Extracted text — DOW-UAP-D48, Department of the Air Force Report, 1996

RESEARCH TRIANGLE INSTITUTE
RTI
Contract No. FO4703-91-C-0112
RTI Report No. RTI/5180/77-43F
September 10, 1996
Modeling Unlikely Space-Booster
Failures in Risk Calculations
Final Report
Prepared for
Department of the Air Force
45th Space Wing (AFSPC)
Safety Office - 45 SW/SE
Patrick AFB, FL 32925
and
Department of the Air Force
30th Space Wing (AFSPC)
19961025 122
Safety Office - 30 SW/SE
Vandenberg AFB, CA 93437
Distribution authorized to US Government agencies and their contractors to protect administrative/
operational use data, 10 September 96. Other requests for this document shall be referred to the 30th Space
Wing (AFSPC) Safety Office (30 SW/SE), Vandenberg AFB, CA 93437, or 45th Space Wing (AFSPC)
Safety Office (45 SW/SE), Patrick AFB, FL 32925.
DTIC QUALITY INSPECTED 2
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Contract No. FO4703-91-C-0112
RTI Report No. RTI/5180/77-43F
Task No. 10/95-77, Subtask 2.0
September 10, 1996
Modeling Unlikely Space-Booster
Failures in Risk Calculations
Final Report
Prepared by
James A. Ward, Jr.
Robert M. Montgomery
of
Research Triangle Institute
Center for Aerospace Technology
Launch Systems Safety Department
Prepared for
Department of the Air Force
45th Space Wing (AFSPC)
Safety Office - 45 SW/SE
Patrick AFB, FL 32925
and
Department of the Air Force
30th Space Wing (AFSPC)
Safety Office - 30 SW/SE
Vandenberg AFB, CA 93437
Distribution authorized to US Government agencies and their contractors to protect administrative/
operational use data, 10 September 96. Other requests for this document shall be referred to the 30th Space
Wing (AFSPC) Safety Office (30 SW/SE), Vandenberg AFB, CA 93437, or 45th Space Wing (AFSPC)
Safety Office (45 SW/SE), Patrick AFB, FL 32925.
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1. AGENCY USE ONLY (Leave blank)
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September 10, 1996
Final
4. TITLE AND SUBTITLE
5. FUNDING NUMBERS
Modeling Unlikely Space-Booster Failures in Risk Calculations
C: FO4703-91-C-0112
TA: 10/95-77
6. AUTHOR(S)
James A. Ward, Jr.
Robert M. Montgomery
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
8. PERFORMING ORGANIZATION
REPORT NUMBER
Research Triangle Institute
ACTA, Inc.
3000 N. Atlantic Avenue
Skypark 3
RTI/5180/77-43F
Cocoa Beach, FL 32931
23430 Hawthorne Blvd., Suite 300
Torrance, CA 90505
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)
10. SPONSORING / MONITORING
AGENCY REPORT NUMBER
Department of the Air Force (AFSPC)
Department of the Air Force (AFSPC)
30th Space Wing
45th Space Wing
305W-TR-96-12
Vandenberg AFB, CA 93437
Patrick AFB, FL 32925
Mr. Martin Kinna (30 SW/SEY)
Louis J. Ullian, Jr. (45 SW/SED)
11. SUPPLEMENTARY NOTES
* Subcontractor
** Prime Contractor
12a. DISTRIBUTION/AVAILABILITY STATEMENT
12b. DISTRIBUTION CODE
Distribution authorized to US Government agencies and their contractors to protect
administrative/operationa use data, 10 September 96. Other requests for this document shall
be referred to the 30th Space Wing (AFSPC) Safety Office (30 SW/SE), Vandenberg AFB, CA
93437, or 45th Space Wing (AFSPC) Safety Office (45 SW/SE), Patrick AFB, FL 32925.
D
13. ABSTRACT (Maximum 200 words)
Missile and space-vehicle performance histories contain many examples of failures that cause, or have the
potential to cause, significant vehicle deviations from the intended flight line. In RTI's risk-analysis program,
DAMP, such failures are referred to as Mode-5 failure responses. Although Mode-5 failure responses are much
less likely to occur than those that result in impacts near the flight line, risk-analysis studies are incomplete without
them. This report shows how impacts from Mode-5 failures are modeled in program DAMP. The impact density
function used for this purpose contains two shaping constants that control the rate at which the density function
drops in value as the angular deviation from the flight line and the impact range increase. Certain Mode-5
malfunctions are simulated, and the two shaping constants then chosen by trial and error so that impacts from the
simulated malfunctions and the theoretical density function are in close agreement. An appendix to the report
contains a listing and brief narrative failure history of the Atlas, Delta, and Titan missile and space-vehicle launches
from the Eastern and Western Ranges from the beginning of each program through August 1996. Each entry
gives the vehicle configuration, whether the flight was a success, the flight phase in which any anomalous behavior
occurred, and a classification of vehicle behavior in accordance with defined failure-response modes.
14. SUBJECT TERMS
15. NUMBER OF PAGES
launch risk, unlikely failure modeling, booster failure probabilities
180
16. PRICE CODE
17. SECURITY CLASSIFICATION
18. SECURITY CLASSIFICATION
19. SECURITY CLASSIFICATION
20. LIMITATION OF ABSTRACT
OF REPORT
OF THIS PAGE
OF ABSTRACT
Unclassified
Unclassified
Unclassified
SAR
NSN 7540-01-280-5500
Standard Form 298 (Rev. 2-89)
Prescribed by ANSI Std. 239-18
298-102
Abstract
Missile and space-vehicle performance histories contain many examples of failures that
cause, or have the potential to cause, significant vehicle deviations from the intended
flight line. In RTI's risk-analysis program, DAMP, such failures are referred to as
Mode-5 failure responses. Although Mode-5 failure responses are much less likely to
occur than those that result in impacts near the flight line, risk-analysis studies are
incomplete without them. This report shows how impacts from Mode-5 failures are
modeled in program DAMP. The impact density function used for this purpose
contains two shaping constants that control the rate at which the density function drops
in value as the angular deviation from the flight line and the impact range increase.
Certain Mode-5 malfunctions are simulated, and the two shaping constants then chosen
by trial and error so that impacts from the simulated malfunctions and the theoretical
density function are in close agreement.
An appendix to the report contains a listing and brief narrative failure history of the
Atlas, Delta, and Titan missile and space-vehicle launches from the Eastern and
Western Ranges from the beginning of each program through August 1996. Each entry
gives the vehicle configuration, whether the flight was a success, the flight phase in
which any anomalous behavior occurred, and a classification of vehicle behavior in
accordance with defined failure-response modes. Various filtering or data weighting
techniques are described. The empirical data are then filtered to estimate (1) failure
probabilities for Atlas, Delta, and Titan, and (2) percentages of future failures that will
result in Mode-5 (and other Mode) responses.
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Table of Contents
1. Introduction
1
2. Examples Showing Need for Mode 5
3
3. Understanding the Mode-5 Failure Response
7
3.1 Effects of Mode-5 Shaping Constants
9
3.2 Effects of Shaping Constant on DAMP Results
9
4. Methodology for Assessing Failure Probabilities
13
4.1 The Parts-Analysis Approach
13
4.2 The Empirical Approach
15
5. Computation of Failure Probabilities
16
5.1 Overall Failure Probability
16
5.2 Relative and Absolute Probabilities for Response Modes
24
5.3 Relative Probability of Tumble for Response-Modes 3 and 4
30
6. Shaping Constants Through Simulation
31
6.1 Malfunction Turn Simulations
31
6.1.1 Random-Attitude Failures
31
6.1.2 Slow-Turn Failures
32
6.1.3 Factors Affecting Malfunction-Turn Results
33
6.1.4 Malfunction-Turn Results for Atlas IIAS
35
6.2 Shaping Constants for Atlas IIAS
37
6.2.1 Optimum Mode-5 Shaping Constants
37
6.2.2 Launch-Area Mode-5 Risks
49
6.2.3 Effects of Mode-5 Constants on Ship-Hit Contours
51
6.2.4 Range Distributions of Theoretical and Simulated Impacts
58
6.3 Shaping Constants for Delta-GEM
60
6.3.1 Optimum Mode-5 Shaping Constants
61
6.3.2 Launch-Area Mode-5 Risks
64
6.4 Shaping Constants for Titan IV
65
6.5 Shaping Constants for LLV1
69
6.6 Shaping Constants for Other Launch Vehicles
72
7. Potential Future Investigations
73
8. Summary.
74
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Appendix A. Failure Response Modes in Program DAMP
79
Appendix B. Shaping-Constant Effects on Mode-5 Impact Distributions
81
Appendix C. Filter Characteristics
90
Appendix D. Launch and Performance Histories
96
D.1 Basic Data
96
D.1.1 Data Sources
96
D.1.2 Assignment of Failure-Response Modes
98
D.1.3 Assignment of Flight Phase
98
D.1.4 Representative Configurations
100
D.2 Atlas Launch and Performance History
101
D.2.1 Atlas Launch History
103
D.2.2 Atlas Failure Narratives
115
D.3 Delta Launch and Performance History
133
D.3.1 Delta Launch History
136
D.3.2 Delta Failure Narratives
142
D.4 Titan Launch and Performance History
146
D.4.1 Titan Launch History
149
D.4.2 Titan Failure Narratives
157
D.5 Thor Launch and Performance History (Not Including Delta)
164
D.5.1 Thor and Thor-Boosted Launch History
164
D.5.2 Thor and Thor-Boosted Failure Narratives
167
References
171
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Table of Figures
Figure 1. Joust Impact Trace Showing a Mode-5 Failure Response
6
Figure 2. Atlas IIAS Risk Contours for Inner-Ear Injury with A = 3.0
11
Figure 3. Atlas IIAS Risk Contours for Inner-Ear Injury with A = 3.5
12
Figure 4. Filter Factor Results for Representative Configurations of Atlas
23
Figure 5. Combined Random-Attitude and Slow-Turn Results
36
Figure 6. Atlas IIAS Breakup Percentages for Random-Attitude Turns
37
Figure 7. Atlas IIAS Impacts with No Breakup
39
Figure 8. Atlas IIAS Impacts with Breakup
40
Figure 9. Atlas IIAS Simulation Results with B = 1,000
42
Figure 10. Atlas IIAS Simulation Results with B = 50,000
44
Figure 11. Atlas IIAS Simulation Results with B = 100,000
45
Figure 12. Atlas IIAS Simulation Results with B = 500,000
46
Figure 13. Atlas IIAS Simulation Results with B = 5,000,000
47
Figure 14. Effects of Breakup q-alpha on A for Atlas IIAS
49
Figure 15. Mode-5 Density-Function Values at Three Miles
51
Figure 16. Atlas IIAS Mode-5 Ship-Hit Contours with A = 3.00
53
Figure 17. Atlas IIAS All-Mode Ship-Hit Contours with A = 3.00
54
Figure 18. Atlas IIAS Mode-5 Ship-Hit Contours with A = 3.45
55
Figure 19. Atlas IIAS All-Mode Ship-Hit Contours with A = 3.45
56
Figure 20. Atlas IIAS Mode-5 Ship-Hit Contours with A = 6.30
57
Figure 21. Atlas IIAS All-Mode Ship-Hit Contours with A = 6.30
58
Figure 22. Impact-Range Distributions
59
Figure 23. Delta-GEM Breakup Percentages
61
Figure 24. Delta-GEM Simulation Results with B =1,000
62
Figure 25. Delta-GEM Simulation Results with Best-Fit Shaping Constants
63
Figure 26. Titan IV Breakup Percentages
65
Figure 27. Titan Simulation Results with B = 1,000
66
Figure 28. Titan Simulation Results with Best-Fit Shaping Constants
67
Figure 29. LLV1 Breakup Percentages
69
Figure 30. LLV1 Simulation Results with B = 1,000
70
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Figure 31. LLV1 Simulation Results with Best-Fit Shaping Constants
71
Figure 32. f-Ratios for Ranges from 1 to 25 Miles
86
Figure 33. Percentage of Impacts Between Flight Line and Any Radial
87
Figure 34. Percentage of Impacts in 5-Degree Sectors
88
Figure 35. Exponential Weights for Fading-Memory Filters
93
Figure 36. Recursive Filter Factor for Last Data Point
94
Figure 37, Atlas Launch Summary
102
Figure 38. Delta Launch Summary
135
Figure 39. Titan Launch Summary
148
Figure 40. Thor Launch Summary
164
Table of Tables
Table 1. Effects of Mode-5 Shaping Constant A on Atlas IIA Risks
10
Table 2. Predicted Failure Probabilities for Representative Configurations
17
Table 3. Predicted Failure Probabilities for All Configurations
18
Table 4. Comparison of Weighting Percentages
19
Table 5. Filter Factor Influence on Weighting Percentages
21
Table 6. Failure Probabilities for Atlas, Delta, and Titan
24
Table 7. Number of Atlas Failures - All Configurations (532 Flights)
25
Table 8. Number of Delta Failures - All Configurations (232 Flights)
25
Table 9. Number of Titan Failures - All Configurations (337 Flights)
25
Table 10. Number of Eastern-Range Thor Failures (85 Flights)
25
Table 11. Number of Failures for All Vehicles (1186 Flights)
26
Table 12. Date of Most Recent Failure
26
Table 13. Percentage Weighting for Sample of 1186 Launches
27
Table 14. Response-Mode Occurrence Percentages
27
Table 15. Recommended Response-Mode Percentages for Flight Phases 0 - 2
28
Table 16. Recommended Response-Mode Percentages for Flight Phases 0 - 1
29
Table 17. Absolute Failure Probabilities for Response Modes 1-5
29
Table 18. Percent of Response Modes 3 and 4 That Tumble
30
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Table 19. Sample Impact Distribution for Atlas IIAS with No Breakup
41
Table 20. Shaping Constants for Atlas IIAS
48
Table 21. Shaping Constants and Related Risks for Atlas IIAS
50
Table 22. Best-Fit Conditions for Atlas IIAS
52
Table 23. Shaping Constants and Related Risks for Delta-GEM
64
Table 24. Shaping Constants for Titan IV
68
Table 25. Shaping Constants for LLV1
72
Table 26. Summary of A Values for B = 1,000
72
Table 27. Failure Probabilities for Atlas, Delta, and Titan
75
Table 28. Recommended Response-Mode Percentages for Flight Phases 0 -2
75
Table 29. Recommended Response-Mode Percentages for Flight Phases 0 - 1
75
Table 30. Absolute Failure Probabilities for Response Modes 1 - 5
76
Table 31. Summary of A Values for B = 1,000
77
Table 32. Summary of Optimum Mode-5 Shaping Constants
77
Table 33. Effect on f-Ratio of Varying Mode-5 Constant A (B = 1000) - Part 1
82
Table 34. Effect on f-Ratio of Varying Mode-5 Constant A (B = 1000) - Part 2
83
Table 35. Effect on f-Ratio of Varying Mode-5 Constant B (A = 3) - Part 1
84
Table 36. Effect on f-Ratio of Varying Mode-5 Constant B (A = 3) - Part 2
85
Table 37. Filter Application for Failure Probability
95
Table 38. Flight-Phase Definitions
99
Table 39. Flight Phases by Launch Vehicle
99
Table 40. Summary of Atlas Vehicle Configurations
101
Table 41. Atlas Launch History
103
Table 42. Summary of Delta Vehicle Configurations
133
Table 43. Delta Launch History
136
Table 44. Summary of Titan Vehicle Configurations
147
Table 45. Titan Launch History
149
Table 46. Thor Launch History
165
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1. Introduction
The debris from most launch vehicles that fail catastrophically tend to impact close to the
intended flight line. Typical failures that produce such results are premature thrust
termination, stage ignition failure, tank rupture or explosion, or rapid out-of-control
tumble. Less likely malfunctions may cause a vehicle to execute a sustained turn away
from the flight line. Examples are control failures that cause the rocket engine to lock in a
fixed position near null, or failures leading to erroneous orientation of the guidance
platform. Such failures should not be ignored, since they may produce nearly all or a
significant part of the risks to population centers that are more than a mile or SO uprange or
many miles away from the flight line. Consequently, RTI has been tasked to estimate the
probabilities of occurrence of these less-likely failures, and to determine optimum values
for the shaping constants of the associated impact-density function.
RTI has developed a prototype risk-analysis program (1) to analyze the level of risk in the
launch area when ballistic missiles and space vehicles are launched, and (2) to provide
guidelines for launch operations and launch-area risk management. This program, "facility
DAMage and Personnel injury" (DAMP), uses information about the launch vehicle, its
trajectory and failure responses, and facilities and populations in the launch area to estimate
hit probabilities and casualty expectations. When a missile or space vehicle malfunctions,
people and facilities may be subjected to significant risks from falling inert debris, or from
overpressures and secondary debris produced by a stage, component, or large propellant
chunk that explodes on impact. Although fire, toxic materials, and radiation may also
subject personnel to significant danger, these hazards are not addressed in program DAMP.
Hazards are greatest in the launch area and along the intended flight line, but lesser
hazards exist throughout the area inside the impact limit lines. Small hazards exist even
outside these lines if the flight termination system fails or other unlikely events occur.
In computing launch-area risks, DAMP makes no attempt to model vehicle failures per
se. A list of possible failures for any vehicle would be extensive, and variations in
failures from vehicle to vehicle would complicate the modeling process. Instead,
DAMP models failure responses. Regardless of the exact nature of the failures that can
occur, there are only six possible response modes that affect risks on the ground, five
for failure responses, and one to model the behavior of a normal vehicle. The six
modes are described in Appendix A. It can be seen from the descriptions that impacts
resulting from failure-response Modes 1, 2, and 3 occur at most a mile or two from the
launch point, while those from Mode 4 can only occur near the flight line, even though the
vehicle may tumble before breakup or destruct. Although the hazards outside the launch
area and away from the flight line may be small, vehicle flight tests through the years have
demonstrated that finite hazards do exist in these areas. Such hazards are due almost
entirely to Mode-5 failure responses, even through the probability of a Mode-5 failure may
be only a small part of the total failure probability. The Mode-5 failure-response,
theoretical though it is, was developed to reflect the facts that: (1) unlikely vehicle failures
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can cause impacts uprange or well away from the intended flight line, and (2) some vehicle
failures cannot logically be classified as Response Modes 1, 2, 3, or 4.
In keeping with the above, the Mode-5 impact-density function was developed with the
characteristics listed below. The function, which fills the void left by Modes 1 through 4, is
sufficiently robust to include all possible impacts, yet seemingly comports with observed
test results.
(1) Impacts can occur in any direction from the launch point and at any range within
the vehicle's energy capabilities.
(2) At any given impact range from the launch point, the likelihood of impact
decreases as the angular deviation from the flight line increases, becoming least
likely in the uprange direction. For any fixed angular deviation from the flight
line, the likelihood of impact decreases as the impact range increases.
(3) At fixed impact ranges near the launch point, the impact density function changes
gradually as the impact direction swings 180° from downrange to uprange. As
the impact range increases, the decrease in the density function becomes
progressively more and more rapid with change in impact direction. In other
words, the greater the impact range, the more rapidly the density function
changes with angular deviation from the flight line.
As modeled in DAMP, the effects of destruct action on the Mode-5 density function are
accounted for in the launch area by supplementing impacts inside the impact limit lines
with those that would occur outside the impact limit lines if no destruct action were taken.
The Mode-5 failure-response methodology was fully developed in an earlier RTI report¹.
As pointed out there, the shape of the impact density function can be controlled somewhat
through the selection of shaping constants that appear in the defining equation. Intuition
suggests that the constants should be vehicle dependent, since (1) ruggedly built missiles
would, after a malfunction, be more likely to impact well away from the flight line than
would a fragile space vehicle that tends to break up before deviating significantly, and
(2) certain vehicles, after a malfunction, tend to stabilize and continue thrusting at large
angles of attack, while other vehicles that experience similar malfunctions tend to tumble.
Hit probabilities computed by program DAMP for targets located more than two miles or
so uprange from the pad or more than a few miles from the flight line, are due almost
entirely to the Mode-5 impact-density function. Thus, the assumed probability of
occurrence of a Mode-5 response as well as the selected Mode-5 constants are of
considerable importance.
The tasking for this study is set forth as Task No. 10/95-77, Paragraph 2.0, of Contract
FO4703-91-C-0112. The primary purpose of the tasking is: "Perform a study to
determine the best values for Mode-5 failure probability and the Mode-5 density-
function shaping constant A." Although not explicitly included in the statement of work,
the study also develops absolute failure probabilities for Atlas, Delta, and Titan, and
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relative probabilities of occurrence for all failure-response modes for these vehicles, LLV1,
and other new launch systems.
Although it may be reasonable to establish the relative probability of occurrence of a
Mode-5 failure response by empirical means, the number of Mode-5 failures is too small to
have any hope of establishing accurate values for the shaping constants from this sample
alone. Inadequate descriptions of vehicle behavior in the available historical records and
uncertainty in impact location following a malfunction add to the difficulty of classifying
failure responses. In view of the limited data available for vehicles that have experienced
Mode-5 failures, the values chosen for the Mode-5 constants must depend on simulations of
vehicle behavior following failure.
2. Examples Showing Need for Mode 5
The need for a Mode-5 response or some similar response mode (or a multiplicity of other
response modes) can be seen from the following vehicle performance descriptions extracted
from Appendix D:
(1) Atlas 8E, 24 Jan 61. Missile stability was lost at about 161 seconds, some 30
seconds after BECO, probably due to failure of the servo-amplifier power supply.
The sustainer engine shut down at 248 seconds, and the vernier engines about 10
seconds later. Impact occurred 1316 miles downrange and 215 miles crossrange.
(2) Titan M-4, 6 Oct 61. A one-bit error in the W velocity accumulation caused impact
86 miles short and 14 miles right of target.
(3) Atlas 145D (Mariner R-1), 22 July 62. Booster stage and flight appeared normal
until after booster staging at guidance enable at about 157 seconds. Operation of
guidance rate beacon was intermittent. Due to this and faulty guidance equations,
erroneous guidance commands were given based on invalid rate data. Vehicle
deviations became evident at 172 seconds and continued throughout flight with a
maximum yaw deviation of 60° and pitch deviation of 28° occurring at 270
seconds. The vehicle deviated grossly from the planned trajectory in azimuth and
velocity, and executed abnormal maneuvers in pitch and yaw. The missile was
destroyed by the RSO at 293.5 seconds, some 12 seconds after SECO.
(4) Atlas SLV-3 (GTA-9), 17 May 66. Vehicle became unstable when B2 pitch control
was lost at 121 seconds. Loss of pitch control resulted in a pitch-down maneuver
much greater than 90°. Guidance control was lost at 132 seconds. After BECO,
the vehicle stabilized in an abnormal attitude. Although the vehicle did not
follow the planned trajectory, SECO (at 280 seconds), VECO (at 298 seconds), and
Agena separation occurred normally from programmer commands.
(5) Atlas 95F (ABRES/AFSC), 3 May 68. Immediately after liftoff the telemetered roll
and yaw rates indicated that the missile was erratic. During the first 10 seconds of
flight the missile yawed hard to the left. It then began a hard yaw to the right,
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crossed over the flight line and continued toward the right destruct line. Shortly
thereafter the missile apparently pitched up violently and the IIP began moving
back toward the beach. The missile was destructed at about 45 seconds when the
altitude was about 14,000 feet and the downrange distance about 9 miles. Major
pieces impacted less than a mile offshore, indicating uprange movement of the
impact point during the last part of thrusting flight.
(6) Delta Intelsat III, 18 Sep 68. Due to loss of rate gyro, undamped pitch oscillations
began at 20 seconds. A series of violent maneuvers followed at 59 seconds.
During the 13-second period while these maneuvers continued, the vehicle
pitched down some 270°, then up 210°, and then made a large yaw to the left. At
72 seconds the vehicle regained control and flew stably in a down and leftward
direction until 100 seconds. At this time, with the main engine against the pitch
and yaw stops, the destabilizing aerodynamic forces became so large that quasi-
control could no longer be maintained. The first stage broke up at 103 seconds.
The second stage was destroyed by the RSO at 110.6 seconds. Major pieces
impacted about 12 miles downrange and 2 miles left of the flight line.
(7) Delta Pioneer E, 27 Aug 69. First-stage hydraulics system failed a few seconds
before first-stage burnout (MECO). The vehicle pitched down, yawed left, rolled
counterclockwise driving all gyros off limits, and then tumbled. Second-stage
separation and ignition occurred while the vehicle was out of control. After about
20 seconds, the second stage regained control in a yaw-right, pitch-up attitude. It
flew stably in this attitude for about 240 seconds until destroyed by the safety
officer at T+484 seconds.
(8) Atlas 68E, 8 Dec 80. Flight appeared normal until 102.7 seconds when the lube oil
pressure on the B2 booster engine suddenly dropped. At 120.1 seconds, the
engine shut down, followed 385 msec later by guidance shutdown of the B1
engine. The asymmetric thrust during shutdown caused yaw and roll rates that
the flight control system could not correct. As a result, attitude control was lost
and the thrusting sustainer pivoted the missile to a retrofire attitude before the
vehicle could be stabilized. After the booster package was jettisoned, the missile
was stabilized and decelerating in the retrofire mode by 148 seconds. The
sustainer continued thrusting in this attitude until 282.9 seconds when reentry
heating apparently caused sustainer shutdown and vehicle breakup.
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It is obvious from the response-mode definitions in Appendix A that none of the described
vehicle failures can be considered as a Mode 1, 2, or 3 response, or a Mode-4 on-trajectory
failure.* Except possibly for (2), it also seems apparent that none can be modeled as either a
rapid tumble or a slow turn.
*
Although prompt destruct action during any of the described flights might have resulted in a Mode-4
classification, the safety officer typically needs several seconds to evaluate data after a malfunction.
Quick action is contrary to safety philosophy if impact limit lines are not threatened and the destruct
system is not at risk, since additional flight time enhances the user's opportunity to pinpoint the
nature of the problem.
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A good illustration of a Mode-5 failure response occurred during launch of Prospector
(Joust) on the Eastern Range in June 1991. The Joust consists of a single-stage Castor IV-A
solid-propellant rocket motor and a payload module. The "vehicle made a radical pitch-up
maneuver due to aft-skirt structural failure at approximately T+14 Seconds." [2] The
vacuum instantaneous impact trace from the RSO console is shown in Figure 1. If the
safety officer had taken destruct action during the time interval from 18 to 25 seconds,
impact would have been well away from the flight line.
CYBER A
UNCLASSIFIED
IP MAP 1
JOUST1761-A
20 SEC.
+ 30.0
+
30 0
ALTER
PRIME
1.17B
CNTRAVES3
SKIN
ON TRACK
ON TRACK
1.0 DELAY
25 SEC.
1.0 DELAY
18 SEC.
30 SEC.
+ 12 CHEV
15 CHEV
19.7 5L0
16.3 3 SLO
32.2 SHT
30.1 SHT
0.1 RGT
15 SEC.
0.7 LFT
4.2 LOW
4 1 LOW
170 HDG
78 HDG
245 VEL
625 VEL
2 ALT
2 ALT
0.14
CNTRAVES3
SKIN
ON TRACK
ON TRACK
0.5 DELAY
0.5 DELAY
+
4 GREEN
Figure 1. Joust Impact Trace Showing a Mode-5 Failure Response
As still another example of a Mode-5 failure response, a guided Red Tigress sounding
rocket was launched from Pad 20 at Cape Canaveral on 20 Aug 91. Within a second or
two after clearing the launcher, the rocket made a near 90° right turn, and flew stably in
this direction until destroyed by the safety officer at 23.3 seconds. Pieces impacted
some two or three miles from the launch pad. This failure might have been classified
as a Mode-2 response if destruct action had been taken shortly after launch.
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3. Understanding the Mode-5 Failure Response
Unlike failure response Modes 3 and 4, response Mode 5 (and also Mode 2) is not a direct
function of time from launch. For Modes 3 and 4, the mean point of impact (MPI) for each
debris class is fixed, once the failure time is established. At each instant there is only one
possible location for the MPI for each debris class. On the other hand, the Mode-5 impact-
density function for each debris class consists of a primary part and a secondary
superimposed part. The primary impact-density function accounts for impact variability
due to the erratic flight of the vehicle. It is used to determine the probability that the mean
piece in a debris class resulting from vehicle breakup falls in a given area (say on a building
or open field). The secondary density function accounts for debris dispersion due to
vehicle breakup and to aerodynamic effects during free fall. It is used to determine the
probability that fragments from the class actually hit a building or field. In other words, the
primary impact-density function is used to compute the probability that the secondary
function is centered in some specified area; the secondary function, which describes the
distribution of class pieces about the mean point, is then used to compute the probability
that one or more class pieces impacts on the specified population center or area.
The primary part of the Mode-5 impact density function, which was presented as Eq. (9.5)
in Ref. [1], is reproduced here as Eq. (1):
Ce^⁺⁺R
(1)
where R is the range from the launch point in miles, Φ* is the angle in radians between the
uprange direction and a line from the pad through the impact point, R is the impact-range
rate in miles per second. A and C are dimensionless shaping constants, and shaping-
constant D is in miles. For a Mode-5 response, there is by definition an earliest time of
occurrence Tₚ (pitch-over time) and a latest time of occurrence TB (burnout, orbital injection,
or some other specified termination time). The specific time in this span at which a Mode-5
response manifests itself is of no consequence, although the duration of the span must be
considered in assigning a probability of occurrence for a Mode-5 response.
Given that a Mode-5 response has occurred, the probability that the center of the secondary
function lies in some region or on some building (population center) is determined by
integrating the primary impact-density function for the class over the region or building.
The primary function depends on range (R) and direction (Φ) from the launch point to the
population center, but not directly on time from launch. The primary function does,
*
As an aid to understanding, the supplement of Φ, designated as Θ, is used in plots and tables in this
report.
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however, involve the quantity R which is expressed explicitly as a function of R and only
implicitly as a function of time. Values of R from the nominal trajectory are differenced to
compute R.
The secondary Mode-5 impact-density function is circular normal in form and expressed by
the equation
2 f(d)
(2)
where d is the distance from the impact point of the mean piece to the center of the target,
and σᶜ is the standard deviation (dispersion) for the debris class. The fact that the center of
the secondary impact-density function (or secondary MPI for a debris class) lies on some
population center does not necessarily mean that pieces in the class hit the center. The
probability that one or more pieces actually hits the pop center is determined by integrating
the secondary impact-density function over the center and combining results for all pieces
in the class. The dispersions for the secondary function are computed by root-sum-
squaring individual dispersions* arising from the effects of winds, vehicle-breakup
velocities, and drag uncertainties for the class. They are computed from the nominal
trajectory, and can be explicitly expressed as a function of impact range. Since the pop
center can also be hit if the MPI of the secondary density function lies outside the pop
center, all possible mutually=exclusive locations of the secondary function that can result in
impact on the pop center must be considered. For each mutually-exclusive location, the
probability that one or more class pieces impacts on the pop center is calculated, and the
results combined to obtain the total hit probability for the class.
The Mode-5 primary impact-density function is modeled SO it is independent of how the
impact point arrives at a particular location. For example, there are myriad paths that a
vehicle can travel to impact at a location two miles crossrange left from the launch pad.
Figure 1 shows one such way for a Joust vehicle that failed at 15 seconds, but four seconds
later had moved the impact point uprange and crossrange to a position two miles
crossrange left from the launch point. Another way to place the impact point two miles
crossrange left is for the vehicle to fly in the wrong direction (north instead of east) from
liftoff.
Although numerous failure mechanisms and vehicle behaviors can lead to a Mode-5
response and impact in a particular area, the exact mechanism and behavior are irrelevant.
All such possibilities are assumed to be accounted for by Eq. (1). Four specific failures that
produce Mode-5 responses are easily described: (1) a re-orientation of the guidance
platform, (2) insertion of an erroneous spatial target into the guidance system, (3) locking of
the engine nozzle in a fixed position near null thus producing a near-constant angular
*
These dispersions are a subset of the Mode-4 impact dispersions.
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acceleration of the vehicle body and a slow turn of the velocity vector, (4) erroneous
accumulation of velocity bits by the guidance system. Many other Mode-5 responses are so
convoluted that they defy description or categorization.
3.1 Effects of Mode-5 Shaping Constants
The primary part of the Mode-5 impact-density function was presented previously as
Eq. (1). As originally formulated, the function contained three shaping constants. If both
numerator and denominator of the equation are divided by the constant C, and B is
substituted for D/C, one unnecessary constant disappears so that the function may be
expressed as follows:
e⁴⁶ +B/R
f(R,Φ)=
=
(3)
The values chosen for the shaping constants A and B that appear in Eq. (3) influence, but do
not change, the basic nature of the Mode-5 impact-density function. For many years values
of A = 2.5 and B = 1000 were used in the Eastern Range ship-hit computations, although in
more recent risk studies the value of A has been increased to 3.0. This increase resulted
from the observation that, in recent years, vehicles that experience Mode-5 failure responses
seem less likely than earlier developmental vehicles to deviate significantly from the
intended flight line. To see how A and B affect the distribution of Mode-5 impacts, and to
further understanding of the function, the results of choosing various values of A and B are
provided in Appendix B.
3.2 Effects of Shaping Constant on DAMP Results
As pointed out in the Introduction, two important types of constant parameters
required by DAMP for risk estimations must be determined. They are: (1) probability
of a Mode-5 failure response, and (2) values of the Mode-5 shaping constants A and B,
currently set at 3.0 and 1000, respectively. As will be demonstrated later, DAMP
results are far more sensitive to changes in A than in B.
The following cases illustrate the effects that constant A has on calculated risks.
Case 1: Baseline Risks for Atlas IIA
In the baseline risk analysis for Atlas IIA¹, the probability of a Mode-5 failure response
was estimated at 12.5% of the total failure probability during the first 120 seconds of
flight. Even so, risks resulting from Mode-5 responses accounted for about 90% of the
total risks for people inside the impact limit lines (ILL). Table 1 indicates the range of
risks inside the ILLs for day launches from Pad A using various estimates of the
shaping constant A and a value of B = 1000.
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Table 1. Effects of Mode-5 Shaping Constant A on Atlas IIA Risks
B = 1,000
Percent of Mode-5
Casualty Expectancy (x 10⁶) inside ILLs
Constant A
IPs Uprange
Mode 5
Total for all Modes
2.5
28.6
246
259.9
3.0
20.7
136
149.4
3.5
14.6
58.9
72.7
4.0
10.0
30.5
44.3
The results in the third column are directly proportional to the probability that a Mode-
5 failure occurs. For the Atlas IIA analysis, a value of 1/200 = 0.005 was assumed.
Case 2: Risk Contours for Atlas IIAS
Definitions of Flight Hazard Area and Flight Caution Area may be based on the risk
contours for inner-ear injury. Constant A can have a significant effect on the location of
the 10⁶ contour, as illustrated in Figure 2 and Figure 3 for the Atlas IIAS. For these
figures, the Mode-5 absolute probability of occurrence was 0.005, constant A was 3.0
and 3.5, and constant B was 1000.
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11
96/01/6
Figure 2. Atlas IIAS Risk Contours for Inner-Ear Injury with A = 3.0
1)
is
-
10 -4 4
Mode-5 - 5 A = 3.0
10 - -6 6
Inner Ear Injury In
Atlas IIAS
10 -5 5
Inner Ear In Injury
10⁻⁶
4
10
10.5
Atlas IIAS
- Mode-5 A = 3.5
10⁻⁴
OF
Figure 3. Atlas IIAS Risk Contours for Inner-Ear Injury with A = 3.5
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4. Methodology for Assessing Failure Probabilities
A primary purpose of this study is to develop estimates of the relative probabilities of
occurrence of a Mode-5 failure response for Atlas, Delta, Titan, and as a by-product, for
other launch vehicles as well. Natural fallouts of this effort are the relative probabilities of
occurrence of other failure-response modes used in program DAMP as well as overall
vehicle failure probabilities. There are at least two approaches commonly used in
estimating launch-vehicle failure probabilities: (1) a so-called parts-analysis or engineering
approach, involving an engineering assessment of the reliability of various parts and
components comprising each missile subsystem, and the effects of a part, component or
subsystem failure; and (2) an empirical statistical approach based on actual launch results.
There are serious problems with both approaches.
4.1 The Parts-Analysis Approach
A description of this approach, its difficulties and shortcomings, are discussed in some
detail in a draft report by Booz Allen & Hamilton, Inc.¹⁴¹ prepared in 1992 for the Air Force
Space Command. Since we cannot improve on the ideas and words expressed by
Booz
Allen, we quote the following from that report:
"The engineering approach for calculation of launch vehicle success rates is based
on measurement/estimation of piece-part reliabilities and their combination into
reliability block models of the launch system. These block models include
consideration of the criticality of individual components, the presence (or absence)
of redundant capabilities, the likelihood that one component failure might cause a
failure in another component, as well as other needed data. By combining the
individual piece-part reliabilities in this model, the engineering approach produces
an overall reliability estimate for the launch system.
"The engineering approach has several significant limitations that tend to reduce
confidence in its results. First, the approach assumes that the interrelationships
among and between sub-systems are understood sufficiently to enable
development of a reliability block diagram. This assumption is highly
questionable in complex systems, such as space launch vehicles, whose operational
histories include many anecdotes regarding unexpected relationships between
"independent' sub-systems.
"The second drawback of the engineering approach is that it assesses the reliability
of the system in a perfectly assembled condition. As a result, it assesses reliability
without regard to manufacturing, processing, or operations variations and errors."
Effects typically overlooked or ignored include:
a. Improper installation of components
b. Erroneous computer programs
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C. Insertion of improper computer programs
d. Support-personnel fatigue
A third limitation of the parts-analysis approach discussed in Ref. [4] deals with the
subjectivity and invalid assumptions often used to estimate piece/component reliabilities.
Here Booz Allen quotes from a report by the Office of Technology Assessment, and we
do likewise:
"The design reliability of proposed vehicles is generally estimated using:
Data from laboratory tests of vehicle systems (e.g., engines and avionics) and
components that have already been built;
Engineer's judgments about the reliability achievable in systems and
components that have not been built;
Analyses of whether a failure in one system or component would cause other
systems and components, or the vehicle to fail; and
Assumptions (often tacit) that:
the laboratory conditions under which systems were tested precisely
duplicate the conditions under which the systems will operate,
the conditions under which the system will operate are those under which
they were designed to operate,
the engineer's judgments about reliability are correct, and
the failure analyses considered all circumstances and details that influence
reliability.
Such engineering estimates of design reliability are incomplete and subjective..."
Effects influencing reliability that the analyst may fail to consider include:
a. Lightning strikes
b. Aging effects, particularly for solid propellants
C. Corrosion
d. Insufficient heat or cold insulation for critical components
e. Icing
f. Erroneous antennae patterns or instrumentation
Booz
Allen concludes as follows:
"Finally, due to its nature, the engineering approach can not account for
undetected design flaws. (If these flaws were detected, and could be modeled,
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they would be corrected.) However, experience has shown that design flaws do
cause failures in operational launch systems, and will likely do so in the future."
The major objection to the parts-analysis approach, hinted at above but not actually
expressed, is that all such approaches involve either explicitly or implicitly a so-called K-
factor. The K-factor is included in the reliability calculations in an attempt to compensate
for the fact that the environment in which a part or system is tested is not the same as the
flight environment. Since the K-factor is surely not the same for all components and
systems, multiple values must be assumed and the entire process becomes highly
subjective.
In view of the objections and limitations just presented, in this report the parts-analysis
approach is not considered in assessing vehicle reliability or in estimating the relative
probabilities of occurrence of the various failure-response modes.
4.2 The Empirical Approach
A seemingly more objective way to evaluate vehicle reliability (or conversely, vehicle
failure probabilities) is by examining the actual performance of flight-tested vehicles. In
support of this approach, the following is quoted from the Office of Technology
Assessment⁵⁵ report previously referenced:
"The only completely objective method of estimating a vehicle's probability of
failure is by statistical analysis of number of failures observed in identical vehicles
under conditions representative of those under which future launches will be
attempted."
Although we agree with the Office of Technology Assessment statement, the obvious
difficulty with this approach is that no such sample of identical vehicles exists or is ever
likely to exist.
In their report⁴¹ previously referenced, Booz Allen makes the same point in different words
by stating that "the empirical approach has one significant drawback in that it can not
project the effects of changes in the launch systems". The effects of such changes can only
be assessed objectively by further flight testing.
The difficulty in projecting success rates (or failure rates) from past tests to future tests is
clearly recognized. Nevertheless, RTI has relied exclusively on this method to estimate the
relative probabilities of occurrence for the various failure-response modes. Even so, total
objectivity cannot be claimed since, as will be seen later, the answers depend to a large
extent on how the performance data are filtered, and how big a risk one wants to take that
the true failure probability is underestimated.
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5. Computation of Failure Probabilities
The test results for Atlas, Delta, and Titan in the tables of Appendix D have been used
for three primary purposes:
(1) To predict or estimate the overall probability that each vehicle will fail during the
various phases of flight (see Table 39, Appendix D, for flight-phase definitions).
(2) To establish the relative and overall probabilities for Response Modes 1 through 5.
(3) To establish the relative frequency of tumble for Response Modes 3 and 4.
5.1 Overall Failure Probability
To predict failure probabilities for Atlas, Delta, and Titan, the test results in
Appendix D for representative configurations (i.e., "1" in last column) have been
filtered using three different weighting techniques described in Appendix C:
(1) Equal weighting
(2) Index-count weighting
(3) Exponential weighting
In computing filtered or weighted failure probabilities, a test is assigned a score of one
to indicate the occurrence of a failure or some anomalous behavior, and a score of zero
if no failure occurred. Admittedly, there may be disagreements about the classification
of a few flights, since the launch agency may consider as successful or partially
successful some flights that are shown as failures in Appendix D. To avoid such
disagreements, it is better to think of some non-normal events, particularly those
occurring late in flight, as anomalies rather than failures. The flight phases, as shown
in column 2 of Table 2 and defined in Appendix D.1.3, are inclusive; e.g., flight phase
"0 - 3" includes phases 0, 1, 1.5, 2, 2.5, and 3. An 'NA' in the response-mode column in
the tables of Appendix D indicates that some failure or anomalous behavior has had an
effect on the final orbit or impact point without producing additional risks to people on
the ground or necessarily failing the mission. In the failure-probability calculations of
Table 2 and Table 3, an 'NA' has been considered as a success for all flight phases
except "0 - 5", irrespective of the phase in which the failure or anomalous behavior took
place. Only in flight phase "0-5" is an 'NA' response considered a failure. The
filtered results for representative configurations (defined in Appendix D.1.4) are given
in Table 2 for six flight phases. For flights with multiple entries in the Response-Mode
and Flight-Phase columns (e.g., see Appendix D.2.1, No. 257), the first listed value was
used in the filtering process.
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Table 2. Predicted Failure Probabilities for Representative Configurations
Filter Technique
Sample
Flight
Equal
Index
Expon.
Expon.
Expon
Failures
Vehicle
Phase
Weight
Count
F = 0.99
F = 0.98
F = 0.97
/Total
Atlas
0
0
0
0
0
0
0/7
0 - 1
0.0256
0.0253
0.0245
0.0219
0.0186
4/156
0 - 2
0.0449
0.0385
0.0387
0.0313
0.0243
7/156
0 - 3
0.0769
0.0715
0.0714
0.0643
0.0568
12/156
0 - 4
0.0833
0.0811
0.0801
0.0740
0.0663
13/156
0 - 5 *
0.1090
0.1100
0.1078
0.1019
0.0929
17/156
Delta
0
0
0
0
0
0
0/125
0 - 1
0.0160
0.0126
0.0134
0.0104
0.0075
2/125
0 - 2
0.0160
0.0126
0.0134
0.0104
0.0075
2/125
0 - 3
0.0160
0.0126
0.0134
0.0104
0.0075
2/125
0 - 4
0.0160
0.0126
0.0134
0.0104
0.0075
2/125
0 - 5 *
0.0640
0.0447
0.0535
0.0469
0.0442
8/125
Titan
0
0.0306
0.0210
0.0225
0.0292
0.0352
3/98
0 - 1
0.0234
0.0305
0.0314
0.0403
0.0470
4/171
0 - 2
0.0409
0.0496
0.0514
0.0642
0.0750
7/171
0 - 3
0.0526
0.0581
0.0597
0.0689
0.0773
9/171
0 - 4
0.0526
0.0581
0.0597
0.0689
0.0773
9/171
0 - - 5 *
0.1111
0.1167
0.1188
0.1284
0.1358
19/171
* Includes response mode 'NA'
It is apparent from the data in Table 2 that estimates of future vehicle reliability depend
on the filtering (i.e., weighting) technique applied. Since there are many ways to
perform the filtering, all generally producing slightly different results, the choice of
method to use in deriving empirical failure probabilities cannot be totally objective.
Subjective decisions must also be made about which past configurations to consider as
representative of future vehicles, which flight tests to include in the sample, how to
weight the individual flights, and, in unusual cases, whether to consider a flight a
success or a failure, and to which flight phase to attribute a failure. Except for data
weighting (i.e., choice of filter), these decisions were made for Atlas, Delta, and Titan
before computing the failure probabilities shown in Table 2.
For Atlas and Delta, it can be seen from Table 2 that the predicted failure probabilities
computed with the exponential filter decrease as the value of F decreases. Since a
decreasing F means more emphasis on recent data and less emphasis on the old, the
launch reliability for these vehicles is apparently improving. The reverse seems to be
true for Titan, suggesting either that Titan reliability is not improving or, possibly, that
improvements that have been or are being made to the vehicle are not yet fully
reflected in the test results. For Atlas and Delta, the computed failure probabilities
based on equal weighting are higher than for all other filters, and the predicted failure
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probabilities using index-count filtering are larger than those for exponential filtering.
For Titan, the results are mixed, further suggesting that Titan reliability has not
improved in recent years.
For comparison purposes, the same filtering techniques have been applied to all flight
tests shown in the tables of Appendix D, regardless of configuration. The results are
presented in Table 3.
Table 3. Predicted Failure Probabilities for All Configurations
Filter Technique
Sample
Flight
Equal
Index
Expon.
Expon.
Expon.
Failures
Vehicle
Phase
Weight
Count
F = 0.99
F = 0.98
F = 0.97
/Total
Atlas
0
0
0
0
0
0
0/7
0 - 1
0.1053
0.0641
0.0422
0.0273
0.0190
56/532
0 - 2
0.1711
0.0990
0.0555
0.0311
0.0204
91/532
0 - 3
0.2086
0.1261
0.0802
0.0559
0.0455
111/532
0 - 4
0.2143
0.1330
0.0873
0.0627
0.0511
114/532
0 - 5 *
0.2575
0.1671
0.1150
0.0866
0.0725
137/532
Delta
0
0
0
0
0
0
0/196
0 - 1
0.0172
0.0164
0.0148
0.0110
0.0077
4/232
0 - 2
0.0259
0.0232
0.0201
0.0133
0.0085
6/232
0 - 3
0.0431
0.0279
0.0263
0.0150
0.0089
10/232
0 - 4
0.0431
0.0279
0.0263
0.0150
0.0089
10/232
0 - 5 *
0.1078
0.0766
0.0740
0.0536
0.0459
25/232
Titan
0
0.0306
0.0137
0.0187
0.0281
0.0349
3/98
0 - 1
0.0534
0.0319
0.0351
0.0399
0.0467
18/337
0- 2
0.1424
0.0771
0.0719
0.0662
0.0750
48/337
0 - 3
0.1632
0.0924
0.0830
0.0711
0.0770
55/337
0 - 4
0.1662
0.0942
0.0840
0.0712
0.0771
56/337
0 - 5 *
0.1958
0.1369
0.1326
0.1277
0.1346
66/337
* Includes response mode 'NA'
A comparison of Table 2 and Table 3 shows that in most cases, but not all, exponential
filtering produces failure probabilities for the representative configuration samples that
are smaller than the corresponding probabilities for the all-configuration samples. The
fact that most differences between corresponding samples are relatively small attests to
the effectiveness of the exponential filter in down-weighting early launch failures. This
is not the case for equal weighting of tests, where the predicted failure probabilities
based on all configurations are up to 3.6 times as large.
With respect to the weighting of missile and space-vehicle performance data, RTI
favors an exponential filter over either the equal-weight or index-count filters.
Weighting percentages for the three filters are given in Table 4 for sample sizes of 4 to
1,000. Except for small samples, the percentages produced by equal weighting place
too much emphasis on old data, thus failing to account for the learning process and
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hardware improvements that have taken place through the years. For samples
approaching 100 or so, it seriously over-weights the old data and under-weights the
more recent events. Although equal weighting does not seem suitable for this
application, it could be appropriate in other large-sample situations, for example,
predicting the failure probability of devices that are all manufactured at the same time
by the same process, and tested to the same standards.
Table 4. Comparison of Weighting Percentages
Sample
Last +
Last 5
Last 10
Last 25
Last 50
Last
Size
Filter *
Point
Points
Points
Points
Points
Half
4
Expon.
25.8
-
-
-
-
51.0
Index
40.0
-
-
-
-
70.0
Equal
25.0
-
-
-
-
50.0
10
Expon.
10.9
52.5
100.0
-
-
52.5
Index
18.2
72.7
100.0
-
-
72.5
Equal
10.0
50.0
100.0
-
-
50.0
20
Expon.
6.0
28.9
55.0
-
-
55.0
Index
9.5
42.9
73.8
-
-
73.8
Equal
5.0
25.0
50.0
-
-
50.0
100
Expon.
2.3
11.1
21.1
45.7
73.3
73.3
Index
2.0
9.7
18.9
43.6
74.8
74.8
Equal
1.0
5.0
10.0
25.0
50.0
50.0
200
Expon.
2.0
9.8
18.6
40.4
64.7
88.3
Index
1.0
4.9
9.7
23.4
43.7
74.9
Equal
0.5
2.5
5.0
12.5
25.0
50.0
500
Expon.
2.0
9.6
18.3
39.7
63.6
99.4
Index
0.4
2.0
4.0
9.7
19.0
75.0
Equal
0.2
1.0
2.0
5.0
10.0
50.0
1000
Expon.
2.0
9.6
18.3
39.7
63.6
99.996
Index
0.1
1.0
2.0
4.9
9.7
75.0
Equal
0.1
0.5
1.0
2.5
5.0
50.0
* F = 0.98 for exponential filter
+ "Last" refers to the most recent data point
The index-count filter has serious deficiencies when applied to either small or large
samples of missiles and space vehicles. For small samples, too much emphasis is
placed on recent data. For a sample of four, 40% of the total weight is given to the last
test, and 70% to the last two tests. For a sample of ten, 18.2% of the total weight is
given to the last test and 72.7% to the last five tests. The reliability improvement rate
implied by these weightings seems too optimistic unless there were serious design
flaws in the early configurations that were discovered and corrected. Since many types
of failures surely exist that occur only once in 50 or once in 100 or more launches, the
tenth launch may be no better than the first for predicting the probability of occurrence
of such failures. For large samples, the index-count filter under-weights current data
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more and more as the sample size increases. For samples of 200, 500, and 1000, the
weighting of the last 50 tests are, in each case, 43.7%, 19.0%, and 9.7% of the total
weight. For samples of 100 or more, no matter how large, the index-count filter assigns
25% of the data weight to the oldest half of the data sample - too much in RTI's
opinion.
For missiles and space vehicles, the data weightings imposed by the exponential filter
(F = 0.98) appear reasonable. For small samples less than 20 or so, there is little
difference between equal and exponential weightings. For sample sizes near 80, the
index-count and exponential filters produce similar results. For sample sizes of 200
and more, the weights assigned to the most recent 5, 10, 25, and 50 tests are essentially
constant, showing the fading-memory nature of the exponential filter.
The denominator of the exponential-filter equation [Eq. (18), Appendix C] is a
geometric series that asymptotically approaches a limit of [1/(1 - F)] as n approaches
infinity. For F = 0.98, that limit is 50. Thus, the last data point, which is always given a
weight of one, can never be weighted less than 2% of the total, no matter how large the
sample. For samples of 200 and 300, the oldest half of the data receives only 11.7% and
5% of the total weight. For samples of 500 and larger, the oldest half of the data sample
is essentially omitted altogether. The exponential filter is clearly a fading-memory
filter, as it should be for space-vehicle performance data.
Having decided upon the exponential filter as the best method for weighting missile
and space-vehicle performance data, a filter constant F must be chosen. To see how
data weighting varies with filter-factor value, weighting percentages for various
samples were computed for representative configurations of Atlas, Delta, and Titan
using values of F from 0.96 to 0.995. The results are shown in Table 5.
9/10/96
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Table 5. Filter Factor Influence on Weighting Percentages
Vehicle
Filter
Last
Last 10
Last 50
Last
Last 100
Pt. Ratio
(sample)
Cons't
Point
Points
Points
Half
*
Points
last: first
Atlas
0.96
4.01
33.6
87.2
96.0
98.5
560
(156)
0.97
3.03
26.5
78.9
91.5
96.1
112
0.98
2.09
19.1
66.4
82.9
90.6
22.9
0.99
1.26
12.1
49.9
68.7
80.1
4.7
0.995
0.92
9.0
40.9
59.7
72.7
2.2
Delta
0.96
4.02
33.5
87.5
92.9
98.9
158
(125)
0.97
3.07
26.9
80.0
87.3
97.4
43.7
0.98
2.17
19.9
69.1
78.3
94.3
12.2
0.99
1.40
13.4
55.2
65.6
88.6
3.5
0.995
1.07
10.5
47.6
58.2
84.7
1.9
Titan
0.96
4.00
33.5
87.1
97.1
98.4
1030
(171)
0.97
3.02
26.4
78.6
93.2
95.8
177
0.98
2.07
18.9
65.7
85.1
89.6
31.0
0.99
1.22
11.7
48.1
70.5
77.2
5.5
0.995
0.87
8.5
38.5
60.8
68.5
2.3
* Last half + 1 if sample size is odd
Although the choice of a filter constant cannot be completely objective, use of a value
less than 0.97 or greater than 0.99 produces undesirable weightings. For F = 0.96, for
example, the most recent test result for Titan is weighted 1030 times that for the oldest
test; the last 50 data points receive 87.1% of the total weighting, leaving only 12.9% for
the first 121 flights; the last 100 flights receive 98.4% of the total weighting thus, in
effect, omitting the oldest 71 flights from the solution.
At the high end of the F spectrum, a value of 0.995 fails to down-weight the old test
results sufficiently. Using Atlas as an example, the most recent data point (1/31/96) is
weighted only 2.2 times that of the oldest data point (8/14/64). The oldest half of the
data, stretching from 8/14/64 to 3/06/73, receives 40% of the total weight, and the
earliest 56 launches, comprising 36% of the data, receive 27% (100 - 73) of the total
weight. This is not too different from equal weighting of tests, a procedure that fails to
acknowledge the improvements in Atlas reliability that have taken place over a period
of 32 years.
In choosing a value of F, an attempt is made to strike a suitable balance between two
contrary objectives:
(1) to down-weight substantially those failures for which the probability of
occurrence has been greatly reduced through redesign and replacement of
components, improved test procedures, and the like;
9/10/96
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(2) to down-weight only slightly, or not at all, those failures that are random in
nature, that can still occur in replacement components, or that occur only once in
100 or several hundred launches in components that have not yet failed.
No matter what technique is employed, filtering is at best a compromise. The perfect
filter would somehow down-weight to some extent or entirely those failures that have
been "fixed" or made less likely, without down-weighting those random failures with
unknown causes. The filters considered in this study have no such capabilities; they
produce a result based solely on the launch sequence, and where in the sequence
failures have occurred.
In predicting vehicle failure probabilities from empirical data, large representative
samples are essential for a good estimate, and the more reliable the vehicle, the greater
the need for a large sample. For example, if some characteristic exists in exactly 1% of a
population, the probability is 0.37 that it will not appear in a random sample of 100,
and 0.61 that it will not appear if the sample size is 50. If the characteristic exists in 2%
of the population, it fails to appear about 36% of the time in a random sample of 50.
For reasons presented above, the data samples for Atlas, Delta, and Titan have been
made as large as possible consistent with the notion of representative configurations, as
set forth in Ref. [4]. In RTI's judgment, the value of F that best weights the performance
data is 0.98, although a value anywhere in the interval 0.97 to 0.99 cannot be ruled out.
For consistency in data weighting, the same values of F have been used for all vehicle
programs. The differences in predicted failure probability that result from these three
F's are illustrated in Figure 4 for Atlas. The plots show the inverse relationship
between filter volatility and the value of F. For F = 0.97 vis-à-vis larger values, it can be
seen that the filtered failure probability jumps higher with each failure and drops at a
faster rate with each successful launch that follows.
9/10/96
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0.12
0.11
-
F = 0.97
F = 0.98
0.10
F = 0.99
0.09
0.08
Filtered Failure Probability
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.00
0
20
40
60
80
100
120
140
160
Sample Index (newer
Figure 4. Filter Factor Results for Representative Configurations of Atlas
In summary, it must be recognized that there is no "correct" value for F, and that it is
even difficult to argue generally that one value of F is better than another. In RTI's
view, values of F below 0.97 place too much emphasis on a relatively small sample of
recent launches. Values above 0.99 extend the sample so far back in time that too little
emphasis is placed on improvements in design, materials, and operational procedures.
In any event, the value chosen for F is crucial in arriving at a predicted failure
probability. For the more conservative, a value of 0.99 can be chosen; the optimistic
might chose 0.97.
Since most risk-analysis studies that RTI makes are concerned with the launch area,
failure probabilities beyond flight-phase 2 are of minor interest. The overall failure
probabilities shown in Table 6 have, with one exception, been extracted from Table 2
for F = 0.98. Where a best estimate is called for, RTI plans to use these probabilities in
future launch-area risk analyses for the 45 SW/SE unless directed otherwise, or until
additions to the data samples in Appendix D justify changes.
9/10/96
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Table 6. Failure Probabilities for Atlas, Delta, and Titan
Predicted Failure Probability *
Flight Phase
Flight Phase
Vehicle
0 1
0 - 2
Atlas
0.022
0.031
Delta
0.010
0.013
Titan
0.040
0.064
* Exponential filter with F = 0.98
For Delta, the predicted failure probabilities shown in Table 2 for flight-phases 0 1
and 0 - 2 are the same, since no second-stage failure has occurred in the 125 flights
included in the representative sample. Obviously, this does not mean that the
probability of a Delta second-stage failure is zero. As stated earlier, the choice of F is a
judgment matter with the most reasonable range for F considered to be 0.97 ≤ F ≤ 0.99.
To show a difference in failure probabilities between Delta flight phases, a value of
F = 0.98 has been used for flight phases 0 - 1, and 0.99 for flight phases 0 - 2. It is an
interesting coincidence that the same value of 0.013 is obtained using F = 0.98 and all
Delta configurations (see Table 3). Another way to estimate the Delta second-stage
failure probability is to calculate an upper confidence limit at some suitable level for an
event that has occurred zero times in 125 trials. At the 80% confidence level, the
reliability is at least 0.987, SO the failure probability during second-stage burn (flight
phases 1.5 - 2) is no bigger than 0.013.
5.2 Relative and Absolute Probabilities for Response Modes
For Atlas, Delta, and Titan vehicles, failure-response Modes 1, 2, and 3 are much less
likely to occur than Modes 4 and 5. Since the probabilities of occurrence for the less-
likely modes may be only one in a thousand or less, such responses may not have
occurred at all in the flight tests of representative configurations. In fact, in the
combined samples for Atlas, Delta, and Titan, only 16 failures have occurred during
flights phases 0 - 2. None of the 16 resulted in response-modes 1, 2, or 3. Because of
the small number of failures in the representative configuration samples, the relative
probabilities of occurrence for Modes 1 through 5 have been estimated using results
from all vehicle configurations and launches shown in Appendix D. The rationale for
this approach is that, except for obvious problems that have been corrected, other
changes made through the years to improve vehicle reliability have reduced the
probabilities of occurrence of all response modes more or less proportionally. The
greater significance of more recent vehicle modifications and test results is accounted
for by using an exponential filter to estimate overall failure probabilities. Thus, if
Mode-1 failures occurred more frequently in the distant past than in recent years, the
weighting process reduces the significance of the earlier Mode-1 responses in the
relative probability-of-occurrence calculations. As tabulated from Appendix D, the
number (count) of failures by response mode and flight phase for Atlas, Delta, Titan,
and Eastern-Range Thor launches are given in Table 7 through Table 10. Thor launches
9/10/96
24
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from the Western Range were not included since available performance records were
incomplete. The results for the four vehicles are combined in Table 11. Table 12 gives
last-occurrence dates by response mode for each launch vehicle.
Table 7. Number of Atlas Failures - All Configurations (532 Flights)
Flight
Failure-Response Mode
3 & 4
Phase
1
2
3
4
5
'NA'
Tumble
0
0
0
0
0
0
0
0
0 - 1
7
1
2
38
8
4
11
0 - 2
7
1
2
66
15
13
19
0 - 3
7
1
2
86
15
18
25
0- 4
7
1
2
89
15
21
27
0 - 5
7
1
2
89
15
23
27
Table 8. Number of Delta Failures - All Configurations (232 Flights)
Flight
Failure-Response Mode
3 & 4
Phase
1
2
3
4
5
'NA'
Tumble
0
0
0
0
0
0
0
0
0 - 1
0
0
0
2
2
5
0
0 - 2
0
0
0
4
2
10
1
0 - 3
0
0
0
7
3
12
1
0 - 4
0
0
0
7
3
13
1
0 - 5
0
0
0
7
3
15
1
Table 9. Number of Titan Failures - All Configurations (337 Flights)
Flight
Failure-Response Mode
3 & 4
Phase
1
2
3
4
5
'NA'
Tumble
0
0
0
0
3
0
0
1
0 - 1
2
2
0
13
1
0
5
0 - 2
2
2
0
39
5
3
10
0 - 3
2
2
0
46
5
5
11
0 - 4
2
2
0
47
5
7
11
0 - 5
2
2
0
47
5
10
11
Table 10. Number of Eastern-Range Thor Failures (85 Flights)
Flight
Failure-Response Mode
3 & 4
Phase
1
2
3
4
5
'NA'
Tumble
0
0
0
0
0
0
0
0
0 - 1
4
1
1
15
4
1
3
0 - 2
4
1
1
20
5
3
3
0 - 3
4
1
1
22
5
3
3
0- 4
4
1
1
22
5
4
3
0 - 5
4
1
1
22
5
5
3
9/10/96
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Table 11. Number of Failures for All Vehicles (1186 Flights)
Flight
Failure-Response Mode
3 & 4
Phase
1
2
3
4
5
'NA'
Tumble
0
0
0
0
3
0
0
1
0 - 1
13
4
3
68
15
11
19
0 - 2
13
4
3
129
27
29
33
0 - 3
13
4
3
161
28
38
40
0- 4
13
4
3
165
28
45
42
0- 5
13
4
3
165
28
53
42
Table 12. Date of Most Recent Failure
Response
Vehicle
Mode
Atlas
Delta
Titan
Thor*
1
03/02/65
none
12/12/59
04/19/58
2
12/18/81
none
05/01/63
12/30/58
3
04/25/61
none
none
07/21/59
4
08/22/92
05/03/86
10/05/93
03/24//64
5
12/08/80
08/27/69
11/30/65
01/24/62
* Last Thor launch was 02/23/65
For the reasons advanced previously, an exponential filter has been used to estimate
relative probabilities of occurrence for Modes 1 through 5 and the fraction of Mode-3
and Mode-4 failures that tumble while the vehicle is thrusting. The percentage
weightings for various data samples are shown in Table 13 for values of F from 0.980 to
0.999. Because of the large size of the composite sample (1186), the filter-control
constant of 0.98 used previously to estimate absolute failure probabilities for individual
vehicles does not seem suitable for estimating relative probabilities for the individual
response modes. Use of 0.98 would effectively place 98.2% of the total weight on the
most recent 200 tests thus, in effect, eliminating the earliest 986 tests from the solution.
These are the very tests needed to provide an adequate sample of failures from which
to estimate relative frequencies of occurrence of the individual response modes.
9/10/96
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Table 13. Percentage Weighting for Sample of 1186 Launches
Filter
Last
Last 100
Last 200
Last 300
Last 500
Point Ratio
Constant
Point
Points
Points
Points
Points
Last:First
0.999
0.14
13.7
26.1
37.3
56.7
3.3
0.996
0.40
33.3
55.6
70.6
87.3
1.2 X 10²
0.995
0.50
39.5
63.5
78.0
92.1
3.8 X 10²
0.994
0.60
45.3
70.0
83.6
95.1
1.3 X 10³
0.993
0.70
50.5
75.5
87.9
97.0
4.2 X 10³
0.992
0.80
55.2
79.9
91.0
98.2
1.4 X 10⁴
0.991
0.90
59.5
83.6
93.4
98.9
4.5 X 10⁴
0.990
1.00
63.4
86.6
95.1
99.3
1.5 X 10⁵
0.980
2.00
86.7
98.2
99.8
99.996
3.9 X 10¹¹
The value of F = 0.999 is considered inappropriate because, as seen in Table 13, the
weighting factor applied to the most recent datum is only 3.3 times that applied to the
oldest test result from 39 years ago. The most recent 200 and 300 points in the sample
comprising 16.8% and 25.2% of the data receive only 26.1% and 37.3% of the total
weight. This is not too different from equal weighting of data, which is appropriate
only if the relative frequency of occurrence of each response mode has not changed
significantly through the years. On the other hand, use of F = 0.99 effectively throws
out the oldest 600 to 700 launches that are sorely needed for an adequate sample size.
The results of the filtering process are given in Table 14 for failures during flight phases
0 2.
Table 14. Response-Mode Occurrence Percentages
Filter
Response Mode
Factor
1
2
3
4
5
0.999
7.39
2.27
1.70
73.30
15.34
0.996
2.24
4.35
0.37
80.37
12.67
0.995
1.32
4.92
0.19
82.59
10.98
0.994
0.73
5.26
0.09
84.57
9.35
0.993
0.39
5.37
0.04
86.25
7.95
0.992
0.20
5.31
0.02
87.68
6.78
0.991
0.11
5.13
0.01
88.92
5.84
0.990
0.05
4.87
0.00
90.02
5.06
0.980
0.00
1.86
0.00
96.81
1.33
The results in Table 14 show that the percentages of occurrence for response-modes 2
and 4 are relatively insensitive to filter-factor values, while the percentages for
Modes 1, 3, and 5 decrease as filter memory (filter factor) decreases. This suggests that
occurrences of Modes 1, 3, and 5 have been decreasing over the years, while Modes 2
and 4 occurrences have not changed much. Although it cannot be argued convincingly
9/10/96
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that 0.993 is superior to 0.992 or 0.994, or even values outside this interval, a value of
0.993 was chosen.
This section has thus far described a rationale for selecting a filtering process and filter
constant to estimate percentages of occurrence of failure-response modes for Atlas,
Delta, and Titan launch vehicles. These are mature launch systems with improved
reliability as a result of years of experience and corrections of problems. Although the
designs of new launch vehicles may be based to some extent on mature systems, new
systems are expected to fail at a higher rate. For vehicles with liquid-propellant stages
burning at liftoff, the percentages of occurrence of the various response modes are more
likely to be similar to the earlier versions of Atlas, Delta, and Titan than to current
vehicles. For lack of any other data, for such new liquid-propellant systems the relative
percentages for the five failure-response modes have been calculated using the total
combined sample of Atlas, Delta, Titan, and Thor with a filter constant of 0.999 (almost
equal weighting).
For new solid-propellant vehicles, use of F = 0.999 results in a Mode-1 percentage that
seems much too high. All of the 13 Mode-1 failures in the composite sample (Table 11)
involved liquid-propellant vehicles, whereas none of the Atlas, Delta, or Titan
configurations with solid-propellant boosters have experienced a Mode-1 response. On
the other hand, use of F = 0.993 that is applied for mature launch systems seems to
reduce the probability of a Mode-5 response too much, since a Red Tigress vehicle and
a Joust vehicle launched at the Cape in 1991 both experienced Mode-5 failure responses
(see Section 2). As a compromise between new and mature liquid-propellant vehicles,
a value of F = 0.996 has been assumed for new solid-propellant vehicles. The
percentages shown in Table 15 for flight phases 0 - 2 have been obtained from Table 14.
Similar information for flight phases 0 - 1 are given in Table 16. In future risk studies
for the 45 SW/SE, RTI plans to use these relative percentages for mature and new
systems.
Table 15. Recommended Response-Mode Percentages for Flight Phases 0 - 2
Response
Mature Launch
New Solid Systems
New Liquid Systems
Mode
Systems (F = 0.993)
(F = 0.996)
(F = 0.999)
1
0.4
2.2
7.4
2
5.4
4.3
2.3
3
0.1
0.4
1.7
4
86.2
80.4
73.3
5
7.9
12.7
15.3
9/10/96
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Table 16. Recommended Response-Mode Percentages for Flight Phases 0 - 1
Response
Mature Launch
New Solid Systems
New Liquid Systems
Mode
Systems (F = 0.993)
(F = 0.996)
(F = 0.999)
1
0.5
3.4
10.7
2
7.4
6.6
4.3
3
0.1
0.6
2.4
4
81.9
74.5
67.0
5
10.1
14.9
15.6
Absolute probabilities of occurrence for response Modes 1 through 5 can be obtained by
multiplying the absolute failure probabilities for flight phases 0- - 1 and 0 - 2 (Table 6)
by the relative failure probabilities in Table 15 and Table 16. The results are shown in
Table 17. Probabilities are listed to six decimal places to show differences, not because
all figures are actually significant. To obtain these results, more precise values for
relative probabilities of occurrence were used than shown in Table 15 and Table 16.
Table 17. Absolute Failure Probabilities for Response Modes 1- - 5
Vehicle:
Atlas
Delta
Titan
Flight
0 - 1
0 - 2
0 - 1
0- 2
0- 1
0- 2
Phase:
(0-170 sec)
(0-280 sec)
(0-270 sec)
(0-630 sec)
(0-300 sec)
(0-540 sec)
Mode 1
0.000119
0.000121
0.000054
0.000051
0.000216
0.000250
Mode 2
0.001637
0.001665
0.000744
0.000698
0.002976
0.003437
Mode 3
0.000011
0.000012
0.000005
0.000005
0.000020
0.000026
Mode 4
0.018007
0.026738
0.008185
0.011212
0.032740
0.055200
Mode 5
0.002226
0.002465
0.001012
0.001034
0.004048
0.005088
Total
0.022
0.031
0.010
0.013
0.040
0.064
For each vehicle, the absolute probabilities for Modes 1, 2, and 3 differ slightly for flight
phases 0 - 1 and 0 - 2. This difference is due to the unequal data weighting produced
by the exponential filter. If equal data weighting had been applied, the absolute
probabilities for these modes would have been identical as expected, since Modes 1, 2,
and 3 cannot occur beyond flight phase 1.
Differences in absolute probabilities for Modes 4 and 5 for flight phases 0 - 1 and 0 - 2
can also be seen in the table. A part of this difference may result from unequal data
weighting, but primarily it is due to the obvious fact that fewer Mode 4 and 5 failures
have occurred during flight phase 0 - - 1 than during the longer span of flight phase 0 - 2.
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5.3 Relative Probability of Tumble for Response-Modes 3 and 4
Exponential filters with values of F from 0.98 to 0.999 have been used to estimate the
percentage of Mode-3 and Mode-4 responses that terminate with a thrusting tumble.
Results are given in Table 18 for flight phases 0 - 2 and 0 - 5. For launch-area risk
calculations, only flight phases 0 - 2 are of interest. The data sample was a
chronological composite of all Atlas, Delta, Titan, and Thor tests and configurations
shown in Appendix D. To several decimal places at least, the values in the table are
determined entirely from Mode-4 responses, since the last vehicle to experience a
Mode-3 response (4/25/61) is weighted out of the solution: The results in Table 18 are
based on a total sample size of 1,186 flight tests.
Table 18. Percent of Response Modes 3 and 4 That Tumble
Filter Factor
Flight Phases 0 - 2
Flight Phases 0 - 5
0.999
25.0
25.0
0.996
26.3
27.0
0.993
27.3
28.6
0.990
28.3
30.1
0.980
31.3
34.8
Through flight phase 2, there were 33 tumbles out of a total of 132 Mode-3 and Mode-4
responses. Through flight phase 5, there were 42 tumbles out of 168 Mode-3 and
Mode-4 responses.
As seen from Table 13, the smaller the filter factor, the greater the weight placed on
recent test data. In view of this, it is apparent from Table 18 that the percentage of
Mode-4 responses that end with a thrusting tumble has been increasing gradually. The
same conclusion is reached for flight phases 0 - 2 and 0 - 5. In recognition of this
gradual increase, in future studies RTI will assume that approximately one-third of
Mode-3 and Mode-4 failure responses end with a thrusting tumble.
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6. Shaping Constants Through Simulation
Since adequate test data are not available to establish the Mode-5 shaping constants
empirically, other methods are needed for this purpose. It will be recalled that, after
vehicle pitchover, any malfunction with the potential to cause a substantial deviation
from the intended flight line is, by definition, a Mode-5 failure response. The
malfunction need not actually cause a large deviation to be classified as a Mode-5
response. One such class of failures leading to a Mode-5 response has been termed a
random-attitude failure. Such responses can result from guidance and control failures
that lead to erroneous orientation of the guidance platform or an erroneous spatial
target. Another class of failures that can cause sustained deviation away from the flight
line is the slow turn, where the engine nozzle, in effect, locks in some fixed position,
generally but not necessarily near null. Both types of malfunctions have been
investigated in an attempt to estimate numerical values for Mode-5 shaping constants A
and B. Basically, the idea is to (1) run a large sample of random-attitude and slow-turn
failures, (2) calculate the percentages of impacts in five-degree sectors from 0° to 180°,
(3) compare these percentages with those obtained from the Mode-5 impact density
function when specific values are assigned to A and B, and (4) assign values to A and B
until the best possible fit is obtained between the simulated-turn impacts and the
theoretical Mode-5 impacts.
6.1 Malfunction Turn Simulations
6.1.1 Random-Attitude Failures
A guidance and control failure leading to a fixed erroneous direction of thrust is
termed a random-attitude failure. Such failures represent a subset of possible Mode-5
failure responses. Random-attitude failures can be used to establish the maximum
possible region of impact, given that a vehicle has flown normally for a specified period
of time. For this purpose RTI has developed a Random-Attitude Failure Impact Point
(RAFIP) program written in Fortran (3900 lines of code) for execution on a personal
computer.
Using a Monte Carlo approach, program RAFIP first selects a starting time and then a
random thrust direction on the attitude sphere, with all directions having the same
chance of being chosen. Each Monte-Carlo run is begun using the nominal vehicle
position and velocity at the selected start time, assuming an instantaneous change in
thrust direction. Thrust is applied continuously in the selected random direction, and
the equations of motion are numerically integrated until one of four conditions is
satisfied: (1) final stage burnout occurs, (2) the vehicle impacts while thrusting,
(3) orbital insertion occurs, (4) the vehicle breaks up due to aerodynamic forces
For conditions (1) and (4), the trajectory is extended to impact using Kepler's equations.
For condition (3), an impact point does not exist. The process just described is repeated
9/10/96
31
RTI
for a suitably large sample so the distribution of resulting impact points will, for all
practical purposes, represent all possible impact points, irrespective of the actual nature
of the failure.
Depending on vehicle breakup characteristics and failure time, a vehicle that
experiences a random-attitude failure may break up at the instant of failure, or after a
few seconds into the turn, or not at all. In making the calculations, three separate
breakup thresholds and a no-breakup case were investigated. With respect to vehicle
breakup, the assumption was made that the vehicle would break up if qα exceeded a
specified constant limit, where q is the dynamic pressure and α is the total angle of
attack. Although the breakup qα may well be a complicated function of Mach number
and other parameters, this simplistic approach was taken.
Random-attitude-failure calculations were made individually for Atlas, Delta, Titan,
and LLV1 starting shortly after pitchover and continuing to some convenient time such
as a stage burnout when the vehicle could no longer endanger the launch area.
Theoretically, the Mode-5 impact density function extends downrange until the
instantaneous impact point vanishes. Since this study is concerned with evaluation of
density-function parameters for launch-area risk analysis, the random-attitude
calculations were stopped at a staging event when the vehicle no longer had sufficient
energy to return the impact point to the launch area. Using trajectory data for each
vehicle, program RAFIP was run to generate 10,000 impact-point samples at each
starting time. Calculations were made at ten-second intervals.
6.1.2 Slow-Turn Failures
Certain types of guidance and control failures can cause the thrusting engine to gimbal
to null or a near-null position: Such failures can produce what is herein called a slow
turn. For various reasons, after an engine is commanded to null it may not thrust
precisely through the center of gravity, e.g., structural misalignments, shifting center of
gravity, canted nozzles. Since, like random-attitude failures, slow turns constitute a
subset of Mode-5 failure responses, they have been investigated using RTI program
RAFIP. The following assumptions have been made in making the calculations:
(1) The effective thrust offset of a "nulled" engine is normally distributed with a zero
mean and a standard deviation of 0.1°.
(2) A fixed thrust offset results in a constant angular acceleration of the airframe, and
thus a constant angular acceleration of the thrust vector.
(3) For small thrust misalignments, the angular acceleration of the airframe is
proportional to the angular thrust misalignment.
At each time point, the angular acceleration produced by small thrust offsets was
estimated from the malfunction turn data provided to the safety office by the range
user. Malfunction turns for the Atlas IIAS were provided for three gimbal angles, the
smallest being one degree. For each gimbal angle, the results were plotted as
9/10/96
32
RTI
cumulative angle turned versus time. Since the slope of the curve (i.e., the turning rate)
is greatest when the thrust (and thus airframe) is directed at right angles to the velocity
vector, the average angular acceleration during the first 90° of rotation was obtained
from the equation
(4)
so that
(5)
where t is the elapsed time from the beginning of the tumble turn until the airframe has
rotated approximately 90°. If the assumption is made that the angular acceleration is
directly proportional to the thrust offset angle (i.e., nozzle deflection), the angular
acceleration Θd for any small deflection angle becomes
(6)
where Θ is the angular acceleration computed from Eq. (5) for deflection angle δ (1° for
Atlas IIAS), and δd is some small deflection angle.
Using the Atlas IIAS data, angular accelerations ё were computed at ten-second
intervals from the programming time of 15 seconds to 275 seconds for δ = 1°. For each
starting time, a normal distribution with zero mean and a standard deviation of 0.1°
was sampled to obtain an initial thrust misalignment δd to substitute in Eq. (6). The
resulting angular acceleration θd was applied throughout the turn. Slow-turn
calculations were made in a manner analogous to the random-attitude turns, using the
reference trajectory to obtain the starting position and velocity components. The slow
turn was assumed to occur in a randomly oriented plane containing the starting
velocity vector. Each turn was carried out until one of the four conditions listed in
Section 6.1.1 for random-attitude turns was met. For conditions (1) and (4), impact
points were calculated and, along with thrusting impacts from condition (2), summed
for each five-degree sector from 0° to 175°. At each starting time, 10,000 impact-point
calculations were made.
6.1.3 Factors Affecting Malfunction-Turn Results
Random-attitude turns and slow turns are only subsets of the totality of Mode-5 failure
responses. As discussed earlier in Section 3, other types of behavior following a Mode-
5 failure are numerous and largely impossible to categorize, much less simulate.
Ideally, impact distributions from all types of Mode-5 responses should be combined
before results are compared with those obtained from the theoretical Mode-5 impact
9/10/96
33
RTI
density function. Since this could not be done in general, impacts from only the two
types of malfunction turns were considered. Several factors affect the results of the
simulations:
a. Weighting of turn data: Both random-attitude and slow-turn simulations were
made for Atlas IIAS. In combining impacts from the two data sets, random-
attitude turns were assumed to be three times as likely to occur as slow turns. A
factor of three was selected since, among the Mode-5 failure responses in the
performance summaries for Atlas, Delta, and Titan, random-attitude turns
appeared to occur about three times as often as slow turns. In many cases, lack of
detailed information made it difficult to decide whether a Mode-5 response
should be considered as a random-attitude turn, a slow turn, or some other type
of failure. The relative weighting of turns makes little difference, however, since
the impact distribution for the two types of turns are similar (as shown later in
Figure 5), and since the weighted composite must lie between the two. It was
assumed that similar results would be obtained for Delta, Titan, and LLV1, so
slow-turn computations were not made for these vehicles, cutting the number of
time-consuming simulations in half.
b. Breakup qα: In the turn calculations, the assumption was made that vehicle
breakup would occur if a certain value of qa was reached. In addition to the no-
breakup case which is considered unrealistic, separate runs were made for three
constant values of qα: 5,000, 10,000, and 20,000 deg-lb/ft². As stated previously,
the determination of vehicle breakup is, in reality, much more involved than this
simplistic approach would suggest. However, to add realism to the malfunction-
turn calculations, use of a simple approach seemed better than none at all. For
Titan IV, allowable (but not breakup) qα's were provided as functions of Mach
number. The maximum permissible value and corresponding Mach number for
Titan/Centaur, Titan/NUS, and Titan/IUS were, respectively, 6819 deg-lb/ft² at
Mach No. 0.77, 5332 deg-lb/ft² at Mach No. 0.815, and 17,000 deg-lb/ft² at Mach
No. 0.325. For Atlas, Delta, and LLV1 vehicles, no breakup qa data were
available. The breakup qα's used in the calculations bracket the range of
permissible qα's for the Titan vehicles.
C. End time TB: The simulated impact distributions from random-attitude failures
and slow turns were compared with impact distributions computed from the
Mode-5 theoretical impact-density function. For the comparisons to be
meaningful, the value selected for TB in the Mode-5 impact-density equation and
the stop time for thrusting-turn simulations must be the same. To some extent,
the shaping constants A and B derived by fitting the theoretical and simulated
impact data depend on TB, since the percentage of impacts in each 5° sector
depends on TB. However, after A and B have been established for a particular T₆,
using a different TB in the DAMP calculations has no effect on computed risks
provided an adjustment is made in the probability of occurrence of a Mode-5
9/10/96
34
RTI
response. Referring to Eq. (3), the right-hand member must be multiplied by the
probability P₅ of a Mode-5 response to obtain absolute probabilities. Except for TB
itself (and to a slight degree, shaping constants A and B), the quantities in the
equation do not depend on TB. Thus if TB and P₅ are both changed so that p₅/(T₃ -
Tₚ) remains constant, the computed risks are unchanged.
If destruct action (i.e., impact limit lines) is included in the DAMP calculations,
the supplemental risks* resulting from that action must be accounted for. In this
case, the termination time has a minor influence on results, since it affects the
number of impacts that would occur beyond the impact limit lines without
destruct that are forced inside when destruct action is taken. If destruct action is
omitted, the value of TB is immaterial (i.e., supplemental Mode-5 risks are non-
existent) provided that the impact range along the reference trajectory at time TB
exceeds the range to all targets of interest. (Except in this paragraph,
supplemental Mode-5 risks are not addressed in this present report.)
d. Vacuum calculations: Atmospheric effects were accounted for in determining
when vehicle breakup would occur and, to some extent, during each thrusting
turn by using accelerations from the nominal trajectory. To reduce computer time
and cost of this study, vacuum calculations were made during free fall after
vehicle breakup or burnout. Although this increased impact dispersions
somewhat, vacuum results should not be drastically different from those
obtainable using a maximum-beta piece. In theory at least, different mode-5
shaping constants exist for each debris class. In view of the uncertainties in
vehicle breakup conditions and characteristics, and in the overall process of
simulating Mode-5 malfunctions, attempts to derive unique shaping constants for
each debris class did not seem justified.
6.1.4 Malfunction-Turn Results for Atlas IIAS
For Atlas IIAS, the distribution of impacts for simulated random-attitude turns, slow
turns, and a weighted combination (75% random-attitude and 25% slow turn) are
shown in Figure 5. Since the impact distribution (i.e., the percentages of impacts in 5°
sectors) for the weighted composite was not significantly different from that for
random-attitude failures, slow-turn computations were not made for Delta, Titan, and
LLV1.
*
See Ref. [1], Section 10.
9/10/96
35
RTI
100
Atlas IIAS Failures through 280 sec
2
Breakup q-alpha = 20,000 deg-lb/ft
Random-attitude turns
Stow turns
Combined turns (0.75 random + 0.25 slow)
10
Percent in 5-deg sector (%)
1
0.1
0
20
40
60
80
100
120
140
160
180
Angle From Flight Path (deg)
Figure 5. Combined Random-Attitude and Slow-Turn Results
9/10/96
36
RTI
6.2 Shaping Constants for Atlas IIAS
6.2.1 Optimum Mode-5 Shaping Constants
Since the dynamic pressures that can cause the Atlas IIAS to break up were not
available, random-attitude failures were simulated for a no-breakup case and for three
breakup qα's: 20,000 deg-lb/ft2, 10,000 deg-lb/ft2, and 5,000 deg-lb/ft². For each case,
270,000 trajectories were run, giving a total of 1,080,000. It turned out that the value
chosen for the breakup qa was critical in determining shaping constant A, since the
lower the qa, the less the thrusting time before breakup, and the higher the percentages
of impacts in sectors near the flight line.
For Atlas IIAS, the effects of qa on breakup are shown in Figure 6 where, for the
selected qα's, the percentages of random-attitude turns that result in breakup before
280 seconds are plotted against failure time.
100
Atlas IIAS
90
q-alpha in deg-lb/ft2
80
q-alpha = 5,000
70
-
q-alpha = 10,000
q-alpha = 20,000
Breakup Percent (%)
60
50
40
30
20
10
0
0
40
80
120
160
200
240
280
Failure Time (sec)
Figure 6. Atlas IIAS Breakup Percentages for Random-Attitude Turns
For failures between 10 and 30 seconds, most breakups do not occur at failure, but later
in flight after the vehicle has built up significant velocity. For failures between 40 and
105 seconds, more than 80% breakup occurs, even for qα's as high as 20,000 deg-lb/ft².
9/10/96
37
RTI
In this region, breakup occurs at or shortly after vehicle failure. Beyond 170 seconds,
the dynamic pressure between failure and 280 seconds stays sufficiently low so that the
vehicle remains intact.
The dramatic differences in impact distributions that can result at certain times during
flight if the vehicle is subject to aerodynamic breakup can be seen by comparing the
impact footprints in Figure 7 and Figure 8. Both patterns show 10,000 impact points
from random-attitude failures of the Atlas IIAS at 130 seconds. Figure 7 is for no
breakup, and Figure 8 is for a breakup qα of 5,000 deg-lb/ft².
The data in Table 19 comprise an example of a 270,000-point sample of random-attitude
failures run at 10-second intervals from 15 to 275 seconds. (For brevity, only every-
other failure time is shown in the table.) Ten thousand impacts are computed at each
failure time. Five-degree sectors are identified in the left-hand column. For each time,
the number of impacts in each 5° sector is shown in the column for that time. The total
number of impacts for all failure times and the percentages of impacts in each sector are
given in the last two columns of the table.
9/10/96
38
RTI
9/10/96
1
1
Atlas IIAS Impacts
Random-Attitude Failures at 130 sec.
Thrust to 280 sec.
No Breakup
39
Figure 7. Atlas IIAS Impacts with No Breakup
RTI
9/10/96
1
-
Atlas IIAS Impacts
Random-Attitude Failures at 130 sec.
Thrust to 280 sec.
Breakup q-alpha = 5,000 deg-lb/ft2
40
Figure 8. Atlas IIAS Impacts with Breakup
RTI
Table 19. Sample Impact Distribution for Atlas IIAS with No Breakup
Failure Time (sec)
Ang.
15
35
55
75
95
115
135
155
175
195
215
235
255
275
All
%
0
255
300
411
487
608
835
1107
1843
3333
4092
5386
7906
10000
10000
87746
32.50
5
279
314
388
465
575
808
1082
1762
3065
3827
4206
2094
0
0
38474
14.25
10
261
316
427
495
627
744
975
1652
2820
2081
408
0
0
0
21265
7.88
15
298
329
354
464
558
730
945
1445
782
0
0
0
0
0
12195
4.52
20
274
319
378
421
566
670
845
1292
0
0
0
0
0
0
8875
3.29
25
287
316
349
406
525
641
776
1203
0
0
0
0
0
0
8189
3.03
30
257
339
337
415
452
505
617
800
0
0
0
0
0
0
6893
2.55
35
299
336
381
368
405
506
550
3
0
0
0
0
0
0
5883
2.18
40
275
293
388
374
409
454
520
0
0
0
0
0
0
0
5593
2.07
45
299
298
310
397
366
412
441
0
0
0
0
0
0
0
5285
1.96
50
242
282
331
346
323
352
378
0
0
0
0
0
0
0
4535
1.68
55
280
308
282
303
314
292
331
0
0
0
0
0
0
0
4005
1.48
60
272
308
289
306
293
299
260
0
0
0
0
0
0
0
3827
1.42
65
288
262
279
300
294
286
256
0
0
0
0
0
0
0
3666
1.36
70
250
275
326
281
264
243
205
0
0
0
0
0
0
0
3483
1.29
75
283
261
272
271
238
232
170
0
0
0
0
0
0
0
3321
1.23
80
273
266
249
272
234
194
111
0
0
0
0
0
0
0
3022
1.12
85
287
274
241
242
219
191
96
0
0
0
0
0
0
0
2888
1.07
90
235
285
246
230
226
171
70
0
0
0
0
0
0
0
2778
1.03
95
303
283
280
235
180
136
55
0
0
0
0
0
0
0
2815
1.04
100
292
283
268
215
190
126
49
0
0
0
0
0
0
0
2620
0.97
105
279
254
246
211
200
108
30
0
0
0
0
0
0
0
2571
0.95
110
283
267
237
204
168
114
27
0
0
0
0
0
0
0
2448
0.91
115
261
255
230
178
162
120
18
0
0
0
0
0
0
0
2346
0.87
120
311
263
251
211
167
98
17
0
0
0
0
0
0
0
2321
0.86
125
276
255
225
189
155
62
11
0
0
0
0
0
0
0
2239
0.83
130
266
251
227
195
126
86
8
0
0
0
0
0
0
0
2246
0.83
135
283
259
227
176
128
77
8
0
0
0
0
0
0
0
2221
0.82
140
286
244
184
186
169
63
5
0
0
0
0
0
0
0
2138
0.79
145
305
243
187
180
118
59
8
0
0
0
0
0
0
0
2102
0.78
150
251
225
178
166
128
72
8
0
0
0
0
0
0
0
1895
0.70
155
293
259
199
151
113
68
2
0
0
0
0
0
0
0
2103
0.78
160
253
213
220
177
127
59
6
0
0
0
0
0
0
0
1952
0.72
165
254
242
203
172
115
68
2
0
0
0
0
0
0
0
2008
0.74
170
298
256
195
171
127
60
6
0
0
0
0
0
0
0
2034
0.75
175
312
267
205
140
131
59
5
0
0
0
0
0
0
0
2018
0.75
Total
10000
10000
10000
10000
10000
10000
10000
10000
10000
10000
10000
10000
10000
10000
270000
100.00
9/10/96
41
RTI
In Figure 9, the percentages of impacts in 5° sectors from 0° to 180° have been plotted
for Atlas IIAS random-attitude turns out to 280 seconds. (It should be remembered that
random-attitude turns are representative of combined random-attitude and slow turns.)
For B = 1000, theoretical Mode-5 impact percentages are also plotted in the figure for
best-fit values of A obtained by trial and error.
100
Atlas HAS Random-Attitude Failures through 280 sec
Breakup q-alpha in deg-lb/ft²
no breakup
20,000
10,000
5,000
10
Percent in 5-deg sector (%)
B = 1,000
A = 1.90
A = 2.75
A = 3.20
A = 3.45
1
0.1
0
20
40
60
80
100
120
140
160
180
Angle From Flight Path (deg)
Figure 9. Atlas IIAS Simulation Results with B = 1,000
By observing curve shapes, it can perhaps be seen that no single value of A causes a
theoretical impact distribution and a distribution of impacts from random-attitude
turns to match closely over the entire range of 5° sectors. Attempts to improve the
match on one end of the curve by selecting a different A merely degrades the match on
9/10/96
42
RTI
the other end. It is possible, however, to obtain fairly close agreement over sectors*
from ±80° to ±180°, as seen in Figure 9. Since for Atlas IIAS there are few, if any,
significant population centers in the launch area outside these sectors (i.e., within ±80°
of the flight line), failure of the curves to match closely near the flight line is of little
consequence. If a better data match is considered desirable for computing risks to
population centers within ±80° of the flight line (e.g., ships), either a different A can be
selected for use with B = 1,000 or other values of A and B can be derived. If only a
single value of B is used, no matter what the value, a good match between theoretical
and simulated data is not possible over the entire 180° sector for various breakup qα's.
Before becoming too concerned about lack of a data match between 0° and 80°, it
should be remembered that many types of Mode-5 responses cannot be simulated, so
that the malfunction-turn impact distributions plotted in Figure 9 are only a subset of
all possible Mode-5 impacts. Based on twelve Mode-5 failure responses for which
impact data are available, it is believed that inclusion of the "non-simulatable" Mode-5
responses would considerably improve the match in the sector from ±10° to ±80°.
Another mitigating factor is that risks near the flight line are totally dominated by
Mode-4 failure responses.
To see how data matching is affected by selecting widely differing values of B, the
theoretical Mode-5 impact distributions were computed for B = 50,000, 100,000, 500,000,
and 5,000,000. Best-fit values for A were again determined by trial and error. Results
are shown in Figure 10 through Figure 13 along with the same impact distributions for
random-attitude turns plotted in Figure 9.
*
For other values of B and qa, close agreement is possible from ±60° to ±180°.
9/10/96
43
RTI
100
Atlas HAS Random-Attitude Failures through 280 sec
2
Breakup q-alpha in deg-lb/ft
no breakup
20,000
10,000
5,000
10
Percent in 5-deg sector (%)
B = 50,000
A = 3.15
A = 4.10
-
-
A = 4.50
A = 4.75
1
0.1
0
20
40
60
80
100
120
140
160
180
Angle From Flight Path (deg)
Figure 10. Atlas IIAS Simulation Results with B = 50,000
9/10/96
44
RTI
100
Atlas IIAS Random-Attitude Failures through 280 sec
Breakup q-alpha in deg-lb/ft²
no breakup
20,000
10,000
5,000
10
Percent in 5-deg sector (%)
B = 100,000
A = 3.40
A = 4.30
A = 4.75
A = 5.00
1
0.1
0
20
40
60
80
100
120
140
160
180
Angle From Flight Path (deg)
Figure 11. Atlas IIAS Simulation Results with B = 100,000
9/10/96
45
RTI
100
Atlas HAS Random-Attitude Failures through 280 sec
2
Breakup q-alpha in deg-lb/ft
no breakup
20,000
10,000
5,000
10
Percent in 5-deg sector (%)
B = 500,000
A = 4.00
A = 4.80
A = 5.30
A = 5.55
1
0.1
0
20
40
60
80
100
120
140
160
180
Angle From Flight Path (deg)
Figure 12. Atlas IIAS Simulation Results with B = 500,000
9/10/96
46
RTI
100
Atlas IIAS Random-Attitude Failures through 280 sec
Breakup q-alpha in deg-lb/ft²
no breakup
20,000
10,000
5,000
10
Percent in 5-deg sector (%)
B = 5,000,000
A = 4.75
A = 5.65
A = 6.10
A = 6.30
1
0.1
0
20
40
60
80
100
120
140
160
180
Angle From Flight Path (deg)
Figure 13. Atlas IIAS Simulation Results with B = 5,000,000
9/10/96
47
RTI
The five values of B and the corresponding best-fit values of A used to compute the
Mode-5 distributions shown in Figure 9 through Figure 13 are tabulated in Table 20. It
is apparent that the value of A is dependent on both qα and B. In general, if a larger
value of B is selected, a larger value of A is required to effect a fit with the random-
attitude-turn data. On the other hand, if the breakup qa is increased, the required
value of A must be decreased. Only qα is critical since, as shown later, any value of B,
together with its corresponding value of A, can be used in the launch-area risk
computations if significant targets do not lie within ±80° of the flight line.
Table 20. Shaping Constants for Atlas IIAS
Breakup qa
(deg-lb/ft²)
B
A
none
1,000
1.90
20,000
2.75
14,000 *
3.00 *
10,000
3.20
5,000
3.45
none
50,000
3.15
20,000
4.10
10,000
4.50
5,000
4.75
none
100,000
3.40
20,000
4.30
10,000
4.75
5,000
5.00
none
500,000
4.00
20,000
4.85
10,000
5.30
5,000
5.55
none
5,000,000
4.75
20,000
5.65
10,000
6.10
5,000
6.30
* interpolated
9/10/96
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RTI
Because of the uncertainties in breakup conditions, the values of A for each B in Table
20 have been plotted against qa in Figure 14. By reading from the plots, a value of A
for the five values of B can be obtained for any breakup qa deemed appropriate
between 5,000 and 20,000 deg-lb/ft².
6.5
B = 5,000,000
6.0
5.5
B = 500,000
5.0
Mode-5 Constant A
B = 100,000
4.5
B = 50,000
4.0
3.5
B = 1,000
3.0
Atlas IIAS
2.5
0
5000
10000
15000
20000
25000
Breakup q-alpha (deg-lb/ft²)
Figure 14. Effects of Breakup q-alpha on A for Atlas IIAS
6.2.2 Launch-Area Mode-5 Risks
The twenty sets of A and B shown in Table 20 were used to compute Mode-5 launch-
area risks for population centers inside the impact limit lines for an Atlas IIAS daytime
launch of a Telstar-4 payload from Pad 36A. Results of these and two other cases are
given in Table 21. The Mode-5 Ec in the first line (old baseline case) of Table 21 is
presented for comparison only. It was obtained from data in the first line of Table 45 of
an earlier RTI study¹³¹. In Ref. [3], the total Atlas IIAS failure probability for the first
two minutes of flight was set at 0.04, with the probability of a Mode-5 failure response
assumed to be 0.005. The second line in Table 21 shows the result of a recomputation of
the Mode-5 baseline risks, again with B = 1000 and A = 3, using newly derived values
for the total failure probability and for a Mode-5 failure response. For flight phases 0 -
2, a total failure probability of 0.031 was assumed, as extracted from Table 6 for
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RTI
F = 0.98. The conditional probability of a Mode-5 response was assumed to be 0.08
(from the last line of Table 15), so the absolute probability was 0.031 X 0.08 = 0.0025.
For the remaining cases in Table 21, the same assumptions were made for the total
failure probability and for the probability of a Mode-5 response.
Table 21. Shaping Constants and Related Risks for Atlas IIAS
TB
Breakup qα
Mode-5 Ec
P₅
(sec)
(deg-lb/ft²)
B
A
(x 10⁶)
0.005
118
14,000 *
1,000
3.00
227
(baseline)
0.0025
280
14,000 *
1,000
3.00
49.1
(new P₅ & TB)
0.0025
280
none
1,000
1.90
139.8
20,000
2.75
73.7
10,000
3.20
33.4
5,000
3.45
19.8
0.0025
280
none
50,000
3.15
144.9
20,000
4.10
75.6
10,000
4.50
37.1
5,000
4.75
21.8
0.0025
280
none
100,000
3.40
144.8
20,000
4.30
79.8
10,000
4.75
36.1
5,000
5.00
21.1
0.0025
280
none
500,000
4.00
143.6
20,000
4.85
79.9
10,000
5.30
35.9
5,000
5.55
20.8
0.0025
280
none
5,000,000
4.75
144.8
20,000
5.65
77.7
10,000
6.10
34.2
5,000
6.30
22.0
* Interpolated from Figure 14
As seen from Table 21, the Mode-5 risks are highly dependent on A and insensitive to
the value chosen for B provided a proper choice is made for A. Even for values of B as
different as 1,000 and 5,000,000, the Mode-5 risks (qα = 5,000) differ by only 12%. This
difference drops for all other values of B. In fact, the differences probably have more to
do with the choice of A than to any inherent difference in results due to the choice of B.
For Atlas IIAS, 24% of the total Mode-5 Ec in the launch area is due to one population
center, and 51% of the total Ec to only five population centers (see page 49 of Ref [3]). If
values of A had been chosen so that theoretical distributions and random-attitude-turn
distributions more nearly matched for the radial directions to these population centers,
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RTI
the differences in calculated Mode-5 risks for the different values of B would surely
have been less.
Further understanding of why small differences in Ec exist can be gained by plotting
values of the Mode-5 density function computed from Eq. (3) This has been done in
Figure 15 for a range of three miles using values of A and B from Table 21 for
qα = 5,000 deg-lb/ft². Since Eq. (3) does not include a factor to account for the
probability of a Mode-5 failure, the values plotted in the figure are conditional impact
probabilities per square mile. For the sector from 120° to 180°, which is where most
population centers are located, the density-function value for B = 5,000,000 is largest
and for B = 1,000 is smallest. Results consistent with this are shown in Table 21, where
the largest and smallest Ec's are for B = 5,000,000 and B = 1,000, respectively.
10⁻²
A = 3.45, B = 1,000
-
- A = 4.75, B = 50,000
A = 5.00, B = 100,000
10⁻³
A = 5.55, B = 500,000
Mode-5 Density-Function Value
A = 6.30, B = 5,000,000
10⁻⁴
10⁻⁵
0
20
40
60
80
100
120
140
160
180
Theta (deg)
Figure 15. Mode-5 Density-Function Values at Three Miles
6.2.3 Effects of Mode-5 Constants on Ship-Hit Contours
In the preceding section, certain values were assigned to B and, by trial and error, best-
fit values of A were found. For every breakup qα and every B, it was possible to find a
value of A that produced good agreement between theoretical and simulated impact
data over 5° sectors from ±100° to ±180° (see Figure 10 through Figure 13). In some
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cases the agreement gradually deteriorated for angles below ±100° while, in other cases,
agreement was remarkably good to ±40°. Below this, agreement was generally poor
except in a region between +3° and ±6° where the theoretical and simulated curves
crossed.
As pointed out previously, for Atlas pad locations at the Cape essentially all significant
population centers (except ships) are located in the sectors from ±100° to ±180°. Thus
any B with the corresponding best-fit value of A can be used to compute launch-area
risks, irrespective of the assumed breakup qα. In unusual cases at the Cape or at other
launch locations, population centers may be located outside sectors of good agreement
for some B's. If such situations arise, a value of B should be used in the risk
calculations that produces the best fit over the largest sector possible, generally ±40° to
±180°. The values of B producing this result are listed in Table 22 as functions of
breakup conditions.
Table 22. Best-Fit Conditions for Atlas IIAS
Breakup
Conditions
B
A
none
50,000
3.15
20,000
100,000
4.30
10,000
100,000
4.75
5,000
5,000,000
6.30
Although the selected values of A produce poor agreement in the sectors from 0° to
+40°, this does not mean that good agreement in this region is impossible. Instead, it
means that the value of A required to produce good agreement in the ±40° sectors will
produce poor agreement elsewhere. In special situations where the only population
centers of interest are within ±40° of the flight line, other values of A can be derived for
use in the risk calculations.
From a practical standpoint, the effort required to find a value of A that produces a
better fit within ±40° or so of the flight line is unnecessary. Within this sector, the
Mode-4 failure response, which is almost 11 times more likely to occur than a Mode-5
response, totally dominates the computed risks. As verification, the DAMP program
was run for the Atlas IIAS vehicle, and ship-hit contours plotted for three vastly
different pairs of A's and B's. The results are shown in Figure 16 through Figure 21,
where the total failure probability during the first two minutes of flight was assumed to
be 0.04, and the probabilities of Mode-4 and Mode-5 responses were 0.033 and 0.005,
respectively. For each A and B, ship-hit contours were computed for Mode 5 alone,
and then for all response modes. As expected, some downrange extension occurred in
the Mode-5 contours as the value of A was increased, since the higher the value of A,
the more concentrated impacts are near the flight line. When all response modes were
included in the calculations, contour differences were almost imperceptible, showing
the total dominance of Mode 4. If the calculations were remade with a Mode-4
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RTI
response 10.9* instead of 6.6 (0.033 ÷ 0.005 = 6.6) times as likely as a Mode-5 response,
the differences in contours would be even less.
15
Atlas IIAS
----- - - 10⁻⁶ 10-5
Mode 5 P₁
10
5
Crossrange Distance (nm)
0
-5
-10
B = 1,000
A = 3.00
-15
-5
0
5
10
15
20
25
Downrange Distance (nm)
Figure 16. Atlas IIAS Mode-5 Ship-Hit Contours with A = 3.00
*
From Table 15, 86.2 ÷ 7.9 = 10.9.
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RTI
15
-4
Atlas IIAS
10
10⁻⁵
All Mode P1
10⁻⁶
10
5
Crossrange Distance (nm)
0
-5
-10
B = 1,000
A = 3.00
-15
-5
0
5
10
15
20
25
Downrange Distance (nm)
Figure 17. Atlas IIAS All-Mode Ship-Hit Contours with A = 3.00
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RTI
15
Atlas IIAS
-
10⁻⁵
Mode 5P₁
10⁻⁶
10
5
Crossrange Distance (nm)
0
-5
-10
B = 1,000
A = 3.45
-15
-5
0
5
10
15
20
25
Downrange Distance (nm)
Figure 18. Atlas IIAS Mode-5 Ship-Hit Contours with A = 3.45
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RTI
15
Atlas IIAS
10⁴
All Mode P₁
10
10⁶
10
5
Crossrange Distance (nm)
0
-5
-10
B = 1,000
A = 3.45
-15
-5
0
5
10
15
20
25
Downrange Distance (nm)
Figure 19. Atlas IIAS All-Mode Ship-Hit Contours with A = 3.45
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RTI
15
Atlas IIAS
- 10⁻⁶ 10-5
Mode 5 P₁
10
5
Crossrange Distance (nm)
0
-5
-10
B = 5,000,000
A = 6.30
-15
-5
0
5
10
15
20
25
Downrange Distance (nm)
Figure 20. Atlas IIAS Mode-5 Ship-Hit Contours with A = 6.30
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RTI
15
Atlas IIAS
10
All Mode P₁
10⁻⁶
10
5
Crossrange Distance (nm)
0
-5
-10
B = 5,000,000
A = 6.30
-15
-5
0
5
10
15
20
25
Downrange Distance (nm)
Figure 21. Atlas IIAS All-Mode Ship-Hit Contours with A = 6.30
6.2.4 Range Distributions of Theoretical and Simulated Impacts
Earlier discussions had to do with how well the angular part of the Mode-5 impact
density function could be made to agree with angular data derived from simulated
random-attitude turns. A similar procedure was used to test agreement between the
range part of the Mode-5 impact density function and the simulated data. For this
purpose, beginning at 15 seconds random-attitude turns were made at 2-second
intervals out to 279 seconds, assuming no breakup and breakup qα's of 5,000 and
20,000 deg-lb/ft². At each time, 2,000 trajectories and impact points were computed,
giving a total sample of 266,000 for each breakup condition. For each impact point, the
range from the pad was computed, and the total number of impacts calculated in 10-
mile range intervals out to 350 miles. Impacts beyond this range were placed in a
single range category. The percentage of impacts in each range interval was then
computed and plotted as shown in Figure 22.
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RTI
100
Atlas IIAS
Theoretical
2
Breakup q-alpha = 5,000 deg-lb/ft
2
-
Breakup q-alpha = 20,000 deg-lb/ft
10
No Breakup
Percent Impacts in 10-nm Interval
1
0.1
0
50
100
150
200
250
300
350
Impact Range (nm)
Figure 22. Impact-Range Distributions
Theoretical impact percentages for the same 10-mile range intervals were obtained by
integrating the Mode-5 impact-density function [Eq. (3)] between the angle limits of
zero and π, and between the range limits of R₁ and R₂, and doubling the results. The
percentages are plotted in Figure 22. As pointed out in more detail at the end of
Appendix B, the percentage of impacts in any range interval is independent of the
values of A and B.
Figure 22 shows that the range impact distributions for theoretical Mode-5 impacts and
random-attitude failures for breakup qα's between 5,000 and 20,000 deg-lb/ft² are in
excellent agreement out to 50 miles. Theoretical percentages and random-attitude
percentages for qα = 5,000 deg-lb/ft² (considered to be the most realistic value) are in
good agreement out to 190 miles. Beyond that the differences appear fairly large,
magnified as they are by the logarithmic scale, although the maximum absolute
difference is only 0.4%. The steep rise in all curves at 350 miles is artificially created by
lumping all impacts beyond 350 miles into one range interval instead of 10-mile
intervals.
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6.3 Shaping Constants for Delta-GEM
Although less extensive, the computations made and graphs plotted to establish Mode-
5 shaping constants for Delta parallel those described in Section 6.2 for Atlas IIAS. The
approach may be summarized as follows:
(1) Calculate impact points from 10,000 simulated random-attitude turns made at 10-
second intervals from programming time at 6 seconds until staging at 270 seconds
(260,000 simulations total). The impact points from these turns, which produce
impact results similar to slow turns, are assumed to be representative of the
totality of Mode-5 impacts.
(2) Determine the percentages of impacts in 5° sectors from 0° to 180°.
(3) For assumed values of A and B, compute the percentages of impacts in the same
5° sectors from the theoretical Mode-5 impact-density function.
(4) By trial and error, find values of A and B that provide a best fit between the
simulated and theoretical impact data.
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RTI
6.3.1 Optimum Mode-5 Shaping Constants
The percentage of Delta vehicles that break up during simulated random-attitude turns
are plotted against failure time in Figure 23. The same breakup qα's used in the
Atlas IIAS calculations were used here. It can be seen from the figure that over 50% of
the vehicles break up, either immediately or eventually, if a turn begins between about
10 and 115 seconds.
100
Delta-GEM
90
q-alpha in deg-lb/ft 2
80
q-alpha = 5,000
70
q-alpha = 10,000
Breakup Percent (%)
60
q-alpha = 20,000
50
40
30
20
10
0
0
40
80
120
160
200
240
280
Failure Time (sec)
Figure 23. Delta-GEM Breakup Percentages
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RTI
Figure 24 shows the percentages of malfunction-turn impacts in 5° sectors for no
breakup and for breakup qα's of 20,000, 10,000, and 5,000 deg-lb/ft². For B = 1,000,
theoretical Mode-5 impacts are also plotted using best-fit values of A. This value of B
was chosen since it is currently used by-RTI in making launch-area risk studies for the
45th Space Wing. In the sectors from ±80° to ±180°, where most of the population
centers are located, fairly good data fits were possible for all breakup qα's except 5,000
deg-lb/ft. No value of A could be found to produce a good fit with B = 1,000. The
bottom plot in Figure 25 shows that an excellent fit between malfunction-turn and
theoretical data is possible for qα = 5,000 deg-lb/ft² if a different choice of B is made.
100
Delta-GEM Random-Attitude Failures through 270 sec
Breakup q-alpha in deg-lb/ft2
no breakup
20,000
10,000
10
5,000
B = 1,000
Percent in 5-deg sector (%)
A = 1.90
A = 2.90
A = 3.10
A = 4.30
1
0.1
0.01
0
20
40
60
80
100
120
140
160
180
Angle From Flight Path (deg)
Figure 24. Delta-GEM Simulation Results with B = 1,000
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The simulated impact percentages plotted in Figure 25 are identical with those shown
in Figure 24. The theoretical percentages in Figure 25 were obtained by trying various
combinations of B and A until the best possible fit was obtained in the sectors from ±60°
to ±180°. From these plots it seems apparent that a reasonable fit between malfunction-
turn and theoretical Mode-5 impact data can be found for any qα between 5,000 and
20,000 deg-lb/ft².
100
Delta-GEM Random-Attitude Failures through 270 sec
Breakup q-alpha in deg-lb/ft2
no breakup
20,000
10,000
10
5,000
Percent in 5-deg sector (%)
A = 2.60, B = 10,000
A = 3.15, B = 2,000
A = 3.35, B = 2,000
A = 3.50, B = 4
1
0.1
0.01
0
20
40
60
80
100
120
140
160
180
Angle From Flight Path (deg)
Figure 25. Delta-GEM Simulation Results with Best-Fit Shaping Constants
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6.3.2 Launch-Area Mode-5 Risks
Using values of A and B from Figure 24 and Figure 25, program DAMP was run to
compute Mode-5 launch-area risks for population centers inside the impact limit lines
for a Delta-GEM/GPS-10 daytime launch from Pad 17A. Results from these and two
other cases are shown in Table 23. The Mode-5 Ec in the first line (old baseline case) is
presented for comparison. It was obtained from the first line of Table 55 of an earlier
RTI study¹³¹. In that study, the total Delta failure probability during the first 130
seconds of flight was set at 0.02, with the probability of a Mode-5 response assumed to
be 0.0025. The second line in Table 23 shows the result of a recomputation of the Mode-
5 risks, again with B = 1,000 and A = 3, using failure probabilities derived earlier in this
report. From Table 6 and Table 15, the failure probability during flight phases 0 - 2 is
0.013, and the relative frequency of occurrence of a Mode-5 response is 0.08. The
absolute probability of a Mode-5 response thus becomes 0.013 X 0.08 ≡ 0.001.
Table 23. Shaping Constants and Related Risks for Delta-GEM
TB
Breakup qα
Mode-5 Ec
P₅
(sec)
(deg-lb/ft2)
B
A
(x 10⁻⁶)
0.0025
130
12,000 *
1,000
3.00
394
(baseline)
0.001
270
12,000 *
1,000
3.00
88.8
(new P₅ & TB)
0.001
270
none
1,000
1.90
220.0
20,000
2.90
104.4
10,000
3.10
74.1
5,000
4.30
5.2
0.001
270
none
10,000
2.60
224.4
20,000
2,000
3.15
102.4
10,000
2,000
3.35
72.0
5,000
4
3.50
5.1
* Interpolated from data contained in Figure 24
As in the case of Atlas, Table 23 again shows that the risks in the launch area are highly
dependent on qa and thus on A, but relatively insensitive to changes in B if a proper
value is selected for A. For example, if qα = 10,000, the computed risks for B = 1,000
(A = 3.10) and B = 2,000 (A = 3.35) differ by less than 3%. For the no-breakup cases
where B = 1,000 and then 10,000, the computed risks in the launch area differ by less
than 2%.
Launch-area risks are highly dependent on the vehicle's capability to withstand
aerodynamic forces. Except early in flight, low-strength vehicles generally break up
quickly after a malfunction turn begins. The later such turns occur, the more likely
pieces are to impact downrange of the launch point, thus lessening risks to uprange
populations. The effects of vehicle strength on risk are clearly seen in Table 23 where,
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RTI
for example, the risks are over 20 times as great if the vehicle's breakup qα is 20,000
rather than 5,000 deg-lb/ft².
6.4 Shaping Constants for Titan IV
Mode-5 shaping constants for Titan IV were developed as described in Section 6.3 for
Delta, except that a total of 290,000 simulations were run between the programming
time of 18 seconds and staging at 300 seconds. The percentage of vehicles that break up
during simulated random-attitude turns are plotted against failure time in Figure 26.
The same qα's used with Atlas and Delta were used here, and similar breakup results
were obtained.
100
Titan IV
90
q-alpha in deg-lb/ft²
80
q-alpha = 5,000
70
-
- q-alpha = 10,000
Breakup Percent (%)
60
q-alpha = 20,000
50
40
30
20
10
0
0
40
80
120
160
200
240
280
Failure Time (sec)
Figure 26. Titan IV Breakup Percentages
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RTI
Figure 27 shows the percentages of malfunction-turn impacts in 5° sectors for no
breakup and for breakup qα's of 20,000, 10,000, and 5,000 deg-lb/ft². For B = 1,000,
theoretical Mode-5 impact distributions are also plotted in the figure using best-fit
values of A. This value of B was chosen since it is currently used by RTI in making
launch-area risk studies for 45 SW/SE. Within the sectors from ±60° to ±180°, where
most population centers are located, data fits are reasonably good. As seen in the next
figure, the divergence for the no-breakup case can be greatly reduced by selecting other
values for B and A.
100
Titan IV Random-Attitude Failures through 300 sec
Breakup q-alpha in deg-lb/ft²
no
breakup
20,000
10,000
5,000
10
B = 1,000
Percent in 5-deg sector (%)
A = 2.00
A = 2.95
A = 3.25
A = 3.50
1
0.1
0
20
40
60
80
100
120
140
160
180
Angle From Flight Path (deg)
Figure 27. Titan Simulation Results with B = 1,000
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RTI
The simulated impact distributions plotted in Figure 28 are identical to those shown in
Figure 27. The theoretical Mode-5 percentages were obtained by testing various
combinations of B and A until a good fit between the simulated malfunction-turn
results and theoretical impact-distribution data was obtained in the sectors from ±60° to
±180°. Although somewhat better fits may be possible for the lower breakup qα's, the
effort to find them did not seem worthwhile, since the A's and B's shown in the figure
produced fits that were more than adequate in the sectors where the population centers
are located.
100
Titan IV Random-Attitude Failures through 300 sec
Breakup q-alpha in deg-lb/ft²
no breakup
20,000
10,000
5,000
10
A = 2.70, B = 10,000 =
Percent in 5-deg sector (%)
A = 3.15, B = 2,000
A = 3.25, B = 1,000
A = 3.50, B = 1,000
1
0.1
0
20
40
60
80
100
120
140
160
180
Angle From Flight Path (deg)
Figure 28. Titan Simulation Results with Best-Fit Shaping Constants
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The best-fit values of B and A shown in Figure 27 and Figure 28 are tabulated for
convenient reference in Table 24. For breakup qα's of 10,000 and 5,000 deg-lb/ft², the
currently-used value of B = 1,000 provided a better data fit than other values of B that
were investigated.
Table 24. Shaping Constants for Titan IV
TB
Breakup qa
(sec)
(deg-lb/ft²)
B
A
300
none
1,000
2.00
20,000
2.95
10,000
3.25
5,000
3.50
300
none
10,000
2.70
20,000
2,000
3.15
10,000
1,000
3.25
5,000
1,000
3.50
Risk calculations in the launch area were not made for Titan IV.
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6.5 Shaping Constants for LLV1
Shaping constants for LLV1 were developed as described in Section 6.3 for Delta,
except that a total of 290,000 simulations were made between the programming time of
1 second and staging at 290 seconds. The percentages of vehicles that break up during
simulated random-attitude turns are plotted in Figure 29. As expected, the results are
similar to those shown previously for Atlas, Delta, and Titan although, due to its higher
acceleration, the rapid drop-off from near 100% breakup occurs at an earlier time for
the LLV1 than for the other vehicles.
100
LLV1
90
q-alpha in deg-lb/ft 2
80
q-alpha = 5,000
70
-
q-alpha = 10,000
Breakup Percent (%)
60
q-alpha = 20,000
50
40
30
20
10
0
0
40
80
120
160
200
240
280
Failure Time (sec)
Figure 29. LLV1 Breakup Percentages
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RTI
Figure 30 shows the percentage of malfunction-turn impacts in 5° sectors for no
breakup, and for breakup qa's of 20,000, 10,000, and 5,000 deg-lb/ft². The three
breakup qα's produced impact distributions that were surprisingly similar, possibly
due to the vehicle's higher acceleration. Theoretical Mode-5 impact distributions are
also plotted in the figure for B = 1,000 and best-fit values of A. This value of B was
chosen since it is currently used by RTI in making launch-area risk studies for
45 SW/SE. For all except the no-breakup case, values of A were found that produced
good fits between the malfunction-turn and Mode-5 impact distributions in the sectors
from ±60° to ±180°.
100
LLV1 Random-Attitude Failures through 290 sec
2
Breakup q-alpha in deg-lb/ft
no breakup
20,000
10,000
10
5,000
B = 1,000
Percent in 5-deg sector (%)
A = 1.85 =
A = 2.60
A = 2.70
A = 2.75
1
0.1
0.01
0
20
40
60
80
100
120
140
160
180
Angle From Flight Path (deg)
Figure 30. LLV1 Simulation Results with B = 1,000
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Figure 31 shows that a good fit for the no-breakup case is possible if higher values of B
and A are used. The simulated malfunction-turn impact distributions for the breakup
cases plotted in this figure are identical with those in Figure 30. Since the theoretical
percentages for B = 1,000 produced excellent fits, these values were simply replotted in
Figure 31. For the no-breakup case, various combinations of B and A were tried before
arriving at the plot shown in the figure.
100
LLV1 Random-Attitude Failures through 290 sec
2
Breakup q-alpha in deg-lb/ft
no breakup
20,000
10,000
10
0
5,000
Percent in 5-deg sector (%)
A = 2.45, B = 10,000
A = 2.60, B = 1,000
A = 2.70, B = 1,000
A = 2.75, B = 1,000
1
0.1
0.01
0
20
40
60
80
100
120
140
160
180
Angle From Flight Path (deg)
Figure 31. LLV1 Simulation Results with Best-Fit Shaping Constants
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The best-fit values of B and A from Figure 30 and Figure 31 have been listed for
convenient reference in Table 25. It is interesting to note that, for all breakup
conditions, the currently-used value of B = 1,000 provided a better data fit than any
other B that was investigated.
Table 25. Shaping Constants for LLV1
T₈
Breakup qα
(sec)
(deg-lb/ft²)
B
A
290
none
1,000
1.85
20,000
2.60
10,000
2.70
5,000
2.75
290
none
10,000
2.45
20,000
1,000
2.60
10,000
1,000
2.70
5,000
1,000
2.75
No launch-area risk calculations were made for LLV1.
6.6 Shaping Constants for Other Launch Vehicles
Procedures for developing Mode-5 shaping constants A and B are fully described in
this report. For Atlas, Delta, Titan, and LLV1, best-fit values of A were derived for four
breakup conditions (1) for the currently-used value of B = 1,000, and (2) for optimum-fit
values of B. For any new launch vehicle requiring risk calculations, the same
procedures should be followed to obtain suitable values for A and B.
As an alternative and less time-consuming process, values of A and B can be estimated
by comparing the new vehicle with one of the four vehicles referred to above and listed
in Table 26. If the configuration and trajectory of the new vehicle and one of the listed
vehicles are similar, values of A and B shown in the table for that vehicle and the
assumed breakup condition can be used. There may, of course, be no similarity
between the new vehicle and any of the listed vehicles. In that event and depending on
assumed breakup conditions, one of the mean values shown in the last row of the table
can be selected until better values can be developed.
Table 26. Summary of A Values for B = 1,000
IP Range (nm)
Breakup qa (deg-lb/ft²)
Vehicle
at 30 sec
5,000
10,000
20,000
None
Atlas IIAS
0.3
3.45
3.20
2.75
1.90
Delta-GEM
5.2
4.30
3.10
2.90
1.90
Titan IV
1.9
3.50
3.25
2.95
2.00
LLV1
33.4
2.75
2.70
2.60
1.85
Other vehicles
3.5
3.1
2.8
1.9
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7. Potential Future Investigations
Because of contract limitations on funds and the deadline for publishing the report,
certain interesting facets of the Mode-5 modeling process could not be fully
investigated. Several such issues are listed below in considered order of importance:
(1) Effects on shaping constants A and B of using more precise breakup (qα)
conditions during malfunction-turn simulations.
(2) Effects on shaping constants A and B (and thus overall risks) if different values of
TB are used in computing theoretical and simulated impacts (e.g., TB
corresponding to burnout of zero, first, and second stages).
(3) Effects on shaping constants A and B if drag is accounted for in computing free-
fall impact points after a malfunction turn. (Shaping constants could be
determined for maximum, minimum, and intermediate ballistic coefficients, then
interpolated for other values. This more accurate approach would ultimately
require extensive modifications to DAMP.)
(4) Effects on shaping constants A and B if sectors smaller than 5° are used to
compare theoretical and simulated impact data (e.g., 1° or 2°).
(5) Effects on relative failure probabilities for solid-propellant vehicles if unclassified
solid-propellant vehicles or declassified test results are used in the historical data
samples (e.g., Pershing, Polaris, Poseidon, Trident).
Other tasks that should be performed at some point in the future include:
(a) Update absolute failure probabilities for Atlas, Delta, Titan, and perhaps other
vehicles.
(b) Develop suitable shaping constants A and B for new vehicles. (In this regard, see
Section 6.6)
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8. Summary
In RTI's risk-computation program DAMP, vehicle failures per se are not considered.
Instead each catastrophic failure is assumed to produce one of five failure responses,
and it is these response modes that are modeled in DAMP. Although most catastrophic
failures result in impacts near the flight line, less likely malfunctions may cause debris
to fall either uprange or well away from the flight line. In DAMP, vehicle failures with
this potential are, for the most part, classified as Mode-5 failure responses. The
resulting impacts are modeled by a rather formidable-looking density function that
includes two shaping constants (A and B) that strongly influence the nature of the
impact-density function. To obtain absolute probabilities (or risks), the function must
be multiplied by-a probability-of-occurrence factor (p₅). The primary purpose of this
study was to determine the best values for A, B, and P₅ for various vehicle programs.
Other objectives not explicitly included in the statement of work were to develop
absolute failure probabilities for Atlas, Delta, and Titan and to derive relative
probabilities of occurrence for the five failure-response modes in DAMP.
Although some risk analyses may ignore unlikely failure-response modes, Section 2
demonstrates the need for a Mode-5 response - or some similar response - through
brief descriptions of actual vehicle flights. Section 3 and Appendix B provide the
reader with a fuller understanding of the nature and intricacies of the Mode-5 impact-
density function. Together, they show how density-function shaping is affected by
values of A and B, and in particular how the Atlas IIAS launch-area risk contours
change if the value of A is changed.
Section 4 is a philosophical discussion of methods of assessing vehicle failure
probability (or reliability). Two approaches are discussed, one strictly empirical, the
other a parts-analysis method that involves the assignment of failure probabilities to
individual parts, components, and systems. Although difficulties exist with both
approaches, the empirical method was chosen to estimate both absolute and relative
failure probabilities.
As the first step in estimating failure probabilities empirically, performance histories
were gathered, summarized, and tabulated (Appendix D) by launch date for Atlas,
Delta, and Titan vehicle launches from the Eastern and Western Ranges, and for Thor
launches from the Eastern Range. Obtaining this information, and assigning response
modes and associated flight phases for each failure consumed a large portion of the
effort expended on this task.
A filtering (i.e., data weighting) technique was selected (see Section 5.1 and
Appendix C) and applied to the launch failure data to estimate overall failure
probabilities by flight phase (see Section D.1.3) for Atlas, Delta, and Titan vehicles. The
recommended failure probabilities are based on test results involving only those
vehicle configurations that are considered to be representative of current launch
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configurations (see Section D.1.4). The results, summarized previously in Table 6 of
Section 5.1, are repeated here in Table 27. Flight phases 0 - 1 go from liftoff through
first-stage or booster cutoff, while flight phase 2 extends through second-stage or
sustainer cutoff. Although failure probabilities for all flight phases are listed in Table 2,
only malfunctions during flight phases 0 through 1 have significant effects on launch-
area risks.
Table 27. Failure Probabilities for Atlas, Delta, and Titan
Predicted Failure Probability
Flight Phase
Flight Phase
Vehicle
0 - 1
0 2
Atlas
0.022
0.031
Delta
0.010
0.013
Titan
0.040
0.064
Absolute overall failure probabilities for Atlas, Delta, and Titan were based only on
flight results from "representative" vehicle configurations. Because of the small
number of failures in the individual representative samples, test results for all
configurations (including Thor) were combined into a single sample and filtered to
estimate relative failure probabilities for the five failure-response modes in program
DAMP (see Section 5.2). The results for flight phases 0 - 2 and 0 - 1, together with
recommended values for new launch systems, were summarized in Table 15 and Table
16, respectively, and are repeated here in Table 28 and Table 29.
Table 28. Recommended Response-Mode Percentages for Flight Phases 0 -2
Response
Mature Launch
New Solid Systems
New Liquid Systems
Mode
Systems (F = 0.993)
(F = 0.996)
(F = 0.999)
1
0.4
2.2
7.4
2
5.4
4.3
2.3
3
0.1
0.4
1.7
4
86.2
80.4
73.3
5
7.9
12.7
15.3
Table 29. Recommended Response-Mode Percentages for Flight Phases 0 - 1
Response
Mature Launch
New Solid Systems
New Liquid Systems
Mode
Systems (F = 0.993)
(F = 0.996)
(F = 0.999)
1
0.5
3.4
10.7
2
7.4
6.6
4.3
3
0.1
0.6
2.4
4
81.9
74.5
67.0
5
10.1
14.9
15.6
For Atlas, Delta, and Titan, absolute probabilities for the individual response modes
were obtained by multiplying absolute failure probabilities from Table 27 by the
relative probabilities shown in the second columns of Table 28 and Table 29. The
results, presented originally in Table 17, are repeated below in Table 30. To obtain
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these results, the relative probabilities used were more precise than those given in
Table 28 and Table 29. No pretense is made that all figures in Table 30 are actually
significant.
Table 30. Absolute Failure Probabilities for Response Modes 1- - 5
Vehicle:
Atlas
Delta
Titan
Flight
0 1
0 2
0- 1
0 2
0 - 1
0 - - 2
Phase:
(0-170 sec)
(0-280 sec)
(0-270 sec)
(0-630 sec)
(0-300 sec)
(0-540 sec)
Mode 1
0.000119
0.000121
0.000054
0.000051
0.000216
0.000250
Mode 2
0.001637
0.001665
0.000744
0.000698
0.002976
0.003437
Mode 3
0.000011
0.000012
0.000005
0.000005
0.000020
0.000026
Mode 4
0.018007
0.026738
0.008185
0.011212
0.032740
0.055200
Mode 5
0.002226
0.002465
0.001012
0.001034
0.004048
0.005088
Total
0.022
0.031
0.010
0.013
0.040
0.064
The same chronological composite sample used to estimate relative failure probabilities
for the failure-response modes was used to estimate the conditional probability that a
Mode-3 or Mode-4 response terminates with a rapid tumble. This was found to be
about one-third (see Section 5.3).
Because the empirical data were insufficient to determine Mode-5 density-function
shaping constants A and B, an alternate approach was used. Basically, for each of four
vehicles (Atlas, Delta, Titan, and LLV1), Mode-5 failure responses were simulated at a
series of failure times. The simulated malfunctions investigated were random-attitude
turns and slow turns. At each time, 10,000 impact points were computed. The
percentages of impacts in 5° sectors from 0° (downrange) to 180° (uprange) were
determined. These were compared with the percentages obtained in the same sectors
from the theoretical Mode-5 impact-density function when specific values were
assigned to A and B. By trial and error, values of A and B producing a good match
between the two sets of percentages were established (see Section 6). After best-fit
values were determined, the impact percentages for Atlas IIAS in 10-mile range
increments were checked to verify that the range part of the Mode-5 impact-density
function was consistent with impact ranges resulting from 266,000 simulated Mode-5
failure responses (see Section 6.2.4).
Since the impact distributions resulting from simulated malfunction turns were highly
dependent upon the dynamic pressure (qα) assumed to cause vehicle breakup, shaping
constants A and B were likewise dependent on breakup assumptions. Three breakup
qα's and a no-breakup case were investigated by simulating 270,000 malfunction turns
for each of the four conditions. Although a qα of 5,000 deg-lb/ft² is considered most
likely applicable for Atlas, Delta, and Titan, shaping constants for all breakup
conditions were provided earlier in Section 6.
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Traditionally, a value of B = 1,000 has been used by the 45 SW/SE in ship-hit
calculations, and by RTI in performing launch-area risk analyses for the 45 SW/SE.
Using this value of B, for each vehicle values of A were found that produced a good
match between simulated and theoretical data. The results for qα = 5,000, 10,000, and
20,000 deg-lb/ft² are given in Table 31. As discussed earlier in the report, no single
value of A could be found that produced a good fit over the entire 180° sector, although
with one exception a good match did exist in the uprange portion of the sector from
about ±90° to ±180°. For launches from Cape Canaveral, most population centers are
located in this uprange sector. For any launch-area population centers located in the
downrange sector, the risks are almost surely dominated by the Mode-4 failure
response.
Table 31. Summary of A Values for B = 1,000
Flight
TB
Breakup qa (deg-lb/ft²)
Vehicle
Phase
(sec)
5,000
10,000
20,000
Atlas IIAS
0 - 2
280
3.45
3.20
2.75
Delta-GEM
0 - 1
270
4.30
3.10
2.90
Titan IV
0 - 1
300
3.50
3.25
2.95
LLV1
0 - 2
290
2.75
2.70
2.60
Other vehicles
---
---
3.5
3.1
2.8
Other values of B were investigated to find combinations of B and A that provided the
best possible data fits over the largest possible portion of the 0° to 180° sector.
Although no combinations of A and B could be found that produced good fits for the
entire 180° sector, the values shown in Table 32 extended the fit from the uprange
direction to within about 40° of the downrange direction.
Table 32. Summary of Optimum Mode-5 Shaping Constants
Flight
TB
Breakup qα
Vehicle
Phase
(sec)
(deg-lb/ft²)
B
A
Atlas
0 - 2
280
5,000
5,000,000
6.30
Delta
0 - 1
270
5,000
4
3.50
Titan
0 - 1
300
5,000
1,000
3.50
LLV1
0 - 2
290
5,000
1,000
2.75
Launch-area risk calculations were made for Atlas and Delta to ascertain the effects of
using radically different values of A and B in the Mode-5 impact-density function. For
example, for a breakup qα of 5,000 deg-lb/ft2, values of A = 3.45 and B = 1,000 from
Table 31 and A = 6.30 and B = 5,000,000 from Table 32 were used to determine total
Mode-5 launch-area risks for an Atlas IIAS launch from Complex 36. The total risks
differed by about 10%. (Other results for Atlas IIAS are given in Table 21, and for Delta
in Table 23.) Other calculations for Atlas and Delta show that the value of B is not
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important in the launch-area risk calculations provided an appropriate value of A is
selected.
Since a good data match within ±40° of the flight line was not found, the effect of this
on ship-hit calculations was investigated. It was discovered that the values chosen for
A and B made no significant difference, since the risks to shipping near the flight line
are totally dominated by the Mode-4 failure response (see Section 6.2.3).
Mode-5 baseline risks for Atlas and Delta were recomputed using newly derived
values for (1) shaping constants A and B, (2) the overall vehicle failure probability, and
(3) the relative probabilities of occurrence of the individual failure-response modes.
Results were then compared with baseline risks computed in prior RTI studies. For
Atlas, Mode-5 launch-area risks were reduced by a factor between 3 to 11, the exact
value depending on the assumed breakup qα for the vehicle. For Delta, the reduction
factor was between 4 and 75, with the exact value again depending on assumed
breakup conditions.
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Appendix A. Failure Response Modes in Program DAMP
In program DAMP, no attempt is made to model vehicle behavior for failure of specific
systems and components. A list of such failures and possible behaviors for any vehicle
would be extensive, and variations from vehicle to vehicle would complicate the
modeling process, or make it almost impossible. Instead, failure responses are modeled
in DAMP without regard to the specific failure that causes the response. There are only
six possible response modes in DAMP, five for failures, and one to model the behavior
of a normal vehicle. The six vehicle-response modes are described in layman's
language as follows; technical descriptions are provided in Ref. [1].
Mode 1: Vehicle topples over or falls back on the launch point after a rise of, at
most, a few feet. Propellants deflagrate or explode with some assumed TNT
equivalency.
Mode 2: Vehicle loses control at or shortly after liftoff, with all flight directions
equally likely. Destruct is transmitted as soon as erratic flight is confirmed, usually
no later than six to twelve seconds after launch. For each vehicle, a latest destruct
time is established that is used in computing the maximum impact distance for
pieces, given that a Mode-2 response has occurred.
Mode 3: Vehicle fails to pitch-program normally, producing near-vertical flight
while thrusting at normal levels. Vehicle may tumble rapidly out of control at any
point during vertical flight resulting in spontaneous breakup, or may be destroyed
when destruct criteria are violated. The mode is terminated by destruct action if
the vehicle reaches the so-called "straight-up" time without programming. This
time varies with launch vehicle and with mission, but usually occurs (at Cape
Canaveral Air Station) between 30 and 70 seconds after launch.
Mode 4: Vehicle flies within normal limits until some malfunction terminates
thrust, causes spontaneous breakup, or results in destruct by flight-control
personnel. Breakup may or may not be preceded by a rapid tumble while the
vehicle is still thrusting but, in any event, vehicle debris and components impact
near the intended flight line.
Mode 5: Vehicle may impact in any direction from the launch point within its
range capability. At any range, impacts are most likely to occur along the flight
line, becoming less likely as the angular deviation from the flight line increases. As
the impact range increases, weighting is progressively increased to favor the
downrange direction. In any fixed direction, the impact probability decreases as
the impact range increases. Flight may terminate spontaneously due to complete
loss of vehicle stability or because of destruct action. Outside the launch area, any
malfunction with the potential to cause a substantial deviation from the intended
flight direction is classified as a Mode-5 failure response. By definition, Mode-5
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responses begin at vehicle pitch-over or programming for vertically-launched
missiles, and at liftoff for those not launched vertically.
Mode 6: Unlike impacts from response Modes 1 through 5, Mode-6 impacts result
from normal flights and normal impacts of separated stages and components.
Jettisoned components are assumed to be non-explosive. For each impacting stage
or component, a mean point of impact and bivariate-normal impact dispersions in
downrange and crossrange components are assumed. The impact dispersions
include the effects of variations in vehicle performance, drag uncertainties, and
winds.
Of the five failure-response modes, only Mode 5 is modeled to allow for the possibility
of failure of the flight termination system, since vehicles experiencing other failure
responses tend to impact within the impact limit lines. In DAMP, risk computations for
Modes 2 through 4 are based on the assumption that the flight termination system is
successfully employed when required. Failure responses originally classified as
Mode 2, 3, or 4 may be reclassified as Mode 5 if the flight termination system fails or
subsequent vehicle performance does not conform with the original response-mode
definition. Risks associated with vehicle failure responses accompanied by a failure of
the flight termination system are assumed to be adequately modeled in DAMP by
Mode 5.
The five failure-response modes modeled in DAMP are sufficient to account for all
anomalous impacts in the estimation of risks. However, some vehicle failures and
anomalous behaviors have an effect on mission success without increasing risks to
people and property on the ground. These behaviors have been assigned Mode NA
(not applicable) in the response-mode column of the launch-history tables in
Appendix D.
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Appendix B. Shaping-Constant Effects on Mode-5 Impact Distributions
The values chosen for shaping constants A and B that appear in the Mode-5 impact-density
function [Eq. (3)] have a significant effect on the angular distribution of impacts about the
launch point. This Appendix shows the effects of A and B on (1) the ratio of impacts along
the downrange line to any other radial through the launch point, and (2) the percentages of
impacts in various sectors relative to the downrange line.
Following the procedures outlined in Section 9.7 of Reference [1], it is interesting to observe
the effects of varying the constants A and B. This is done in terms of a so-called f-ratio,
which is expressed in Ref. [1] as Eq. (9.19), and is repeated here:
(7)
The ratio shows how much more likely impact is to occur along the flight line (where Φ = π)
than along some other radial line that makes an angle Θ (Θ = π - φ) with the flight line.
Table 33 and Table 34 present f-ratios for values of A = 2.5, 3.0, 3.5, and 4.0, and B = 1000
for impact ranges from one to 25 miles. Table 35 and Table 36 show the effects of halving
and doubling the constant B for a fixed value of A = 3.0.
Before citing numerical examples, it should be emphasized that the data in Table 33
through Table 36 are derived from the primary Mode-5 impact-density function and, as
such, they indicate likelihood ratios for the location of the secondary Mode-5 density
functions. A secondary function, it will be remembered, describes the dispersion of a
debris class about the impact point of the mean piece in the class. Thus, referring to Table
34 with A = 3.0, it can be seen that the secondary impact-density function for a debris class
is 4.7 times more likely to be centered 10 miles downrange along the flight line (Θ = 0°) than
10 miles from the launch point along a radial line that makes a 30° angle with the flight line.
As another example, the secondary function (i.e., the impact point for the mean piece in a
debris class) is 82.2 times more likely to be located 25 miles downrange along the flight line
than 25 miles crossrange (Θ = 90°), and assuming no destruct action, that it is
303.2/82.2 = 3.7 times more likely to be located 25 miles crossrange than 25 miles uprange
(Θ = 180°).
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Table 33. Effect on f-Ratio of Varying Mode-5 Constant A (B = 1000) - Part 1
R=1nm
R=5nm
180 - Φ
A = 2.5
A = 3.0
A = 3.5
A = 4.0
A = 2.5
A = 3.0
A = 3.5
A = 4.0
0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
5
1.2
1.3
1.3
1.4
1.2
1.3
1.4
1.4
10
1.3
1.6
1.8
2.0
1.5
1.7
1.8
2.0
15
1.5
2.0
2.4
2.8
1.8
2.2
2.5
2.8
20
1.7
2.5
3.3
4.0
2.2
2.8
3.4
4.0
25
1.9
3.1
4.3
5.6
2.6
3.6
4.6
5.7
30
2.1
3.7
5.8
7.9
3.1
4.5
6.1
8.1
35
2.3
4.5
7.6
11.1
3.7
5.8
8.3
11.4
40
2.5
5.3
9.8
15.5
4.3
7.3
11.1
16.1
45
2.6
6.2
12.6
21.5
4.9
9.2
14.9
22.8
50
2.8
7.0
15.9
29.5
5.7
11.4
19.9
32.1
55
2.9
7.9
19.7
40.2
6.4
14.1
26.3
45.1
60
3.0
8.7
24.0
53.8
7.2
17.1
34.7
63.1
65
3.1
9.5
28.5
70.7
7.9
20.6
45.2
87.8
70
3.2
10.2
33.1
91.0
8.6
24.3
58.2
121.4
75
3.3
10.8
37.6
113.9
9.3
28.5
73.8
166.3
80
3.3
11.3
41.8
138.6
10.0
32.5
92.1
224.8
85
3.4
11.7
45.5
163.6
10.5
36.5
112.6
299.2
90
3.4
12.1
48.7
187.4
11.1
40.4
134.7
390.1
95
3.4
12.3
51.4
208.9
11.5
44.1
157.4
496.7
100
3.5
12.6
53.5
227.2
11.9
47.3
179.9
615.2
105
3.5
12.7
55.2
242.2
12.3
50.2
200.9
739.7
110
3.5
12.9
56.5
254.1
12.5
52.7
219.9
862.9
115
3.5
13.0
57.6
263.1
12.8
54.7
236.4
977.7
120
3.5
13.1
58.3
270.0
13.0
56.4
250.2
1079.0
125
3.5
13.2
58.9
275.0
13.2
57.8
261.4
1164.0
130
3.5
13.2
59.4
278.6
13.3
58.9
270.4
1232.6
135
3.6
13.3
59.7
281.2
13.4
59.8
277.4
1286.0
140
3.6
13.3
59.9
283.1
13.5
60.5
282.8
1326.5
145
3.6
13.3
60.1
284.5
13.6
61.1
286.9
1356.7
150
3.6
13.3
60.2
285.4
13.6
61.5
290.0
1378.8
155
3.6
13.3
60.3
286.1
13.7
61.8
292.3
1394.8
160
3.6
13.4
60.4
286.6
13.7
62.1
294.1
1406.3
165
3.6
13.4
60.5
286.9
13.7
62.3
295.4
1414.6
170
3.6
13.4
60.5
287.2
13.8
62.4
296.3
1420.5
175
3.6
13.4
60.5
287.3
13.8
62.6
297.0
1424.7
180
3.6
13.4
60.5
287.5
13.8
62.6
297.6
1427.6
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Table 34. Effect on f-Ratio of Varying Mode-5 Constant A (B = 1000) - Part 2
R = 10 nm
R = 25 nm
180 - 0
A = 2.5
A = 3.0
A = 3.5
A = 4.0
A = 2.5
A = 3.0
A = 3.5
A = 4.0
0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
5
1.2
1.3
1.4
1.4
1.2
1.3
1.4
1.4
10
1.5
1.7
1.8
2.0
1.5
1.7
1.8
2.0
15
1.9
2.2
2.5
2.8
1.9
2.2
2.5
2.8
20
2.3
2.8
3.4
4.0
2.3
2.8
3.4
4.0
25
2.8
3.6
4.6
5.7
2.9
3.7
4.6
5.7
30
3.4
4.7
6.2
8.1
3.6
4.8
6.2
8.1
35
4.1
6.0
8.4
11.5
4.4
6.1
8.4
11.5
40
4.9
7.7
11.3
16.2
5.3
7.9
11.4
16.3
45
5.8
9.8
15.3
23.0
6.5
10.2
15.5
23.1
50
6.8
12.4
20.5
32.4
7.9
13.2
20.9
32.7
55
8.0
15.7
27.5
45.8
9.6
16.9
28.3
46.2
60
9.3
19.7
36.7
64.5
11.5
21.6
38.1
65.4
65
10.7
24.4
48.8
90.6
13.7
27.5
51.2
92.3
70
12.1
29.9
64.3
126.7
16.2
34.8
68.7
130.2
75
13.5
36.3
84.1
176.4
19.0
43.8
91.7
183.1
80
15.0
43.4
108.6
243.9
22.1
54.5
121.8
256.9
85
16.4
51.1
138.4
333.9
25.4
67.3
160.6
358.9
90
17.8
59.1
173.5
451.4
28.8
82.2
209.9
498.3
95
19.0
67.3
213.3
600.5
32.4
98.9
271.3
686.6
100
20.1
75.3
256.8
782.9
35.9
117.3
345.7
936.0
105
21.2
82.9
302.1
996.3
39.4
137.0
433.3
1258.3
110
22.1
89.8
347.2
1233.5
42.7
157.2
532.8
1662.1
115
22.9
96.0
390.2
1482.5
45.9
177.4
641.3
2148.4
120
23.5
101.4
429.4
1728.6
48.7
196.9
754.5
2707.0
125
24.1
106.0
463.6
1957.9
51.3
215.0
867.2
3315.0
130
24.6
109.9
492.6
2159.9
53.5
231.5
974.6
3939.0
135
25.0
113.0
516.4
2329.5
55.5
245.9
1072.3
4542.1
140
25.3
115.5
535.5
2466.0
57.2
258.3
1158.0
5092.0
145
25.6
117.6
550.4
2572.4
58.6
268.8
1230.3
5567.4
150
25.8
119.2
562.0
2653.1
59.9
277.4
1289.7
5959.9
155
26.0
120.5
570.8
2713.1
60.9
284.5
1337.3
6271.7
160
26.1
121.5
577.5
2757.1
61.7
290.1
1374.6
6512.1
165
26.3
122.2
582.5
2789.0
62.4
294.6
1403.5
6693.0
170
26.4
122.8
586.3
2812.0
63.0
298.2
1425.6
6826.7
175
26.4
123.3
589.1
2828.4
63.4
301.0
1442.3
6924.4
180
26.5
123.7
591.2
2840.1
63.8
303.2
1454.9
6994.9
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Table 35. Effect on f-Ratio of Varying Mode-5 Constant B (A = 3) - Part 1
R =1 nm
R = 5 nm
180
B = 500
B = 1000
B = 2000
B = 500
B = 1000
B = 2000
0
1.0
1.0
1.0
1.0
1.0
1.0
5
1.3
1.3
1.2
1.3
1.3
1.3
10
1.6
1.6
1.5
1.7
1.7
1.7
15
2.1
2.0
1.9
2.2
2.2
2.1
20
2.7
2.5
2.3
2.8
2.8
2.7
25
3.4
3.1
2.7
3.6
3.6
3.4
30
4.2
3.7
3.1
4.7
4.5
4.3
35
5.2
4.5
3.6
6.0
5.8
5.4
40
6.4
5.3
4.1
7.7
7.3
6.6
45
7.7
6.2
4.5
9.8
9.2
8.1
50
9.2
7.0
5.0
12.4
11.4
9.8
55
10.8
7.9
5.3
15.7
14.1
11.7
60
12.4
8.7
5.7
19.7
17.1
13.7
65
14.1
9.5
6.0
24.4
20.6
15.8
70
15.8
10.2
6.2
29.9
24.3
17.8
75
17.3
10.8
6.4
36.3
28.5
19.9
80
18.7
11.3
6.6
43.4
32.5
21.8
85
20.0
11.7
6.7
51.1
36.5
23.5
90
21.1
12.1
6.8
59.1
40.4
25.0
95
22.0
12.3
6.9
67.3
44.1
26.3
100
22.8
12.6
7.0
75.3
47.3
27.5
105
23.4
12.7
7.0
82.9
50.2
28.4
110
23.9
12.9
7.1
89.8
52.7
29.1
115
24.3
13.0
7.1
96.0
54.7
29.7
120
24.6
13.1
7.1
101.4
56.4
30.2
125
24.9
13.2
7.1
106.0
57.8
30.6
130
25.1
13.2
7.1
109.9
58.9
30.9
135
25.3
13.3
7.2
113.0
59.8
31.2
140
25.4
13.3
7.2
115.5
60.5
31.3
145
25.5
13.3
7.2
117.6
61.1
31.5
150
25.5
13.3
7.2
119.2
61.5
31.6
155
25.6
13.3
7.2
120.5
61.8
31.7
160
25.6
13.4
7.2
121.5
62.1
31.8
165
25.7
13.4
7.2
122.2
62.3
31.8
170
25.7
13.4
7.2
122.8
62.4
31.8
175
25.7
13.4
7.2
123.3
62.6
31.9
180
25.7
13.4
7.2
123.7
62.6
31.9
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Table 36. Effect on f-Ratio of Varying Mode-5 Constant B (A = 3) - Part 2
R = 10 nm
R = 25 nm
180 - Φ
B = 500
B = 1000
B = 2000
B = 500
B = 1000
B = 2000
0
1.0
1.0
1.0
1.0
1.0
1.0
5
1.3
1.3
1.3
1.3
1.3
1.3
10
1.7
1.7
1.7
1.7
1.7
1.7
15
2.2
2.2
2.2
2.2
2.2
2.2
20
2.8
2.8
2.8
2.8
2.8
2.8
25
3.7
3.6
3.6
3.7
3.7
3.6
30
4.7
4.7
4.5
4.8
4.8
4.7
35
6.1
6.0
5.8
6.2
6.1
6.0
40
7.9
7.7
7.3
8.0
7.9
7.8
45
10.2
9.8
9.2
10.4
10.2
9.9
50
13.0
12.4
11.4
13.4
13.2
12.7
55
16.7
15.7
14.1
17.3
16.9
16.1
60
21.2
19.7
17.1
22.3
21.6
20.3
65
26.9
24.4
20.6
28.7
27.5
25.3
70
33.9
29.9
24.3
36.8
34.8
31.3
75
42.3
36.3
28.3
47.0
43.8
38.5
80
52.3
43.4
32.5
59.7
54.5
46.6
85
63.9
51.1
36.5
75.4
67.3
55.5
90
77.1
59.1
40.4
94.5
82.2
65.2
95
91.7
67.3
44.1
117.4
98.9
75.3
100
107.3
75.3
47.3
144.4
117.3
85.5
105
123.5
82.9
50.2
175.4
137.0
95.4
110
139.7
89.8
52.7
210.1
157.2
104.7
115
155.4
96.0
54.7
247.9
177.4
113.3
120
170.1
101.4
56.4
287.7
196.9
120.9
125
183.5
106.0
57.8
328.3
215.0
127.5
130
195.3
109.9
58.9
368.2
231.5
133.1
135
205.5
113.0
59.8
406.3
245.9
137.7
140
214.1
115.5
60.5
441.4
258.3
141.5
145
221.2
117.6
61.1
472.8
268.8
144.6
150
227.0
119.2
61.5
500.3
277.4
147.1
155
231.7
120.5
61.8
523.6
284.5
149.0
160
235.4
121.5
62.1
543.2
290.1
150.5
165
238.4
122.2
62.3
559.3
294.6
151.7
170
240.7
122.8
62.4
572.3
298.2
152.7
175
242.5
123.3
62.6
582.7
301.0
153.4
180
244.0
123.7
62.6
591.0
303.2
154.0
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The f-ratios in Table 33 and Table 34 (also in Table 35 and Table 36) have been plotted in
Figure 32 for A = 3.0 and B = 1000. Reading from the 10-mile plot for Θ = 90°, it can be seen
that a vehicle experiencing a Mode-5 response is about 60 times more likely to impact along
the flight line than along the 90-degree radial. Essentially the same value (actually 59.1)
appears in Table 34.
300
A = 3.0
B = 1000
250
R = 1 nm
-
-
R = 5 nm
200
R = 10 nm
R = 25 nm
f-Ratio
150
100
50
0
0 20 40 60 80 100 120 140 160 180
Angular Deviation From Downrange (deg)
Figure 32. f-Ratios for Ranges from 1 to 25 Miles
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There are other ways to show how the value chosen for A affects the Mode-5 impact
density function. For five values of A, the plots in Figure 33 show the percentages* of
Atlas IIAS impacts that lie between the flight line and any radial line through the launch
point that makes an angle Θ with respect to the flight line. If A = 3.0, it can be seen that
approximately 46% of all Mode-5 impacts lie between 0° and 20°. If A is 4.0, the percentage
of impacts between 0° and 20° increases to about 64%.
100
90
80
70
60
Percent
50
Data for Atlas IIAS
40
B = 1000
30
A = 1.0
-
A = 2.0
20
A = 3.0
A = 4.0
10
A = 5.0
0
0
20
40
60
80
100
120
140
160
180
Theta (deg)
Figure 33. Percentage of Impacts Between Flight Line and Any Radial
*
The Mode-5 impact density function must be integrated numerically to arrive at the values plotted in
Figure 33. Since the quantity R that appears in the density function is trajectory dependent,
somewhat different curves would be obtained for other trajectories and vehicles.
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Another way to show how the value of A affects Mode-5 impacts is illustrated in Figure 34.
For the same values of A used previously in Figure 33, the graphs in Figure 34 show the
percentages of impacts in any 5° sector between radials that make angles of Θ° and (Θ + 5)°
with respect to the flight line. It is interesting to note that if A is set equal to 1.0 with
B = 1,000, impacts in all 5° sectors are approximately the same, thus resulting in an
impact-density function that is essentially uniform in direction.
Data for Atlas IIAS
B = 1000
A = 1.0
A = 2.0
10
A = 3.0
A = 4.0
Percent in 5-deg Sector (%)
A = 5.0
1
0.1
0
20
40
60
80
100
120
140
160
180
Angle from Flight Path, Theta (deg)
Figure 34. Percentage of Impacts in 5-Degree Sectors
For A = 1, the Mode-5 impact-density function is essentially the same as a density
function formerly used in the Launch Risk Analysis (LARA) Program at the Western
Range to model gross azimuth failures. This response mode was called the Gross
Flight Deviation Failure (GFDF) mode. In LARA the range and azimuth portions of the
GFDF density function were assumed to be independent. Impact azimuths were
uniformly distributed, while the range density function can be represented as
f(R) = TB p R
(8)
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where p is the probability of occurrence of the GFDF mode, TB is the stage burn time,
and R is the rate of change of the impact range. The function cannot be applied early
in flight before programming when R is essentially zero. The range portion of the
Mode-5 impact-density function used in DAMP reduces to essentially the same form. If
Eq. (3) is integrated between the limits of zero and π, the conditional Mode-5 density
function reduces to
(9)
where Tₚ is the programming time, and TB and R are as previously defined. To obtain
absolute values, f(R) must of course be multiplied by the probability of occurrence of a
Mode-5 failure response.
Although the GFDF density function may be a suitable model for random-attitude
failures occurring at or a few seconds after programming, the performance histories in
Appendix D indicate that such failures are no more likely to occur at programming
than at any other time. Thus, there appears to be no need for including a GFDF mode
per se in the risk calculations, since all random-attitude failures are accounted for by
the Mode-5 density function. However, if for some obscure reason inclusion of a GFDF
response mode is desired, two approaches are possible: (1) run the GFDF mode
separately in DAMP (by using Mode-5 with A = 1) while zeroing out all other response
modes; (2) modify DAMP to handle two separate Mode-5 density functions, each with
its own values of A and B. Obviously approach (2) is much more involved and time
consuming to implement.
Although it may not be obvious, the probability of impact in any annular range interval
obtained by integrating the Mode-5 density function between the interval boundaries is
independent of the values assigned to A and B. If Eq. (3) is integrated between the
angle limits of zero and π (and only for these limits), the A's and B's cancel leaving the
probability of impact between R₁ and R2 as a function of impact range alone. With a
change of variable, the probability of impacting between R₁ and R2 becomes a simple
function of time (see pages 84 and 85 of Ref. [1] for details).
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Appendix C. Filter Characteristics
Estimating launch-vehicle failure probabilities using empirical launch data is an
uncertain process when the sample size is small and the data are obtained from an
evolving system. One approach that may be used to estimate failure probabilities is to
perform a least-squares fit to trial outcome values (0 = success, 1 = failure). For mature
launch vehicles, failure probabilities have decreased markedly from their early
experimental days. For new programs, empirical data may be scant or nonexistent.
One decision that must be made involves the type of function to fit to the data. The
true nature of the failure-rate function may be unknown or extremely complex, or there
may be insufficient data to estimate a complex function. The easiest calculation is made
when a constant failure-rate function is assumed. However, available data appear to
indicate that failure rates decrease as a program matures, at least up to a point. If it can
be assumed that launch-vehicle failure probabilities decrease over time (i.e., as the
number of launches increases), then some non-constant function (perhaps linear or
exponential) can be chosen for the fit, or the data weighted as a function of time. In
estimating Atlas reliability, General Dynamics⁶⁶ chose the latter option by adopting the
Duane model. This model is based on the assumption that the mean number of
launches between failures increases when causes of failure are corrected. Although this
may be the case up to a point, eventually reliability seems to level off at a fairly
constant value. Consequently, for mature programs RTI has chosen to fit the failure-
rate function to a constant. Such a fit can be based on simple least squares using a
fixed-length sliding-window filter to allow for changes in the estimated value over
time, or on a least squares fit with unequal weighting.
If a constant function is fit to a set of data using least squares with equal weighting of
data, the solution is given by the mean:
(10)
Consider the following example:
x₁=6 =
x₂=5
x₃=7
Then,
X=6+5+7-18=6 6+5+7
(11)
Recursively,
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(12)
For the equally-weighted case, the recursive filter factor an = 1/n.
Using the same example, with X, = 0,
X₁ X₁ = x₁ = 6
(13)
In general terms, this recursive formulation of the least squares solution is called an
expanding-memory filter, as opposed to a sliding-window or fixed-length filter. In an
expanding-memory filter, the solution is always based on the entire data set. In the
equally-weighted case, all data points have an equal influence on the solution,
regardless of their locations in the sequence.
It can be seen that in the limit as n becomes very large, an approaches zero. That is,
each data point in the sequence is accorded a decreased weight due to the increased
number of points being fit. If the data being fit should actually describe a constant, this
is exactly what is desired. Normally, however, the function that the data should fit is
unknown, and a constant function is used merely as an approximation to smooth or
edit the data. What is desired is a recursive least squares fit that assigns a decreasing
weight to data of increasing age, so the fit de-weights data points used in earlier
recursions.
In a fading-memory filter, the weighting factor decreases as time recedes into the past,
so that the importance of any given datum will decrease as the age of the datum
increases. An example of such a filter is one in which each datum is weighted by its
count or index number in the sequence:
i
xᵢ
Xₙ
=
(14)
i=1
Using the same numerical example as before, where X₁ = 6, X2 = 5, and X3 = 7,
X = 1.6+2.5+3.7 1+2+3 =
(15)
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For the recursive form of this filter, where each datum is weighted by its position in the
chronological sequence, the recursive filter factor for the nth point is given by
(16)
n(n+1)
i=1
Using Eq. (12),
(17)
Xs=5.33+ (7 (7-5.33)=6.17
The "memory" (i.e., importance) of older data in this filter fades at a rate dictated by
the filter. In this case, the 50th value is 50 times more important than the first, and the
100th value is twice as important as the 50th and 100 times more important than the first.
The exponentially-weighted filter provides the analyst with more flexibility. This filter
uses F' as a weighting factor, where the filter-control constant F is a value chosen
between zero and one, and i is the "age-count" of the ith data point. For this filter, i = 0
now designates the current or latest data point, i=1 designates the immediately
preceding or next-to-last data point, etc., so the data points are indexed in reverse
chronological order starting with zero. The weighted least-squares solution is
n-1
Xₙ₋ᵢ
Xₙ
=
n-1
(18)
Fi
i=0
Using F = 0.9 and the same example as before,
(.9)°(7)+(9)'(5)+(9)*(6)
=
(19)
= -7+45+486 - 1636 - 604 16.36
The weighting of each data point for sample sizes up to 300 is shown in Figure 35 for
values of F from 0.8 to 1.0. For F = 1, all points in the sample are weighted equally. For
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F = 0.8, only the most recent 25 or so data points contribute to the final result, since all
older data points are essentially weighted out of the solution.
1.0
F = 1 (equally weighted)
0.9
F = 0.999
0.8
F = 0.998
0.7
0.6
F = 0.995
Data Weight (Fⁿ⁻¹)
0.5
F # 0.99
0.4
0.3
F = 0.98
0.2
F = 0.95
0.1
F=0.9
F=0.8
0.0
0
50
100
150
200
250
300
Data Index (older ->)
Figure 35. Exponential Weights for Fading-Memory Filters
For the exponentially-weighted fading-memory filter, it can be shown that the
recursive filter factor used in Eq. (12) is
an = 1-Fn an = 1-Fⁿ 1-F
(20)
Since 0≤F≤1, an in Eq. (20) does not approach zero as n approaches infinity (as the
other two filters do), but instead approaches the value (1 - F). If F = 0, then an = 1 for all
n, the filter has no memory at all, and the filtered value always equals the last
measurement. In the limit as F approaches one, L'Hospital's rule can be applied to
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show that an approaches 1/n, the filter-factor value for the equally-weighted case, and
the filter memory no longer fades. For values of F between zero and one, the rate at
which the filter memory fades decreases as F increases. The analyst can control the rate
at which the filter memory fades by selecting an appropriate value of F.
As the number of points n increases, the value of an used in the recursive exponential-
filter equation decreases continuously as it asymptotically approaches 1 - F. For any
given n, a larger an means more emphasis is placed on the current data point and less
on previous points. That is, the larger the recursive filter factor an, the faster the filter
memory fades. Filter factors for sample sizes up to 300 points are shown in Figure 36
for six different filters. Early in the data-index count (n less than 30), the filter based on
index-number weighting has the fastest fading memory, since for 30 data points or
fewer the filter has the largest filter factors. After 160 points or so, the index-weighted
filter fades at a slower rate than the exponential filter with F = 0.99. Consequently,
users of index-count-based fading filters frequently calculate a filter factor for some
maximum value of n that is then applied to all subsequent data points as well. For
example, if a maximum count of about 180 is used for n; this filter from that point on
will behave similarly to the exponentially-fading filter with F = 0.99.
1
0.1
F = 0.95
Recursive Filter Factor
F = 0.98
F = 0.99
0.01
Index weighting
F = 0.995
Filter memory fades faster ->
Equal weighting
0.001
0
50
100
150
200
250
300
Number of Data Points in Sample
Figure 36. Recursive Filter Factor for Last Data Point
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The fading-memory recursive filter, defined by Eqs. (12) and (20), can be applied to
launch test results to estimate failure probability. For this application the values to be
filtered are the test outcomes, with 0 representing a successful launch, and 1
representing a failure or anomalous behavior. Given a series of outcomes, the filtered
result after each launch in the series represents the estimate of failure probability at that
point. Filtered results for two filter-control constants are shown in Table 37 for a
hypothetical series of ten launches for which all but the second and fourth flights were
successful.
Table 37. Filter Application for Failure Probability
F = 0.98
F = 0.90
Index
Outcome
Filter factor, an
Fail. Prob.
Filter factor, an
Fail. Prob.
1
0
1.0000
0.0
1.0000
0.0
2
1
0.5051
0.5051
0.5263
0.5263
3
0
0.3401
0.3333
0.3690
0.3321
4
1
0.2576
0.5051
0.2908
0.5263
5
0
0.2082
0.3999
0.2442
0.3978
6
0
0.1752
0.3299
0.2132
0.3129
7
0
0.1517
0.2798
0.1917
0.2529
8
0
0.1340
0.2423
0.1756
0.2085
9
0
0.1203
0.2132
0.1632
0.1745
10
0
0.1093
0.1899
0.1535
0.1477
In this example, estimated failure probabilities are shown for two values of the filter
constant that force the filter to fade at two different rates. After ten launches the
estimated failure probability using F = 0.98 is 0.1899. For the faster fading-memory
filter (F = 0.90), the result is 0.1477. Both estimates are less than that obtained by equal
weighting, since the two failures occurred early in the sequence. Note that after four
launches (2 successes and 2 failures) both filtered estimates exceed 0.5, since one of the
two failures occurred during the fourth flight.
If the 1's and O's used in the example to represent failures and successes were reversed,
the same filter would provide estimates of probability of success.
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Appendix D. Launch and Performance Histories
D.1 Basic Data
In support of the empirical approach to use post-test results to estimate future vehicle
failure rates, the performance histories for Atlas, Delta, Titan, and Thor missiles/
vehicles were studied. Results are summarized in Appendix D as follows:
Appendix D.2: Atlas Launch and Performance History
Appendix D.3: Delta Launch and Performance History
Appendix D.4: Titan Launch and Performance History
Appendix D.5: Thor Launch and Performance History
The histories include all Atlas, Delta, and Titan launches from the Eastern and Western
Ranges prior to 1 September 1996. For Thor, only Eastern Range launches are included,
since this summary was completed before it was decided not to use Thor results in
predicting failure probabilities for Delta. The Atlas, Titan, and Thor summaries
include both weapons systems tests and space flights, while the Delta summary
includes only space flights.
For each vehicle, each section of the appendix is divided into two parts:
(1) A tabular summary listing all launches in chronological order by sequence
number, a mission identifier, launch date, vehicle configuration, launch range, the
failure-response mode to which any failure has been assigned, the flight phase in
which the failure or anomalous behavior occurred, and a configuration flag (0 or
1) indicating whether the vehicle is sufficiently representative of current vehicles
to be included in the data sample used to predict vehicle reliability.
(2) A brief narrative - necessarily brief in most cases due to lack of information -
describing the general nature of the failure or the behavior of the vehicle after
failure, or the effects of the failure on flight parameters.
D.1.1 Data Sources
The vehicle performance summaries and histories were collected primarily from the
following sources:
(1) "Eastern Range Launches, 1950 - 1994, Chronological Summary", 45th Space Wing
History Office.¹⁷¹
(2) Extension to (1) updating the launch summary through 30 December 1995. [8]
(3) "Vandenberg AFB Launch Summary", Headquarters 30th Space Wing, Office of
History, Launch Chronology, 1958 - 1995. [9]
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(4) "Spacelift Effective Capacity: Part 1 - Launch Vehicle Projected Success Rate
Analysis", Draft prepared by Booz Allen & Hamilton, Inc. 19 February 1992,
prepared for Air Force Space Command Launch Services Office. [4]
(5) Isakowitz, Steven J., (updated by Jeff Samella), International Reference Guide to
Space Launch Systems, Second Edition, published and distributed by AIAA in
1995.
[10]
(6) Smith, O. G., "Launch Systems for Manned Spacecraft", Draft, July 23, 1991. [11]
(7) "Comparison of Orbit Parameters - Table 1", prepared by McDonnell Douglas
Space Systems Company, Delta launches through 4 Nov 95.
(8) Missiles/Space Vehicle Files, 45th Space Wing, Wing Safety, Mission Flight
Control and Analysis (SEO), 1957 through 1995. [13]
(9) Missile Launch Operations Logs, 30th Space Wing, copies provided via ACTA,
Inc., (Mr. James Baeker), 1963 through 1995. [14]
(10) "Titan IV, America's Silent Hero", published by Lockheed Martin in Florida Today,
13 Nov 95. [15]
(11) "Atlas Program Flight History" (through April 1965), General Dynamics Report
EM-1860, 26 April 1965. [16]
(12) Fenske, C. W., "Atlas Flight Program Summary", Lockheed Martin, April 1995. [17]
(13) Brater, Bob, "Launch History", Lockheed Martin FAX to RTI, March 13, 1996. [18]
(14) Several USAF Accident/Incident Reports for Atlas and Titan failures. [19]
(15) Quintero, Andrew H., "Launch Failures from the Eastern Range Since 1975",
Aerospace memo, February 25, 1996, provided to RTI by Bill Zelinsky.[20]
(16) Set of "Titan Flight Anomaly/Failure Summary" since 1959, received from
Lockheed Martin, April 4, 1996. [21]
(17) Chang, I-Shih, "Space Launch Vehicle Failures (1984 - 1995)", Aerospace Report
No. TOR-96(8504)-2, January 1996. [22]
There were numerous discrepancies in the source data, particularly with regard to
launch date and vehicle configuration. Some sources apparently list launch dates in
local time, others use Greenwich time, and in some cases the same source may use both
with no indication of which is which. Most of the launch dates shown in Appendix D
agree with those in the Eastern Range and Western Range summaries published by the
respective History offices. Since the dates on these summaries are not consistently local
or Greenwich, neither are the dates listed in Appendix D. Although launch dates are
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used to order the vehicle tests for filtering, whether the dates are inconsistently in local
or Greenwich times is inconsequential. In most cases, the ordering is not affected by a
one-day change in launch date. In rare cases where the order of two launches might be
inadvertently reversed, the filtering calculations are unaffected if the interchanged
flights are both failures or both successes. Even when this is not the case, the effect on
the final results for samples greater than one-hundred is negligible.
Configuration discrepancies also existed in the source data as, for example, the listing
of the same Atlas vehicle as a IIA in one source and as a IIAS in another. In rare cases,
a launch may have been called a success in one document and a failure in another, with
little or no data provided to make it clear whether the difference in classification was
due to error or different success criteria. Although a considerable effort was made to
eliminate errors and discrepancies in Appendix D, there can be no assurance that the
effort was 100% successful.
D.1.2 Assignment of Failure-Response Modes
In the tabular historical summaries in Appendix D, the column labeled "Response
Mode" refers to the failure-response modes in program DAMP. The numbers 1
through 5 in this column correlate with the failure-response modes described in
Appendix A. The letter "T" following either a "3" or "4" indicates that the vehicle
executed a thrusting tumble before breakup or destruct. An "NA" (i.e., not applicable)
appearing in the column means that some anomalous behavior caused stages or
components to impact outside their normal impact areas without necessarily failing the
flight, or that the anomalous behavior resulted in an unplanned orbit that may or may
not have interfered with mission objectives. If the response-mode column is blank,
either the flight was a success, or there was no information in the data sources to
indicate otherwise.
In some cases where the data sources contained only sketchy or incomplete
information, assignment of the response mode involved some speculation: Mostly, this
situation arose in trying to decide between response modes 4 and 5 or between modes 4
and 4T or, in rare cases, what mode to assign when the vehicle response did not exactly
fit any of the response-mode definitions.
D.1.3 Assignment of Flight Phase
The number shown in the "Flight Phase" column in the tabular summaries of
Appendix D indicates the phase of vehicle flight in which the failure or anomalous
behavior occurred. Definitions of flight phase are given in Table 38. The assigned
numbers are arbitrary, but were chosen in a way that suggests the vehicle stage that
failed or the stage that was thrusting when the failure occurred.
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Table 38. Flight-Phase Definitions
Flight Phase
Description
0
SRM auxiliary thrust phase
1
First-stage thrust phase if no auxiliary SRM's carried, or
First-stage thrust phase after SRM separation
1.5
Attitude-control phase after first-stage thrust phase or between
first and second-thrust phases
2
Second-stage thrust phase
2.5
Attitude-control phase after second thrust phase or between
second and third-thrust phases
3
Third-stage thrust phase, or third thrust phase if second stage is
restartable
3.5
Attitude-control phase after third thrust phase or between
third and fourth thrust phases
4
Fourth thrust phase, or
Upper stage/payload thrust phase
5
Attitude control phase after Flight Phase 4, or orbital phase
In some cases, two flight phases are listed opposite an entry, e.g., 2 and 5. This means
that some failure or anomalous behavior occurred during the second-stage thrusting
period that did not prevent the attainment of an orbit, but did result in an abnormal
final orbit. Other somewhat arbitrary decisions were necessary in assigning a flight
phase when an expended stage failed to separate, or an upper stage failed to ignite. If,
for example, the first and second stages failed to separate, any of flight phase 1, 1.5, or 2
could be assigned, depending on the exact cause of the failure. The detailed
information needed to make the proper choice was sometimes lacking.
Table 39 is provided to assist in understanding how flight phases were assigned for
Atlas, Delta/Thor, and Titan vehicles.
Table 39. Flight Phases by Launch Vehicle
Flight Phase
Atlas
Delta/Thor
Titan
0
Castor burn
Castor/GEM burn
SRM solo
1
Atlas booster
First-stage burn
Stage 1
1.5
Booster separation
Vernier solo - Sep 1/2
Stage-1 separation
2
Sustainer
Second-stage burn
Stage 2
2.5
Vernier/ACS solo
Coast between stg 2/3
Vernier solo
3
Agena/Centaur
Third-stage burn
TS/Centaur/IUS
3.5
-
Coast after stg 3
-
4
Second burn
Second burn
Second burn
5
Orbit
Orbit
Orbit
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D.1.4 Representative Configurations
The last column in the tables in Appendix D indicates whether the vehicle
configuration is considered sufficiently similar to current and future vehicles for the
test result to be included in the representative data sample used to predict absolute
reliability. A "1" in the column indicates that the test result is included, while a "0"
indicates that it is excluded. There are likely to be differences of opinion about which
past configurations are representative and which are not. In determining which to
include, RTI has relied entirely on the Booz Allen & Hamilton report⁴¹ referred to
earlier. When faced with the same problem, Booz
Allen
established
the
following
criteria for deciding whether past configurations were sufficiently similar to current
configurations:
(1) Genealogy: Is the current system a direct or indirect derivative of the historical
configuration?
(2) Operations: Is the current system operated in the same manner as the historical
configurations (e.g., ICBM versus space-launch vehicle)?
(3) Composition: Does the current system use the same types of elements (i.e., SRMs,
upper stage, etc.)?
Based on these criteria and other factors, Booz
Allen
decided
to
use
test
results
from
flights of the following vehicle configurations to predict future success rates:
Atlas: SLV-3 and later configurations to include SLV-3A, SLV-3C, SLV-3D, G, H, I, II,
IIA, IIAS. (Excluded: Atlas A, B, C, LV-3A, 3B, 3C, D, E, F)
Delta: 291X and later configurations to include 391X, 392X, 492X, 592X, 692X, 792X.
Titan: Titan IIIC and later configurations to include IIIB, IIID, IIIE, 34B, 34D, III/CT,
IV, II-SLV.
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D.2 Atlas Launch and Performance History
Atlas space-launch vehicles, originally manufactured by General Dynamics and
currently by Lockheed Martin, derived from the Atlas ICBM series developed in the
1950s. The primary one-and-one-half-stage vehicle played a major role in early lunar
exploration activities (the unmanned Ranger, Lunar Orbiter, and Surveyor programs),
and planetary probes (Mariner and Pioneer). Table 40 shows a summary of Atlas
configurations since the beginning of the program.[10]
Table 40. Summary of Atlas Vehicle Configurations
Configuration
Description
A
ICBM single-stage test vehicle
B, C
ICBM 11/2-stage test vehicle
D
ICBM and later space-launch vehicle
E,F
First an ICBM (1960), then a reentry test vehicle (1964), then a
space-launch vehicle (1968)
LV-3A
Same as D except Agena upper stage
LV-3B
Same as D except man-rated for Project Mercury
SLV-3
Same as LV-3A except reliability improvements
SLV-3A
Same as SLV-3 except stretched 117 inches
LV-3C
Integrated with Centaur D upper stage
SLV-3C
Same as LV-3C except stretched 51 inches
SLV-3D
Same as SLV-3C except Centaur uprated to D-1A and Atlas
electronics integrated with Centaur (no longer radio guided)
G
Same as SLV-3D but Atlas stretched 81 inches
H
Same as SLV-3D except with E/F avionics and no Centaur
I
Same as G except strengthened for 14-ft payload fairing, ring laser
gyro added
II
Same as I except Atlas stretched 108 inches, engines uprated,
hydrazine roll-control added, verniers deleted, Centaur stretched
36 inches
IIA
Same as II except Centaur RL-10s engines uprated to 20K lbs
thrust and 6.5 seconds Isp increase from extendible RL-10 nozzles
IIAS
Same as IIA except 4 Castor IVA strap-on SRMs added
Atlas A, B, and C were developmental ICBMs. Atlas D, E, and F configurations were
deployed as operational ICBMs during the 1960s. During that time, some Atlas Ds
were modified as space-launch vehicles in the LV series: LV-3A, 3B, and 3C. The
Standardized Launch Vehicle (SLV) series derived from a need to reduce lead times in
transforming Atlas missiles to space-launch vehicles. The SLV series began with the
SLV-3 vehicle, which used an Agena upper stage. The G and H vehicles evolved from
the SLV series. Eventually the I, II, IIA, and IIAS configurations were developed with
the aim of also supporting commercial launches.
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Atlas vehicles are fueled by a mixture of liquid oxygen and kerosene (RP-1). The latest
IIAS configuration also incorporates Castor IVA solid-rocket motors. The early Atlas
core vehicle included a sustainer, verniers, and two booster engines, all ignited prior to
liftoff. In the Atlas II, IIA, and IIAS vehicles, the vernier engines have been replaced by
a hydrazine roll-control system. Of the four Castor SRBs on the IIAS, two are ground
lit and two are air lit some 60 seconds later. Atlas vehicles are now typically integrated
with the Centaur upper stage vehicle that is fueled with liquid oxygen and liquid
hydrogen. Earlier flights used an Agena upper stage.
The entire Atlas history through 1995 is depicted rather compactly in bar-graph form in
Figure 37. The solid-block portion of each bar indicates the number of launches during
the calendar year for which vehicle performance was entirely normal, in so far as could
be determined. The clear white parts forming the tops of most bars show the number
of launches that were either failures or flights where the launch vehicle experienced
some sort of anomalous behavior. Every launch with an entry in the response mode
column in Table 41 falls in this category. Such behavior did not necessarily prevent the
attainment of some, or even all, mission objectives.
50
45
40
Failure/Anomaly
Normal Performance
35
Number of Atlas Missions
30
25
20
15
10
5
0
55
60
65
70
75
80
85
90
95
Launch Year
Figure 37. Atlas Launch Summary
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RTI
D.2.1 Atlas Launch History
The data in Table 41 summarize the flight performance of all Atlas and Atlas-boosted
space-vehicle launches since the program began in June 1957. A launch sequence
number is provided in the first column, a mission ID and launch date in columns 2
and 3. The vehicle configuration or Atlas booster number is given in the fourth
column, while the fifth column shows whether the launch took place from the Eastern
or Western Range. The last three columns in the table show, respectively, the response
mode assigned by RTI to any failure or anomalous behavior that occurred, the flight
phase in which it occurred, and whether the vehicle configuration is considered
representative for the purposes of predicting future Atlas reliability. Launches through
sequence number 532 were used in the filtering process to estimate failure rate.
Table 41. Atlas Launch History
Launch
Vehicle
Test
Response
Flight
Rep.
No.
Mission/ID
Date
Configuration
Range
Mode
Phase
Conf.
1
Weapons System (WS)
06/11/57
4A
ER
4T
1
0
2
WS
09/25/57
6A
ER
4
1
0
3
WS
12/17/57
12A
ER
0
4
WS
01/10/58
10A
ER
0
5
WS
02/07/58
13A
ER
4
1
0
6
WS
02/20/58
11A
ER
4T
1
0
7
WS
04/05/58
15A
ER
4
1
0
8
WS
06/03/58
16A
ER
0
9
WS
07/19/58
3B
ER
4T
1
0
10
WS
08/02/58
4B
ER
0
11
WS
08/28/58
5B
ER
4
2.5
0
12
WS
09/14/58
8B
ER
4
2.5
0
13
WS
09/18/58
6B
ER
4
1
0
14
WS
11/17/58
9B
ER
4
2
0
15
WS
11/28/58
12B
ER
0
16
SCORE
12/18/58
10B LV-3A/AGENA
ER
0
17
WS
12/23/58
3C
ER
0
18
WS
01/15/59
13B
ER
5
1
0
19
WS
01/27/59
4C
ER
5
2
0
20
WS
02/04/59
11B
ER
0
21
WS
02/20/59
5C
ER
4
2
0
22
WS
03/18/59
7C
ER
4
1
0
23
WS
04/14/59
3D
ER
4
1
0
24
WS
05/18/59
7D
ER
4
1
0
25
WS
06/06/59
5D
ER
4
2
0
26
WS
07/21/59
8C
ER
0
27
WS
07/28/59
11D
ER
0
28
WS
08/11/59
14D
ER
0
29
WS
08/24/59
11C
ER
0
30
MERCURY (test)
09/09/59
10D LV-3B
ER
4
2
0
31
DESERT HEAT
09/09/59
12D
WR
0
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RTI
Launch
Vehicle
Test
Response
Flight
Rep.
No.
Mission/ID
Date
Configuration
Range
Mode
Phase
Conf.
32
WS
09/16/59
17D
ER
4
2.5
0
33
WS
10/06/59
18D
ER
0
34
WS
10/09/59
22D
ER
0
35
WS
10/29/59
26D
ER
4
2.5
0
36
WS
11/04/59
28D
ER
NA
2
0
37
WS
11/24/59
15D
ER
NA
2.5
0
38
ABLE (PIONEER)
11/26/59
20D LV-3A/AGENA
ER
4
1
0
39
WS
12/08/59
31D
ER
0
40
WS
12/18/59
40D
ER
0
41
WS
01/06/60
43D
ER
0
42
WS
01/26/60
44D
ER
0
43
DUAL EXHAUST
01/26/60
6D
WR
4
2 & 2.5
0
44
WS
02/11/60
49D
ER
0
45
MIDAS I
02/26/60
29D LV-3A/AGENA A
ER
4
2.5
0
46
WS
03/08/60
42D
ER
4
2.5
0
47
WS
03/10/60
51D
ER
1
1
0
48
WS
04/07/60
48D
ER
1
1
0
49
QUICK START
04/22/60
25D
WR
0
50
LUCKY DRAGON
05/06/60
23D
WR
3
1
0
51
WS
05/20/60
56D
ER
0
52
MIDAS II
05/24/60
45D LV-3A/AGENA A
ER
0
53
WS
06/11/60
54D
ER
0
54
WS
06/22/60
62D
ER
4
2.5
0
55
WS
06/27/60
27D
ER
0
56
WS
07/02/60
60D
ER
4
2
0
57
TIGER SKIN
07/22/60
74D
WR
5
1
0
58
MERCURY 1
07/29/60
50D LV-3B
ER
4
1
0
59
WS
08/09/60
32D
ER
0
60
WS
08/12/60
66D
ER
0
61
GOLDEN JOURNEY
09/12/60
47D
WR
4
2
0
62
WS
09/16/60
76D
ER
0
63
WS
09/19/60
79D
ER
0
64
ABLE 5 (PIONEER)
09/25/60
80D LV-3A/AGENA
ER
4T
2.5 & 3
0
65
HIGH ARROW
09/29/60
33D
WR
4
1
0
66
WS
10/11/60
3E
ER
5
2
0
67
Gibson Girl
10/11/60
57D LV-3A/AGENA A
WR
NA
3 & 5
0
68
DIAMOND JUBILEE
10/12/60
81D
WR
4
1
0
69
WS
10/13/60
71D
ER
0
70
WS
10/22/60
55D
ER
0
71
WS
11/15/60
83D
ER
0
72
WS
11/29/60
4E
ER
5
2
0
73
ABLE 5B (PIONEER)
12/15/60
91D LV-3A/AGENA
ER
4
1
0
74
HOT SHOT
12/16/60
99D
WR
0
75
WS
01/23/61
90D
ER
0
76
WS
01/24/61
8E
ER
5
2
0
77
Jawhawk Jamboree
01/31/61
70D LV-3A/AGENA A
WR
NA
2
0
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RTI
Launch
Vehicle
Test
Response
Flight
Rep.
No.
Mission/ID
Date
Configuration
Range
Mode
Phase
Conf.
78
MERCURY 2
02/21/61
67D LV-3B
ER
0
79
WS
02/24/61
9E
ER
0
80
WS
03/13/61
13E
ER
4
2
0
81
WS
03/24/61
16E
ER
4
1.5
0
82
MERCURY 3
04/25/61
100D LV-3B
ER
3
1
0
83
WS
05/12/61
12E
ER
0
84
LITTLE SATIN
05/24/61
95D
WR
0
85
WS
05/26/61
18E
ER
0
86
SURE SHOT
06/07/61
27E
WR
4
1
0
87
WS
06/22/61
17E
ER
4
1
0
88
WS
07/06/61
22E
ER
0
89
Polar Orbit (Midas III)
07/12/61
97D, LV-3A/AGENA B
WR
0
90
WS
07/31/61
21E
ER
0
91
WS
08/08/61
2F
ER
0
92
NEW NICKEL
08/22/61
101D
WR
0
93
RANGER 1
08/23/61
111D LV-3A/AGENA
ER
NA
4
0
94
WS
09/08/61
26E
ER
4
2
0
95
First Motion (Samos III)
09/09/61
106D LV-3A/AGENA B
WR
1
1
0
96
MERCURY 4
09/13/61
88D LV-3B
ER
0
97
WS
10/02/61
25E
ER
0
98
WS
10/05/61
30E
ER
0
99
Big Town (Midas IV)
10/21/61
105D LV-3A/AGENA B
WR
NA
2
0
100
WS
11/10/61
32E
ER
4T
1
0
101
RANGER 2
11/18/61
117D LV-3A/AGENA
ER
NA
4
0
102
WS
11/22/61
4F
ER
0
103
Round Trip (Samos IV)
11/22/61
108D LV-3A/AGENA B
WR
4T
2
0
104
MERCURY 5
11/29/61
93D LV-3B
ER
0
105
BIG PUSH
11/29/61
53D
WR
0
106
WS
12/01/61
35E
ER
0
107
BIG CHIEF
12/07/61
82D
WR
0
108
WS
12/12/61
5F
ER
5
2
0
109
WS
12/19/61
36E
ER
0
110
WS
12/20/61
6F
ER
4T
2
0
111
Ocean Way (Samos V)
12/22/61
114D LV-3A/AGENA B
WR
NA
2
0
112
BLUE FIN
01/17/62
123D
WR
0
113
BLUE MOSS
01/23/62
132D
WR
0
114
RANGER 3
01/26/62
121D LV-3A/AGENA B
ER
NA
2 & 5
0
115
WS
02/13/62
40E
ER
0
116
BIG JOHN
02/16/62
137D
WR
NA
1.5
0
117
MERCURY 6
02/20/62
109D, LV-3B
ER
0
118
CHAIN SMOKER
02/21/62
52D
WR
4
1
0
119
SILVER SPUR
02/28/62
66E
WR
4T
1.5 & 2
0
120
Loose Tooth
03/07/62
112D, LV-3A/AGENA B
WR
0
121
CURRY COMB I
03/23/62
134D
WR
0
122
WS
04/09/62
11F
ER
1
1
0
123
Night Hunt
04/09/62
110D LV-3A/AGENA B
WR
NA
1
0
9/10/96
105
RTI
Launch
Vehicle
Test
Response
Flight
Rep.
No.
Mission/ID
Date
Configuration
Range
Mode
Phase
Conf.
124
CURRY COMB II
04/11/62
129D
WR
0
125
RANGER 4
04/23/62
133D, LV-3A/AGENA B
ER
0
126
Dainty Doll
04/26/62
118D, LV-3A/AGENA B
WR
0
127
BLUE BALL
04/27/62
140D
WR
0
128
AC-1 (SUBORBITAL)
05/08/62
104D LV-3C/CENT. D
ER
4
1
0
129
CANNONBALL FLYER
05/11/62
127D
WR
0
130
MERCURY 7
05/24/62
107D, LV-3B
ER
0
131
Rubber Gun
06/17/62
115D, LV-3A/AGENA B
WR
4
3
0
132
ALL JAZZ
06/26/62
21D
WR
0
133
LONG LADY
07/12/62
141D
WR
0
134
EXTRA BONUS
07/13/62
67E
WR
4
2 & 2.5
0
135
Armored Car
07/18/62
120D, LV-3A/AGENA B
WR
0
136
FIRST TRY
07/19/62
13D
WR
0
137
MARINER 1 (VENUS)
07/22/62
145D LV-3A/AGENA B
ER
5
2
0
138
HIS NIBS
08/01/62
15F
WR
0
139
Air Scout
08/05/62
124D, LV-3A/AGENA B
WR
0
140
PEG BOARD
08/09/62
8D
WR
0
141
PEG BOARD II
08/09/62
87D
WR
4
2.5
0
142
CRASH TRUCK
08/10/62
57F
WR
5
1
0
143
WS
08/13/62
7F
ER
0
144
MARINER 2 (VENUS)
08/27/62
179D LV-3A/AGENA B
ER
NA
2
0
145
WS
09/19/62
8F
ER
0
146
BRIAR STREET
10/02/62
4D
WR
4
2
0
147
MERCURY 8
10/03/62
113D, LV-3B
ER
0
148
RANGER 5
10/18/62
215D LV-3A/AGENA B
ER
NA
5
0
149
WS
10/19/62
14F
ER
0
150
CLOSED CIRCUITS
10/26/62
159D
WR
0
151
WS
11/07/62
16F
ER
0
152
After Deck
11/11/62
128D, LV-3A/AGENA B
WR
0
153
ACTION TIME
11/14/62
13F
WR
4
1
0
154
WS
12/05/62
21F
ER
0
155
DEER PARK
12/12/62
161D
WR
0
156
Bargain Counter
12/17/62
131D, LV-3A/AGENA B
WR
4T
1
0
157
OAK TREE
12/18/62
64E
WR
4T
1
0
158
FLY HIGH
12/22/62
160D
WR
4
2
0
159
BIG SUE
01/25/63
39D
WR
4
1
0
160
FAINT CLICK
01/31/63
176D
WR
0
161
FLAG RACE
02/13/63
182D
WR
0
162
PITCH PINE
02/28/63
188D
WR
0
163
ABRES-1
03/01/63
134F
ER
0
164
TALL TREE 3
03/09/63
102D
WR
5
1
0
165
TALL TREE 2
03/11/63
64D
WR
0
166
TALL TREE 1
03/15/63
46D
WR
4T
2
0
167
TALL TREE 5
03/15/63
63F
WR
0
168
LEADING EDGE
03/16/63
193D
WR
4T
2
0
169
KENDALL GREEN
03/21/63
83F
WR
4
2.5
0
9/10/96
106
RTI
Launch
Vehicle
Test
Response
Flight
Rep.
No.
Mission/ID
Date
Configuration
Range
Mode
Phase
Conf.
170
TALL TREE 4
03/23/63
52F
WR
4
1
0
171
BLACK BUCK
04/24/63
65E
WR
NA
2.5
0
172
ABRES-2
04/26/63
135F
ER
0
173
Damp Clay
05/09/63
119D, LV-3A/AGENA B
WR
0
174
MERCURY 9
05/15/63
130D, LV-3B
ER
0
175
DOCK HAND
06/04/63
62E
WR
0
176
HARPOON GUN
06/12/63
198D
WR
0
177
Big Four
06/12/63
139D, LV-3A/AGENA B
WR
4T
1
0
178
GO BOY
07/03/63
69E
WR
0
179
Fish Pool
07/12/63
201D, LV-3A/AGENA D
WR
0
180
Damp Duck
07/18/63
75D, LV-3A/AGENA B
WR
0
181
SILVER DOLL
07/26/63
24E
WR
4
2
0
182
BIG FLIGHT
07/30/63
70E
WR
0
183
COOL WATER I
07/31/63
143D
WR
0
184
PIPE DREAM
08/24/63
72E
WR
0
185
COOL WATER II
08/28/63
142D
WR
0
186
Fixed Fee
09/06/63
212D, LV-3A/AGENA D
WR
0
187
COOL WATER III
09/06/63
63D
WR
4
1
0
188
COOL WATER IV
09/11/63
84D
WR
4T
2.5
0
189
FILTER TIP
09/25/63
71E
WR
4T
2
0
190
HOT RUM
10/03/63
45F
WR
1
1
0
191
COOL WATER V
10/07/63
163D
WR
4
1
0
192
VELA 1 & 2
10/16/63
197D, LV-3A/AGENA D
ER
0
193
Hay Bailer
10/25/63
224D, LV-3A/AGENA D
WR
0
194
ABRES-3
10/28/63
136F
ER
4T
2
0
195
HICKORY HOLLOW
11/04/63
232D
WR
0
196
COOL WATER VI
11/13/63
158D
WR
4
1
0
197
AC-2
11/27/63
126D, LV-3C/CENTAUR D
ER
0
198
LENS COVER
12/18/63
233D
WR
0
199
Rest Easy
12/18/63
227D, LV-3A/AGENA D
WR
0
200
DAY BOOK
12/18/63
109F
WR
0
201
RANGER 6
01/30/64
199D, LV-3A/AGENA B
ER
0
202
BLUE BAY
02/12/64
48E
WR
4
2
0
203
Upper Octane
02/25/64
285D, LV-3A/AGENA D
WR
0
204
ABRES-4
02/25/64
5E
ER
0
205
Ink Blotter
03/11/64
296D, LV-3A/AGENA D
WR
0
206
ABRES-5
04/01/64
137F
ER
0
207
HIGH BALL
04/03/64
3F
WR
1
1
0
208
PROJECT FIRE
04/14/64
263D, LV-3A/AGENA D
ER
0
209
Anchor Dan
04/23/64
351D, LV-3A/AGENA D
WR
0
210
Big Fred
05/19/64
350D, LV-3A/AGENA D
WR
0
211
IRON LUNG
06/18/64
243D
WR
0
212
AC-3
06/30/64
135D, LV-3C/CENT. D
ER
4
3
0
213
Quarter Round
07/06/64
352D, LV-3A/AGENA D
WR
0
214
VELA3&4
07/17/64
216D, LV-3A/AGENA D
ER
0
215
RANGER 7
07/28/64
250D, LV-3A/AGENA D
ER
0
9/10/96
107
RTI
Launch
Vehicle
Test
Response
Flight
Rep.
No.
Mission/ID
Date
Configuration
Range
Mode
Phase
Conf.
216
KNOCK WOOD
07/29/64
248D
WR
0
217
LARGE CHARGE
08/07/64
110F
WR
0
218
Big Sickle
08/14/64
7101, SLV-3A/AGENA D
WR
1
219
GALLANT GAL
08/27/64
57E
WR
4
2
0
220
BIG DEAL
08/31/64
36F
WR
0
221
OGO-1
09/04/64
195D, LV-3A/AGENA B
ER
0
222
BUTTERFLY NET
09/15/64
245D
WR
0
223
BUZZING BEE
09/22/64
247D
WR
0
224
Slow Pace
09/23/64
7102, SLV-3/AGENA D
WR
1
225
Busy Line
10/08/64
7103, SLV-3/AGENA D
WR
1
226
Boon Decker
10/23/64
353D, LV-3A/AGENA D
WR
0
227
MARINER 3
11/05/64
289D, LV-3A/AGENA D
ER
4
4
0
228
MARINER 4
11/28/64
288D, LV-3A/AGENA D
ER
0
229
BROOK TROUT
12/01/64
210D
WR
0
230
OPERA GLASS
12/04/64
300D
WR
0
231
Battle Royal
12/04/64
7105, SLV-3/AGENA D
WR
1
232
AC-4
12/11/64
146D, LV-3C/CENTAUR D
ER
0
233
STEP OVER
12/22/64
111F
WR
0
234
PILOT LIGHT
01/08/65
106F
WR
0
235
PENCIL SET
01/12/65
166D
WR
0
236
Beaver's Dam
01/21/65
172D/ABRES
WR
4
2&3
0
237
Sand Lark
01/23/65
7106, SLV-3/AGENA D
WR
1
238
RANGER 8
02/17/65
196D, LV-3A/AGENA B
ER
0
239
DRAG BAR
02/27/65
211D
WR
0
240
PORK BARREL
03/02/65
301D
WR
0
241
AC-5
03/02/65
156D, LV-3C/CENT. D
ER
1
1
0
242
Ship Rail
03/12/65
7104, SLV-3/AGENA D
WR
1
243
ANGEL CAMP
03/12/65
154D
WR
0
244
RANGER 9
03/21/65
204D, LV-3A/AGENA B
ER
0
245
FRESH FROG
03/26/65
297D
WR
0
246
Air Pump
04/03/65
7401, SLV-3/AGENA D
WR
1
247
FLIP SIDE
04/06/65
150D
WR
0
248
Dwarf Tree
04/28/65
7107, SLV-3/AGENA D
WR
1
249
PROJECT FIRE
05/22/65
264D, LV-3A/AGENA D
ER
0
250
Bottom Land
05/27/65
7108, SLV-3/AGENA D
WR
1
251
Tennis Match
05/27/65
68D/ABRES
WR
4
1
0
252
OLD FOGEY
06/03/65
177D
WR
0
253
LEA RING
06/08/65
299D
WR
0
254
STOCK BOY
06/10/65
302D
WR
0
255
Worn Face
06/25/65
7109, SLV-3/AGENA D
WR
1
256
BLIND SPOT
07/01/65
59D
WR
0
257
White Pine
07/12/65
7112, SLV-3/AGENA D
WR
4 & 5
2&3
1
258
VELA 5 & 6
07/20/65
225D, LV-3A/AGENA D
ER
0
259
Water Tower
08/03/65
7111, SLV-3/AGENA D
WR
1
260
PIANO WIRE
08/04/65
183D
WR
0
261
SEA TRAMP
08/05/65
147F
WR
0
9/10/96
108
RTI
Launch
Vehicle
Test
Response
Flight
Rep.
No.
Mission/ID
Date
Configuration
Range
Mode
Phase
Conf.
262
AC-6
08/11/65
151D, LV-3C/CENTAUR D
ER
0
263
TONTO RIM
08/26/65
61D
WR
0
264
WATER SNAKE
09/29/65
125D
WR
0
265
Log Fog
09/30/65
7110, SLV-3/AGENA D
WR
1
266
Seething City
10/05/65
34D/ABRES
WR
0
267
GTV-6
10/25/65
5301, SLV-3/AGENA D
ER
4
3
1
268
Shop Degree
11/08/65
7113, SLV-3/AGENA D
WR
1
269
WILD GOAT
11/29/65
200D
WR
0
270
TAG DAY
12/20/65
85D
WR
0
271
Blanket Party
01/19/66
7114, SLV-3/AGENA D
WR
1
272
YEAST CAKE
02/10/66
305D
WR
0
273
LONELY MT.
02/11/66
86D
WR
0
274
Mucho Grande
02/15/66
7115, SLV-3/AGENA D
WR
1
275
SYCAMORE RIDGE
02/19/66
73D
WR
0
276
ETERNAL CAMP
03/04/66
303D
WR
5
1
0
277
GTV-8
03/16/66
5302, SLV-3/AGENA D
ER
1
278
Dumb Dora
03/18/66
7116, SLV-3/AGENA D
WR
1
279
WHITE BEAR
03/19/66
304D
WR
5
2
0
280
Bronze Bell
03/30/66
72D
WR
0
281
AC-8
04/07/66
184D, LV-3C/CENT. D
ER
4T
4
0
282
OAO-1
04/08/66
5001, SLV-3/AGENA D
ER
0
283
Shallow Stream
04/19/66
7117, SLV-3/AGENA D
WR
1
284
CRAB CLAW
05/03/66
208D
WR
4T
1
0
285
SUPPLY ROOM
05/13/66
98D
WR
0
286
Pump Handle
05/14/66
7118, SLV-3/AGENA D
WR
1
287
GTV-9
05/17/66
5303, SLV-3/AGENA D
ER
5
1
1
288
SAND SHARK
05/26/66
41D
WR
0
289
SURVEYOR-1 (AC-10)
05/30/66
290D, LV-3C/CENTAUR D
ER
0
290
GTV-9A
06/01/66
5304, SLV-3/AGENA D
ER
1
291
Power Drill
06/03/66
7119, SLV-3/AGENA D
WR
1
292
OGO-3
06/06/66
5601, SLV-3/AGENA B
ER
1
293
Mama's Boy
06/09/66
7201, SLV-3/AGENA D
WR
1
294
VENEER PANEL
06/10/66
96D
WR
4
2.5
0
295
GOLDEN MT.
06/26/66
147D
WR
0
296
HEAVY ARTILLERY
06/30/66
298D
WR
0
297
Snake Creek
07/12/66
7120, SLV-3/AGENA D
WR
1
298
Stony Island
07/13/66
58D/ABRES
WR
NA
3
0
299
GTV-10
07/18/66
5305, SLV-3/AGENA D
ER
1
300
BUSY RAMROD
08/08/66
149F
WR
4
2
0
301
LUNAR ORBITER 1
08/10/66
5801, SLV-3/AGENA D
ER
1
302
Silver Doll
08/16/66
7121, SLV-3/AGENA D
WR
1
303
Happy Mt.
08/19/66
7202, SLV-3/AGENA D
WR
1
304
GTV-11
09/12/66
5306, SLV-3/AGENA D
ER
1
305
Taxi Driver
09/16/66
7123, SLV-3/AGENA D
WR
1
306
SURVEYOR 2 (AC-7)
09/20/66
194D, LV-3C/CENT. D
ER
NA
5
0
307
Dwarf Killer
10/05/66
7203, SLV-3/AGENA D
WR
1
9/10/96
109
RTI
Launch
Vehicle
Test
Response
Flight
Rep.
No.
Mission/ID
Date
Configuration
Range
Mode
Phase
Conf.
308
LOW HILL
10/11/66
115F
WR
4
1
0
309
Gleaming Star
10/12/66
7122, SLV-3/AGENA D
WR
1
310
AC-9
10/26/66
174D, LV-3C/CENT. D
ER
NA
2
0
311
Red Caboose
11/02/66
7124, SLV-3/AGENA D
WR
1
312
LUNAR ORBITER 2
11/06/66
5802, SLV-3/AGENA D
ER
1
313
GTV-12
11/11/66
5307, SLV-3/AGENA D
ER
1
314
Busy Mermaid
12/05/66
7125, SLV-3/AGENA D
WR
1
315
ATS-B
12/06/66
5101, SLV-3/AGENA D
ER
1
316
Busy Panama
12/11/66
89D/ABRES
WR
0
317
Busy Peacock
12/21/66
7001, SLV-3/AGENA D
WR
1
318
BUSY STEPSON
01/17/67
148F
WR
NA
2.5
0
319
BUSY NIECE
01/22/67
35D
WR
0
320
Busy Party
02/02/67
7126, SLV-3/AGENA D
WR
1
321
LUNAR ORBITER 3
02/04/67
5803, SLV-3/AGENA D
ER
1
322
BUSY BOXER
02/13/67
121F
WR
0
323
Giant Chief
03/05/67
7002, SLV-3/AGENA D
WR
1
324
LITTLE CHURCH
03/16/67
151F
WR
0
325
ATS-A
04/05/67
5102, SLV-3/AGENA D
ER
1
326
BUSY SUNRISE
04/07/67
38D
WR
0
327
SURVEYOR 3 (AC-12)
04/17/67
292D, LV-3C/CENTAUR D
ER
0
328
Busy Tournament
04/19/67
7003, SLV-3/AGENA D
WR
1
329
LUNAR ORBITER 4
05/04/67
5804, SLV-3/AGENA D
ER
1
330
BUSY PIGSKIN
05/19/67
119F
WR
0
331
Busy Camper
05/22/67
7127, SLV-3/AGENA D
WR
1
332
Busy Wolf
06/04/67
7128, SLV-3/AGENA D
WR
1
333
BUCK TYPE
06/09/67
122F
WR
0
334
MARINER 5 (VENUS)
06/14/67
5401, SLV-3/AGENA D
ER
1
335
ABRES (AFSC)
07/06/67
65D
WR
0
336
SURVEYOR 4 (AC-11)
07/14/67
291D, LV-3C/CENTAUR D
ER
0
337
ABRES (AFSC)
07/22/67
114F
WR
0
338
AFSC
07/27/67
92D/ABRES
WR
0
339
BREAD HOOK
07/29/67
150F
WR
0
340
LUNAR ORBITER 5
08/01/67
5805, SLV-3/AGENA D
ER
1
341
SURVEYOR 5 (AC-13)
09/08/67
5901C, SLV-3/CENTAUR D
ER
1
342
ABRES (AFSC)
10/11/67
69D
WR
0
343
ABRES (AFSC)
10/14/67
118F
WR
0
344
ABRES (AFSC)
10/27/67
81F
WR
4T
1
0
345
ATS-C
11/05/67
5103, SLV-3/AGENA D
ER
1
346
SURVEYOR 6 (AC-14)
11/07/67
5902C, SLV-3C/CENTAUR D
ER
1
347
ABRES (AFSC)
11/07/67
94D
WR
0
348
ABRES (AFSC)
11/10/67
113F
WR
0
349
ABRES (AFSC)
12/21/67
117F
WR
0
350
SURVEYOR 7 (AC-15)
01/07/68
5903C, SLV-3C/CENTAUR D
ER
1
351
ABRES (AFSC)
01/31/68
94F
WR
0
352
ABRES (AFSC)
02/26/68
116F
WR
0
353
OGO-E
03/04/68
5602A, SLV-3A/AGENA D
ER
1
9/10/96
110
RTI
Launch
Vehicle
Test
Response
Flight
Rep.
No.
Mission/ID
Date
Configuration
Range
Mode
Phase
Conf.
354
ABRES (AFSC)
03/06/68
74E
WR
0
355
AFSC
04/06/68
107F/ABRES
WR
0
356
ABRES (AFSC)
04/18/68
77E
WR
0
357
ABRES (AFSC)
04/27/68
78E
WR
0
358
ABRES (AFSC)
05/03/68
95F
WR
5
1
0
359
ABRES (AFSC)
06/01/68
89F
WR
0
360
ABRES (AFSC)
06/22/68
86F
WR
0
361
ABRES (AFSC)
06/29/68
32F
WR
0
362
AFSC
07/11/68
75F/ABRES
WR
0
363
DOD (AA-27)
08/06/68
SLV-3A/AGENA D
ER
1
364
ATS-D (AC-17)
08/10/68
5104C, SLV-3C/CENTAUR D
ER
NA
4
1
365
AFSC
08/16/68
7004, SLV-3/BURNER II
WR
4
3
1
366
ABRES (AFSC)
09/25/68
99F
WR
0
367
ABRES (AFSC)
09/27/68
84F
WR
0
368
ABRES (AFSC)
11/16/68
56F
WR
4T
2.5
0
369
ABRES (AFSC)
11/24/68
60F
WR
0
370
OAO-A2 (AC-16)
12/07/68
5002C, SLV-3C/CENTAUR D
ER
1
371
ABRES (AFSC)
01/16/69
70F
WR
0
372
MARINER 6 (MARS) (AC-20)
02/24/69
5403C, SLV-3C/CENTAUR D
ER
NA
1
1
373
AFSC
03/17/69
104F/ABRES
WR
0
374
MARINER 7 (MARS) (AC-19)
03/27/69
5105C, SLV-3C/CENTAUR D
ER
1
375
DOD (AA-28)
04/12/69
SLV-3A/AGENA D
ER
1
376
ATS-E (AC-18)
08/12/69
5402C, SLV-3C/CENTAUR D
ER
1
377
ABRES (AFSC)
08/20/69
112F
WR
0
378
ABRES (AFSC)
09/16/69
100F
WR
0
379
ABRES (AFSC)
10/10/69
98F
WR
4
1
0
380
ABRES (AFSC)
12/03/69
44F
WR
0
381
ABRES (AFSC)
12/12/69
93F
WR
0
382
ABRES (AFSC)
02/08/70
96F
WR
0
383
ABRES (AFSC)
03/13/70
28F
WR
0
384
ABRES (AFSC)
05/30/70
91F
WR
0
385
ABRES (AFSC)
06/09/70
92F
WR
0
386
DOD (AA-29)
06/19/70
SLV-3A/AGENA D
ER
1
387
DOD (AA-30)
08/31/70
SLV-3A/AGENA D
ER
1
388
OAO-B (AC-21)
11/30/70
5003C, SLV-3C/CENTAUR D
ER
4
2
1
389
ABRES (AFSC)
12/22/70
105F
WR
0
390
INTELSAT IV F-2 (AC-25)
01/25/71
5005C, SLV-3C/CENTAUR D
ER
1
391
ABRES (AFSC)
04/05/71
85F
WR
0
392
MARINER 8 (MARS) (AC-24)
05/08/71
5405C, SLV-3C/CENTAUR

[truncated]