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 Consta.nts................................. ".....................................-...... 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 Tum. Simulations...........•...................................................................... 31
          6.1.1 Random-Attitu.de Failures ...............-............................................................... 31
          6.1.2 Slow-Tum Failures ........................................................................................... 32
          6.1.3 Factors Affecting Malfunction-Tum Results ................................................ 33
          6.1.4 Malfunction-Tum 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                                          I
          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 LLVl .................................................................................... 69
      6.6 Shaping Constants for Other Launch Vehicles ....................................................... 72

7. Potential Future Investigations ......................................................................................... 73

8. Summarv:
         ., ............................................................................................................................ 74


9/10/96                                                              ii                                                                   RTI