Research for Hit Probabilities

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CNA COMPUTER PROGRAM 19-69, WEAPON PATTERN EFFECTIVENESS III
June 1, 1974
A Monte Carlo simulation program has been written in FORTRAN to compute hit probabilities of a pattern of weapons against a maneuvering target. The aimpoint is specified, and a bivariate normal aiming error is assumed for the weapon pattern; individual weapons in the pattern are assumed to have bivariate normal (ballistic) dispersion errors. Target initial velocity, time spent in a straight leg, turning radius, and time spent in the turn are specified, and a normal distribution are included. Flow charts, program listing, and sample inputs and outputs are provided.
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PROBABILITIES IN A SEQUENCE OF CORRELATED EVENTS
June 1, 1974
The correlation between gunnery shots is treated by regarding them as repeated dependent trials, the probability of a hit being determined by the success or failure of the previous shot. Relevant results on MARKOV chains are summarized and extended to the case of non-stationary correlation. The system of difference equations is made the basis of the treatment, which provides an IBM computational scheme for finding the probabilities of various numbers of hits, and also explicit formulas for such probabilities in a case which generalizes the Poisson distribution. Illustrative applications are given to gunnery data.
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A MODEL OF CARRIER-SUBMARINE INTERACTIONS
June 1, 1974
Analytic expressions for the probability that a single aircraft carrier, opposed by submarines, can remain on station for a specified length of time are discussed in this research contribution. The threat from both torpedo and cruise-missile submarines is considered, but the threat from aircraft is not. Expressions for expected submarine losses are derived. Expressions are also developed to show how the probability of remaining on station improves as the carrier's resistance to damage increases. A wide variety of ASW force compositions and tactics can be represented in the parameters of the model. Appendix C presents an alternative way to formulate the problem and derive the quantities mentioned above. The two methods produce results that are in excellent agreement. The intention of the authors is to provide a tool that can be used to improve carrier effectiveness through the study of tactics and force interactions.
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AIR-TO-GROUND GUNNERY SIMULATION, CNA COMPUTER PROGRAM 6-70 (PROGRAM AIRTOGR)
June 1, 1974
A computer program employing a Monte Carlo simulation is presented to determine the probability of destroying a rectangular target with air-to-ground gunnery. The effect of correlation of successive aim points is considered, and bivariate normal aiming error and ballistic dispersion are assumed. Included in the report are a flow chart, a listing of the FORTRAN program, and a sample program.
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THE THEORETICAL BASIS OF THE CODE 50 NUCLEAR EXCHANGE MODEL
June 1, 1974
The Code 50 Nuclear Exchange Model is a war game model produced by the LAMBDA Corporation. This research contribution derives and explains the basic mathematical models used in the computer programs of that model, including models of missile and bomber penetration as well as damage calculation, weapon allocation, and kill probability models. Model implementation and integration into the Code 50 program are also demonstrated.
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