Salvo combat model
Encyclopedia
The salvo combat model provides a mathematical representation of missile battles between modern warships. It was developed by Wayne Hughes at the U.S. Naval Postgraduate School in Monterey . The salvo model describes the basic elements of modern missile combat in a very simple way. This is similar to how the Lanchester
square law provides a simple model of modern gun combat .
This exchange of missile fire can be modeled as follows. Let symbol A represent the number of combat units (warships or other weapon platforms) in the Red force at the beginning of the battle. Each one has offensive firepower α, which is the number of offensive missiles accurately fired per salvo at the enemy. Each one also has defensive firepower y, which is the number of incoming enemy missiles intercepted per salvo by its active defenses. Each ship has staying power w, which is the number of enemy missile hits required to put it out of action. Equivalently, one could say that each attacking missile can cause damage equal to a fraction u=1/w of a Red ship.
The Blue force is represented in a similar manner. Blue has B units, each with offensive firepower β, defensive firepower z, and staying power x. Each missile that hits will cause damage v=1/x.
The salvo combat model calculates the number of ships lost on each side using the following pair of equations. Here, ΔA represents the change in the number of Red's ships from one salvo, while ΔB represents the change in the number of Blue ships.
Each equation starts by calculating the total number of offensive missiles being launched by the attacker. It then subtracts the total number of interceptions by the defender. The number of remaining (non-intercepted) offensive missiles is multiplied by the amount of damage caused per missile to get the total amount of damage. If there are more defensive interceptions than offensive missiles, then the total damage is zero; it cannot be negative.
Mathematically, the salvo equations can be thought of as difference equations or recurrence relations. They also fall within the field of operations research
.
A stochastic (or probabilistic) version of the model also exists . In this version, the ship parameters listed above are random variables instead of constants. This means that the result of each salvo also varies randomly. The stochastic model can be incorporated into a computer spreadsheet and used instead of the Monte Carlo method
of computer simulation .
square law equations, with two main differences.
First, the basic salvo equations form a discrete time model, whereas Lanchester's original equations form a continuous time model. Cruise missiles typically are fired in relatively small quantities. Each one has a high probability of hitting its target, if not intercepted, and carries a relatively powerful warhead. Therefore it makes sense to model them as a discrete pulse (or salvo) of firepower.
By comparison, bullets or shells in a gun battle are typically fired in large quantities. Each round has a relatively low chance of hitting its target, and does a relatively small amount of damage. Therefore it makes sense to model them as a small but continuous stream of firepower.
Second, the salvo equations include defensive firepower, whereas Lanchester's original equations include only offensive firepower. Cruise missiles can be intercepted (shot down) by active defenses, such as surface-to-air missiles and anti-aircraft guns. By comparison, it is generally not practical to intercept bullets and shells in a gun battle.
. Offensive firepower represents anti-ship cruise missiles
such as the Harpoon, the Exocet
and the Styx. Defensive firepower represents air defense missiles such as the Standard
, as well as anti-aircraft guns such as the Phalanx
. However, one can adapt the model to other kinds of battles having similar characteristics.
For example, some authors have used it study World War II battles between aircraft carriers , such as the Battle of the Coral Sea
. In this case, the offensive firepower consists of dive bombers and torpedo bombers. The defensive firepower consists of fighter aircraft that try to intercept those bombers.
The model could also describe battles where torpedoes are the main form of offensive firepower, such as in the Battle of Savo Island
. In this case, the defensive firepower would be zero, since so far there is no effective way to actively intercept torpedoes.
The initial goal of such research is to get a better understanding of how the model works. A more important objective is to see what the model might suggest about the behavior of real missile battles. This could help with the development of better modern naval tactics
for attacking with and defending against such missiles.
Lanchester's laws
Lanchester's laws are mathematical formulae for calculating the relative strengths of a predator/prey pair. This article is concerned with military forces....
square law provides a simple model of modern gun combat .
Basic Form
Suppose that two naval forces, Red and Blue, are engaging each other in combat. The battle begins with Red firing a salvo of missiles at Blue. The Blue ships try to shoot down those incoming missiles. Simultaneously, Blue launches a salvo that Red tries to intercept.This exchange of missile fire can be modeled as follows. Let symbol A represent the number of combat units (warships or other weapon platforms) in the Red force at the beginning of the battle. Each one has offensive firepower α, which is the number of offensive missiles accurately fired per salvo at the enemy. Each one also has defensive firepower y, which is the number of incoming enemy missiles intercepted per salvo by its active defenses. Each ship has staying power w, which is the number of enemy missile hits required to put it out of action. Equivalently, one could say that each attacking missile can cause damage equal to a fraction u=1/w of a Red ship.
The Blue force is represented in a similar manner. Blue has B units, each with offensive firepower β, defensive firepower z, and staying power x. Each missile that hits will cause damage v=1/x.
The salvo combat model calculates the number of ships lost on each side using the following pair of equations. Here, ΔA represents the change in the number of Red's ships from one salvo, while ΔB represents the change in the number of Blue ships.
- ΔA = -(βB - yA)u, subject to 0 ≤ -ΔA ≤ A
- ΔB = -(αA - zB)v, subject to 0 ≤ -ΔB ≤ B
Each equation starts by calculating the total number of offensive missiles being launched by the attacker. It then subtracts the total number of interceptions by the defender. The number of remaining (non-intercepted) offensive missiles is multiplied by the amount of damage caused per missile to get the total amount of damage. If there are more defensive interceptions than offensive missiles, then the total damage is zero; it cannot be negative.
Mathematically, the salvo equations can be thought of as difference equations or recurrence relations. They also fall within the field of operations research
Operations research
Operations research is an interdisciplinary mathematical science that focuses on the effective use of technology by organizations...
.
A stochastic (or probabilistic) version of the model also exists . In this version, the ship parameters listed above are random variables instead of constants. This means that the result of each salvo also varies randomly. The stochastic model can be incorporated into a computer spreadsheet and used instead of the Monte Carlo method
Monte Carlo method
Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in computer simulations of physical and mathematical systems...
of computer simulation .
Relation to Lanchester's Laws
The salvo equations are related to the LanchesterLanchester's laws
Lanchester's laws are mathematical formulae for calculating the relative strengths of a predator/prey pair. This article is concerned with military forces....
square law equations, with two main differences.
First, the basic salvo equations form a discrete time model, whereas Lanchester's original equations form a continuous time model. Cruise missiles typically are fired in relatively small quantities. Each one has a high probability of hitting its target, if not intercepted, and carries a relatively powerful warhead. Therefore it makes sense to model them as a discrete pulse (or salvo) of firepower.
By comparison, bullets or shells in a gun battle are typically fired in large quantities. Each round has a relatively low chance of hitting its target, and does a relatively small amount of damage. Therefore it makes sense to model them as a small but continuous stream of firepower.
Second, the salvo equations include defensive firepower, whereas Lanchester's original equations include only offensive firepower. Cruise missiles can be intercepted (shot down) by active defenses, such as surface-to-air missiles and anti-aircraft guns. By comparison, it is generally not practical to intercept bullets and shells in a gun battle.
Types of Warfare
The salvo model primarily represents naval missile battles, such as those that took place during the Falklands WarFalklands War
The Falklands War , also called the Falklands Conflict or Falklands Crisis, was fought in 1982 between Argentina and the United Kingdom over the disputed Falkland Islands and South Georgia and the South Sandwich Islands...
. Offensive firepower represents anti-ship cruise missiles
Anti-ship missile
Anti-ship missiles are guided missiles that are designed for use against ships and large boats. Most anti-ship missiles are of the sea-skimming type, many use a combination of inertial guidance and radar homing...
such as the Harpoon, the Exocet
Exocet
The Exocet is a French-built anti-ship missile whose various versions can be launched from surface vessels, submarines, helicopters and fixed wing aircraft. Hundreds were fired in combat during the 1980s.-Etymology:...
and the Styx. Defensive firepower represents air defense missiles such as the Standard
RIM-67 Standard
The RIM-67 Standard ER is an extended range surface-to-air missile and anti ship missile originally developed for the United States Navy...
, as well as anti-aircraft guns such as the Phalanx
Phalanx CIWS
The Phalanx CIWS is an anti-ship missile defense system. It is a close-in weapon system and was designed and manufactured by the General Dynamics Corporation, Pomona Division...
. However, one can adapt the model to other kinds of battles having similar characteristics.
For example, some authors have used it study World War II battles between aircraft carriers , such as the Battle of the Coral Sea
Battle of the Coral Sea
The Battle of the Coral Sea, fought from 4–8 May 1942, was a major naval battle in the Pacific Theater of World War II between the Imperial Japanese Navy and Allied naval and air forces from the United States and Australia. The battle was the first fleet action in which aircraft carriers engaged...
. In this case, the offensive firepower consists of dive bombers and torpedo bombers. The defensive firepower consists of fighter aircraft that try to intercept those bombers.
The model could also describe battles where torpedoes are the main form of offensive firepower, such as in the Battle of Savo Island
Battle of Savo Island
The Battle of Savo Island, also known as the First Battle of Savo Island and, in Japanese sources, as the , was a naval battle of the Pacific Campaign of World War II, between the Imperial Japanese Navy and Allied naval forces...
. In this case, the defensive firepower would be zero, since so far there is no effective way to actively intercept torpedoes.
Development of Tactics
The salvo combat model can help with research on a variety of issues in naval warfare . For example, one study examined the value of having accurate information about an enemy fleet . Another study looked at how many missiles would be required to achieve a desired probability of success when attacking several targets at once . Researchers have also analyzed the mathematical properties of the model itself .The initial goal of such research is to get a better understanding of how the model works. A more important objective is to see what the model might suggest about the behavior of real missile battles. This could help with the development of better modern naval tactics
Modern naval tactics
The term modern naval tactics refers to tactical doctrines developed after World War II, following the final obsolescence of the battleship and the development of long-range missiles. Since there has been no major naval conflict since World War II, with the exception of the Falklands War, many of...
for attacking with and defending against such missiles.