can cause impacts uprange or well away from the intended flight line, and (2) some vehicle
failures cannot logically be classified as Response Modes 1, 2, 3, or 4.

In- keeping with the above, the Mode-5 impact-density function was developed with the
characteristics listed below. The function, which fills the void left by Modes 1 through 4, is
sufficiently robust to include all possible impacts, yet seemingly comports with observed
test results.

(1)   Impacts can occur in any direction from the launch point and at any range within
      the vehicle's energy capabilities.

(2)   At any given impact range from the launch point, the likelihood of impact
      decreases as the angular deviation from the flight line increases, becoming least.
      likely in the uprange direction. For any fixed angular deviation from the flight
      line, the likelihood of impact decreases as the impact range increases.

(3)   At fixed impact ranges near the launch point, the impact density function changes
      gradually as the impact direction swings 180° from downrange to uprange. As
      the impact range increases, the decrease in the density function becomes
      progressively more and more rapid with change in impact direction. In other
      words, the greater the impact range, the more rapidly the density function
      changes with angular deviation from the flight line.                              •

As modeled in DAMP, the effects of destruct action on the Mode-5 density function are
accounted for in the launch area by supplementing impacts inside the impact limit lines
with those that would occur outside the impact limit lines if no destruct action were taken.
 The Mode-5 failure-response methodology was fully developed in an earlier RTI report111•
 As pointed ·out there, the shape of the impact density function can be controlled somewhat
 through the selection of shaping constants that appear in the defining equation Intuition
 suggests that the constants should be vehicle dependent, since (1) ruggedly built missiles
 would, after a malfunction, be more likely to impact well away from the flight line than
 would a fragile space vehicle that tends to break up before deviating significantly; and
.(2) certain vehicles, after a malfunction, tend to stabilize and •continue thrusting at large
 angles of attack, while other vehicles that experience similar malfunctions tend to tumble.
 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 Thus, the assumed probability of
 occurrence of a Mode-5 response as well as the selected Mode-5 constants are of
 considerable importance.

The tasking for this. study is set _forth as Task No. 10/95-77, Paragraph 2.0, of Contract
FO4703-91-C-0112. The primary purpose of the tasking is: "Perform a study to
determine the best values for Mode-5 failure probability and the Mode-5 density-
function shaping constant A." Although not explicitly included in the statement of work,
the study also develops absolute failure probabilities for Atlas, Delta, and Titan, and

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