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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.
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Figure 1. Joust Impact Trace Showing a Mode-5 Failure Response - UNCLASSIFIED CYBER H IP MAP 1 JOUST1761-A diagram showing trajectory traces at various time intervals (18 SEC, 20 SEC, 25 SEC, 30 SEC) with technical parameters including altitude, velocity, and track data
Atlas IIAS risk contours map showing inner-ear injury zones with concentric circles marked 10^-6, 10^-5, and 10^-4, with Mode-5A notation and A=3.0 parameter
Figure 3. Atlas IIAS Risk Contours for Inner-Ear Injury with A = 3.5
Filter Factor Results for Representative Configurations of Atlas
Atlas IIAS Failures through 280 sec - Breakup q-alpha = 20,000 deg-lb/ft² - Random-attitude turns, Slow turns, Combined turns (0.75 random + 0.25 slow) - Percent in 5-deg sector vs Angle From Flight Path (deg)
Figure 6. Atlas IIAS Breakup Percentages for Random-Attitude Turns
Atlas IIAS Impacts with No Breakup - map showing random-attitude failures at t30 sec thrust to 280 sec with impact footprint overlay
Atlas IIAS Impacts with Breakup - Random-Attitude Failures at 130 sec, Thrust to 230 sec, Breakup q-alpha = 5000 deg-lb/ft²
Figure 9. Atlas IIAS Simulation Results with B = 1,000
Figure 10. Atlas IIAS Simulation Results with B = 50,000 - Graph showing Percent in 5-deg sector (%) vs Angle From Flight Path (deg), with multiple curves for different Breakup q-alpha values in deg-lb/ft
Figure 11. Atlas IIAS Simulation Results with B = 100,000 - Graph showing Atlas IIAS Random-Attitude Failures through 280 sec, plotting Percent in 5-deg sector vs Angle From Flight Path (deg), with multiple curves for different Breakup q-alpha values in deg-lb/ft² (no breakup, 20,000, 10,000, 5,000) and B = 100,000 with A values of 3.40, 4.30, 4.75, and 5.00
Atlas IIAS Random-Attitude Failures through 280 sec - Breakup q-alpha in deg-lb/ft - showing percent in 5-deg sector vs angle from flight path with various breakup values (no breakup, 20,000, 10,000, 5,000) and B=500,000 with A values 4.00, 4.80, 5.30, 5.55
Atlas IIAS Random-Attitude Failures through 280 sec, Breakup q-alpha in deg-lb/ft^2, showing percent in 5-deg sector vs angle from flight path
Figure 14. Effects of Breakup q-alpha on A for Atlas IIAS
Figure 15. Mode-5 Density-Function Values at Three Miles
Atlas IIAS Mode-5 Ship-Hit Contours with A = 3.00, showing crossrange distance vs downrange distance with contour lines for 10^-5 and 10^-6, B = 1,000 and A = 3.00
Atlas IIAS All-Mode Ship-Hit Contours showing crossrange distance (nm) vs downrange distance (nm) with probability contours 10^-4, 10^-5, 10^-6, B = 1,000, A = 3.00
Atlas IIAS Mode-5 Ship-Hit Contours showing crossrange vs downrange distance with probability contours 10^-5 and 10^-8, Mode 5 P_I, B=1,000, A=3.45
Atlas IIAS All-Mode Ship-Hit Contours with A = 3.45, showing crossrange distance (nm) vs downrange distance (nm) with probability contours 10^-4, 10^-5, 10^-6 and parameters B = 1,000, A = 3.45
Atlas IIAS Mode-5 Ship-Hit Contours showing crossrange distance vs downrange distance with probability contours 10^-5 and 10^-6, B = 5,000,000, A = 6.30
Figure 21. Atlas IIAS All-Mode Ship-Hit Contours with A = 6.30
Figure 22. Impact-Range Distributions - Graph showing percent impacts in 10-nm interval vs impact range (nm) with Atlas IIAS theoretical and breakup q-alpha curves
Figure 23. Delta-GEM Breakup Percentages - Graph showing breakup percent vs failure time for three q-alpha values (5,000, 10,000, and 20,000 deg-lb/ft²)
Delta-GEM Random-Altitude Failures through 270 sec, showing Percent in 5-deg sector vs Angle From Flight Path, with breakup q-alpha values and theoretical Mode-5 curves for various A values with B=1,000
Delta-GEM Simulation Results with Best-Fit Shaping Constants showing percent in 5-deg sector vs angle from flight path for various breakup q-alpha values
Figure 26. Titan IV Breakup Percentages - Graph showing Breakup Percent (%) vs Failure Time (sec) for three q-alpha values: 5,000, 10,000, and 20,000 deg-lb/ft²
Figure 27. Titan Simulation Results with B = 1,000 - Graph showing Percent in 5-deg sector vs Angle From Flight Path (deg) with multiple curves for different breakup q-alpha values and no breakup scenarios
Titan IV Random-Attitude Failures through 300 sec, showing Breakup α-alpha in deg-lb/ft² with various parameters (no breakup, 20,000, 10,000, 5,000) and curves for A=2.70, B=10,000; A=3.15, B=2,000; A=3.25, B=1,000; A=3.50, B=1,000. Y-axis: Percent in 5-deg sector (%), logarithmic scale 0.1 to 100. X-axis: Angle From Flight Path (deg), 0 to 180.
Figure 29. LLV1 Breakup Percentages - Graph showing breakup percent vs failure time with three curves for q-alpha values of 5,000, 10,000, and 20,000 deg-lb/ft²
Figure 30. LLV1 Simulation Results with B = 1,000 - Graph showing percent in 5-deg sector vs angle from flight path, with multiple curves for different breakup q-alpha values and A values
LLV1 Simulation Results with Best-Fit Shaping Constants showing percent in 5-deg sector vs angle from flight path for various breakup q-alpha values and shaping constants
Figure 32. f-Ratios for Ranges from 1 to 25 Miles
Figure 33. Percentage of Impacts Between Flight Line and Any Radial - Data for Atlas IIAS B = 1000, showing curves for A = 1.0, 2.0, 3.0, 4.0, 5.0
Data for Atlas IIAS, B = 1000, showing Percent in 5-deg Sector vs Angle from Flight Path, Theta (deg) for A values 1.0, 2.0, 3.0, 4.0, 5.0
Figure 35. Exponential Weights for Fading-Memory Filters
Figure 36. Recursive Filter Factor for Last Data Point
Figure 37. Atlas Launch Summary - Bar graph showing Number of Atlas Missions (0-50) vs Launch Year (55-95), with bars split between Failure/Anomaly (white) and Normal Performance (black)
Figure 38. Delta Launch Summary - Bar graph showing Number of Delta Missions (0-16) vs Launch Year (55-95), with bars split between Failure/Anomaly (white) and Normal Performance (black)
Figure 39. Titan Launch Summary - Bar graph showing Number of Titan Missions (y-axis, 0-30) vs Launch Year (x-axis, 55-95), with bars divided into Normal Performance (solid black) and Failure/Anomaly (clear white)
Figure 40. Thor Launch Summary - Bar graph showing Thor missions by launch year with normal performance and failure/anomaly breakdown