|
Insensitive Munition (IM) tests at some facilities currently use three fragments launched simultaneously to determine the likelihood of detonation. The likelihood of detonation from fragment impact depends on many factors, including the obliquity of the target, the fragment orientation, the impact velocity, and the synergism of the fragments. Synergism is important only if the fragments impact within several fragment widths of each other, and within several microseconds [Ref. 1]. The likelihood of detonation resulting from shock impulse for fragments not impacting within a few fragment widths of each other then depends primarily on the obliquity of the target, the fragment orientation and velocity. This fragment orientation is quantified with an impact angle, θ, which is measured between the normal to a face of the fragment and the reverse direction of the impacted surface normal, as shown in Figure 1. The obliquity is also quantified with an angle, which is measured between the velocity vector of the fragment and reverse direction of the impacted surface normal.
Figure 1 — Fragment Impact Angle.
This paper's discussion of detonation threshold calculations is divided into four parts. First, it outlines two models used to determine Shock to Detonation Transition (SDT). One is used in hydrocodes, while the other is an engineering-based equation. The discussion focuses on how the orientation of the fragment or fragments affects the detonation calculation, and adds perspective to the fragment orientation probability sections that follow.
This paper also reviews the analytic method described in Ref. 2 to determine the probability that a particular impact angle will occur for a cube. This method is based on the area ratio of a subsurface of a sphere containing just the cube to the total surface area of that sphere. The subsurface is that area swept out by the radius of the sphere as it assumes orientations with angles in a given impact angle interval.
In addition, this paper describes an analytic equation for calculating the combined probability of multiple events, knowing the probability of a single event. Although this equation is most certainly given in many texts on probability, it was determined by extrapolation from simple examples. These examples are given for illustration and to validate the equation. The equation is then used to calculate the combined probability of the minimum impact angle for three tumbling fragments, as would occur in an IM test.
Finally, this paper applies analytic methods to calculate the probability of impact angles for the U.S. Proposed NATO Insensitive Munitions (IM) Test Fragment under the assumption of random tumbling. These calculations then allow comparisons between the probability of impact angles for impact of a single cube, triple cubes and the Proposed NATO test fragment.
next page »
|
