Abstract:
A method of simulating the effects of one or more explosive events utilizes a mapping of graphically-valued dots to describe the explosive event at detonation at a plurality of (x,y) positions. A degradation rule is applied to the mapping of dots at each of times t n , for n=1 to N, to yield corresponding mappings of degraded value dots. The degradation rule specifies how the mapping of dots at detonation changes with time. The mapping at detonation and mappings of the degraded value dots are then simultaneously displayed in (x,y) registration with one another.

Description:
ORIGIN OF THE INVENTION 
   The invention described herein was made in the performance of official duties by employees of the Department of the Navy and may be manufactured, used, licensed by or for the Government for any governmental purpose without payment of any royalties thereon. 
   FIELD OF THE INVENTION 
   The invention relates generally to waveform interaction analysis and display of such waveform interaction, and more particularly to a method of simulating effects of one or more explosive events using, for example, pressure and impulse data associated with a single explosive event. 
   BACKGROUND OF THE INVENTION 
   Currently, development testing of obstacle breaching systems requires and has utilized numerous explosive tests. Results have indicated that increases in explosive performance are enhanced by spacing explosive charges from one another and then detonating them nearly simultaneously. More specifically, it was discovered that the shock-on-shock interaction between the discrete charges resulted in a greater destructive ability than that of a single charge of equivalent mass on a pound equivalent basis. Further, it was noted that different spacing between explosive charges yielded different performance results. The above discoveries led to the hypothesis that, for a given explosive charge size, an optimum spacing exists for some minimum number of charges. However, the current approach to determine such optimum spacing relies solely on expensive and dangerous empirical testing using live explosives. 
   SUMMARY OF THE INVENTION 
   Accordingly, it is an object of the present invention to provide a method of simulating the effects of an explosive event over time. 
   Another object of the present invention is to provide a method of simulating the effects of multiple explosive events. 
   Still another object of the present invention is to provide a graphic method of displaying the effects of multiple explosive events occurring at spaced-apart positions. 
   Yet another object of the present invention is to provide a graphic method of displaying the effects of multiple explosive events occurring at spaced-apart positions so that different charge sizes at different spacing intervals can be analyzed. 
   Other objects and advantages of the present invention will become more obvious hereinafter in the specification and drawings. 
   In accordance with the present invention, a method of simulating the effects of an explosive event utilizes a function F(x,y,t) that describes an explosive event. The function defines a mapping of known values at a plurality of (x,y) positions indicative of effects caused by the explosive event at a time of detonation t=t 0 . A degradation rule is applied to the mapping of known values at each of times t n , for n=1 to N, to yield corresponding mappings of degraded values. The degradation rule specifies how the mapping of known values changes with time. The mapping of known values and mappings of degraded values are then simultaneously displayed in (x,y) registration with one another. Each “value” can be represented graphically as a displayed “dot” having its intensity, gray scale or color determined by the magnitude (e.g., pressure, impulse, etc.) of the value associated therewith. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Other objects, features and advantages of the present invention will become apparent upon reference to the following description of the preferred embodiments and to the drawings, wherein corresponding reference characters indicate corresponding parts throughout the several views of the drawings and wherein: 
       FIG. 1  is a block diagram depicting the steps used in simulating the effects of a single explosive event in accordance with the present invention; 
       FIG. 2  is a schematic view of single explosive charge and the effects generated thereby at its time of detonation; and 
       FIG. 3  is a schematic view of multiple, spaced-apart explosive charges. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Referring now to the drawings, and more particularly to  FIG. 1 , a top-level flowchart is shown of the method of simulating the effects of an explosive event in accordance with the present invention. For ease of understanding, the present method will first be described as it relates to a single explosive event. However, the present invention can also be used to simulate the effects of multiple, spaced-apart explosive events (occurring simultaneously or nearly simultaneously) as will be explained further below. The simulation of multiple explosive events is of great use in determining an optimum spacing for a given set of spaced-apart explosive charges. 
   In the present invention, step  100  provides information on the explosive effects associated with a given charge at its time of detonation. In general, the explosive effects are described by a position-based, time-varying, function or F(x,y,t) where the function&#39;s result at time t is a value at an (x,y) coordinate. Typically, the explosive effects are represented by empirically-measured pressure and impulse data which can be mapped on an (x,y) coordinate system. For example,  FIG. 2  illustrates an explosive charge  10  positioned on an (x,y) coordinate axis at position (0,0). At time of detonation or t 0  as it will be referred to herein, pressure and impulse data is known (e.g., empirically measured) at a number of (x,y) positions. The pressure and impulse data at each position can thus be assigned a value that indicates the relative magnitude of the pressure and impulse data at that position. The relative value at each position can be graphically represented as a “dot” (e.g., a pixel, a printed mark, etc.). The resulting “dots”  12  define the mapping of the pressure and impulse data. While only a few-measurement positions are illustrated, the actual number of measurement positions would probably be much greater and can be varied without departing from the scope of the present invention. Indeed, accuracy of the present method improves with the number of known measurements. 
   Each mapped dot  12  graphically represents the relative magnitude of the value associated therewith. For example, in terms of a monochrome, CRT-type display, each dot  12  could have its intensity adjusted in accordance with the value associated with the corresponding pressure and impulse data. In terms of a printed display using only black ink, each dot  12  could have its grey scale adjusted in accordance with the pressure/impulse data value associated therewith. Still further, in terms of color displays/printers, each dot  12  can have its color adjusted in accordance with the pressure/impulse data value associated therewith. 
   With the “a priori” knowledge of the mapping of known values depicted in  FIG. 2 , the present method proceeds at step  102  by applying a degradation rule to the mapping of known values. More specifically, the change in each of dots  12  is projected to the next time increment in accordance with the velocity of the pressure and shock waves generated by explosive charge  10 . Assuming spherical symmetry of shock wave movement at a known velocity, the incremental radial distance that the shock waves move for a given amount of time Δt after time of detonation t 0  can be easily determined. Accordingly, step  102  applies a selected mathematical rule that reduces or degrades the value of each dot  12  at a time t=t 0 +n(Δt) after time of detonation. In terms of the mechanical pressure and impulse waves generated by explosive charge  10 , a suitable degradation rule is defined as the value of each dot  12  reduced by the cube root of the radial distance that the pressure/impulse waves would travel from time of detonation to t 0  a given time t n . It is to be understood that other degradation rules (i.e., transfer functions) could also be used without departing from the scope of the present invention. For example, if shock degradation through a particular material was of interest, one would use a (transfer function) degradation rule that accounted for the material&#39;s properties. 
   Step  104  displays the cumulative effective of the explosive event over time by simultaneously displaying dots  12  at time of detonation t 0  along with each subsequent mapping of degraded dots  12  at each time interval t n  with the dots associated with each time t n  being displayed in (x,y) registration with one another. The process of steps  102  and  104  is repeated for a desired number of N time intervals (e.g., seconds or fractions thereof) after time of detonation as indicated by loop  106 . As a result, by evaluating the intensity, changing gray scale or changing color over the (x,y) mapping, one can calculate/predict the cumulative total effect of the interacting pressure and/or impulse waves (generated by the explosive event) at any given time t n  at any (x,y) position after detonation. Such evaluation can be performed visually or through use of automated analyzers (e.g., densitometers in the case of changing grey scale levels or calorimeters in the case of changing colors). 
   As mentioned above, the present invention can be extended for use in simulating the effects of multiple, spaced-apart explosive events that occur simultaneously or nearly simultaneously. The term “explosive event” as used herein is meant to include impact events such as those caused by high velocity fragments impacting a target or target area. The present invention can also be used to estimate cratering events caused by an impact event. 
   The multiple, spaced-apart explosive events situation is illustrated in  FIG. 3  for a set of line charges where four explosive charges  10 A- 10 D are aligned on the x-axis of the (x,y) coordinate system. Spacing between adjacent ones of charges  10 A- 10 D is given by Δx. While each of charges  10 A- 10 D will typically be the same size charge, this is not required for the present invention. Rather, all that is required is the “a priori” knowledge of the mapping of known values (e.g., pressure and impulse data at time of detonation) for each of charges  10 A- 10 D such as that described above with respect to FIG.  2 . Then, the methodology described above with respect to  FIG. 1  is applied in parallel for each of charges  10 A- 10 D with the simultaneously display step  104  taking place on the same display at any given time t n . As a result, the cumulative total effect of the interacting pressure and/or impulse waves for the set of charges  10 A- 10 D can be seen/analyzed at any given time t n  over the entire (x,y) coordinate area or any part thereof. 
   The present invention can simulate simultaneous detonation of charges  10 A- 10 D such that time of detonation t 0  occurs at the same time for each charge. However, the present invention can also simulate the effects of near simultaneous detonation of charges  10 A- 10 D. For example, sequential detonation of charges  10 A- 10 D can be simulated by delaying each subsequent time of detonation t 0  by same small increment so that each charge&#39;s time of detonation is slightly different. 
   The advantages of the present invention are numerous. Knowledge of a single explosive event at detonation can be parlayed into a prediction of explosive effects over time for one or multiple, spaced-apart explosive events. The method is simple and produces a display that can be examined visually or via automation. The approach will find use in military applications (e.g., mine clearing) and civilian applications (e.g., mining, road construction, etc.). Use of the present invention provides a safe and inexpensive approach to prediction of explosive effects so that both effectiveness and impact on the surrounding environment/community can be evaluated. 
   Although the invention has been described relative to a specific embodiment thereof, there are numerous variations and modifications that will be readily apparent to those skilled in the art in light of the above teachings. It is therefore to be understood that, within the scope of the appended claims, the invention may be practiced other than as specifically described.