Department of the Air Force Report, 1996

acceleration of the vehicle body and a slow turn of the velocity vector, (4) erroneous
accumulation of velocity bits by the guidance system. Many other Mode-5 responses are so
convoluted that they defy description or categorization
3.1 Effects of Mode-5 Shaping Constants
The primary part of the Mode-5 impact-density function was presented previously as
Eq. (1). As originally formulated, the function contained three shaping constants. If both
numerator and denominator of the equation are divided by the constant C, and B is
substituted for D/C, one unnecessary constant disappears so that the function may be
expressed as follows:
(3)
The values chosen for the shaping constants A and B that appear in Eq. (3) influence, but do
not change, the basic nature of the Mode-5 impact-density function For many years values
of A = 2.5 and B = 1000 were used in the Eastern Range ship-hit computations, although in
more recent risk studies the value of A has been increased to 3.0. This increase resulted .
from the observation that, in recent years, vehicles that experience Mode-5 failure responses
seem less likely than earlier developmental vehicles to deviate significantly from the
intended flight line. To see how A and B affect the distribution of Mode-5 impacts, and to
further understanding of the function, the results of choosing various values of A and B are
provided in Appendix B.
3.2 Effects of Shaping Constant on DAMP Results
As pointed out in the Introduction, two important types of constant parameters
required by DAMP for risk estimations must be determined. They are: (1) probability
of a Mode-5 failure response, and (2) valqes of the Mode-5 shaping constants A and B,
currently set at 3.0 and 1000, respectively. As will be demonstrated later, DAMP
results are far more sensitive to changes in A than in B.
The following cases illustrate the effects that constant A has on calculated risks.
Case 1: Baseline Risks for Atlas IIA
In the baseline risk analysis for Atlas IIAm, the probability of a Modew5 failure response
was estimated at 12.5% of the total failure probability during the first 120 seconds of
flight. Even so, risks resulting from Mode-5 responses accounted for about 90% of the
total risks for people inside the impact limit lines (ILL). Table 1 indicates the range of
risks inside the ILLs for day launches from Pad A using various estimates of the
shaping constant A and a value of B = 1000.
9/10/96 9 RTI