Modeling of Unlikely Space-Booster Failures in Risk Calculations

Source file: dow-uap-d48-report-september-1996.pdf Originating agency: U.S. Air Force (AFSPC) / Research Triangle Institute (RTI) Date range: 10 September 1996 Page count: 181 (pages 1–60 read in full detail; the remaining pages are statistical appendices) High-significance pages: 1–10, 16–30, 96–172 (Appendix D with launch history)

Research note: This document is not a UAP (Unidentified Anomalous Phenomena) report. It is a distribution-restricted engineering-statistical report concerning the analysis of missile and space-vehicle launch risk, prepared for the U.S. Air Force. The designation "DOW-UAP-D48" reflects an internal numbering system of the document collection and does not represent any connection to the investigation of unidentified phenomena.

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Official Blurb (from war.gov)

This report describes the Modeling of Unlikely Space-Booster Failures in Risk Calculations, documenting historical launch failure modes and recommending corrective actions to address them using novel modelling techniques.

Summary

This report, authored by James A. Ward, Jr. and Robert M. Montgomery of the Research Triangle Institute (RTI), presents a mathematical methodology for analyzing improbable failures of space vehicles and missiles. The document was developed for the U.S. Air Force's safety office (AFSPC) and serves two primary launch bases: Patrick AFB in Florida (45th Wing) and Vandenberg AFB in California (30th Wing). The report's central purpose is to improve the DAMP (Facility DAMage and Personnel injury) risk-analysis program by more accurately quantifying Mode-5 failures — failures that may cause a vehicle to deviate extremely from its planned flight path and threaten populations far from the normal flight axis.

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Research Article

Introduction

In 1996, a landmark year in the field of space-launch safety, the Research Triangle Institute conducted a deep and comprehensive study for the U.S. Air Force Space Command. Contract number FO4703-91-C-0112, subtask 10/95-77, led to the development of novel mathematical tools for predicting hazard risk arising from space-vehicle failure. The document addresses a fundamental safety question: how can the risk created by those rare failures — in which a vehicle goes out of control and is hurled in an unpredictable direction, far from its intended flight axis — be modeled and quantified?

Structure of the DAMP Analysis Program

The DAMP program, developed by RTI, serves as a central tool for computing hit probabilities and estimating potential casualties during missile launches. The program defines six possible failure-response modes:

Mode 1: Debris impact in the immediate vicinity of the launch point, typically resulting from early thrust termination. Mode 2: Impacts near the flight axis, arising from various types of failures during the thrust phase. Mode 3: Rapid breakup (tumble) causing impacts near the launch point. Mode 4: Impacts along the planned flight axis, resulting from relatively late failures. Mode 5: The rarest and most complex failure, in which the vehicle deviates extremely and is hurled in any possible direction, sometimes very far from the flight axis. Normal mode: Nominal flight with no significant anomaly.

The heart of the study focuses on Mode 5, which, though rare, is responsible for nearly 90% of the total risk to people located outside the normal flight axis. This is an important safety paradox: a low-probability failure creates the majority of risk to distant populations.

Mathematical Definition of the Mode-5 Hit-Density Function

The principal hit-density function for Mode 5 is defined as:

f(R, phi) = [e^(Aphi) + B/R] / {2(T_b - T_p) * [(1/A)(e^(Api) - 1) + B*pi/R] * R * dR}

where:

• R is the distance of the impact point from the launch point (in miles)
• phi is the angle (in radians) between the normal flight direction and the impact direction
• A and B are shaping constants determined experimentally and by simulation methods
• T_b and T_p are the time bounds within which Mode 5 can occur

Constant A controls the rate at which density decreases as the angle from the flight axis increases, and has the greatest influence on the risk-calculation results. Constant B affects the relationship between impact distance and density. The study proved that the value of A is critical to the results, while the value of B has a far more marginal effect.

Failure-Probability Analysis

Atlas, Delta, and Titan

The study analyzed historical launch data for three principal vehicles — Atlas, Delta, and Titan — using an empirical approach based on real flight data. Analysis of a sample of 1,186 launches (532 Atlas, 232 Delta, 337 Titan, and 85 Thor) yielded the following overall failure probabilities (Flight Phases 0–2, exponential filter F=0.98):

• Atlas: 3.1% (approximately 1 in 32 launches)
• Delta: 1.3% (approximately 1 in 77 launches)
• Titan: 6.4% (approximately 1 in 16 launches)

Mode 4 is the most dominant among failures, constituting roughly 86% of failures in mature systems. Mode 5 constitutes roughly 8% of failures but is responsible for a substantial share of the risk to distant populations.

An important trend was revealed: the reliability of Atlas and Delta improves over the years (recent failures are rarer), whereas Titan's reliability showed no clear consistent improvement — pointing to structural problems in design or manufacturing process that are not fully resolved.

Data-Filtering Methods

In selecting probability values, three different weighting methods were examined:

1. Equal Weighting: every past launch is equal to a current launch. This method is counterintuitive and does not account for technological improvements.
2. Index-Count weighting: weight assigned according to more recent results.
3. Exponential Filter (F=0.98): RTI's preferred method, in which recent launches receive exponentially higher weight. This method enables a "fading memory" that reflects technological improvements over time.

Failure Simulation: The Monte Carlo Approach

Because empirical data on Mode-5 failures are extremely rare, the team developed a simulation program named RAFIP (Random-Attitude Failure Impact Point), written in FORTRAN (3,900 lines of code), using a Monte Carlo approach. The software simulates two principal failure types:

Random-Attitude Failure: a failure that causes the vehicle to point in a completely random thrust direction. For each simulation, a random thrust direction is selected over a unit sphere (the attitude sphere), and the vehicle's trajectory is computed to an impact point. Each simulation run for one vehicle included 270,000 to 1,080,000 trajectories.

Slow-Turn Failure: a failure that causes the engine to lock at a small angle near zero (near-null position), causing the vehicle to turn slowly and steadily in an unplanned direction. For Atlas IIAS, 10,000 impact points were computed for each failure time.

A surprising finding: the distribution of impact points for both failure types is very similar, indicating that the risk outcome does not depend so much on the specific failure type as on the vehicle's behavior afterward.

Findings for Specific Vehicles

Atlas IIAS

For Atlas IIAS, the simulation showed that the optimal value of A ranges between 2.75 and 3.45 (for B=1,000), depending on the qalpha (pressure × angle of attack) threshold defining when the vehicle breaks up aerodynamically. The absolute probability of a Mode-5 response was estimated at 0.0025 (0.25%) for flight phases 0–2.

Delta-GEM

Analysis of Delta-GEM yielded values of A slightly lower than those of Atlas. Delta's relatively high qalpha causes higher breakup rates in the early stages of failure.

Titan IV

Titan IV presented different characteristics owing to its large engine mass. The allowable qalpha (not breakup) for Titan/Centaur is 6,819 deg-lb/ft², and for Titan/IUS 17,000 deg-lb/ft². The optimal A values for Titan were found to be higher than those of Atlas.

LLV1

LLV1 (Lockheed Launch Vehicle 1) was a relatively new launch vehicle at the time of writing, so more conservative shaping constants were used for its risk calculations.

Historical Incidents from the Appendix

Appendix D of the report contains a detailed launch history and failure narratives spanning decades. Among the examples cited as evidence of the need for Mode 5:

Atlas 8E, 24 January 1961: Lost stability at second 161, approximately 30 seconds after booster engine cutoff. The sustainer engine was cut off at second 248. The impact point was 1,316 miles downrange and 215 miles to the side.

Atlas 145D (Mariner R-1), 22 July 1962: A guidance-controller problem caused a maximum deviation of 60 degrees in yaw and 28 degrees in pitch. The vehicle was destroyed by the RSO at second 293.5.

Atlas SLV-3 (GTA-9), 17 May 1966: Loss of pitch control at second 121. The vehicle entered an anomalous trajectory and subsequently stabilized in an anomalous attitude.

Delta Intelsat III, 18 September 1968: Owing to a gyroscope failure, undamped pitch oscillations occurred from second 20. The vehicle turned 270 degrees downward and then 210 degrees upward. The first stage broke up at second 103.

Joust (Prospector), June 1991: A Castor IV-A launch vehicle with a Prospector payload performed an extreme pitch-up maneuver due to a structural failure in the aft skirt at T+14 seconds. The vehicle could have impacted far from the flight axis had it not been for the destruct action of the safety officer.

Red Tigress, 20 August 1991: A sounding rocket was launched from Pad 20 at Cape Canaveral, and within a second or two of clearing the pad turned 90 degrees to the right. It flew in this direction until destruction at second 23.3. Debris fell a mile or two from the launch point.

Key Recommendations and Conclusions

On the basis of the comprehensive quantitative analysis, the report reached several key conclusions:

1. Selection of constant A: This is the most critical parameter. For mature systems, a value of A=3.0 with B=1,000 constitutes a reasonable baseline. A higher A value reduces the risk to populations far from the flight axis.

2. Mode-5 probability: For mature systems (F=0.993), the Mode-5 rate is approximately 7.9% of all failures. For new liquid systems, the rate rises to 15.3%.

3. About a third of Mode-3 and Mode-4 failures end in a "thrusting tumble," a trend that increased gradually in the more recent data.

4. Framework for future launches: RTI recommended using the constants computed in this report for all future risk analyses for the 45th Wing (45 SW/SE), unless new data indicate a justified change.

5. Fundamental limitations: The report frankly emphasizes that the quantitative approach is full of uncertainty. A "correct value" cannot be determined with certainty, and every analysis depends on contested assumptions regarding the qalpha threshold, breakup, and specific failure patterns that cannot be simulated.

Historical Significance

The report was written at a pivotal point in the history of American launch safety. In 1996, the U.S. space program faced a transition from aging military missiles to a family of modern launch vehicles. AFSPC sought to deepen its risk-analysis capabilities ahead of additional commercial and scientific launches. The DAMP methodology developed on the basis of this study became a central tool in defining protective zones around launch sites and in planning safe flight paths over populated areas.

From a public-safety perspective, the report proves that even if a Mode-5 failure is rare (less than 1% of all failures), risk analysis must account for it because of its potential impact. The risk to the "warning areas" and "danger areas" established around launch sites depends directly on Mode-5 parameters, and therefore the choice of A and B values directly affects the level of protection citizens receive from the rarest failure.

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Key People

Name	Role	Organization
James A. Ward, Jr.	Lead author	Research Triangle Institute
Robert M. Montgomery	Co-author	Research Triangle Institute
Martin Kinna	Monitoring representative	30 SW/SEY, Vandenberg AFB
Louis J. Ullian, Jr.	Monitoring representative	45 SW/SED, Patrick AFB

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Locations

Location	Role in the document
Patrick AFB, Florida (FL 32925)	Eastern launch base, 45th Wing
Vandenberg AFB, California (CA 93437)	Western launch base, 30th Wing
Cape Canaveral, Florida	Principal public launch site
Cocoa Beach, Florida	RTI location (3000 N. Atlantic Ave)
Torrance, California	ACTA Inc. location (prime contractor)

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Major Failure Incidents

Incident	Date	Vehicle	Brief description	Pages
Atlas 8E	24 January 1961	Atlas 8E	Loss of stability at second 161, impact 1,316 miles off-trajectory	3
Titan M-4	6 October 1961	Titan	Bit error in velocity integration, impact 86 miles short of target	3
Atlas 145D (Mariner)	22 July 1962	Atlas	Faulty guidance controller, 60-degree yaw deviation, destruct at second 293	3
Atlas SLV-3 (GTA-9)	17 May 1966	Atlas	Pitch-control failure at second 121, loss of control	3
Atlas 95F	3 May 1968	Atlas	Anomalous yaw and pitch motions from the first moment, destruct at 14,000 ft	3–4
Delta Intelsat III	18 September 1968	Delta	Gyroscope failure, severe pitch oscillations, impact 12 miles off trajectory	4
Delta Pioneer E	27 August 1969	Delta	Hydraulic failure before MECO, severe yaw and roll, destruct at T+484	4
Atlas 68E	8 December 1980	Atlas	Oil-pressure drop, engine shutdown, uncontrolled yaw and roll, retrofire	4
Joust (Prospector)	June 1991	Castor IV-A	Extreme pitch-up due to structural failure, distinct Mode-5 response	6
Red Tigress	20 August 1991	Sounding Rocket	90-degree right turn immediately after launch, destruct at second 23.3	6

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Notable Quotes

From the official summary:

"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."

On the importance of Mode 5:

"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."

On the limitations of the analysis:

"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."

From Booz Allen and Hamilton (quoted in the report) on design flaws:

"Finally, due to its nature, the engineering approach cannot account for undetected design flaws. (If these flaws were detected, and could be modeled, 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."

On one-third of failures:

"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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This article was written based on a full reading of the accessible pages of the report. The document is purely technical-engineering and is not connected to unidentified phenomena (UAP). The designation "DOW-UAP-D48" is an internal serial number of the document collection and does not represent UAP content.