478. Monte Carlo Techniques as Applied to the A3 Polaris Missile

Paper

Abstract

A concept called ‘performance reliability’ was used in designing the Polaris A3 missile. This concept allows a low percentage of subsystem failures in exchange for increased missile system performance (range or payload). This approach is necessary since the size of a submarine launch tube places restrictions on missile sizing. The only way to increase payload or range without changing launch tube size, therefore, is to improve state of the art, or accept reduced reliability. Naturally, both methods were used in designing the A3, however this paper will discuss only the method of reducing reliability to reduce weight in the second stage flight control subsystem. Once it has been decided to reduce reliability, a method must be used to actually determine analytically the probability of success of a subsystem.
The analytical method finally decided upon was an iterative computer technique using random numbers. This technique is commonly called ‘Monte Carlo.’ The paper will discuss, within the limitations of security, the weight saving of a Monte Carlo designed fluid injection thrust vector control system having a small probability of failure vs. a system designed for worst on worst conditions.
The success of the Monte Carlo Technique in the thrust vector control system led to serious consideration of its use in other areas which are primary weight responsibilities. For example, the tolerances on the c.g.’s and M.I.’s are very tedious to find in closed form, but very easy to find using Monte Carlo – if computer time and talent are available. Another example is the tolerance on weights during burning. The weighed inert weight of a motor includes a certain amount of burnable inert weight, as well as fixed inert weight. Since they are not independent variables, then the problem of finding tolerances on inert weight near burnout of a stage becomes a problem which responds nicely to Monte Carlo, whereas the root-sum-square technique is invalid because it assumes independence of variables.
These cases are discussed, have been used in Polaris analysis, and have provided reasonable answers. Problems arising in their use are also discussed. It is felt that Monte Carlo will come into increased use as an analytical tool.