Effects of lethality in naval combat models

In the context of both discrete time salvo models and continuous time Lanchester models we examine the effect on naval combat of lethality: that is, the relative balance between the offensive and defensive attributes of the units involved. We define three distinct levels of lethality and describe the distinguishing features of combat for each level. We discuss the implications of these characteristics for naval decision‐makers; in particular, we show that the usefulness of the intuitive concept “more is better” varies greatly depending on the lethality level. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

On efficient algorithms for finding efficient salvo policies

We consider the salvo policy problem, in which there are k moments, called salvos, at which we can fire multiple missiles simultaneously at an incoming object. Each salvo is characterized by a probability p_i: the hit probability of a single missile. After each salvo, we can assess whether the incoming object is still active. If it is, we fire the missiles assigned to the next salvo. In the salvo policy problem, the goal is to assign at most n missiles to salvos in order to minimize the expected number of missiles used. We consider three problem versions. In Gould's version, we have to assign all n missiles to salvos. In the Big Bomb version, a cost of B is incurred when all salvo's are unsuccessful. Finally, we consider the Quota version in which the kill probability should exceed some quota Q. We discuss the computational complexity and the approximability of these problem versions. In particular, we show that Gould's version and the Big Bomb version admit pseudopolynomial time exact algorithms and fully polynomial time approximation schemes. We also present an iterative approximation algorithm for the Quota version, and show that a related problem is NP-complete.     

Analysis of artillery shoot‐and‐scoot tactics

Firing multiple artillery rounds from the same location has two main benefits: a high rate of fire at the enemy and improved accuracy as the shooter's aim adjusts to previous rounds. However, firing repeatedly from the same location carries significant risk that the enemy will detect the artillery's location. Therefore, the shooter may periodically move locations to avoid counter‐battery fire. This maneuver is known as the shoot‐and‐scoot tactic. This article analyzes the shoot‐and‐scoot tactic for a time‐critical mission using Markov models. We compute optimal move policies and develop heuristics for more complex and realistic settings. Spending a reasonable amount of time firing multiple shots from the same location is often preferable to moving immediately after firing an initial salvo. Moving frequently reduces risk to the artillery, but also limits the artillery's ability to inflict damage on the enemy.     

火箭助飞鱼雷与空投鱼雷齐射攻潜射击方法

火箭助飞鱼雷与空投鱼雷齐射攻潜是水面舰艇中远距离攻潜的有效方法之一。由于火箭助飞鱼雷和空投鱼雷齐射的平台、弹道不同,为了有效的组织鱼雷的齐射,必须解决相关的问题。因此,从火箭助飞鱼雷与空投鱼雷的作战使用特点出发,首先探讨两雷齐射的定义及实施方法,其次通过计算机仿真研究了实施齐射时的直升机安全问题,并研究了两雷射击的间隔时间,拟合了计算公式。总之,此问题的研究对发挥水面舰艇中远距离反潜作战能力具有一定的意义。     

When is model complexity too much? Illustrating the benefits of simple models with Hughes' salvo equations

The simulations that many defense analysts rely upon in their studies continue to grow in size and complexity. This paper contrasts the guidance that the authors have received—from some of the giants of military operations research—with the current practice. In particular, the analytic utility of Hughes' simple salvo equations is compared with that of the complex Joint Warfighting System (JWARS), with respect to JWARS' key performance parameters. The comparison suggests that a family of analytic tools supports the best analyses. It follows that smaller, more agile, and transparent models, such as Hughes' salvo equations, are underutilized in defense analyses. We believe that these models should receive more attention, use, and funding. To illustrate this point, this paper uses two very simple models (by modern standards) to rapidly generate insights on the value of information relative to force strength. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

反潜鱼雷两雷平行航向齐射最小齐射距离计算方法研究

提出了2种计算反潜鱼雷两雷平行航向齐射最小齐射距离的方法———几何法和概率法,并对2种方法进行了比较.结果表明,概率法比几何法更加实用.所提出的计算方法对今后有关部门设计或改进舰艇指控系统软件具有重要参考价值.     

Effective attacks in the salvo combat model: Salvo sizes and quantities of targets

This article considers two related questions of tactics in the context of the salvo model for naval missile combat. For a given set of targets, how many missiles should be fired to produce an effective attack? For a given available salvo size, how many enemy targets should be fired at? In the deterministic version of the model I derive a simple optimality relationship between the number of missiles to fire and the number of targets to engage. In the stochastic model I employ the expected loss inflicted and the probability of enemy elimination as the main performance measures and use these to derive salvo sizes that are in some sense “optimal.” I find that the offensive firepower needed for an effective attack depends not only on a target's total strength but also on the relative balance between its active defensive power and passive staying power. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

声自导雷平行齐射发现概率解析计算模型

为了准确快速地评估声自导鱼雷平行齐射的作战效能（发现概率）,从鱼雷、目标的相对运动入手,将目标位置及运动随机误差转移到鱼雷航向上;如此建立了计算声自导鱼雷平行齐射发现概率的一重积分解析模型（不考虑鱼雷航行性能误差）和四重积分解析计算模型（考虑鱼雷航行性能误差）。最后以统计模型为标准来验证两个解析模型的正确性。仿真结果显示,对于90%左右的考察态势,解析模型与统计模型的结果差的绝对值在1%之内,另外10%左右的考察态势,也在1%-3%之间。从而验证了所建解析模型的正确性和可行性。     

The salvo combat model with area fire

This article analyzes versions of the salvo model of missile combat where area fire is used by one or both sides in a battle. Although these models share some properties with the area fire Lanchester model and the aimed fire salvo model, they also display some interesting differences, especially over the course of several salvos. Although the relative size of each force is important with aimed fire, with area fire, it is the absolute size that matters. Similarly, although aimed fire exhibits square law behavior, area fire shows approximately linear behavior. When one side uses area fire and the other uses aimed fire, the model displays a mix of square and linear law behavior. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 60: 652–660, 2013     

尾流自导鱼雷双雷二次转角齐射

针对尾流自导鱼雷在小舷角或者大舷角态势下,使用正常的双雷平行齐射有可能导致鱼雷的入尾流角度θ不满足要求(在30°到150°之间)的问题,提出并建立了含θ为参数的双雷二次转角齐射模型,一方面通过鱼雷的二次转角来使入尾流角度满足要求,另一方面通过双雷齐射提高发现概率.仿真结果表明,该方法基本能够满足特殊态势条件下对于发现概率的射击要求,前提条件是要根据不同的态势及不同的目标运动要素情况,选择不同的θ以获得最佳的射击效果.