparator switch means for modulating said highfrequency output signal generated by said microwave generator means with a command signal at the instant when the missile achieves cutoff velocity: and  
  b. command detecting means mounted on the missile 35 for detecting the modulating command and for terminating the powered flight of the missile on detection of the modulating command signal.  
  6. A missle propulsion control system as recited in claim 5 further comprising: transceiver means mounted on the missile and connected to said command detecting means for receiving the signal radiated by said antenna means and for transmitting back toward said antenna means a series of pulse modulated, microwave frequency wave trains, the initial phase of each of said wave trains being controlled by said signal received by said transceiver means.  
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