Patent GB-870302-A (GB)
Title: Electric analogue computer for determining the apparatus position of a satellite
IPC: G01C21/00
Filed: 1959-04-13
Abstract: 870,302. Analogue computers. COLLINS RADIO CO. April 13, 1959 [July 23, 1958], No. 12472/59. Class 37. A computer for computing the position of a satellite (in terms of the declination and the hour angle T) with respect to an observer in terms of a co-ordinate system which has its origin at the observer's location O which involves the conversion of one co-ordinate system to another. Theory.-The radius vector r (Fig. 1), is defined as extending from the centre O of the earth to the satellite 10, the latter having an orbit 11. The components of the vector r are first defined in terms of co-ordinates lying in the orbital plane (X1X2) of the satellite, the coordinate X1 (13) being so directed that it lies both in the equatorial plane (X1<SP>11>X2<SP>11>) and the orbital plane (X1X2) and the co-ordinate X2 (14) lying perpendicular to X1 in the orbital plane. The X2 component is then resolved into rectangular components in the (X2<SP>1>X3<SP>1>) plane, which is perpendicular to X1 at the origin of the X2 co-ordinate, said rectangular components being 16, 17 in the X3<SP>1>X2<SP>1> co-ordinates respectively, where X3<SP>1> (or north) is parallel to the axis of rotation of the earth and X2<SP>1> lies in the equatorial plane. The angle between 14(X2) and 17(X2<SP>1>) is # (equal to the angle of inclination of the orbital plane to the equatorial plane, so that 16 is equal to X2 sin # (14 sin #) and 17 to X2 cos # (14 cos a). The X1 component 13 and the X2<SP>1 >component 17 (both of which lie in the equatorial plane) are then rotated by an angle # which is the angle between component 13 and the meridian 20 of the observer location (until one component coincides with the observer's meridian) and is equal to # - y where # is the angle between the vernal equinox r and meridian 20 and y that between the vernal equinox rand co-ordinate X1<SP>1> the rotated components therefore having co-ordinates in the terrestrial sphere. Component X1<SP>11> (20) is equal to X1<SP>1> cos #+X2<SP>1> sin # and X211 (24) to X2<SP>1> cos # - X1<1> sin #. The components X1<SP>11>, X2<SP>11> and the " north " component 16 of Fig. 1 (or X3<SP>11>) therefore define the position of radius vector r with respect to the centre of the earth. The components X1<SP>11>, X2<SP>11>, X3<SP>11> are then translated into components X1<SP>111>, X2<SP>111>, X3<SP>111> of a system having its origin at the observer's location and each lying parallel to the respective components X1<SP>11>, X2<SP>11>, X3<SP>11> in the terrestrial sphere. The components shown for vector d extending from the observer location to satellite 10 (Fig. 2) are X1<SP>111> (21) X2<SP>111> (22) and X3<SP>111> (23). The length of 21 is equal to the length of 20 in the equatorial plane less R1, the length of 22 is identical with 24 in the equatorial plane and the 'length of 23 is equal to the length of 16 in the equatorial plane less R3 where R is defined as the vector from the centre of the earth to the observer's location and R1 = R cos #, R2 = R sin #, # being the angle between R and the X1<11> co-ordinate (or meridian of the observer's location). Computer (Fig. 5). The main elements in the computer are electro-mechanical resolvers 31- 35 inclusive. Resolver 31, for example, has stator input windings 36, 37 at an electrical 90 degrees to one another coupled to a pair of rotor output windings (also at 90 degrees to one another) and wound on a. shaft 40. Small compensating windings 41, 42 are coupled to input windings 36, 37 respectively and connected in the feedback circuits of buffer amplifiers 43, 44 respectively, the output of which is connected to a respective input winding 36, 37. The operation of the circuit for solving the satellite problem is as follows : an A.C. voltage of amplitude r is applied from potentiometer 48 to the input 45 of resolver 31, the other input thereof being earthed so that the induced rotor output voltages of resolver 31 have amplitudes corresponding to rectangular components of r (i.e. 13, 14) the direction of the output coordinate system (corresponding to angle between co-ordinate X1 (13) on equatorial plane X1<SP>11>X2<SP>11>and the satellite 10). The output voltage corresponding to 14 is applied to one input of resolver 33 (the other input being earthed) the rotor output windings corresponding to the equatorial and north components 16, 17 (or 14 sin #, 14 cos #) the rotor shaft being rotated through an angle a corresponding to the angle of inclination of the orbital plane to the equatorial plane. The voltage corresponding to component 13 (lying in the equatorial plane and that corresponding to component 17 (also in the equatorial plane) are each applied to one input winding of resolver 32 which translates these components into a second set of rectangular co-ordinates rotated through angle # (# - y) by the rotor shaft setting 57. One rotor output voltage of resolver 32 corresponds to component 24 and the other to component 20, and relate to a co-ordinate system having its origin at the centre of the earth. In order to translate this into one having its origin at the location of the observer, the voltage corresponding to component 24 is applied to one terminal of an input winding and a voltage corresponding to R1 (derived from potentiometer arm 49) to the other terminal (to give 21), a voltage corresponding to 20 (equal to 22) being applied to the other input winding. The rotor shaft 65 is driven by a servo system 67, 68, 69 until the voltage across output winding 66 is zero. The voltage across the other output winding will therefore be equal to the vector sum of the input voltages, that is, it will be equal to S the vector sum of 22 and 21 and the position of shaft 65 will correspond to angle T (the hour angle). The output S of resolver 34 is applied to one input winding of resolver 35, one terminal of the other input winding being supplied with a voltage corresponding to 16 and the other terminal with a voltage corresponding to R3 (from potentiometer 50) so that the difference corresponding to 23 will be the actual input to that winding. The output voltage of one output winding of resolver 35 is nulled (as in resolver 34) the output of the other therefore corresponding to the vector sum of the input voltages to the resolver, i.e. to 23+S and therefore to d, and the position of the rotor shaft 74 to the declination.