900,047. Automatic steering control systems; phase-sensitive circuits. NORTH AMERICAN AVIATION Inc. April 20, 1959, No. 13397/59. Class 38 (4). [Also in Groups XXI, XXXVI, XL (b) and XL (c)] Relates to a fire-control system for automatically maintaining a rocket-firing interceptor aircraft on a lead collision course or a lead pursuit course relative to a target aircraft. A lead collision course is one in which the interceptor approaches the target on such a path that when the rocket is automatically fired it follows a path which is an extension of the interceptor path and collides with the target. As shown in Fig. 47B, 514 indicates the present position of the target and 517 indicates its position at a subsequent " timeuntil-hit " T assuming that the target follows a rectilinear track at a constant velocity #V B ; 513 indicates the present position of the interceptor, 515 indicates its position when the rocket is fired and 518 indicates the position it would have reached at the time of hit T if it had maintained its course after firing the rocket. It is seen that where #V I is the velocity vector of the interceptor, R is the " present range " vector of the target from the interceptor and #R A is the " advance range " vector, i.e. the vector from the point 518 to the point 513. The magnitude R A of the vector #R A is given by Vo.Tf, where Vo is the average velocity of the rocket relative to the interceptor and Tf is the time of flight of the rocket; in the lead collision mode described a predetermined value of Vo.Tf is set in manually. A lead pursuit course is one in which the interceptor follows the shortest path to approach the target from behind and is such that the rocket is always aimed with the proper lead angle so that it may be fired at any time. For such a course T= Tf and equation (1) applies if the substitution is made; in the lead pursuit mode described the value of R A =VoT# which makes T=T# is computed automatically. The system disclosed comprises:- (1) an automatic tracking pulse radar which determines the present target range R, Fig. 47B, and maintains the tracking axis i of the radar directed at the target; (2) rate gyros mounted on the radar tracker for determining the angular rates of rotation # i , # j , # k of the orthogonal tracker axis i, j, k. (3) a prediction computer responsive to R, R, # i , # j , # k , the computed true airspeed V I of the interceptor, the azimuth # and elevation Á of the tracking axis i relative to the aircraft orthogonal axis x (roll axis), y (pitch axis), z (yaw axis) and the (undetermined) time-until-hit T to give R Ax /T,R Ay /T and R Az /T, where R Ax , R Ay and R Az are the x, y, and z components of the " advance range " vector #R A , Fig. 47B; (4) a time-until-hit servo responsive to the computed R Ax /T and to the manually-set (lead T collision mode) or computed (lead pursuit mode) input R A =Vo.Tf giving the time-until-hit T which is applied to the prediction computer thereby closing the loop to determine the outputs therefrom; R Az (5) means for combining the outputs- and T R Ay -from the prediction computer with the T pitch and yaw components of the ballistic jump function J/T and gravity drop functions (see below) to give pitch and yaw steering error signals # z and # y which are applied to the auto pilot to maintain the correct course; the steering error signals # y and # z are related to the y and z components of the computed miss distance M, Fig. 38, by In the load collision mode the time of flight Tf of the rocket is computed, Fig. 40 (not shown), as an empirical function of the manual input RA = Vo.T#, the computed airspeed V I , the computed air density ratio #/#0, the average temperature Tp of the rocket propellant (preset) and sin #, where # is the measured pitch angle and the rocket firing circuit is automatically actuated when the computed time of flight Tf is equal to the computed time-unit-hit T. In the lead pursuit mode the input R A =VoT# to the time-of-flight servo is automatically adjusted so that the value of Tf derived therefrom is equal to the value of T derived therefrom in the time-until-hit servo. The pitch and yaw jump functions Jz/T and Jy/T are computed, Figs. 41 and 42 (not shown) in accordance with the following equations:- where V R = Vo+V I is the velocity of the rocket relative to the air space; α is the computed angle of attack of the interceptor, i.e. the angle between the heading line 284, Fig. 38, and the course line 285; # is the preset angle the rocket launching pod makes with the z axis of the interceptor; f is the launching factor; when a rocket is launched in the direction 286, Fig. 38, the heading of the rocket " jumps " by an amount f(α - #) towards the course line 285 so that the initial path of the rocket is along the line 287; in computing the pitch jump function f is computed as an empirical function of the interceptor velocity V I and the measured state pressure P#; in computing the yaw jump function f is assumed to be a preset constant; # is the computed angle of skid. The pitch and yaw components of the gravity drop function are given respectively by G G -cos # cos # and - cos # sin #, where G is an T T empirical function of Vo.Tf, # is the pitch angle and # is the roll angle. Radar, Figs. 4, 6, 13, 15 and Figs. 2, 3, 5, 7, 8, 9, 10, 11, 12, 14, 16, 17 (not shown).-The pulse radar transmitter is coupled to a rectangular TE 01 waveguide 47, Fig. 4, which is coupled by a tapered section 48, Fig. 13, to a rectangular section 49 of increased vertical (E) dimension having a horizontal partition 56, Fig. 13 (side elevation), to form in effect two contiguous rectangular TE 01 waveguides which are coupled by a tapered section 52 to a corresponding structure 36 of increased horizontal (H) dimension such that the two contiguous rectangular waveguides 38, 39 are each capable of sustaining TE 01 and TE 02 modes. The vertical (E) dimensions of the waveguides 38, 39 are then progressively reduced in a tapered section 35, Fig. 7 (not shown), and the ends of the waveguides 38, 39 are folded back and coupled respectively to rectangular apertures 33, 34 in a matching plate 40, Fig. 6, at the focus of a paraboloidal reflector 22, the vertical dimensions of the apertures 33, 34 in the plate 40 being stepped, as shown in Fig. 6, to effect impedance matching. Suitable dimensions for the component parts of the aerial system are given to obtain a 5-6% bandwidth at X band frequencies. During transmission a TE 01 wave is transmitted through the waveguide system to produce a pencil beam symmetrical with respect to the aerial i axis, Figs. 9 and 10 (not shown). If the target is on the i axis then the echo will produce cophasal TE 01 waves in the waveguides 38, 39. If the target is displaced in azimuth, Fig. 9 (not shown) then in each waveguide 38 and 39 there are produced both a fundamental TE 01 wave and a secondary TE 02 wave, Fig. 15, and the TE 02 wave is coupled out through slots 53, 54, Fig. 15, to induce in the side arm 55 of a " duo mode " bridge 21 a secondary TE 01 wave whose amplitude and phase sense relative to the primary TE 01 wave passing through the bridge 21 is proportional to the magnitude and sense of the azimuthal misalignment. If the target is displaced in elevation, Fig. 10 (not shown), then the echo will produce in the waveguides 38 and 39 primary in-phase TE 01 waves (shown by solid arrows in Fig. 13) and out-of-phase TE 01 waves (shown by dotted lines 58 in Fig. 13). At the end of the partition 56, Fig. 13, the primary in-phase waves will combine and travel down the main waveguide 47 but the out-of-phase waves will interact to produce a curved field 59 which induces in a rectangular side arm 20 (horizontal E dimension), Fig. 11 (not shown), a wave whose amplitude and phase-sense relative to the primary wave is proportional to the magnitude and sense of the elevation misalignment. The outputs from the main guide 47 and the side arms 55 and 20 are heterodyned in separate mixers, Fig. 3 (not shown), with outputs from a common local oscillator and applied to separate azimuth and elevation phase-sensitive rectifiers, Fig. 14 (not shown), to give corresponding error signals. Each phase-sensitive rectifier comprises two oppositely-poled rectifiers. The reference input from the main guide 47 is applied in push-pull to the two diodes, the error input from the side arm 20 or 55 is applied in parallel to the diodes and the D.C. output is applied from the junction of two load resistances connected across the diodes through an R.F. choke to a cathode follower. The signal derived from the output from the main guide 47 is also applied to any suitable ranging circuit to give a voltage representing the present target range R. Prediction computer and ballistic circuits, Figs. 35-38 and Figs. 39-41 (not shown).- The first step in the prediction computation is to compute the smoothed components along the radar axes i, j, k of the target velocity #V B . #V B is given by the vector equation As shown in Fig. 35, electrical signals proportional to the angle of attack α and the angle of skid # are applied to potentiometers 234 and 235 which together with potentiometer 232 are controlled by a mechanical true air speed signal V I giving output signals Via, V I # and V I which are applied to resolvers 229, 231 set respectively in accordance with the azimuth # and elevation Á of the radar tracker to give electrical outputs V Ii , V Ij and V Ik . Mechanical signals # i , # j , # k are produced by a servo 215 controlled by the rate gyros 212, 213, 214, an electrical signal R is produced by differentiating at 216 the electrical range signal R from the radar and electrical signals B# j and R# k are derived from the signals R, # j and # k in the multipliers 221 and 222. The resultant signals are then combined according to equations (6), (7) and