Reports/Apollo 17/Apollo-Saturn V Postflight Trajectory AS-512

Reports/Apollo 17/Apollo-Saturn V Postflight Trajectory AS-512
Jump to: navigation, search
This page is still under development.

Contents

Document No. D5-15560-12
Apollo/Saturn V Postflight Trajectory — AS-512
Saturn V Contract No. NAS 8-5608 , Schedule II, Part IX, Task Directive 290 (Part A)
Tracking and Flight Reconstruction
G. T. Pinson
April 11, 1973
D. E. Chichester, Manager, Flight Technology
Boeing Company Space Division Launch Systems Branch
D5-15560-12

[edit] Abstract

This document presents the postflight trajectory for the Apollo/Saturn V AS-512 flight. Included is an analysis of the orbital and powered flight trajectories of the launch vehicle and the free flight trajectories of the expended S-IC and -II stages. Trajectory dependent parameters are provided in earth-fixed launch site, launch vehicle navigation, and geographic polar coordinate systems. The time history of the trajectory parameters for the launch vehicle is presented from guidance reference release to Command Service Module (CSM) separation.

Tables of significant parameters at engine cutoff, stage separation, parking orbit insertion, and translunar injection are included in this document. Figures of such parameters as altitude, surface and cross range, and the magnitude of total velocity and acceleration as a function of range time for the powered flight trajectories are presented.

  • Apollo/Saturn V
  • AS-512
  • Postflight Trajectory Powered Flight Trajectory Orbital Trajectory
  • Spent Stage Trajectory Apollo 17

[edit] Section 1: Summary and introduction

The Apollo Saturn V AS-512 vehicle was launched from Launch Complex 39, Pad A, at the Kennedy Space Center on December 7, 1972, at 00:33:00 A.M. Eastern Standard Time at an azimuth of 90 degrees east of north. Guidance Reference Release ooscurred at -16.960 seconds. First motion occurred at 0.2 second. A roll maneuver was initiated at 12.9 seconds to place the vehicle on a flight azimuth of 91.503 degrees east of north.

All trajectory parameters were close to nominal from liftoff to parking orbit insertion. The vehicle was inserted into parking orbit at 712.65 seconds at an altitude of 170.5 km (92.1 nmi) and a total space-fixed velocity of 7,804.1 m/s (25,604.0 ft/s). The vehicle remained in orbit for approximately two revolutions. The S-IVB stage was restarted during the second revolution at 11,556.6 seconds.

At 11,917.64 seconds, the vehicle was injected into a near-nominal translunar trajectory at an altitude of 313.7 km (169.4 nmi) and a total space-fixed velocity of 10,837.3 m/s (35,555.4 ft/s). At 13,347.6 seconds, the CSM separated from the launch vehicle at an altitude of 6,605.8 km (3,566.8 nmi) and a total space-fixed velocity of 7,725.1 m/s (25,344.8 ft/s).

The impact location of the spent S-IC stage was determined to be 28.219 degrees north latitude and 73.878 degrees west longitude at 551.7 seconds. The impact location of the spent S-II stage was determined to be 20.056 degrees north latitude and 39.604 degrees west longitude at 1,196.9 seconds.

A more detailed description of the postflight mass point launch vehicle trajectory and launch parameters is given in Section 2. The trajectory is divided into the following phases, each discussed in a separate subsection of Section 2:

  1. Ascent (guidance reference release to parking orbit insertion)
  2. Parking orbit (orbit insertion to S-IVB restart preparation)
  3. Second burn (S-IVB restart preparation to translunar injection)
  4. Translunar orbit (translunar injection to CSM separation)
  5. Free flight (expended S-IC and S-II stages)

The trajectories for the first four of the above phases were established from external C-band radar and S-band tracking data and ST-14M inertial platform guidance velocity data. Since no tracking data were available for the S-IC and S-II spent stages, the trajectory phases outlined in (e) above were simulated using actual separation conditions and nominal drag and retrorocket performance data.

Section 3 contains a description of the trajectory reconstruction methods, a summary of the tracking data used in the analysis with the resulting residual plots, and an estimate of the uncertainty 1 the reconstructed trajectory.

Appendix A provides a definition of the symbols, nomenclature, and coordinate systems used in the report. Appendix B is a tabular nistory of selected trajectory parameters in metric units. Appendix C presents the same parameters expresses in English units.


[edit] Section 2: Trajectory description

This section describes the reconstructed trajectory, referenced to the Instrument Unit, by providing plotted histories of pertinent variables and tables of important parameters at significant event times. The complete time history of selected Observed Mass Point Trajectory parameters, in both metric and English units, is tabulated in Appendices B and C, respectively. These tabulations are given in accordance with "Project Apollo Coordinate System Standards" (PACSS, Reference 1) and are in earth-fixed launch site (PACSS10), launch vehicle navigation (PACSS13), and geographic polar (PACSS1) coordinate systems. Computations of the transformations relating the various coordinate systems are based on the earth's spin axis as it was oriented at GRR. For convenience, these systems are described in Appendix A along with a definition of other terms and symbols used.

A comparison of actual and nominal times for significant flight events is presented in Table 2-I. The actual times for these events are taken from Reference 2. The nominal data and times are taken from Reference 3. Range time, which is referenced to Range Time Zero, is used throughout this documentation unless otherwise specified. Range Time Zero was established at 29:33:00 Greenwich Mean Time on December 6, 1972. The Fischer Ellipsoid of 1960 (Reference 4) is used as the representative model for the earth and its gravitational field. All latitude and longitude coordinates are defined with respect to this ellipsoid.

The geographic coordinates for Launch Complex 39, Pad A, at the Kennedy Space Center are as follows:

  • Geodetic Latitude   28.608422 degrees north
  • Longitude   80.604133 degrees west

The height of the Instrument Unit of the launch vehicle above the reference ellipsoid is 111.65m (366.31 ft).

The azimuth alignments are as follows:

  • Launch Azimuth   90.0 degrees east of north
  • Flight Azimuth   91.503 degrees east of north
  • ST-124M Platform   91.504 degrees east of north Azimuth

The flight azimuth, dependent on the launch time, launch day and month, is calculated using polynomial coefficients taken from the guidance presettings in order to aoshieve the desired translunar targeting parameters. The translunar targeting parameters are functions of the moon position, earth parking orbit inclination, earth-moon distance, and moon travel rate.

[edit] 2.1 Ascent phase

The trajectory parameters from guidance referenose release to parking orbit insertion were close to nominal. The space-fixed velocity and altitude at S-IC OECO were 2.0 m/s (6.5 ft/s) greater than nominal and 0.2 km (0.1 nmi) less than nominal, respectively. At S-II OECO, the space-fixed velocity and altitude were 25.6 m/s (84.0 ft/s) and 0.5 km (0.3 nmi) greater than nominal. The altitude was 0.1 km (0.1 nmi) greater than nominal, and the space-fixed velocity was 0.3 m/s (1.0 ft/s) less than nominal at S-IVB first guidance cutoff signal. The maximum acceleration was 37.95 m/s2 (3.87g) during the S-IC phase.

Some significant trajectory parameters are tabulated in Table 2-11 at key events such as Mach 1, maximum acceleration, etc. Trajectory parameters at engine cutoff times are presented in Table 2-III. Table 2-IV shows trajectory parameters at stage separation times.

To supplement these discrete time tabulations, a number of parameters are plotted over the entire ascent phase. Figure 2-1 shows the vehicle ground track and the location of the tracking stations used in the reconstruction. Altitude, surface range, and cross range are plotted versus time in Figures 2-2 through 2-4, respectively. Space-fixed velocity and flight path angle are shown in Figure 2-5. Figure 2-6 gives total inertial acceleration. Dynamic pressure and mach number are plotted in Figure 2-7. The ascent phase trajectory is tabulated in Tables B-I through B-III in metric units, and in Tables C-I through C-III in English units.

[edit] 2.2 Parking orbit phase

The parking orbit phase spans the inerval from insertion to S-IVB restart preparation at 10,978.6 seconds. Figure 2-8 illustrates the vehicle ground track following parking orbit insertion and shows the vehicle location at significant event times (sae Table 2-1).

The S-IVB/LM/CSM was inserted into a near circular earth parking orbit at 712.65 seconds, 4.09 seconds earlier than nominal. Me earlier insertion time resulted mainly from the greater than nominal S-II performance. The parking orbit insertion conditions were close to nominal. Table 2-V gives the actual parking orbit insertion conditions and provides a comparison with the nominal values.

During the parkin; orbit, no major thrusting occurred; however, the orbit was continuously perturbed by low-level LH2 venting. The resulting small velocity perturbations were considered in this analysis. An acceleration model was built from the ST-124M guidance platform velocity data. The guidance velocity data were fitted in segments by polynomials in time. The polynomials were analytically differentiated to model the component accelerations sensed by the guidance platform. Table 2-VI lists the acceleration polynomials derived by this method. Figure 2-9 reflects the best estimate of the total parking orbit acceleration (rss of components) after modeling biases have been removed.

The parking orbit phase is tabulated in Table B-IV in metric units and in Table C-IV in English units.

[edit] 2.3 Second burn phase

The second burn trajectory phase spans the interval from S-IVB restart preparation at 10,978.6 seconds to translunar injection and is divided into two segments. The two segments are the S-IVB restart preparation segment (10,578.6 seconds to 11,500 seconds) and. the S-IVB second burn powered segment (11,500 seconds to TLI). The S-IVB stage was restarted 1.9 seconds earlier than nominal at 11,556.6 seconds (see Table 2-I for significant event times). The vehicle ground track during this trajectory phase is shown in Figure 2-8 as continuation of the parking orbit phase. Vehicle altitude is plotted in Figure 2-10. Figure 2-11 shows the space-fixed velocity and the flight path angle. Total inertial acceleration is shown in Figure 2-12.

The second guidance cutoff signal conditions, depicted in Table 2-III, were near nominal. Cutoff occurred 2.10 seconds later than nominal with the altitude 5.8 km (3.1 nmi) greater than nominal, the space-fixed velocity 4.7 m/s (15.4 ft/s) less than nominal, and the flight path angle 0.]40 degree greater than nominal. The longer S-IVB second burn was a result of the shortened S-IVB first burn time discussed above.

The second burn phase is tabulated in Tables B-V through E-VII in metric units and Tables C-V through C-VII in English units.

The translunar orbit phase spans the interval from injection to S-IVB/CSM separation. Figure 2-8 shows the ground track continued through this trajectory phase.

Translunar injection occurred at 11,917.64 seconds, 2.10 seconds later than nominal (see Table 2-I). The translunar injection conditions were close to nominal. Table 2-VII gives the actual translunar orbit injection conditions and provides a comparison with the nominal values.

Accelerations during the period between translunar injection and CSM separation were treated as in parking orbit, representing them as segmented polynomials. Table 2-V111 lists these polynomial coefficients and time spans. The best estimate of the total translunar orbit acceleration (rss of components) after modeling biases have been removed is plotted in Figure 2-13.

Trajectory parameters at CSM separation (defined as the end of the launch vehicle trajectory) are listed in Table The translunar orbit phase is tabulated in Tables B-V through B-VII in metric units and Tables C-V through C-VII in English units.

[edit] 2.5 Free flight phases

Postflight predictions of earth surface impact parameters for the spent S-IC and S-II stages were computed using a mass point trajectory simulation computer program. S-IC and S-II separation position and velocity data from the postflight trajectory were combined with nominal main propulsion system decay performance and nominal retrorocket performance to initialize the simulation program.

[edit] 2.5.1 S-IC spent stage trajectory

Three separate theoretical trajectories were computed for the spent S-IC stage. These three trajectories represent the following booster atmospheric entry conditions:

  1. Zero-degree angle-of-attack entry
  2. Ninety-degree angle-of-attack entry
  3. Tumbling entry

The tumbling booster case is considered to define actual case impact conditions although no tracking coverage was available for confirmation. Results of the three computed S-IC spent stage trajectories are summarized in Table 2-IX. The ground track is shown in Figure 2-14.

[edit] 2.5.2 S-II spent stage trajectory

Three separate theoretical trajectories, corresponding to the zero-degree, ninety-degree, and tumbling entry conditions were also computed for the spent S-II stage.

The computed results, assuming a tumbling stage, were considered to define stage impact conditions since no tracking coverage of the spent S-II stage was available.

Results of the three computed S-II spent stage trajectories are summarized in Table 2-X. The ground track is shown in Figure 2-14.

[edit] Section 3: Trajectory accuracy

Trajectory reconstruction is an estimation process with the resulting confidence level or accuracy of the trajectory dependent upon the following factors:

  • Quantity of tracking data
  • Quality of tracking data
  • Consistency between tracking and guidance velocity data
  • Continuity between trajectory phases (boost, parking orbit, second burn, and translunar orbit)

These factors vary from flight to flight so that a rigorous statistical error analysis of the reconstructed trajectory is difficult to obtain. However, the extent to which systematic errors can be identified and corrected, plus random errors averaged out, determines the accuracy of the reconstruction. This section summarizes the results for the AS-512 flight and leads to the position and velocity uncertainties for the reconstructed trajectory. In addition, the basic analysis methods used in the reconstruction are presented in this section.

[edit] 3.1 Trajectory reconstruction methods

The trajectory reconstruction process takes place in three stages:

  1. Initial data preparation
  2. Main analysis
  3. Output data processing

The initial data preparation converts the raw tracking and guidance velocity data to a form compatible with the estimation programs. This includes correction for atmospheric refraction (for OCP and GATE), conversion of doppler count to instantaneous range rate, data editing, and data reformatting.

The main analysis effort is conducted with three separate estimation tools. The tools are:

  1. The Guidance and Tracking Evaluation program that uses a Kalman estimation method to fit C-band and S-band measurements during powered and non-powered flight phases. The GATE program employs the Cowell formulation of the differential equations of motion to model tracker angles, range, and instantaneous range rate.
  2. The Orbital Correction Program that uses a weighted least squares estimation method to fit C-band and S-band measurements during non-powered flight phases. The OCP employs the Cowell formulation of the differential equations of motion to model tracker angles, range, and instantaneous range rate.
  3. The Lunar Impact Determination program that uses a Kalman estimation method to fit C-band and S-band measurements during non-powered flight phases. The LID program employs the Encke formulation of the differential equations of motion to model tracker angles, range, and average range rate.

These three tools were used to iteratively develop the separate powered and unpowered flight trajectory segments. Capability exists with the three tools to incorporate end point constraints as required to provide trajectory continuity and consistency. The residual plots (see Paragraph 3.2.2) depicted in this section were produced with the GATE program for the ascent phase and with the LID program for the coast phases.

After the main analysis is completed, the separate trajectory segments are merged together and transformed to several coordinate systems to provide the output trajectory listings and tapes. Included in this output data processing is a rework of the first 20 seconds of the ascent phase to better represent the early launch portion of the trajectory. Also, the engine start, cutoff, and mixture ratio shift transient areas of the powered flight portions of the trajectory are reshaped in order to better represent the conditions and to incorporate the specific event times.

[edit] 3.1.1 Powered flight trajectory determination

The GATE program is used to determine the powered flight phases of the trajectory (ascent phase and second burn powered'segment). Telemetered guidance velocity data from on-board the vehicle are used as generating parameters in conjunction with a comprehensive gravity model to produce a trajectory to fit the available tracking data. The Kalman estimation scheme is generally used to solve for coefficients of a guidance error model and, when desired, for corrections to initial position and velocity.

[edit] 3.1.2 Non-powered flight trajectory determination

The three above mentioned tools were used for non-powered or coasting orbit determination. The OCP uses a polynomial to represent the non-gravitational accelerations (see Section 2.2). The GATE and LID programs use either polynomial or tabular representatiolAs or the perturbing accelerations. The perturbing accelerations are used in conjunction with a comprehensive gravity model to simulate the trajectory used to fit the tracking data. The estimation techniques are applied to obtain, generally, the initial vehicle position and velocity plus acceleration bias terms. For the AS-512 parking orbit, several iterations were made to determine biases needed to adjust the polynomial accelerations to produce a consistent orbit. It was noted that an additional bias was needed during the latter part of the first revolution and the early part of the second revolution to adequately fit the tracking data. The constant terms of the polynomial were adjusted by the biases specified in Table 2-VI from 712.65 to 11,520 seconds. A subsequent set of iterations were then made to determine the additional acceleration needed from 3,600 to 7,200 seconds. These additional biases are also listed in Table 2-VI.

[edit] 3.1.3 Estimation of trajectory segments

With these three programs, the analysis proceeds by successive iterations to eliminate poor-quality and inconsistent tracking data from the solutions. Other estimation controls, such as relative data weights, are varied from run to run until an overall best-estimate trajectory is obtained. State vectors from adjacent segments can be used in a particular segment and weighted appropriately to provide initial or final constraining state vectors. This constraint feature permits the development of a continuous and consistent trajectory when the segments are later merged.

The criteria for evaluating a particular solution include the magnitudes and shapes of tracking residuals (differences between actual tracking and the reconstructed trajectory), the values of the guidance error model coefficients or polynomial bias terms, and the consistency between the separately estimated trajectory segments. A state vector comparison is used for judging the consistency between the various state vectors developed at time points common to two trajectory segments. Generally, the time points used for this state vector consistency judgment are Earth Parking Orbit Insertion, Restart Preparation (somewhere in Timebase 6), and Translunar Injection.

[edit] 3.2 Trajectory data sources

[edit] 3.2.1 Tracking data - Quantity

Time periods for which C-band radar and S-band tracking data were available for AS-512 reconstruction are illustrated in Figure 3-1. The geographic locations of the tracking stations are shown on ground track Figures 2-1 and 2-8 and are itemized in Table 3-I. Most of the tracking data were used except for isolated points cr for data segments which were inconsistent with adjacent data.

The C-band tracking data were provided in azimuth angle, elevation angle, and range measured parameters. These measurements are defined in Reference 1 and are designated as PACSS3a. The USB tracking data were provided in X-angle, Y-angle, range and range rate measured parameters. These, also, are defined in Reference 1, and are designated as PACSS3c and 3d, for the 30-foot and 85-foot antennas, respectively.

As shown in Figure 3-1, adequate data existed in order to determine the AS-512 trajectory. In general, tracking coverage was redundant except for the second burn powered sejment where no tracking data were available.

[edit] 3.2.2 Tracking data - Quality

Measured parameter comparisons between the tracking data and the reconstructed trajectory were calculated as required in the various PACSS3 coordinate systems. The position components of the trajectory in PACSS10 were transformed into the measured parameters of the PACSS3 system appropriate to each tracker. To more accurately model the tracking measurements, precession and nutation of the earth and aberration effects are modeled in the analysis programs. Residual differences or deviations (observed tracking dats minus calculated tracking data, 0-C) were determined for the various tracking data sets. These residual differences are used for assessing the quality of the tracking data as well as determining how well the reconstructed trajectory fits the data.

The ascent phase measured parameter residuals are shown in Figures 3-2 through 3-9. Merritt Island, Patrick, Grand Turk, Bermuda and Antigua C-band residuals are given in Figures 3-2 through 3-7. Residuals for the Merritt Island and Bermuda S-band trackers are shown in Figures 3-8 and 3-9.

Measured parameter residuals during the parking orbit phase are given chronologically in Figures 3-10 through 3-27. Figures 3-10, 3-11, 3-16, and 3-18 give first pass residuals for the Antigua, Carnarvon, Merritt Island and Bermuda C-band radars, respectively. Carnarvon, Hawaii, Goldstone, Texas, Merritt Island and Bermuda S-band first pass residuals are shown in Figure 3-12 through 3-15, 3-17, and 3-19, respectively, Second pass residuals for the Carnarvon and Merritt Island radars are shown in Figures 3-21 and 3-26, respectively. Ascension, Carnarvon, Hawaii, Goldstone, Texas and Merritt Island S-band second pass residuals are given in Figures 3-20, 3-22 through 3-25, and 3-27, respectively. The translunar phase measured parameter residuals are given in Figures 3-28 through 3-30. S-band residuals for the Ascension and Carnarvon trackers are shown in Figures 3-28 and 3-30. Figure 3-29 shows the Carnarvon C-band radar residuals.

It is to be noted that the above measured parameter residuals for all phases of the flight depict the consistent data sets which were used in the reconstruction of the various trajectory phases.

[edit] 3.2.3 Guidance velocity data

Guidance velocity data throughout the separate trajectory phases were received from the ST-124M inertial platform. The velocity data during the powered phases (ascent and second burn) were used directly by the GATE program as non-gravitational generating parameters. Velocity data during the orbit phases (parking and translunar) were fitted with polynomials and used by the OCP, GATE, and LID programs to provide non-gravitational effects (see Paragraphs 2.2 and 2.4, and Figures 2-9 and 2-13).

[edit] 3.3 Consistency between tracking and guidance velocity data

The consistency between tracking and guidance velocity data can be obtained by examining guidance velocity error plots during powered flight trajectory segments. Thesc error plots give the differences between the guidance velocities from the ST-124M platform and those derived from the reconstructed trajectory which fit the tracking data.

The guidance velocity error plots for the ascent phase had reasonable shapes and magnitudes. The maximum error amounted to 0.8 m/s (2.6 ft/s) in the vertical direction, 2.8 m/s (9.2 ft/s) in the crossrange direction, and 0.2 m/s (0.7 ft/s) in the downrange direction, referenced to the launch vehicle platform accelerometer coordinate system (PACSS12).

The downrange and vertical guidance velocity error plots for the second burn powered segment also had reasonable shapes and magnitudes. The crossrange error component had a reasonable shape, but a larger magnitude than has beer observed on previous flights. Guidance analysis has shown the crossrange error magnitude to be compatible with the ascent phase cross-range error magnitude (Reference 2). Due to the constraint of exactly matching restart and TLI vectors, the velocity errors also reflect trajectory uncertainties at 11,500 seconds and TLI. The maximum error amounted to 1.1 m/s (3.6 ft/s) in the vertical direction, 11.8 m/s (38.7 ft/s) in the crossrange direction, and 1.4 m/s (4.6 ft/s) in the downrange direction, referenced to PACSS12.

[edit] 3.4 Continuity between trajectory phases

The continuity between independently estimated trajectory segments is used as one of the indicators of the trajectory accuracy. A measure of the continuity between two adjacent trajectory segments is obtained by differencing the state vectors at a time point common to both segments. As noted in Paragraph 3.1.3, the time points normally used for continuity judgments are parking orbit insertion, a point somewhere during S-IVB restart preparation after TB6, and trans-lunar injection. Comparisons at these time points were made for the AS-512 analysis and are described below. Following these comparisons, the separate trajectory segments were merged together, in the manner also described below, to provide the complete trajectory from GRR to CSM separation.

Comparisons of the state vectors at parking orbit insertion obtained independently by the powered flight and parking orbit analyses yielded excellent -reement. The position and velocity components of the two best-estimate solutions had a spread of 161 m (528 ft) and 0.5 m/s (1.6 ft/s) in the vertical direction, 37 m (121 ft) and 0.5 m/s (1.6 ft/s) in the cross range direction, and 101 m (331 ft) and 0.0 m/s (0.0 ft/s) in the downrange direction, referenced to the earth-fixed launch site coordinate system (PACSS10). Since these differences are very small and since the confidence for the boost trajectory segment is greater at EPO than the parking orbit segment (because the boost fit had available more data near EPO), the EPO point quoted in this document is taken from the boost trajectory segment. The parking orbit segment, however, is generated from the state vector which was obtained by the composite fit of the available parking orbit tracking data.

Since no tracking data were available during the second burn powered segment, a parking orbit state vector at 11,500 seconds range time was used to initialize the second burn powered segment. The confidence in the parking orbit state vector is high due to the excellent fit of the tracking data available during the restart preparation segment.

The second burn powered segment was developed by using the ST-124 guidance data as generating parameters and integrating from the parking orbit state vector at 11,500 seconds to the translunar orbit state vector at translunar injection. Two second burn trajectories were simulateu, one constrained to the TLI vector and one unconstrained. State vector differences at TLI (presented below) between the constrained integration and an unconstrained second burn integration are compatible with possible guidance errors. It should be pointed out that no tracking data were available to establish the post-TLI trajectory until 1,079 seconds after TLI. Also, only two trackers provided data during TB7 (see Figure 3-1). This increases the uncertainties in the TLI vector, and constraining the solution to fit this TLI state vector will cause the guidance errors to reflect these uncertainties. The position and velocity components of the two second burn integrations had a spread at TLI of 901 m (2,956 ft) and 3.4 m/s (11.2 ft/s) in the vertical direction, 2,436 m (7,992 ft) and 8.0 m/s (26.2 ft/s) in the cross range direction, and 1,186 m (3,891 ft) and 3.4 m/s (11.2 ft/s) in the downrange direction, referenced to the PACSS10 system.

Several injection vectors were obtained by solving for different translunar trajectory segments using various tracking data combinations The position and velocity components from a set of these solutions had a spread at TLI of 67 m (220 ft) and 0.9 m/s (3.0 ft/s) in the vertical direction, 1,238 m (4,062 ft) and 1.1 m/s (3.6 ft/s) in the cross range direction and 194 m (636 ft) and 0.1 m/s (0.3 ft/s) in the downrange direction, referenced to the PACSSIO system. The constrained seco.,O burn trajectory was used because the set of TLI solutions were all in good agreement.

As an additional validity check on the translunar phase, the reconstructed CSM separation state vector was propagated forward to lunar impact with the various S-IVB velocity increments modeled. The resultant lunar impact point is in excellent agreement with AS-512 lunar impact points quoted in Reference 2.

As noted above, the TLI state vector from the translunar segment was used for the end of the second burn segment. The continuitl thus provided at TLI plus the continuity at restart, discussed above, provides a completely continuous trajectory from the start of the parking orbit segment to the end of the translunar orbit segment at CSM separation.

As an aid in estimating the traectory accuracy, some of the tracking data throughout the various trajectory phases were transformed into the earth-fixed launch site coordinate system (PACSS10) position components and differenced with the reconstructed trajectory. The resulting residuals or deviations provide a direct indication Lif the spread of the tracking data about the trajectory.

The position deviations during the ascent phase are shown for the "- )and trackers in Figures 3-31 through 3-35. Deviations for parking orbit are shown in Figures 3-36 through 3-48 for the C-band and S-band stations. Trans-lunar deviations are given in Figure 3-49.

Based upon the information Jf the above paragraphs and a priori knowledge, the trajectory uncertainties were conservatively estimated. The uncertainties for the ascent phase are shown in Figure 3-50. At S-IC OECO, the uncertainties in position and velocity components in PACSS10 are ±70 m (±230 ft) and ±0.4 m/s (±1.3 ft/s), respectively. At S-II OECO, the uncertainties in position and velocity components in PACSS10 are ±360 m (11,181 ft) and ±0.7 m/s (2.3 ft/s), respectively. A. insert:.on and throughout the pa/king orbit, the uncertainties in position and velocity components in PACSS10 are ±500 m (±1,640 ft) and ±1.0 m/s (3.3 ft/s), respectively. The trajectory uncertainties increased to ±2,000 m (±6,562 ft) in position components and ±2.0 m/s (±6.6 ft/s) in veiocity components at TLI and throughout the post-TLI trajectory. The total radius and velocity magnitude uncertainties throughout the parking orbit phase are estimated at ±300 m (±984 ft) and ±0.5 m/s (±1.6 ft/s). Similarly, the total radius and velocity magnitude uncertainties throughout the translunar orbit phase are estimated at ±1,500 m (±4,921 ft) and t1.5 m/s (±4.9 ft/s).

[edit] Reference

[edit] References

  • NASA Document SE 008-001-1, "Project Apollo Coordinate System Standards," June 1965.
  • NASA Document MPR-SAT-FE-73-1, "Saturn V Launch Vehicle Flight Evaluation Report - AS-512 Apollo 17 Mission," February 28, 1973.
  • MSFC Memorandum MFT-200-72, "AS-512 Postlaunch Operational Trajectory," December 8, 1972.
  • NASA Document M-D E 8020.008B, "Natural Environment and Physical Standards for the Apollo Program," April 1965.

[edit] Acknowledgement

The analyses presented in this document were conducted under the technical direction of R. McCurdy by the following Saturn Engineering personnel:

  • J. Burgen G. Engels
  • T. Galbraith
  • J. Jaap
  • P. Johnson D. McKellar

Boeing Computer Services

  • W. Case
  • C. Dorries R. Simmons

Questions concerning the information presented should be directed to the technical supervisor of this analysis:

  • G. T. Pinson, JC-40 The Boeing Company Huntsville, Alabama

[edit] Glossary of terms

Altitude
The distance between the vehicle and its subvehicle point on the surface of ale Fischer Ellipsoid.
Ascent Phase
The segment of the vehicle flight from launch to parking orbit insertion.
Average Range Rate
The change in range per unit time computed over a finite interval.
Azimuth Angle
The angle, positive clockwise, from true north to the projection of the range vector on the ground station tangent plane (PACSS3a).
Cross Range
The vehicle lateral position measured in the earth-fixed launch site centered coordinate system (PACSS10).
Descending Node
The angle measured in the equatorial plane from the launch meridian at TGRR to the descending node of the orbit at the specified time.
Dynamic Pressure
The force per unit area of the atmosphere on the vehicle resulting from its motion through the atmosphere.
Elevation Angle
The angle between the range vector and its projection on the ground station tangent plane. This angle is positive above the ground station tangent plane (PACSS3a).
Flight Path Angle
The angle between the vehicle space- fixed velocity vector and a plane normal to a vector from the center of the earth to the vehicle. This angle is positive above the plane.
Heading Angle
The angle between the north direction in a plane normal to a vector from the center of the earth to the vehicle and the projection of the space-fixed velocity vector on the plane.
Inclination
The angle between the earth's north polar axis and the orbital angular momentum vector.
Inertial Acceleration
The magnitude of the vehicle acceleration in the launch vehicle platform accelerometer: coordinate system (PACSS12).
Instantaneous Range Rate
The rate of change of the distance from the receiving tracker to the vehicle at the specified time.
Latitude (geodetic)
The angle between the equatorial plane and the line normal to the ellipsoidal surface at a specified point, measured positive north in the meridian of the point.
Longitude
The angle between the plane of the Greenwich Meridian and the plane of the meridian containing the specified point measured positive eastward from the Greenwich Meridian.
Mach Number
The ratio of the vehicle velocity relative to the surrounding., atmosphere to the speed of sound in the atmosphere.
Measured Parameter
A primary measurement made by any ground station, e.g., elevation angle.
Parking Orbit Phase
The segment of the vehicle flight from parking orbit insertion to S-IVB restart preparation.
Range
The average of the uplink and downlink signal travel distances (PACSS3a, PACSS3c, and PACSS3d).
Second Burn Phase
The segment of the vehicle flight from S-IVB restart preparation to TLI.
Space-Fixed Velocity
The magnitude of the vehicle velocity in the launch vehicle navigation coordinate system (PACSS13).
Subvehicle Point
The point of intersection of the ellipsoidal surface and a line normal to this surface passing through the vehicle center of mass.
Surface Range
The arc length between the launch site and subvehicle point measured along the surface of the Fischer Ellipsoid.
Translunar Orbit Phase
The segment of the vehicle flight from TLI to CSM separation.
X-Angle
30' Antennas - The angle measured in the plane of the ground station prime vertical from the zenith to the projection of the slant range vector onto this plane, positive eastward (PACSS3c)
85' Antennas - The angle measured in the meridian plane of the grcund station from the zenith to the projection of the slant range vector onto this plane, positive southward (PACSS3d)
Y-Angle
30' Antennas - The angle between the slant range vector and its projection onto the plane of the ground station prime vertical, positive when the slant range vector is north of the plane (PACSS3c)
85' Antennas - The angle between the slant range vector and its projection onto the meridian plane of the radar site, positive when the slant range vector is east of the meridian plane (PACSS3d)

[edit] Appendix A: Definitions of trajectory symbols and coordinate systems

XE, YE, ZE, DXE, DYE, DZE, DDXE, DDYE, DDZE
Position, velocity, and acceleration components of vehicle Instrument Unit in Earth-Fixed Launch Site Coordinate System. The origin of this system is at the intersection of Fischer Ellipsoid (1960) and the normal to it which passes through the launch site. The X-axis coincides with the ellipsoid normal passing through the site, positive upward. The Z-axis is parallel to the earth-fixed flight azimuth, defined at guidance reference release time, and is positive down-range. The Y-axis completes a right-handed system. This coordinate system is identical to Standard Coordinate System 10 of Project Apollo Coordinate System Standards, abbreviated as PACSS10.
XS, YS, ZS, DXS, DYS, DZS, DDXS, DDYS, DDZS
Position, velocity, and acceleration components of vehicle Instrument Unit in Launch Vehicle Navigation Coordinate System. The origin of this system is at the center of the earth. The X-axis is parallel to Fischer Ellipsoid normal through the launch site, positive upward. The Z-axis is parallel to the flight azimuth, positive downrange. The Y-axis completes a right-handed system. The direction of the coordinate axes remains fixed in space at guidance reference release. This coordinate system is identical to Standard Coordinate System 13 of Project Apollo Coordinate System Standards, abbreviated as PACSS13.
GC DIST, DEC, GD LAT, LONG
Position components of vehicle Instrument Unit in Geographic Polar Coordinate System. Position in this system is defined by the geocentric distance (GC DIST), geocentric declination (DEC) geodetic latitude (GD LAT), and longitude (LONG). Geocentric distance is the distance from the geocenter to vehicle Instrument Unit. Geocentric declination is the angle between the radius vector of the vehicle and the equatorial plane, positive north of the equatorial plane. Geodetic latitude is the angle between the normal to the Fischer Ellipsoid through the subvehicle point and the equatorial plane, positive north of the equatorial plane. Longitude is the angle between the projection of the radius vector into the equatorial plane and the Greenwich meridian, positive east of the Greenwich meridian. This coordinate system is identical to Standard Coordinate System 1 of Project Apollo Coordinate System Standards, abbreviated as PACSS1.
EF VEL, VEL-AZ, VEL-EL
Earth-fixed velocity of vehicle Instrument Unit in Geographic Polar Coordinate System. Velocity in this system is given in terms of azimuth (VEL-AZ), elevation (VEL-EL) and magnitude of the earth-fixed velocity vector (EF VEL). Azimuth is the angle between the projection of the velocity vector into the local horizontal plane and the north direction in this plane, positive east of north. Elevation is the angle between the velocity vector and the local horizontal plane, positive above the horizontal plane. This coordinate system is identical to Standard Coordinate System 1 of Project Apollo Coordinate System Standards, abbreviated as PACSS1.
SF VEL, FLT-PATH, HEAD
Space-fixed velocity of vehicle Instrument Unit in Geographic Polar Coordinate System. Velocity in this system is given in terms of heading angle (HEAD), flight path angle (FLT-PATH), and magnitude of the space-fixed velocity vector (SF VEL). Heading angle is the angle between the projection of the velocity vector into, the local horizontal plane and the north direction in this plane, positive east of north. Flight path angle is the angle between the velocity vector and the local horizontal plane, positive above the horizontal plane. This coordinate system is identical to Standard Coordinate System 1 of Project Apollo Coordinate System Standards, abbreviated at PACSS1.
ALTITUDE
Perpendicular distance from vehicle Instrument Unit to Fischer Ellipsoid, positive above Fischer Ellipsoid.
RANGE
Surface range, measured along Fischer Ellipsoid from the launch site to the subvehicle point.
TIME
Range time, referenced to nearest integer second before IU umbilical disconnect.

[edit] Appendix B: Time history of trajectory parameters - Metric units

The postflight trajectory, from guidance referen:e release to CSM separation, is tabulated in metric units in Tables B-I through B-VII.

  • Table B-I gives the earth-fixed launch site position, velocity, and acceleration components for the ascent phase of flight.
  • Table B-II gives the launch vehicle navigation position, velocity, and acceleration components for the ascent phase of flight.
  • Table B-III gives the geographic polar coordinates for the ascent phase of flight.
  • Table B-IV gives the geographic polar coordinates for the parking orbit phase of flight.
  • Table B-V gives the earth-fixed launch site position, velocity, and acceleration components for the second burn and translunar phases of flight.
  • Table B-VI gives the launch vehicle navigation position, velocity, and acceleration components for the second burn and translunar phases of flight
  • Table B-VII gives the geographic polar coordinates for the second burn and translunar phases of flight.

[edit] Appendix C: Time history of trajectory parameters - English units

The postflight trajectory, from guidance reference release to CSM separation, is tabulated in English units in Table C-I through C-VII.

  • Table C-I gives the earth-fixed launch site position, velocity, and acceleration components for the ascent phase of flight.
  • Table C-II gives the launch vehicle navigation position, velocity, and acceleration components for the ascent phase of flight.
  • Table C-III gives the geographic polar coordinates for the ascent phase of flight.
  • Table C-IV gives the geographic polar coordinates for the parking orbit phase of flight.
  • Table C-V gives the earth-fixed launch site position, velocity, and acceleration components for the second burn and translunar phases of flight.
  • Table C-VI gives the launch vehicle navigation position, velocity, and acceleration components for the second burn and translunar phases of flight.
  • Table C-VII gives the geographic polar coordinates for the second burn and translunar phases of flight.
Retrieved from "http://www.ehartwell.com/afj/Reports/Apollo_17/Apollo-Saturn_V_Postflight_Trajectory_AS-512"