MERCURY PROJECT SUMMARY (NASA SP-45)

 

7. TRAJECTORY ANALYSIS

 

By JOHN P. MAYER, Asst. Chief for Mission Planning, Flight Operations Division, NASA Manned Spacecraft Center; and CARL R. HUSS, Flight Operations Division, NASA Manned Spacecraft Center

 

Summary

 

[119] A description of the mission analysis studies conducted for Project Mercury is given along with specific examples for the various mission analysis phases.

 

Aborted mission studies constituted about 90 percent of all mission- analysis studies conducted. These studies were necessary from a light- safety standpoint and are considered equally applicable to future manned spacecraft projects. It was found that the basic mission design must be chosen in a flexible manner so that consideration can be given to the changes in mission constraints. Real-time computing has proved extremely valuable in Project Mercury; however, consideration must be given to changes in mission operational plans which cannot be effectively included in the Real Time Computer Complex.

 

Introduction

 

The mission-analysis effort in Project Mercury was conducted in several phases leading up to the flight missions. These phases include the mission analysis supporting the systems design of the spacecraft, the basic operational design of the Mercury missions based on mission requirements and objectives, detailed operational mission analysis for each specific flight, and the formulation of the mission logic to be included in the computer used for inflight real-time control of the missions.

 

Mission Phases

 

In figure 7-1 are shown the important phases of mission-analysis studies. In the early mission-analysis phase, the analysis was specifically for use in spacecraft system design. For example, the maximum loads and heating conditions were determined for structural design, and the spacecraft propulsion performance requirements were determined leading to the design of the retrorocket system. After the spacecraft systems were essentially designed, the mission-analysis effort shifted to the operational phase. In this phase the system design was reasonably fixed and the detailed mission design was then accomplished by taking into account all of the constraints, including spacecraft, launch-vehicle, and operational constraints. The objective in this phase is to design a mission within the capabilities of the actual spacecraft system developed. In this phase of the mission some feedback into system design was made, although these were small changes since the early design proved to be sound.

 

The next mission analysis phase was in the design of specific missions. In this case the mission analysis was specialized to handle the aspects of a particular mission by using the actual performance characteristics of the launch vehicle and spacecraft being used. This phase also included the analysis for the particular operational mission objectives and ground rules developed for these missions.

 

The next phase was the real-time mission analysis phase, which started at the beginning of the launch countdown and lasted until the

 


mission sequence diagram

Figure 7-1. Mission analysis sequence diagram.

 

[120] vehicle was recovered after the mission. In this, calculations were accomplished in real time by a computer; however, the logic and equations used in this computer were developed in the preceding operational mission-analysis phase. Although every effort was made to anticipate all the possibilities that could affect the flight and include them in the real- time computer program, these possibilities were never fully established. Therefore, mission-analysis experts were used as flight controllers and also performed auxiliary computing using off-line computers other than those used in the realtime computing complex during the missions.

 

The next mission-analysis phase was a postflight analysis phase in which the information obtained from actual flights was fedback into the plans for future flights and, in some cases resulted in system modifications to the spacecraft, the launch vehicle, and the ground support system.

 

Some specific examples of mission constraints affecting the analysis are shown in figure 7-2. Some of the spacecraft constraints that must be considered are the performance of the spacecraft propulsion system, the spacecraft control system accuracies, and other system limitations. Some of the ground complex constraints to be considered are performance (which includes the effects of the locations of command stations and command ranges) and system limitations. Constraints involving the launch vehicle which had to be considered were performance, guidance accuracies, and systems limitations. In Project

 


mission operation diagram

Figure 7-2. Operational mission analysis.

 

Mercury the systems limitations of the launch vehicle included heating and load restraints and the guidance radar look angle constraint.

 

The operational constraints to be considered in the are a of launch operations are range safety limits, abort considerations, environmental considerations, landing and recovery considerations, and human factors. Some of the environmental factors that were considered were the effect of atmospheric and geophysic constraints and winds. Consideration had to be given to recovery and landing constraints for both normal and aborted missions and, in all cases, the human tolerances to acceleration loads and motions were considered.

 

Abort considerations resulted in about 90 percent of the mission- analysis studies. Studies were made to provide flight controllers with the information as to when to initiate aborts for maximum pilot safety. Studies were also made to determine allowable tolerances in order to obtain safe miss distances between the launch vehicle and the spacecraft and acceptable lateral loads. Also of importance were the studies to determine the abort recovery areas for all phases of the flight.

 

In order to illustrate some of the techniques used and the results accomplished in the mission-analysis area, a few specific examples from each phase will be discussed.

 

Design Mission Analysis

 

One example of the work performed in the advanced mission analysis phase is illustrated by a study of the immediate post-abort conditions. The selection of the escape-rocket offset involved a compromise between high lateral loads and low miss distances between the spacecraft and the launch vehicle in the high-dynamic-pressure abort phase of launch. For low offset values the probability of exceeding high lateral loads was low; however, the probability of obtaining low miss distances was high. For high values of the offset the opposite is true. Thus, the selection of the offset was made on the basis of minimum combined probability of occurrence of either events. In figure 7-3, the combined probability of exceeding either a dangerous lateral load or an unacceptable miss distance is shown plotted against the escape-rocket offset.

 


graph of rocket escape thrust and mission performance

[121] Figure 7-3. Selection of escape-rocket thrust offset.

 

Operational Mission Analysis

 

A typical example of the operational mission analysis was in the selection of the Mercury orbital elements. The orbital inclination which governed the ground track for Project Mercury was selected because the network facilities established prior to Mercury could be used to good advantage, reentries for the first three orbital passes and the 16th to the 18th passes occurred over the United States, and the orbital ground track fell within the temperate region of the world. In addition, the specific Mercury inclination was affected by launch-abort recovery considerations.

 

The orbital altitude and shape of the Mercury orbit were selected based on launch-vehicle performance, accuracy, and abort operational considerations. These considerations are illustrated in figures 7-4 to 7-7. In figure 7-4 the orbital lifetime is shown plotted against apogee altitude for given perigee altitudes. For Project Mercury it was desired to have minimum lifetime of 36 hours for a 24-hour mission. Since the atmospheric densities at orbital altitudes were not well-defined at the time Project Mercury was initiated, it was believed that 21 conservative value for density must be used for estimating lifetime. The density used in this figure is considered to be a 3a [a = Greek letter sigma], or very conservative, dense atmosphere. From figure 7-4, it can be noted that for an adequate lifetime in a circular orbit at all altitude of 105 nautical miles could have been selected, or an elliptical orbit having the same lifetime could have been selected, for example, an orbit having an 80-mile perigee and a 170-mile apogee.

 


graph contrasting orbit apogee and orbit security

Figure 7-4. Minimum lifetimes for elliptical orbits.

 

The next constraint to be considered is that of launch-vehicle performance. In figure 7-5 the staging time is shown plotted against the insertion or perigee altitude. The curves shown are given for a constant orbital lifetime; that is, the apogee altitude decreases as the insertion altitude increases. For a constant insertion altitude the performance, or excess velocity available above that required ([Greek letter Delta]Vmin), increases with staging time until it reaches a peak value. For greater staging times the performance decreases. The minimum acceptable performance curves are shown in figure 7-5. The increment of velocity [Greek letter Delta] V that defines the acceptable performance is the difference between the velocity at fuel depletion and the planned velocity. Therefore, all of the clear area in the figure would represent acceptable orbital insertion altitudes.

 

The launch-vehicle guidance accuracies are considered in figure 7-6. Since the Atlas launch vehicle used for the Mercury program was guided by a radio guidance system, the guidance accuracy was dependent to some extent on the radar elevation angle at cut-off. In figure 7 6 the minimum elevation angle Emin which was considered acceptable is shown. Again the clear area in the figure is indicative of acceptable orbital insertion conditions. Next, however, the operational considerations must be included. These are shown in figure 7-7. In this [122] case the operational consideration which affected the orbital conditions was the requirement to avoid a landing in Africa for an abort from the minimum acceptable velocity. In this figure the position of the line shown is such that the spacecraft would not land in Africa if an abort were made at the no-go velocity, with allowance for the dispersions on the abort landing area. From figure 7-7 it may be noted that the operational consideration significantly affects the orbital insertion altitudes which could be used for Project Mercury.

 


graph of staging time vs insertion altitude

Figure 7-5. Effect of launch-vehicle performance.

graph of staging time vs insertion altitude

Figure 7-6. Effect of a launch-vehicle guidance.

 

As operational experience was gained in Project Mercury flights, confidence and knowledge in the systems made it possible to reduce to some extent, the original guidance and performance constraints. For example, the minimum elevation angle was reduced after obtaining a better understanding of the effects on guidance accuracy from operational experience with the guidance system.

 


grah show the efects of operational constraints

Figure 7-7. Effect of operational constraints.

 

Specific Mission Analysis

 

A considerable mission-analysis effort is made in the design of each specific Mercury flight. Included in this effort are detailed trajectory calculations for the mission, dispersion calculations, calculations concerning aborts during all phases of the mission, and calculations of retrograde time to be used in the mission. When the flight day arrived, special mission-analysis studies were performed to support the flight. These studies included evaluating the wind effects on the loads on the launch vehicle and determining the landing areas of the spacecraft in aborted missions based on actual wind profiles. In figure 7-8 the effects of the actual winds on the abort landing areas at various times of the flight are shown for the MA-9

 


graph showing the effect of wind on landing location

Figure 7-8. Effects of actual winds on MA-9 abort landing.

 

[123] mission. These calculations were made to enable the recovery forces to be positioned prior to the launch such that they could most easily make an emergency recovery should abort occur.

 

Real-Time Mission Analysis

General Computing Requirements

 

Real-time computing has proved very valuable in Project Mercury for use in flight control and monitoring. The basic computing requirements in real time are as follows:

(1) Powered flight. Pertinent trajectory parameters were computed in order that the status of the launch could be monitored for any indication of all impending abort. The cut-off velocity was used to determine the acceptability of the orbital parameters based on preplanned criteria. In addition, landing points for possible aborts and radar-acquisition data were computed.

(2) Aborted missions. For aborted missions the computer must be programed to select a target recovery area and if necessary compute the time for retrofire to land within this area.

(3) Orbit. In this phase the orbital parameters were predicted with sufficient accuracy to establish the minimum lifetime of the orbit, to predict the retrofire time to land in normal and contingency recovery areas, to determine spacecraft orbital position, to determine acquisition data for all radar sites, and to predict the time of landing for use by recovery forces.

(4) Reentry. During reentry the computer program recalculates and updates the landing point and time of landing, based on conditions at retrofire, in addition to predicting acquisition data for reentry radar stations.

 

Example of Go-No-Go Computation

 

The computation of the go-no-go parameters was probably the most important of the realtime computations. The selection of the Mercury go-no-go criteria which were used in the real-time computing program is shown in figures 7-9 to 7-11. In figure 7-9 the minimum energy for an acceptable Mercury mission is illustrated. The flight-path angle at insertion is plotted against the insertion velocity. The minimum acceptable orbit was defined as that orbit in which the spacecraft could safely complete one orbital pass and land. Because of the

 


graph showing relationship of plight path angle and velocity

Figure 7-9. Determination of minimum acceptable orbit.

diagram of acceptable reentry zones

Figure 7-10. Determination of maximum acceptable orbit.

graph of flight path and velocity

Figure 7-11. Operational go-no-go orbital-insertion criteria.

 

critical flight safety nature of the problem, the minimum orbit was selected on the basis of a very conservative drag coefficient CD and atmospheric density p [Greek letter rho]. The symbol, (CDp)n, shown in figure 7- 12 has been normalized and [124] represents the ratio of the parametric drag coefficient-density product to a nominal value of this product. Therefore, values of (CDp)n which are greater than unity are considered to be conservative. The 99- percent probability curve shown in figure 7-9 was the one selected for the go-no-go criteria. Therefore from a lifetime consideration the conditions would be "go" at velocities higher than this boundary; however, other constraints imposed a limit at higher velocities.

 


graph of alltitude effect on orbit

Figure 7-12. Effects of actual atmosphere on MA-9 orbital lifetime.

 

In figure 7-10 the determination of the maximum energy orbit is illustrated. As the velocity is increased above orbital velocity the apogee increases approximately 1 mile for every 2 feet per second. When the velocity reaches a certain critical value, an area occurs near perigee such that, if the retrorockets were ignited, excessive heating would occur during reentry. As the velocity increases above this value this critical area near perigee extends over most of the orbit and another critical area for initiation of reentry appears near apogee. At this point if reentry were initiated, the reentry loads would become excessive. As the velocity is further increased, a velocity is reached in which these critical areas cover the entire orbital range and a safe reentry would not be possible from any point in the orbit. The operational go-no-go criteria that resulted from these constraints are shown in figure 7-11 where the flight-path angle at cut-off is plotted against the insertion velocity. The region for a minimum acceptable orbit lies within the boundaries shown. For all Project Mercury missions the cut-off velocities were well within the safe boundaries. For the MA-9 mission, for example, the cut-off occurred within the boundary of the symbol shown in this figure.

 

As was previously stated, some auxiliary computing was performed during each mission outside of the real-time computers. An example of this auxiliary computing is shown in figure 7-12 were the effects of the actual atmosphere on the orbital lifetime of the MA-9 mission are shown. In figure 7-12 apogee altitude is plotted against time. Because of the length of the MA-9 mission and the uncertainty of the density of the actual atmosphere on the day of this flight, it was thought necessary to attempt to determine the variation of the actual atmosphere from that used in preflight computations. This calculation was necessary in order to commit the mission to completing 22 passes at a predetermined time during the flight. The lines shown in the figure are for precalculated atmospheric densities which varied from that of the assumed atmosphere. The symbols in this figure indicate the actual apogee obtained during the flight and also that the actual atmosphere was very close to that used in the preflight computations. The actual orbital lifetime for the MA-9 mission would have been about 4.7 days if a reentry were not initiated using the retrorockets.

 

Concluding Remarks

 

The operational experience obtained in mission-analysis studies for Project Mercury has proved valuable for application to other manned space-flight programs. Aborted mission studies constituted about 90 percent of all the mission-analysis studies conducted for Mercury. Although the results of these studies were not required operationally, the amount of effort spent on abort studies is necessary from a flight safety standpoint and will be equally applicable [125] to future manned space projects. It is also evident that the basic mission design must be chosen in a flexible and manner so that consideration can be given to changes in the spacecraft launch vehicle or operational constraints. Real-time computing has proved extremely valuable in Project Mercury; however, it seems that consideration must always be given to changes to mission operational plans which cannot be effectively included in the real-time computing complex. Therefore, auxiliary inflight computing probably should always be considered.


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