density function. Since this could not be done in general, impacts from only the two
types of malfunction turns were considered. Several factors affect the results of the
simulations:

  a. Weighting of tum data: Both random-attitude and slow-tum. simulations were
     made for Atlas HAS. In combining impacts from the two data sets, random-
     attitude turns were assumed to be three times as likely to occur as slow turns. A
     factor of three was selected· since, among the Mode-5 failure responses in the
     performance summaries for Atlas, Delta, and Titan, random-attitude turns
     appeared to occur about three times as often as slow turns. In many cases, lack of
     detailed information made it difficult to· decide whether a Mode-5 response
     should be considered as a random-attitude tum, a slow tum, or some other type
     of failure. The relative weighting of turns makes little difference, however, since
     the impact distribution for the two types of turns are similar (as shown later in
     Figure 5), and since the weighted composite must lie between the two. It was
     assumed that similar results would be obtained for Delta, Titan, and LCVl, so
     slow-turn computations were not made for these vehicles, cutting the number of
     time-consuming simulations in half.

  b. Breakup qa: In the tum calculations, the assumption was made that vehicle
     breakup would occur if a certain value of qa. was reached~ In addition to the no-
     breakup case which is considered unrealistic, separate runs were made for three
     constant values of qa: 5,000, 10,000, and 20,000 deg-lb/ft2. As stated previously,
     the determination of vehicle breakup is, in reality, much more involved than this
     simplistic approach would suggest. However, to add realism to the malfunction-
     tum calculations, use of a simple approach seemed better than none at all. For
     Titan IV, allowable (but not breakup) qa.'s were provided as functions of Mach
     number. The maximum permissible value and corresponding Mach number for
     Titan/Centaur, Titan/NUS~ and Titan/lUS were, respectively, 6819 deflb/ft2 at
     Mach No. 0.77, 5332 deg-lb/ft2 at Mach No. 0.815, and 17,000 deg-lb/ft at Mach
     No. 0.325. For Atlas, Delta, and LLVl vehicles, no breakup qa. data were
     available. The breakup qa.'s used in the calculations bracket the range of
     permissible qa.'s for the Titan vehicles.

 c. End time T5 : The simulated impact distributions from random-attitude failures
    and slow turns were compared with impact distributions computed from the
    Mode-5 theoretical impact-density function.       For the comparisons to be
    meaningful, the value selected for T5 in the Mode-5 impact-density equation and
    the stop time for thrusting-turn simulations must be the same. To some extent,
    the shaping constants A and B derived by fitting the theoretical and simulated
    impact data depend on TJY since the percentage of impacts in each 5° sector
    depends on TB. However, after A and B have been established for a particular TJY
    using a different TB in the DAMP calculations has no effect on computed risks
    provided an adjustment is made in the probability of occurrence of a Mode-5


9/10/96                                   34                                        RTI