Modeling Unlikely Space-Booster Failures in Risk Calculations

## Document Type

Technical Report (Final Report)

## Classification

Administrative/Operational Use Data (Distribution authorized to US Government agencies and contractors)

## Page Description

Title page and cover memoranda of a research report on space-booster failure risk analysis.

## Dates

## Organizations

## Locations

## Document Identifiers

## Title

"Modeling Unlikely Space-Booster Failures in Risk Calculations"

## Notes

Document is marked "DTC QUALITY INSPECTED" indicating technical review compliance.

## Document Type

Technical Report - Credits and Contract Page

## Dates

## People

## Organizations

## Locations

## Document Identifiers

## Classification

Distribution authorized to US Government agencies and contractors for administrative/operational use data.

## Document Type

Technical Report - Form Documentation Page (Standard Form 298)

## Classification

Unclassified

## Report Details

## Authors

## Organizations

## Key Personnel

## Subject Terms

## Document Statistics

## Abstract Summary

Report addresses modeling of Mode-5 (unlikely) failure responses in space-vehicle launches. Covers failure probabilities for Atlas, Delta, and Titan missiles and provides failure history narratives from Eastern and Western Ranges through August 1996.

## Document Type

Technical Report - Table of Contents Pages

## Page Description

Continuation of front matter tables of contents and list of figures/tables

## Figures Referenced

## Tables Referenced

## Content Structure

## Organizations Referenced

## Document Type

Technical Report - Table of Figures and Tables

## Page Description

Comprehensive listing of all figures (31 total) and tables (18 total) referenced in report

## Figures Listed

## Tables Listed

## Key Vehicles Covered

## Organization

## Document Type

Technical Report - Table of Contents (Text Pages)

## Page Description

Detailed table of contents for main body of report showing section structure and page numbers

## Sections

1. **Introduction** (page 1)

2. **Examples Showing Need for Mode 5** (page 3)

3. **Understanding the Mode-5 Failure Response** (page 7)

- 3.1 Effects of Mode-5 Shaping Constants (page 9)

- 3.2 Effects of Shaping Constant on DAMP Results (page 9)

4. **Methodology for Assessing Failure Probabilities** (page 13)

- 4.1 The Parts-Analysis Approach (page 13)

- 4.2 The Empirical Approach (page 15)

5. **Computation of Failure Probabilities** (page 16)

- 5.1 Overall Failure Probability (page 16)

- 5.2 Relative and Absolute Probabilities for Response Modes (page 24)

- 5.3 Relative Probability of Tumble for Response-Modes 3 and 4 (page 30)

6. **Shaping Constants Through Simulation** (page 31)

7. **Potential Future Investigations** (page 73)

8. **Summary** (page 74)

## Appendices

## Date

9/10/96

## Document Type

Technical Report - Appendix Contents

## Page Description

Continuation of front matter showing appendix structure and major content sections

## Appendix D: Launch and Performance Histories

## References Section

Page 171

## Date

9/10/96

## Document Type

Technical Report - Body Text (Section 1: Introduction - continued)

## Page Description

Continuation of opening material with figure listing continuation

## Figures Listed (Continuation)

## Tables Listed (Selected)

## Document Organization

Foundational material for main technical content beginning with Introduction section

## Date

9/10/96

## Document Type

Technical Report - Abstract

## Classification

Unclassified

## Page Description

Formal abstract summarizing purpose and scope of entire 180-page technical report

## Key Concepts Explained

## Methodology

## Data Coverage

## Results

## Date

9/10/96

## Document Type

Technical Report - Section 1: Introduction (Main Body)

## Page Description

Opening section explaining purpose, background, and framework of Mode-5 failure analysis in launch vehicle risk assessment

## Key Concepts

## Program Description

## Analysis Framework

## Organizations Referenced

## Date

9/10/96

## Document Type

Technical Report - Section 1: Introduction (Continuation)

## Page Description

Continued explanation of Mode-5 failure response methodology and mathematical framework

## Mode-5 Characteristics

**Defined by three key properties:**

1. **Impact Range and Direction**: Impacts can occur in any direction from launch point at any range within vehicle's energy capabilities

2. **Angular Deviation Effects**:

- Likelihood of impact decreases as angular deviation from flight line increases

- Becomes least likely in uprange direction

- For fixed angular deviation, impact likelihood decreases with range increase

3. **Density Function Behavior**:

- At fixed impact ranges near launch point: impact density changes gradually as impact direction swings 180° from downrange to uprange

- As impact range increases: decrease in density function becomes progressively more rapid with change in direction

- Greater impact range means more rapid density function change with angular deviation

## Destruct Action Effects

## Vehicle Dependency

## Critical Importance

## Study Tasking

## Date

9/10/96

## Document Type

Technical Report - Section 1: Introduction (Continuation)

## Page Description

Continuation of study scope and methodology, addressing data limitations and simulation approaches

## Data Challenge

## Study Approach

## Study Objectives (Additional to Primary Task)

Beyond primary task to determine Mode-5 constants, study also develops:

1. **Absolute failure probabilities** for Atlas, Delta, and Titan

2. **Relative probabilities** of occurrence for all failure-response modes

3. Applications to LLV1 and other new launch systems

## Organizations

## Technical Framework

## Date

9/10/96

## Document Type

Technical Report - Section 2: Examples Showing Need for Mode 5

## Page Description

Eight detailed examples of historical vehicle failures demonstrating why Mode-5 response classification is necessary

## Historical Examples Documented

**(1) Atlas 8E, 24 Jan 61**

**(2) Titan M-4, 6 Oct 61**

**(3) Atlas 145D (Mariner R-1), 22 July 62**

**(4) Atlas SLV-3 (GTA-9), 17 May 66**

**(5) Atlas 95F (ABRES/AFSC), 3 May 68**

**(6) Delta Intelsat III, 18 Sep 68**

**(7) Delta Pioneer E, 27 Aug 69**

**(8) Atlas 68E, 8 Dec 80**

## Analysis Note

None of these described vehicle failures can be classified as Mode 1, 2, or 3 response, or standard Mode-4 on-trajectory failure. Except possibly example (2), none can be modeled as either rapid tumble or slow turn.

## Date

9/10/96

## Document Type

Technical Report - Discussion and Footnote

## Page Description

Analysis of historical examples and clarification of safety procedures

## Classification Analysis

From the eight historical examples on previous pages, the document states:

"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."

**Exception noted**: Except possibly for example (2) (Titan M-4), it seems apparent that none can be modeled as either a rapid tumble or a slow turn.

## Safety Philosophy Footnote

**Important clarification**: "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."

## Key Points

1. **Safety Officer Procedure**: Needs time to evaluate telemetry data before taking destruct action

2. **Risk Assessment**: Only activates destruct system if immediate threat to impact limit lines exists

3. **System Integrity**: Must ensure destruct system itself is not at risk before committing to action

4. **Information Gathering**: Additional flight time allows better problem diagnosis

## Purpose

This footnote explains why vehicles that could theoretically be classified as Mode-4 responses (on-trajectory failures) through immediate destruct action are instead allowed to continue flying, resulting in Mode-5 classification.

## Date

9/10/96

## Document Type

Technical Report - Case Study Examples of Mode-5 Failure Response

## Page Description

Two recent documented examples demonstrating Mode-5 failure response with RSO console impact trace diagram

## Case Study 1: Prospector (Joust) Launch

**Figure 1 Details** (Joust Impact Trace - JOUST1761-R):

## Case Study 2: Red Tigress Sounding Rocket

## Key Insight

Both examples demonstrate that Mode-5 failure responses result from vehicle malfunctions that cause sustained deviations from intended flight line, where the safety officer must make judgment calls about timing of destruct action based on incomplete information during flight.

## Date

9/10/96

Technical section on Mode-5 failure response analysis. Discusses impact-density functions for debris dispersion modeling in launch vehicle risk assessment.

## Observations

## Assessments

## References

## Page Number

7 (dated 9/10/96, RTI)

Continuation of Mode-5 failure response analysis with secondary impact-density function and practical failure mechanisms.

## Observations

## Failure Mechanisms

Four specific Mode-5 failure types described:

1. Re-orientation of guidance platform

2. Insertion of erroneous spatial target into guidance system

3. Locking of engine nozzle in fixed position near null, producing near-constant angular acceleration and slow velocity vector turn

4. Erroneous accumulation of velocity bits by guidance system

## Assessments

## Page Number

8 (dated 9/10/96, RTI)

Effects of Mode-5 shaping constants on impact-density function and DAMP risk assessment results.

## Observations

## Section 3.1: Effects of Mode-5 Shaping Constants

## Section 3.2: Effects of Shaping Constant on DAMP Results

## Assessments

## Page Number

9 (dated 9/10/96, RTI)

Case study 1 showing effects of Mode-5 shaping constant A on Atlas IIA baseline risks with tabular results.

## Case 1: Baseline Risks for Atlas IIA

## Observations - Table 1: Effects of Mode-5 Shaping Constant A on Atlas IIA Risks

B = 1,000 constant across all rows

## Assessments

## Case 2: Risk Contours for Atlas IIAS

Definitions of Flight Hazard Area and Flight Caution Area may be based on risk contours for inner-ear injury.

## Page Number

10 (dated 9/10/96, RTI)

Risk contour visualization for Atlas IIAS showing inner-ear injury risk zones with shaping constant A = 3.0. Complex cartographic representation with multiple concentric zones and labeled areas.

## Observations

## Locations

## Assessments

## Page Number

11 (dated 9/10/96, RTI)

Risk contour visualization for Atlas IIAS showing inner-ear injury risk zones with shaping constant A = 3.5. Comparative cartographic representation to page 020 with modified constant value.

## Observations

## Locations

## Assessments

## Page Number

12 (dated 9/10/96, RTI)

Section 4: Methodology for Assessing Failure Probabilities. Introduces two primary approaches for estimating launch-vehicle failure probabilities with critical analysis of each method's limitations.

## Observations

## Section 4.1: The Parts-Analysis Approach

Extensive discussion with quotations from Booz-Allen & Hamilton, Inc. (1992) draft report for Air Force Space Command.

Key limitations of parts-analysis approach:

K-factor criticism:

## Organizations

## Assessments

## Page Number

13 (dated 9/10/96, RTI)

Continuation of Section 4.1 (Parts-Analysis Approach) and introduction of Section 4.2 (Empirical Approach). Detailed critique of engineering reliability assessment methodologies and transition to statistical approach.

## Section 4.1 Continued

Booz-Allen conclusion: Engineering approach cannot account for undetected design flaws. However, experience shows design flaws do cause operational launch system failures and will likely continue.

## Section 4.2: The Empirical Approach

## Observations

## Assessments

## Page Number

14 (dated 9/10/96, RTI)

Section 5: Computation of Failure Probabilities. Details empirical approach for predicting failure probabilities and establishing response mode distributions.

## Section 5: Computation of Failure Probabilities

Three primary purposes for test results analysis (Atlas, Delta, Titan from Appendix D tables):

1. Predict overall probability each vehicle will fail during various flight phases (see Table 39, Appendix D for flight-phase definitions)

2. Establish relative and overall probabilities for Response Modes 1 through 5

3. Establish relative frequency of tumble for Response Modes 3 and 4

## Section 5.1: Overall Failure Probability

Prediction methodology for Atlas, Delta, Titan:

## Observations

Representative configuration results presented in Table 2 for six flight phases.

## Assessments

## Page Number

16 (dated 9/10/96, RTI)

Table 2: Predicted Failure Probabilities for Representative Configurations. Comprehensive data table showing failure probability estimates for Atlas, Delta, and Titan across multiple flight phases and filtering techniques.

## Table 2 Observations

### Atlas (156 total flights, representative configuration)

Flight phases 0 through 0-5* with sample failures/total:

### Delta (125 total flights)

### Titan (171 total flights)

*Includes response mode 'NA'

## Assessments

## Page Number

17 (dated 9/10/96, RTI)

Table 3: Predicted Failure Probabilities for All Configurations. Comparative data showing failure probabilities when including all flight test configurations rather than representative samples only.

## Table 3 Observations

### Atlas (532 total flights, all configurations)

Flight phases 0 through 0-5*:

### Delta (232 total flights, all configurations)

### Titan (337 total flights, all configurations)

*Includes response mode 'NA'

## Comparative Analysis

Comparison of Table 2 (representative configurations) vs Table 3 (all configurations):

## Assessments

## Page Number

18 (dated 9/10/96, RTI)

Table 4: Comparison of Weighting Percentages. Comprehensive analysis of how three filtering techniques (Exponential, Index-count, Equal) distribute weight across data samples of varying sizes.

## Table 4 Observations

### Key Findings by Sample Size

**Sample = 4:**

**Sample = 10:**

**Sample = 20:**

**Sample = 100:**

**Sample = 200:**

**Sample = 500:**

**Sample = 1000:**

*F = 0.98 for exponential filter

+"Last" refers to most recent data point

## Assessments

Index-count filter deficiencies:

## Page Number

19 (dated 9/10/96, RTI)

Detailed analysis of exponential filter characteristics and selection of optimal filter constant F for missile/space-vehicle performance data weighting.

## Observations

Exponential filter equation denominator is geometric series asymptotically approaching [1/(1-F)] as n approaches infinity.

## Section on Filter Constant Selection

## Selection Objectives

## Assessments

## Page Number

20 (dated 9/10/96, RTI)

Table 5: Filter Factor Influence on Weighting Percentages. Analysis of how exponential filter constant F (ranging 0.96-0.995) affects data weighting across Atlas, Delta, and Titan samples.

## Table 5 Observations

### Atlas (156 flights)

### Delta (125 flights)

### Titan (171 flights)

*Last half + 1 if sample size is odd

## Critical Analysis

### F = 0.96 Issues

### F = 0.995 Issues

### Optimal Range

## Assessments

## Page Number

21 (dated 9/10/96, RTI)

Conclusion of Section 5.1 discussing selection of exponential filter constant F, with detailed enumeration of two contrary objectives guiding F selection and preliminary assessment of optimal values.

## Section: Filter Constant Selection (Continued from page 20)

1. Down-weight substantially those failures for which probability of occurrence has been greatly reduced through redesign and replacement of components, improved test procedures, and related improvements

2. (Objective continues but text truncated on visible portion)

## Observations

## Vehicles and Data Volumes

## Assessment of Weighting Effects

From Table 5 analysis:

## Overall Assessment

## Organizations Cited

## Page Number

21 (dated 9/10/96, RTI)

Technical discussion of filtering methodology for failure probability predictions and data weighting approaches. Contains narrative text and Figure 4 showing filter factor results for Atlas representative configurations.

## Dates

## Organizations

## Key Content

### Filter Factor Analysis

### Sample Size Principles

### Data Samples

### Figure 4

Shows inverse relationship between filter volatility and F value for Atlas across sample index 0-160, with three curves for F = 0.97, 0.98, and 0.99

Continuation of filter factor analysis with Figure 4 graphical presentation and interpretation of filter factor selection rationale for future risk studies.

## Dates

## Organizations

## Key Content

### Filter Factor Selection Rationale

### Future Risk Analysis Plans

### Figure 4 Interpretation

Demonstrates that filter factor choice significantly affects predicted failure probability trajectory over launch sequence history

Failure probability data for Atlas, Delta, and Titan vehicles with response mode analysis. Contains Table 6 showing predicted failure probabilities and Table 7-10 showing failure counts by response mode.

## Dates

## Organizations

## Key Content

### Table 6: Failure Probabilities (Exponential filter F = 0.98)

**Atlas:**

**Delta:**

**Titan:**

### Delta Second-Stage Analysis

### Response Mode Probabilities

### Failure Count Tables

### Note

Thor Western Range flights excluded due to incomplete performance records

Detailed failure count tables for all launch vehicles across flight phases and failure-response modes.

## Dates

## Organizations

## Key Content

### Table 7: Atlas Failures - All Configurations (532 Flights)

Failure-response modes by flight phase (0 through 0-5):

### Table 8: Delta Failures - All Configurations (232 Flights)

### Table 9: Titan Failures - All Configurations (337 Flights)

### Table 10: Eastern-Range Thor Failures (85 Flights)

Combined failure analysis across all vehicles and last-occurrence dates for each failure mode. Contains Tables 11-12 with aggregate data and temporal information.

## Dates

## Organizations

## Key Content

### Table 11: Number of Failures for All Vehicles (1186 Total Flights)

Aggregate across Atlas, Delta, Titan, Thor by flight phase (0 through 0-5):

### Table 12: Date of Most Recent Failure by Response Mode and Vehicle

**Mode 1 Last Occurrence:**

**Mode 2 Last Occurrence:**

**Mode 3 Last Occurrence:**

**Mode 4 Last Occurrence:**

**Mode 5 Last Occurrence:**

### Notes

Filter weighting analysis and response-mode occurrence percentages. Contains Table 13 showing percentage weightings across filter constants and Table 14 showing response-mode occurrence percentages.

## Dates

## Organizations

## Key Content

### Table 13: Percentage Weighting for Sample of 1186 Launches

Shows weighting distribution across filter constants (0.999 to 0.980):

**At F = 0.999:**

**At F = 0.990:**

**At F = 0.980:**

### Filter Factor Appropriateness

### Table 14: Response-Mode Occurrence Percentages (Flight Phases 0-2)

Selection of filter constant for mature and new launch systems, with recommended response-mode percentages for different vehicle categories.

## Dates

## Organizations

## Key Content

### Filter Constant Selection Rationale

### New Liquid-Propellant Systems

### New Solid-Propellant Systems

### Table 15: Recommended Response-Mode Percentages for Flight Phases O-2

**Mature Launch Systems (F = 0.993):**

**New Solid Systems (F = 0.996):**

**New Liquid Systems (F = 0.999):**

Recommended response-mode percentages for flight phases 0-1 and methodology for calculating absolute failure probabilities by response mode.

## Dates

## Organizations

## Key Content

### Table 16: Recommended Response-Mode Percentages for Flight Phases 0-1

**Mature Launch Systems (F = 0.993):**

**New Solid Systems (F = 0.996):**

**New Liquid Systems (F = 0.999):**

### Absolute Probability Calculation Method

### Observations

Absolute failure probabilities for individual response modes across three launch vehicles and analysis of differences between flight phases.

## Dates

## Organizations

## Key Content

### Table 17: Absolute Failure Probabilities for Response Modes 1-5

**Atlas:**

**Delta:**

**Titan:**

### Analysis Notes

Analysis of phase-dependent failure probabilities and explanation of differences between flight phases for different response modes.

## Dates

## Organizations

## Key Content

### Mode 1-3 Phase Differences

### Mode 4-5 Phase Differences

### Proportional Relationships

### Data Quality Notes

Analysis of tumble response characteristics for failure modes 3 and 4, including filter-based estimation methodology and observed trends.

## Dates

## Organizations

## Key Content

### Section 5.3: Relative Probability of Tumble for Response-Modes 3 and 4

### Methodology

### Table 18: Percent of Response Modes 3 and 4 That Tumble

**Flight Phases 0-2:**

**Flight Phases 0-5:**

### Observed Trends

### Sample Data

### Future Assumption

Introduction to Mode-5 shaping constants determination through simulation, explaining the need for simulation-based approach and overview of methodology.

## Dates

## Organizations

## Key Content

### Section 6: Shaping Constants Through Simulation

### Rationale for Simulation Approach

### Mode-5 Failure Classification

### Simulation Methodology

1. Run large sample of random-attitude and slow-turn failures

2. Calculate percentages of impacts in five-degree sectors from 0° to 180°

3. Compare with percentages from Mode-5 impact density function

4. Assign values to shaping constants A and B until best fit obtained

### Section 6.1: Malfunction Turn Simulations

### Random-Attitude Failure Program (RAFIP)

### RAFIP Monte Carlo Process

1. Select starting time

2. Select random thrust direction on attitude sphere (all directions equally likely)

3. Begin with nominal vehicle position/velocity at start time

4. Apply instantaneous change in thrust direction

5. Numerically integrate equations of motion until one of four conditions:

- Final stage burnout

- Vehicle impacts while thrusting

- Orbital insertion

- Vehicle breaks up from aerodynamic forces

6. For burnout/breakup: extend trajectory to impact using Kepler's equations

7. For orbital insertion: no impact point exists

### Calculation Scope

Detailed explanation of random-attitude failure calculations and slow-turn failure methodology for Mode-5 impact distribution analysis.

## Dates

## Organizations

## Key Content

### Section 6.1.2: Slow-Turn Failures

### Definition and Mechanism

### Slow-Turn Calculation Assumptions

1. Effective thrust offset of "nulled" engine normally distributed with zero mean and 0.1° standard deviation

2. Fixed thrust offset results in constant angular acceleration of airframe and thrust vector

3. For small thrust misalignments, angular acceleration proportional to angular thrust misalignment

### Atlas IIAS Slow-Turn Data

### Angular Acceleration Calculation

### Small Deflection Proportionality

### Slow-Turn Simulation Process

Analysis of factors affecting malfunction-turn simulation results, including weighting methodology, breakup thresholds, end-time considerations, and vacuum calculation approaches.

## Dates

## Organizations

## Key Content

### Section 6.1.3: Factors Affecting Malfunction-Turn Results

### Data Limitations

### Factor a: Weighting of Turn Data

### Factor b: Breakup qa (Dynamic Pressure × Angle of Attack)

### Titan Vehicle Data

### Atlas, Delta, LLV1

### Factor c: End Time T5

### Destruct Action Considerations

### Factor d: Vacuum Calculations

Presentation of malfunction-turn simulation results for Atlas IIAS showing combined random-attitude and slow-turn impact distributions with supporting figure.

## Dates

## Organizations

## Key Content

### Section 6.1.4: Malfunction-Turn Results for Atlas IIAS

### Simulation Results

### Key Findings

### Implications for Other Vehicles

### Figure 5: Combined Random-Attitude and Slow-Turn Results

Graph showing percent in 5-degree sector (log scale, 0.1-100%) vs angle from flight path (0-180 degrees)

**Three curves displayed:**

1. Random-attitude turns (circle markers)

2. Slow turns (square markers)

3. Combined turns (75% random, 25% slow) (diamond markers)

**Curve Characteristics:**

Technical analysis of Atlas IIAS launch vehicle risk assessment, specifically addressing Mode-5 failure response shaping constants and ship-hit contour computations.

## Technical Content

### Subjects

### Key Parameters and Data

### Analysis Notes

### References

### Date

9/10/96

### Organization

RTI (page 52)

Graph and mathematical discussion of Atlas IIAS Mode-5 ship-hit contours with parametric analysis.

## Content

### Figure 16 Details

Atlas IIAS Mode-5 Ship-Hit Contours

### Mathematical Content

### Technical Discussion

### Footnote

### Date

9/10/96

### Organization

RTI (page 53)

Graph showing Atlas IIAS all-mode ship-hit contours with combined failure response distribution analysis.

## Content

### Figure 17 Details

Atlas IIAS All-Mode Ship-Hit Contours

### Technical Purpose

Demonstrates combined effect of all failure response modes on impact distribution, showing dominance of Mode-4 response in overall risk computation.

### Key Observation

When all response modes included in calculations, contour differences compared to Mode-5 alone are almost imperceptible, validating the dominance assertion.

### Date

9/10/96

### Organization

RTI (page 54)

Graph showing Atlas IIAS Mode-5 ship-hit contours with alternative parameter set.

## Content

### Figure 18 Details

Atlas IIAS Mode-5 Ship-Hit Contours

### Parameter Sensitivity

Demonstrates effect of increased A value (3.45 vs 3.00) on impact concentration near flight line. More concentrated distribution expected with higher A.

### Date

9/10/96

### Organization

RTI (page 55)

Graph showing Atlas IIAS all-mode ship-hit contours with parameter set B=1,000, A=3.45.

## Content

### Figure 19 Details

Atlas IIAS All-Mode Ship-Hit Contours

### Technical Analysis

Comparison case showing all-mode impacts with increased A parameter. Contours demonstrate broader distribution than Mode-5 alone due to Mode-4 contribution.

### Date

9/10/96

### Organization

RTI (page 56)

Graph showing Atlas IIAS Mode-5 ship-hit contours with extreme parameter values.

## Content

### Figure 20 Details

Atlas IIAS Mode-5 Ship-Hit Contours

### Technical Significance

Demonstrates effect of maximum breakup scenario (qa = 5,000 deg-lb/ft² with B = 5,000,000). Results in most concentrated impact distribution near flight line, reflecting high structural integrity and distributed fragmentation pattern.

### Date

9/10/96

### Organization

RTI (page 57)

Graph and technical discussion of Atlas IIAS all-mode ship-hit contours with extreme parameters and introduction of range distribution analysis.

## Content

### Figure 21 Details

Atlas IIAS All-Mode Ship-Hit Contours

### Section 6.2.4: Range Distributions of Theoretical and Simulated Impacts

#### Methodology

#### Parameters

### Technical Purpose

Testing agreement between range component of Mode-5 impact-density function and simulated random-attitude data.

### Date

9/10/96

### Organization

RTI (page 58)

Graph and analysis of impact range distributions for Atlas IIAS with theoretical and simulated data comparison.

## Content

### Figure 22 Details

Impact-Range Distributions

#### Data Series

#### Key Findings

### Methodology

### Technical Note

Percentage of impacts in any range interval independent of values of A and B

### Date

9/10/96

### Organization

RTI (page 59)

Introduction and methodology section for Delta-GEM shaping constants development.

## Content

### Section 6.3: Shaping Constants for Delta-GEM

#### Overview

Computations and graphs to establish Mode-5 shaping constants for Delta parallel those for Atlas IIAS (Section 6.2), though less extensive.

#### Methodology Summary

Four-step approach:

1. **Impact Point Calculation**

- 10,000 simulated random-attitude turns

- 10-second intervals from programming time (6 seconds) to staging (270 seconds)

- Total: 260,000 simulations

- Impact points assumed representative of totality of Mode-5 impacts

2. **Angle Distribution Analysis**

- Determine percentages of impacts in 5° sectors from 0° to 180°

3. **Theoretical Computation**

- For assumed values of A and B, compute percentages in same 5° sectors

- Use Mode-5 impact-density function

4. **Parameter Optimization**

- Trial and error method

- Find values of A and B providing best fit between simulated and theoretical data

### Date

9/10/96

### Organization

RTI (page 60)

Graph showing Delta-GEM vehicle breakup percentages versus failure time with multiple breakup scenarios.

## Content

### Section 6.3.1: Optimum Mode-5 Shaping Constants

### Figure 23 Details

Delta-GEM Breakup Percentages

#### Breakup Scenarios

#### Key Observations

### Technical Context

Same breakup qa values used in Atlas IIAS calculations applied to Delta-GEM analysis.

### Date

9/10/96

### Organization

RTI (page 61)

Comprehensive graph showing Delta-GEM malfunction-turn impact distributions with multiple breakup scenarios and parameter variations.

## Content

### Figure 24 Details

Delta-GEM Simulation Results with B = 1,000

#### Data Series

### Key Findings

### Date

9/10/96

### Organization

RTI (page 62)

Graph showing optimized Delta-GEM simulation results with best-fit shaping constants across all breakup scenarios.

## Content

### Figure 25 Details

Delta-GEM Simulation Results with Best-Fit Shaping Constants

#### Data Series and Parameter Sets

### Technical Achievement

Excellent fit between malfunction-turn and theoretical Mode-5 impact data possible for any qa between 5,000 and 20,000 deg-lb/ft² with appropriate parameter selection.

### Methodology Note

Best-fit optimization conducted by trying various combinations of B and A until best possible agreement achieved in ±60° to ±180° sectors (where population centers located).

### Date

9/10/96

### Organization

RTI (page 63)

Technical analysis of Delta-GEM launch-area Mode-5 risks with parametric sensitivity study.

## Content

### Section 6.3.2: Launch-Area Mode-5 Risks

#### Methodology

DAMP program used to compute Mode-5 launch-area risks for population centers inside impact limit lines. Case study: Delta-GEM/GPS-10 daytime launch from Pad 17A.

### Table 23: Shaping Constants and Related Risks for Delta-GEM

| Ps | Tb (sec) | Breakup qa (deg-lb/ft²) | B | A | Mode-5 Ec (x 10⁴) |

|----|----------|------------------------|-------|--------|-----------|

| 0.0025 | 130 | 12,000* | 1,000 | 3.00 | 394 |

| | | (baseline) | | | |

| 0.001 | 270 | 12,000* | 1,000 | 3.00 | 88.8 |

| | | (new p&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 in Figure 24

### Key Findings

#### Risk Dependence on qa and A

#### Quantitative Examples

#### Vehicle Strength Effects

#### Critical Observation

Risks over 20 times greater if vehicle breakup qa is 20,000 rather than 5,000 deg-lb/ft²

### References

### Date

9/10/96

### Organization

RTI (page 64)

Introduction to Titan IV Mode-5 shaping constants development with breakup analysis graph.

## Content

### Section 6.4: Shaping Constants for Titan IV

#### Overview

Mode-5 shaping constants for Titan IV developed using methodology described in Section 6.3 for Delta, with extended sampling:

### Figure 26 Details

Titan IV Breakup Percentages

#### Breakup Scenarios

#### Key Observations

### Technical Context

Demonstrates structural response characteristics of larger Titan IV vehicle to aerodynamic forces during failure scenarios.

### Date

9/10/96

### Organization

RTI (page 65)

Comprehensive graph showing Titan IV malfunction-turn impact distributions with parametric analysis and optimization discussion.

## Content

### Figure 27 Details

Titan IV Simulation Results with B = 1,000

#### Data Series

### Key Findings

#### Sector Performance

#### Parameter Selection

#### Technical Assessment

Reasonable agreement achieved in population-center sectors, with optimization possible for specific breakup scenarios through alternative parameter combinations.

### Optimization Note

Figure 28 (referenced but not shown on this page) would demonstrate best-fit shaping constants for Titan IV similar to Delta-GEM Figure 25 analysis.

### Date

9/10/96

### Organization

RTI (page 66)

Technical analysis of Titan IV Random-Attitude Failures through 300 seconds. Figure 28 displays simulation results with best-fit shaping constants for Mode-5 impact distribution modeling. Content includes comparative graph showing theoretical percentages derived from testing various combinations of parameters (B and A constants) to achieve good fit between simulated malfunction-turn results and theoretical impact-distribution data.

## Observations

## Assessments

## Shaping Constants (from Figure 28)

## References

Summary table of shaping constants for Titan IV vehicle. Table 24 presents best-fit values of B and A parameters for convenient reference, organized by thrust burning time (T_B) and breakup dynamic pressure (qa) conditions.

## Observations

## Data - Table 24: Shaping Constants for Titan IV

| T_B (sec) | Breakup qa (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 |

## Assessments

Introduction to LLV1 shaping constants development methodology (Section 6.5). Describes simulation procedures and presents Figure 29 showing LLV1 breakup percentages as function of failure time and dynamic pressure conditions.

## Observations

## Breakup Percentages (Figure 29)

## Methodology

## Assessments

Analysis of LLV1 malfunction-turn impact distributions with fixed B parameter value. Figure 30 displays percentage of impacts in 5-degree sectors for no-breakup case and three breakup dynamic pressure conditions (qa values of 20,000, 10,000, and 5,000 deg-lb/ft²).

## Observations

## Shaping Constants (from Figure 30)

For no-breakup case and each breakup condition:

## Methodology

## Assessments

Analysis of LLV1 malfunction-turn impact distributions using optimized shaping constants. Figure 31 presents simulation results with best-fit shaping constants combining higher values of both B and A parameters to achieve improved overall fit across impact sectors.

## Observations

## Shaping Constants (from Figure 31)

Best-fit values for LLV1:

## Methodology

## Assessments

Summary table of best-fit shaping constants for LLV1 vehicle (Table 25) and introduction to methodology for developing shaping constants for other launch vehicles (Section 6.6).

## Observations

## Data - Table 25: Shaping Constants for LLV1

| T_B (sec) | Breakup qa (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 |

## Methodology (Section 6.6)

## Assessments

Summary table of A parameter values for B = 1,000 (Table 26) across reference launch vehicles and breakup conditions. Provides basis for estimating shaping constants for new or unstudied launch vehicles.

## Data - Table 26: Summary of A Values for B = 1,000

| Vehicle | IP Range (nm) at 30 sec | Breakup qa (deg-lb/ft²) | | | |

| | | 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 | 3.5 | 3.1 | 2.8 | 1.9 |

## Observations

## Methodology

## Assessments

Section 7: Potential Future Investigations. Lists identified research areas and limitations encountered during study due to contract funding constraints and publication deadlines.

## Observations

## Potential Future Investigations (in priority order)

1. Effects on shaping constants A and B of using more precise breakup (qa) conditions during malfunction-turn simulations

2. Effects on shaping constants A and B (and overall risks) if different T_B values used in computing theoretical and simulated impacts

- Example: T_B corresponding to burnout of zero, first, and second stages

3. Effects on shaping constants A and B if drag accounted for in computing freefall impact points after malfunction turn

- Could determine constants for maximum, minimum, and intermediate ballistic coefficients, then interpolate

- Would require extensive modifications to DAMP program

4. Effects on shaping constants A and B if sectors smaller than 5° used to compare theoretical and simulated impact data

- Example: 1° or 2° sectors instead of 5°

5. Effects on relative failure probabilities for solid-propellant vehicles if unclassified solid-propellant vehicles or declassified test results used in historical data samples

- Example vehicles: Pershing, Polaris, Poseidon, Trident

## Future Tasks

## Assessments

Section 8: Summary. Comprehensive overview of report objectives, methodology, and key findings. Summarizes primary purpose of study and other implicit objectives regarding failure-response modes and risk computation.

## Observations

## Methodology Summary

## Key Process Steps

1. Performance histories gathered and tabulated by launch date for Atlas, Delta, Titan, Thor (Appendix D)

2. Filtering technique applied (Section 5.1, Appendix C) to launch failure data

3. Overall failure probabilities estimated by flight phase

4. Recommended probabilities based on representative vehicle configurations (Section D.1.4)

5. Results from representative configurations form basis of absolute probabilities (Table 27)

6. Relative failure probabilities estimated from combined samples (Tables 28-29)

## Assessments

Continuation of Section 8 Summary with failure probability data tables and Mode-5 shaping constant methodology description.

## Data - Table 27: Failure Probabilities for Atlas, Delta, and Titan

| Vehicle | Flight Phase O-1 | Flight Phase O-2 |

|---------|------------------|------------------|

| Atlas | 0.022 | 0.031 |

| Delta | 0.010 | 0.013 |

| Titan | 0.040 | 0.064 |

## Observations

## Data - Table 28: Recommended Response-Mode Percentages for Flight Phases O-2

| Response Mode | Mature Launch Systems (F = 0.993) | New Solid Systems (F = 0.996) | New Liquid Systems (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% |

## Data - Table 29: Recommended Response-Mode Percentages for Flight Phases O-1

| Response Mode | Mature Launch Systems (F = 0.993) | New Solid Systems (F = 0.996) | New Liquid Systems (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% |

## Methodology - Mode-5 Shaping Constants

## Assessments

Continuation of Mode-5 methodology and presentation of absolute failure probabilities for individual response modes (Table 30).

## Observations

## Data - Table 30: Absolute Failure Probabilities for Response Modes 1-5

| Vehicle: | Atlas | | Delta | | Titan | |

|---|---|---|---|---|---|---|

| Flight Phase: | 0-1 (0-170 sec) | 0-2 (0-280 sec) | 0-1 (0-270 sec) | 0-2 (0-630 sec) | 0-1 (0-300 sec) | 0-2 (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 |

## Assessments

Analysis of traditional and optimized shaping constants for Mode-5 impact distribution modeling. Describes practical methodology using B = 1,000 (established value) and development of optimized B and A combinations.

## Observations

## Data - Table 31: Summary of A Values for B = 1,000

| Vehicle | Flight Phase | T_B (sec) | Breakup qa (deg-lb/ft²) | | |

| | | | 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 |

## Observations on Optimization

## Data - Table 32: Summary of Optimum Mode-5 Shaping Constants

| Vehicle | Flight Phase | T_B (sec) | Breakup qa (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 |

## Assessments

Analysis of launch-area risk calculation results comparing traditional and optimized shaping constants. Demonstrates sensitivity of Mode-5 risk calculations to parameter choices and provides risk reduction factors from previous RTI studies.

## Observations

## Risk Recomputation Results

Mode-5 baseline risks for Atlas and Delta recomputed using newly derived values:

1. Shaping constants A and B

2. Overall vehicle failure probability

3. Relative probabilities of occurrence of individual failure-response modes

## Risk Reduction Factors

**Atlas**: Mode-5 launch-area risks reduced by factor of 3 to 11

**Delta**: Mode-5 launch-area risks reduced by factor of 4 to 75

## Assessments

## Observations

## Failure Response Modes

**Mode 1: Immediate Ground Impact**

**Mode 2: Loss of Control at Liftoff**

**Mode 3: Pitch-Program Failure**

**Mode 4: Normal Flight Until Malfunction**

**Mode 5: Anomalous Direction Impacts**

**Mode 6: Normal Flight Impacts** (not failure mode)

## Key Distinctions

## Assessments

## Observations

## Methodology

**f-ratio Formula** (from Section 9.7 of Reference 1, Equation 9.19):

f-ratio = (e^(Aπ + B/R)) / (e^(Aφ + B/R))

## Data Tables Referenced

**Table 33 and 34**: f-ratios for A values of 2.5, 3.0, 3.5, 4.0; B = 1,000

**Table 35 and 36**: Effects of halving and doubling constant B

## Example Analysis (A = 3.0)

## Key Concept

## Assessments

Numerical data table presenting f-Ratio values for varying Mode-5 constants.

## Content

**Table 33. Effect on f-Ratio of Varying Mode-5 Constant A (B = 1000) - Part 1**

Columns show values for A = 2.5, A = 3.0, A = 3.5, A = 4.0

180-φ angle values range from 0° to 180° in 5-degree increments

## References

Continuation of f-Ratio numerical data table for Mode-5 constant variation analysis.

## Content

**Table 34. Effect on f-Ratio of Varying Mode-5 Constant A (B = 1000) - Part 2**

Columns show values for A = 2.5, A = 3.0, A = 3.5, A = 4.0

180-φ angle values from 0° to 180° in 5-degree increments

## References

Numerical data table for Mode-5 constant B variation analysis with fixed A = 3.

## Content

**Table 35. Effect on f-Ratio of Varying Mode-5 Constant B (A = 3) - Part 1**

Columns show values for B = 500, B = 1000, B = 2000

180-φ angle values from 0° to 180° in 5-degree increments

Pattern shows inverse relationship between B value and f-ratio results.

## References

Continuation of Mode-5 constant B variation data table.

## Content

**Table 36. Effect on f-Ratio of Varying Mode-5 Constant B (A = 3) - Part 2**

Columns show values for B = 500, B = 1000, B = 2000

180-φ angle values from 0° to 180° in 5-degree increments

## References

Analytical text explaining f-ratio data interpretation with reference to Figure 32.

## Content

Discusses f-ratio tables (33, 34, 35, 36) and their graphical representation in Figure 32.

**Key observation:** For A = 3.0 and B = 1000, reading from 10-mile plot at θ = 90°, a vehicle experiencing Mode-5 response is approximately 60 times more likely to impact along flight line than along 90-degree radial. The actual value in Table 34 is 59.1.

**Figure 32: f-Ratios for Ranges from 1 to 25 Miles**

## References

Analysis of Mode-5 impact density function behavior with varying constant A parameter.

## Content

**Discussion:** Shows how the value chosen for A affects Mode-5 impact density function. Examines percentages of Atlas IIAS impacts lying between flight line and any radial through launch point at angle θ from flight line.

**Key findings:**

**Figure 33: Percentage of Impacts Between Flight Line and Any Radial**

**Note:** Mode-5 impact density function requires numerical integration. Results vary for different trajectories and vehicles since R is trajectory-dependent.

## References

Analysis showing Mode-5 impact distribution in angular sectors with varying A parameter values.

## Content

**Discussion:** Another presentation method for A parameter effects on Mode-5 impacts. Shows percentages of impacts in any 5-degree sector between radials making angles 0° and (0+5)° from flight line.

**Key observation:** When A = 1.0 with B = 1000, impacts in all 5-degree sectors are approximately the same, resulting in essentially uniform directional impact-density function.

**Figure 34: Percentage of Impacts in 5-Degree Sectors**

**Historical reference:** Mode-5 with A = 1 equivalent to Gross Flight Deviation Failure (GFDF) mode formerly used in Launch Risk Analysis (LARA) Program at Western Range.

**GFDF characteristics:** Range and azimuth portions assumed independent. Impact azimuths uniformly distributed. Range density function: f(R) = p/(Tₐ·R)

## References

Mathematical analysis of GFDF model and Mode-5 density function equivalence.

## Content

**Mathematical formulation:**

GFDF range density function cannot be applied early in flight before programming when R ≈ 0.

Mode-5 density function integration (Eq. 3, limits 0 to π) reduces to:

f(R) = 1/((Tₐ - Tₚ)·R) [Equation 9]

Absolute values obtained by multiplying f(R) by Mode-5 failure probability.

**Discussion:** GFDF suitable for random-attitude failures at programming or shortly after. Performance histories (Appendix D) show such failures no more likely at programming than other times.

**Key insight:** No need to include separate GFDF mode in risk calculations since all random-attitude failures accounted for by Mode-5 density function.

**Alternative approaches if GFDF inclusion desired:**

1. Run GFDF separately using Mode-5 with A = 1 (zero other response modes)

2. Modify DAMP for two separate Mode-5 density functions with own A, B values

**Property:** Probability of impact in annular range interval (integrating Mode-5 density between interval boundaries) independent of A and B values. When integrated 0 to π, A and B cancel, leaving probability function of range alone.

## References

Introduction to Appendix C on filter characteristics and methodology.

## Content

**Appendix C. Filter Characteristics**

**Context:** Estimating launch-vehicle failure probabilities using empirical launch data is uncertain with small sample sizes and evolving systems.

**Approach:** Least-squares fit to trial outcome values (0 = success, 1 = failure).

**Observation:** Mature launch vehicles show marked decrease in failure rates from early experimental days. New programs may have scant or nonexistent empirical data.

**Key decision:** Type of function to fit. True nature may be unknown, complex, or insufficient data for complex function.

**Simple approach:** Constant failure-rate function assumed.

**Reality:** Available data indicate failure rates decrease as program matures. Launch-vehicle failure probabilities decrease over time (as launches increase).

**Options:**

**RTI approach for mature programs:** Fit failure-rate function to constant using:

**Mathematical foundation:** Constant function least-squares solution given by mean:

X̄ = (1/n)Σxᵢ [Equation 10]

**Example:** Three values (6, 5, 7) yield mean = 6

## References

Recursive filter formulation and expanding-memory filter analysis.

## Content

**Recursive formulation of least-squares solution:**

X̄ₙ = X̄ₙ₋₁(1-aₙ) + xₙ(aₙ) [Equation 12]

X̄ₙ = X̄ₙ₋₁ + aₙ(xₙ - X̄ₙ₋₁)

For equally-weighted case: recursive filter factor aₙ = 1/n

**Example recursion with X₀ = 0:**

**Expanding-memory filter characteristics:**

**Issue:** Unknown true function; constant used as approximation to smooth/edit data.

**Desired property:** Recursive least-squares fit assigning decreasing weight to older data, de-weighting earlier recursions.

**Fading-memory filter:** Weighting factor decreases as time recedes into past. Importance of datum decreases with age.

**Example weighted by count/index:**

X̄ₙ = Σ(i·xᵢ) / Σi [Equation 14]

## References

Index-weighted recursive filter formulation and exponentially-weighted filter analysis.

## Content

**Index-weighted fading-memory filter (position in sequence weighting):**

**Example recursion using Eq. 12:**

**Memory property:** 50th value 50 times more important than first; 100th value 100 times more important than first.

**Exponentially-weighted filter:**

X̄ₙ = Σ(Fⁱ·xₙ₋ᵢ) / Σ(Fⁱ) [Equation 18]

**Example using F = 0.9 with sample (6, 5, 7):**

X̄₃ = [0.9⁰(7) + 0.9¹(5) + 0.9²(6)] / [0.9⁰ + 0.9¹ + 0.9²]

= (7 + 4.5 + 4.86) / 2.71

= 16.36 / 2.71 = 6.04 [Equation 19]

**Weighting characteristics (Figure 35):**

## References

Exponential weighting properties and filter factor characteristics with graphical analysis.

## Content

**Exponentially-weighted filter properties:**

**Boundary conditions:**

**Fading rate control:** Analyst controls memory fade rate by selecting appropriate F value.

**Filter behavior as n increases:**

**Figure 35: Exponential Weights for Fading-Memory Filters**

**Figure 36: Recursive Filter Factor for Last Data Point**

## References

Detailed comparison of recursive filter factors across different filter types and sample sizes.

## Content

**Filter factor behavior analysis:**

**Index-number weighting behavior:**

**Key insight:** As n increases, aₙ for exponential filter decreases continuously, approaching (1-F) asymptotically.

**Practical implications:**

**Figure 36 key observations:**

Shows recursive filter factor (log scale, 0.001 to 1) vs. number of data points (0-300):

Early phase (n < 30): Index-weighting has steepest drop, most aggressive weighting of recent data.

## References

Application of fading-memory recursive filter to launch test results for failure probability estimation.

## Content

**Application methodology:** Fading-memory recursive filter (Eqs. 12, 20) applied to launch test outcomes to estimate failure probability.

**Data representation:**

**Table 37: Filter Application for Failure Probability**

Hypothetical series of 10 launches (all successful except flights 2 and 4):

Index | Outcome | F=0.98 Filter factor, aₙ | F=0.98 Fail. Prob. | F=0.90 Filter factor, aₙ | F=0.90 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

**Key results:**

**Application note:** Reversing 1's and 0's provides probability of success estimates.

## References

Introduction to Appendix D on launch and performance histories methodology.

## Content

**Appendix D. Launch and Performance Histories**

**D.1 Basic Data**

**Purpose:** Support empirical approach using post-test results to estimate future vehicle failure rates.

**Scope:** Performance histories for four launch vehicle families:

**Appendix structure:**

**Data coverage:**

**Data organization per vehicle (two-part structure):**

**(1) Tabular Summary listing chronologically:**

**(2) Narrative description:**

**D.1.1 Data Sources**

## References

Bibliography and methodology section of a launch vehicle reliability analysis report. Contains source citations (references 4-17) for space launch system data, and discusses data discrepancies regarding launch dates, vehicle configurations, and launch success/failure classifications.

## References

1. Booz•Allen & Hamilton, Inc. - "Spacelift Effective Capacity: Part 1 - Launch Vehicle Projected Success Rate Analysis" (19 February 1992)

2. Isakowitz, Steven J. (updated by Jeff Samella) - "International Reference Guide to Space Launch Systems, Second Edition" (published AIAA 1995)

3. Smith, O. G. - "Launch Systems for Manned Spacecraft" (Draft, 23 July 1991)

4. McDonnell Douglas Space Systems Company - "Comparison of Orbit Parameters - Table 1" (Delta launches through 4 Nov 95)

5. 45th Space Wing - Missiles/Space Vehicle Files (1957-1995)

6. 30th Space Wing - Missile Launch Operations Logs (1963-1995, via ACTA Inc., James Baeker)

7. Lockheed Martin - "Titan IV, America's Silent Hero" (Florida Today, 13 Nov 95)

8. General Dynamics - "Atlas Program Flight History" (Report EM-1860, 26 April 1965)

9. Lockheed Martin - "Atlas Flight Program Summary" (April 1995, C. W. Fenske)

10. Lockheed Martin - "Launch History" (FAX to RTI, Bob Brater, 13 March 1996)

11. USAF Accident/Incident Reports for Atlas and Titan failures

12. Aerospace - "Launch Failures from the Eastern Range Since 1975" (Andrew H. Quintero memo, 25 February 1996)

13. Lockheed Martin - "Titan Flight Anomaly/Failure Summary" (received 4 April 1996)

14. Aerospace - "Space Launch Vehicle Failures (1984-1995)" (Report No. TOR-96(8504)-2, I-Shih Chang, January 1996)

## Assessments

## Redactions

None evident

*Report date: 9/10/96 | Page: 97 | RTI*

Continuation of methodology section covering failure-response mode assignment, flight phase definitions, and representative vehicle configuration criteria for launch vehicle reliability analysis.

## Observations

**Failure-Response Modes:**

**Flight Phase Assignment:**

**Representative Configurations:**

## Assessments

*Report date: 9/10/96 | Page: 98 | RTI*

Two reference tables defining flight phase classifications and their mapping to specific launch vehicle types (Atlas, Delta/Thor, Titan).

## Tables

**Table 38: Flight-Phase Definitions**

| Flight Phase | Description |

|---|---|

| 0 | SRM auxiliary thrust phase |

| 1 | First-stage thrust phase (if no auxiliary SRMs) or after SRM separation |

| 1.5 | Attitude-control phase after first-stage or between first and second thrust phases |

| 2 | Second-stage thrust phase |

| 2.5 | Attitude-control phase after second thrust or between second and third thrust phases |

| 3 | Third-stage thrust phase or third thrust phase (if second stage restartable) |

| 3.5 | Attitude-control phase after third thrust 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 |

**Table 39: Flight Phases by Launch Vehicle**

| 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 | Second burn |

| 4 | Second burn | Second burn | Second burn |

| 5 | Orbit | Orbit | Orbit |

## Assessments

*Report date: 9/10/96 | Page: 99 | RTI*

Final methodology section covering representative vehicle configuration criteria and selection rationale based on Booz•Allen & Hamilton criteria for predicting future launch vehicle reliability.

## Organizations

## Observations

**Representative Configuration Criteria:**

**Three-Part Criteria (Booz•Allen established):**

1. **Genealogy**: Is current system a direct or indirect derivative of historical configuration?

2. **Operations**: Is current system operated same manner as historical (e.g., ICBM vs space-launch)?

3. **Composition**: Does current system use same element types (SRMs, upper stage, etc.)?

**Included Configurations for Future Predictions:**

## Assessments

*Report date: 9/10/96 | Page: 100 | RTI*

Overview of Atlas space-launch vehicle program history, configuration evolution, and performance summary including technical specifications and bar-graph visualization of launch performance 1955-1995.

## Organizations

## Observations

**Atlas Origins and Development:**

**Fuel System:**

**Engine Configuration:**

**Configuration Evolution (Table 40):**

| Configuration | Description |

|---|---|

| A | ICBM single-stage test |

| B, C | ICBM 1½-stage test |

| D | ICBM and later space-launch |

| E, F | ICBM (1960), reentry test (1964), space-launch (1968) |

| LV-3A | D with Agena upper stage |

| LV-3B | D man-rated for Project Mercury |

| SLV-3 | LV-3A with reliability improvements |

| SLV-3A | SLV-3 stretched 117 inches |

| LV-3C | Integrated with Centaur D |

| SLV-3C | LV-3C stretched 51 inches |

| SLV-3D | SLV-3C with Centaur uprated to D-1A |

| G | SLV-3D with Atlas stretched 81 inches |

| H | SLV-3D with E/F avionics, no Centaur |

| I | G with strengthened payload fairing, ring laser gyro |

| II | I with Atlas stretched 108 inches, engines uprated, hydrazine roll control, Centaur stretched 36 inches |

| IIA | II with Centaur RL-10s uprated to 20K lbs thrust |

| IIAS | IIA with 4 Castor IVA strap-on SRMs |

**Historical Phases:**

**Performance Summary (Figure 37):**

*Report date: 9/10/96 | Page: 101-102 | RTI*

Beginning of comprehensive Atlas launch history table (Table 41) documenting flight performance from June 1957 through sequence number 532. Contains mission IDs, launch dates, vehicle configurations, test ranges, response modes, flight phases, and representativeness designations.

## Dates

**Launch Period**: June 1957 - 1961 (entries 1-77 visible)

**Notable Programs/Missions:**

## Observations

**Test Ranges:**

**Vehicle Configurations (Representative sample):**

**Response Modes:**

**Flight Phases:**

**Representativeness:**

## Assessments

*Report date: 9/10/96 | Page: 103 | RTI*

Continuation of Atlas launch history table (Table 41) covering sequences 32-77, spanning September 1959 to January 1961. Documents WS, Mercury, Ranger, and Midas missions with vehicle configurations, test ranges, and response modes.

## Dates

**Period**: 09/16/59 - 01/31/61

**Specific Missions:**

## Observations

**Vehicle Configurations:**

**Test Range Distribution:**

**Failure Modes:**

**Flight Phases for Failures:**

**Representativeness:**

## Assessments

*Report date: 9/10/96 | Page: 104 | RTI*

Continuation of Atlas launch history table covering sequences 78-123, spanning February 1961 to April 1962. Documents Mercury, Ranger, Mariner, and various reconnaissance mission launches.

## Dates

**Period**: 02/21/61 - 04/09/62

**Major Missions:**

## Observations

**Vehicle Configurations Evolution:**

**Test Ranges:**

**Response Modes:**

**Flight Phases:**

**Representativeness:**

## Assessments

*Report date: 9/10/96 | Page: 105 | RTI*

Continuation of Atlas launch history table covering sequences 124-169, spanning April 1962 to March 1963. Documents continuation of Ranger, Mariner, and various AFSC/DOD missions.

## Dates

**Period**: 04/11/62 - 03/21/63

**Major Missions:**

## Observations

**Vehicle Configurations:**

**Test Ranges:**

**Response Modes:**

**Flight Phases:**

**Representativeness:**

## Assessments

*Report date: 9/10/96 | Page: 106 | RTI*

Continuation of Atlas launch history table covering sequences 170-215, spanning March 1963 to July 1964. Documents Lunar Orbiter, Surveyor, and various reconnaissance mission launches with transition toward higher-reliability configurations.

## Dates

**Period**: 03/23/63 - 07/28/64

**Major Missions:**

## Observations

**Vehicle Configurations:**

**Test Ranges:**

**Response Modes:**

**Flight Phases:**

**Representativeness:**

## Assessments

*Report date: 9/10/96 | Page: 107 | RTI*

Continuation of Atlas launch history table covering sequences 216-261, spanning July 1964 to August 1965. Primarily unmanned reconnaissance and scientific missions with focus on SLV-3/AGENA D standardized configurations.

## Dates

**Period**: 07/29/64 - 08/05/65

**Major Missions:**

## Observations

**Vehicle Configurations:**

**Test Ranges:**

**Response Modes:**

**Flight Phases:**

**Representativeness:**

## Assessments

*Report date: 9/10/96 | Page: 108 | RTI*

Continuation of Atlas launch history table covering sequences 262-307, spanning August 1965 to October 1966. Marks period of high standardization with SLV-3/AGENA D configurations and introduction of Surveyor lunar missions.

## Dates

**Period**: 08/11/65 - 10/05/66

**Major Missions:**

## Observations

**Vehicle Configurations:**

**Test Ranges:**

**Response Modes:**

**Flight Phases:**

**Representativeness:**

## Assessments

*Report date: 9/10/96 | Page: 109 | RTI*

Continuation of Atlas launch history table covering sequences 308-353, spanning October 1966 to March 1968. Period of increased Surveyor missions and transition toward advanced Centaur-based configurations for planetary missions.

## Dates

**Period**: 10/11/66 - 03/04/68

**Major Missions:**

## Observations

**Vehicle Configurations:**

**Test Ranges:**

**Response Modes:**

**Flight Phases:**

**Representativeness:**

## Assessments

*Report date: 9/10/96 | Page: 110 | RTI*

Continuation of Atlas launch history table covering sequences 354-399, spanning March 1968 to January 1972. Period of declining launch frequency with focus on planetary (Mariner), communications (INTELSAT), and continued reconnaissance missions.

## Dates

**Period**: 03/06/68 - 01/22/72

**Major Missions:**

## Observations

**Vehicle Configurations:**

**Test Ranges:**

**Response Modes:**

**Flight Phases:**

**Representativeness:**

## Assessments

*Report date: 9/10/96 | Page: 111 | RTI*

Final section of Atlas launch history table (Table 41) entries 354-399 spanning March 1968 to January 1972. Represents end of comprehensive historical record with focus on mature platform configurations supporting planetary and communications missions.

## Dates

**Coverage Period**: 03/06/68 - 01/22/72 (entries 354-399)

**Final Programs:**

## Organizations

## Observations

**Vehicle Configuration Summary:**

**Test Range Distribution:**

**Response Mode Summary:**

**Representativeness Final Assessment:**

## Assessments

*Report date: 9/10/96 | Page: 111 | RTI*

*End of Table 41 (Atlas Launch History) - Sequence 1-399 spanning June 1957 to January 1972*

## Status

Readable with content

## Doc Type

Technical report - launch vehicle test data table

## Classification

RTI (Rocket Test Information)

## Page Description

Flight test sequence table (rows 400-445) containing Atlas/satellite mission launch records with columns for flight number, mission/ID, launch date, vehicle configuration, test range, response mode, and flight phase.

## Dates

## Organizations

## Observations

## Notes

Table format shows systematic testing of Atlas launch vehicle variants carrying payloads from 1972-1978.

## Status

Readable with content

## Doc Type

Technical report - launch vehicle test data table (continuation)

## Classification

RTI (Rocket Test Information)

## Page Description

Flight test sequence table (rows 446-491) continuing Atlas/satellite mission launch records with same column structure as page 121. Dates span 1978-1987.

## Dates

## Organizations

## Observations

## Notes

Represents period of mature Atlas program with operational military and commercial satellite launches.

## Status

Readable with content

## Doc Type

Technical report - launch vehicle test data table (continuation)

## Classification

RTI (Rocket Test Information)

## Page Description

Flight test sequence table (rows 492-535) documenting Atlas/satellite missions 1988-1996. Continues systematic flight test record from pages 121-122.

## Dates

## Organizations

## Observations

## Notes

Represents evolution of Atlas program through 1990s with increasing satellite constellation launches.

## Status

Readable with content

## Doc Type

Technical report - failure analysis narrative

## Classification

RTI (Rocket Test Information)

## Section

D.2.2 Atlas Failure Narratives

## Page Description

Beginning of detailed failure narratives for Atlas launch vehicle. Covers failures #1, 2, 5, 6, 7 from the 1950s.

## Dates

## Technical Failures Documented

### 4A (11 June 57)

### 6A (25 Sep 57)

### 13A (7 Feb 58)

### 11A (20 Feb 58)

### 15A (5 Apr 58)

## Observations

## Status

Readable with content

## Doc Type

Technical report - failure analysis narrative (continuation)

## Classification

RTI (Rocket Test Information)

## Section

D.2.2 Atlas Failure Narratives (continued)

## Page Description

Failure narratives for Atlas flights #9, 11, 12, 13, 14, 18, 19, 21.

## Dates

## Technical Failures Documented

### 3B (19 July 58)

### 5B (28 Aug 58)

### 8B (14 Sep 58)

### 6B (18 Sep 58)

### 9B (17 Nov 58)

### 13B (15 Jan 59)

### 4C (27 Jan 59)

### 5C (20 Feb 59)

## Observations

## Status

Readable with content

## Doc Type

Technical report - failure analysis narrative (continuation)

## Classification

RTI (Rocket Test Information)

## Section

D.2.2 Atlas Failure Narratives (continued)

## Page Description

Failure narratives for Atlas flights #22-37, covering period March 1959-November 1959.

## Dates

## Technical Failures Documented

### 7C (18 Mar 59)

### 3D (14 Apr 59)

### 7D (18 May 59)

### 5D (6 June 59)

### 10D Mercury (9 Sep 59)

### 17D (16 Sep 59)

### 26D (29 Oct 59)

### 28D (4 Nov 59)

### 15D (24 Nov 59)

## Observations

## Status

Readable with content

## Doc Type

Technical report - failure analysis narrative (continuation)

## Classification

RTI (Rocket Test Information)

## Section

D.2.2 Atlas Failure Narratives (continued)

## Page Description

Failure narratives for Atlas flights #38-57, spanning November 1959-July 1960.

## Dates

## Technical Failures Documented

### 20D Able M (26 Nov 59)

### 6D Dual Exhaust (26 Jan 60)

### 29D Midas I (26 Feb 60)

### 42D (8 Mar 60)

### 51 D (10 Mar 60)

### 48D (7 Apr 60)

### 23D Lucky Dragon (6 May 60)

### 62D (22 June 60)

### 60D (2 July 60)

### 74D Tiger Skin (22 July 60)

## Observations

## Status

Readable with content

## Doc Type

Technical report - failure analysis narrative (continuation)

## Classification

RTI (Rocket Test Information)

## Section

D.2.2 Atlas Failure Narratives (continued)

## Page Description

Failure narratives for Atlas flights #58-73, covering July 1960-December 1960.

## Dates

## Technical Failures Documented

### 50D Mercury (29 July 60)

### 47D Golden Journey (12 Sep 60)

### 80D Able V/Pioneer (25 Sep 60)

### 33D High Arrow (29 Sep 60)

### 3E (11 Oct 60)

### 57D LV-3A/Agena A Gibson Girl (11 Oct 60)

### 81D Diamond Jubilee (12 Oct 60)

### 4E (29 Nov 60)

### 91D (15 Dec 60)

## Observations

## Status

Readable with content

## Doc Type

Technical report - failure analysis narrative (continuation)

## Classification

RTI (Rocket Test Information)

## Section

D.2.2 Atlas Failure Narratives (continued)

## Page Description

Failure narratives for Atlas flights #76-93, covering January 1961-August 1961.

## Dates

## Technical Failures Documented

### 5E (24 Jan 61)