Rendezvous and Docking for Ats-V Despin
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STUDY OF AUTOMATED RENDEZVOUS AND DOCKING FOR ATS-V DESPIN N7 1-29 6~ 1 AA~I~?J~B. R) - - ----- U (PIES C I(NASA CRO RI RADNUBR (CATEGORY) FINAL REPORT VOLUME 2 OF 2 I SD 71-286, S Rproduediby- INFORMATIONNA~OA TECHNIAL SERVICE U S Deportment of Commerce Springfield VA 22151 k SpaeDMaRon 1014NortAmerican RlodCl @l Space Division North American Rockwell FINAL REPORT ON A STUDY OF AUTOMATED RENDEZVOUS AND DOCKING FOR ATS-V DESPIN Volume 2 of 2 Volumes Appendices February 1971 Contract NASW-2136 Prepared for NASA Goddard Space Flight Center Greenbelt, Maryland ?: SD 71-286 A1b Space Division @IN NorthAmencan Rockwell PREFACE NR has completed a study in accordance with the Statement of Work in NASA Contract NASW-2136, "Study of Automated Rendezvous and Docking for ATS-V Despin". Work was performed for NASA Headquarters under the technical direction of J. R. Burke and for the NASA Goddard Space Flight Center under the techni cal direction of J. Phenix. Their contribution and guidance to the study is gratefully acknowledged. This final report, SD 71-286, presents the results of the study. It consists of 2 Volumes: Volume I - Text; Volume 2 - Appendices (Calculations and pertinent reports generated during the study). This is Volume 2 - Appendices. SD 71-286 Space Division 9 NorthArnencan Rockwell CONTENTS Appendix A - Spin Axis Precession For Required Apogee Burn Attitude Appendix B - Simulation Requirements Document Appendix C - Piloted Docking Simulation Study Appendix D - Post Contact Docking Analysis Appendix E - Typical Procurement Specification PRECEDIG PAGE BLANK NOT FILMED V SD 71-286 i%Space Division North American Rockwell APPEND IX A SPIN AXIS PRECESSION FOR REQUIRED APOGEE BURN ATTITUDE As described in Section 2 of the report, the RMU spin axis must be rotated through 1480 during the transfer orbit. The torque vector must be applied along an axis normal to the major axis of the transfer ellipse, normal to the spin vector in the plane of desired precession. Because of the spin, the torque is applied by means of periodic synchronized torsional reaction jet impulses. The angular velocity of the RMU about its spin axis, WN, will be between 40 RPM and 60 RPM. The sun sensor will be used to synchronize the cycling of the applied couples. Since this precession will be initiated soon after perigee injection, an almost full propellant load will exist with a resulting nominal pressure of 170 psi. The corresponding mean-thrust level for intervals greater than 100 m-sec will be approximately 1.8 lb force per thruster. The distance between thruster pairs about the transverse axis is 54.4 inches. Thus, the expected nominal torque Tnom during the time the couple is applied is: T = 4x 1.8 = 8.1ft-Ibs nom 12 Consider the precession scheme where four sets of two actuators are sequenced to produce couples, -r/2 radians of spin apart. This sequence could cycle let numbers (1-8), (7-6), (5-12), (2-10) in that order (seereaction jet logic, Section 7). Note that any wobble-countering couple required during the time the precession takes place can be obtained from the respective alternates of the above sequence, namely (3-9), (3-11), (4-11), (4-9), without interferring with the precession cycle. Let 9 th denote the half-angle of spin over which the couple acts. Let & (A0) denote the precession angle obtained per revolution of the RMU. Then, gth 8 Tno m Wx Cos (wxt)dt= 8 Tnom Sin L cXxlx Ix x Here Tnom = nominal torque 8.1 ft-lbs A-1S SID 71-286 Space Division ?D North Amencan Rockwell 2 of inertia about spin axis - 57 flug-ft Ix = moment w = spin rate = 60 rpm nominal and 40 rpm minimum 9 So that from (1), 6 (.) = .0288 (Sin th ) rad/rev x 60 rpm 9 .0648 (Sin th) rad/rev (OWx= 40 rpm) The number of .revolutions required to achieve a given precession angle AO is then: .A0A(Nrev)A$(the total number of precession increments =4 Nrev) Thn total time required to complete a precession thru AO is: tpr =(N)ev 2 Tr 7 (. x 4 InomSin 0th So that for (A$) = 148 deg = 2.58 rad (Nrev) = 89.6 (for o =60 rpm) re14 8 0 = 8- x, = 39.8 (for wx =40 rpm) Sin 9th Similarly: (tprpr)1480 Sin89.6 gthx' sec (for co =60 rpm) - 59.7__ sec (for w =40 rpm) Sin 9th x The propellant weight required to achieve a given (A $) is: 2 W = F tpr 8 gth . , where Is= spec impulse of propellant prpsp = 200 sec (assumed) Fa = force per actuator = 1.8 lbs (assumed) A-2 SD 71-286 Space Division NorthAmerican Rockwell So that for A 1480 (Wprop) 1480 = 2.06 )bs1h for (& = 60 rpm) = 1.37 (St 9 th Ibs for = 40 rpm A plot of (tpr)148a and (Wprap) vs 9 th is shown in Figure 2-10. A near optimal choice is 9th = 450* Here (tpr) is a near minimum with no appreciable cost in propellant weight increase. For the purpose of this analysis, the precession trhusting half-angle is assumed fixed at gth = 450 for the open loop precession to achieve A,0 = 148 degrees. The following parameters then result for the 1480 open loop precession W =60 rpm W =40 rpm x x Time to complete A '=1480, (tp) 148o 126 sec 84 sec Total number of precession increments, N I =4N rev- 507 225 Magnitude of precession increments = 1/4 8 (A ) 5.08 mr 11.45 mr Impulse bit time interval per increment 250 m sec 375 m sec Precession Error Analysis The error in orientation after precession consists of a component in the precession plane, Ee and a pointing error normal to the precession plane, e . It will be con venient t6 represent tkese two error angles as vectors, a permissible approximation since these will be small angles (e8 < e4, < 1/4 rad). All error quantities are assumed 3 a values. A-3 SD 71-286 Qh Space Division " NorthAmencan Rockwell The individual contributors to this attitude error are identified as follows: Pal 1. Error due to POLANG Attitude Determination - E0 The value of this total error after a minimum of 1.5 hours of ground station POLANG smoothing can be assumed at 0.50 or = 8.7 mr. Since the POLANG sensitive axis is nearly normal to the spin when the measurement is required, a propagation coefficient of 1 .0 is used so that Pal E =8.7 mr No capability for measurement in the 9 direction is provided. SSA SSA 2. Error due to sun sensor attitude determination, E E ) Since the sun direction = 450 with respect to the nodal line and the apogee spin orientation (where measurement is required) is at -22 degree from the equatorial plane, the sun sensor error propagation coefficient is approximately 1/Sin 500 = 1.3 for both 9 and $ directions. With an expected instrument error of 0.5 degree, this results in: SSA SSA = = 11.3 mr 3. Error due to sun sensor error in synchronizing precession torque axis, SSP E If the precession vector is constantly offset by 0.5 due to sun sensor error (pessimistic), the accumulated error normal to the precession plane is (0.5/57.3) A$, So: SSP SSP =0, 6 = 0.00873 (A (P ) mr 4. Errors due to the actuator pairs supplying the precession torque increments. These error contributions are best described as four individual contributions: "A-4 SD 71-286 d& Space Division North Amencan Rockwell (a) Impulse bit repetition error due to the variation in the average force from given actuator from the expected mean for any given increment. The expected maximum repetition error is 6%. Since two independent actuators form a given couple, the resulting torquing uncertainy is: 1 x 06 = .0415,; and is averaged over the total number of increments, N1 for a given A, Further, this error contribution is confined to the O-plane only. Thus, the impulse bit repetition error becomes afr afr 60 S -0,_ A mr (b) Impulse bit bias error for a given actuator is assumed as 4% max. This bias is correlated for a given actuator with the eight individual jets independent of each other. Again, this contribution is confined to the $-plane so that: afb afb 40 E9 01 E = (A0) mr. (c) Impulse bit centroid repetition error. This contributor is confined to the 9-plane since centroid shift timing for a given torque increment is equiva lent to a shift in the precession axis. The magnitude of the max centroid shift from pulse-to-pulse is assumed at 6%. It results in precession axis tilt of [6 (0th)] where 9 th is spin angle corresponding to the pulse width - 450 . This error is averaged over the total number of pre cession increments. The term arises from the two jets used for a given increment. Thus, the impulse bit centroid repetition error becomes: acr acr 47.2 ( A mr, E0 -0 2WI (d) Impulse bit centroid bias error. This contributor again is confined to the 9 plane. It is correlated for a given actuator and averaged over the eight ihdependent jets used per spin cycle. The maximum magnitude of the centroid bias is 4%. Thus acb acb 31.4 ()mr, 0 A-5 SD 71-286 0 Space Division North Amencan Rockwell (5) Torquing Increment Quantization error. The maximum value of this con tributor is simply 1/2 (precession increment), so that aq aq E =0, E 2.5 mr (for wx=60rpm) 5.7 mr (for w = 40rpm) x (6) Torque Integration Error.