response. Referring to Eq. (3), the right-hand member must be multiplied by the
       probability p5 of a Mode-5 response to obtain absolute probabilities. Except for TB
       itself (and to a slight degree, shaping constants A and B), the quantities in the
       equation do not depend on TB. Thus if TB and p 5 are both changed so that p/(TB -
       Tp) remains constant, the computed risks are unchanged.

       If destruct action (i.e., impact limit lines) is included in the DAMP calculations,
       the supplemental risks* resulting from that action must be accounted for. In this
       case, the termination time has a minor influence on results, since it affects the
       number of impacts that would occur beyond the impact limit lines without
       destruct that are forced inside when destruct action is taken. If destruct action is
       omitted, the value of TB is immaterial (i.e., supplemental Mode-5 risks are non-
       existent) provided that the impact range along the reference trajectory at time TB
       exceeds the range to all targets of interest. (Except in this paragraph,
       supplemental Mode-5 risks are not addressed in this present report.)
    d. Vacuum calculations: Atmospheric effects were accounted for in determining
        when vehicle breakup would occur and, to some extent, during each thrusting
        tum by using accelerations from the nominal trajectory. To reduce computer time
        and cost of this study, vacuum calculations were made during free fall after
        vehicle breakup or burnout. Although this increased impact dispersions
        somewhat, vacuum results should not be drastically different from those
        obtainable using a maximum-beta piece. In theory at least, different mode-5
        shaping constants exist for each debris class. In view of the uncertainties in
        vehicle breakup conditions and characteristics, and in the overall process of
      • simulating Mode-5 malfunctions, attempts to derive unique shaping constants for
        each debris class did not seem justified.
6.1.4 Malfunction-Turn Results for Atlas IIAS
For Atlas IIAS, .the distribution of impacts for simulated random-attitude turns, slow
turns, and a weighted combination (75% random-attitude and 25% slow tum) are
shown in Figure 5. Since the impact distribution (i.e., the percentages of impacts in 5°
sectors) for the weighted composite was not significantly different from that for
random-attitude failures, slow-turn computations were not made for Delta, Titan, and
LLVl.




*   See Ref. [1], Section 10.


9/10/96                                      35                                        RTI