Models of Combat

[herwin]

Ref: Helmbold, Robert L. (1971) "Air Battles and Ground Battles--A Common Pattern?", Rand Report P-4548, January 1971

Helmbold is known in the combat modelling community for demonstrating that break-point models of engagement termination are invalid.

The reference discusses models of combat and points out that air and ground combat appear to follow the same pattern. He starts by discussing the testing of complex combat models, pointing out that there are two approaches available:

1. Replay historical battles and show that the model reproduces the historical outcomes.

2. Find regularities or patterns in the historical battle data and then verify that the model exhibits the same patterns.

The replay approach fails because it requires information on the exact location and manoeuvres of the forces engaged, the amount of ammunition fired, and the manner in which the fire is allocated to the opposing targets. This information is hard to find and in any case tends to build the battle outcome into the game by assumption. He recommends the second approach: demonstrating that regularities are replicated.

The regularities he identifies apply to both land and air operations and are couched in the following terms:

Assume you have two forces, x and y. He uses a Lanchester Law formulation:

3. dx/dt = - D y
4. dy/dt = -A x

D and A are the activity parameters and D/A is the activity ratio between attacker and defender.

5. D/A = (x(0)*x(0) - x(t)*x(t))/(y(0)*y(0) - y(t)*y(t))

You can also consider the fractional strengths a(t) and d(t) of the forces left at time t:

6. a(t) = x(t)/x(0)
7. d(t) = y(t)/y(0)

The losing side almost always (90+% of the time) has the smaller fractional strength at the end of the battle. You can write differential equations for a and d:

8. da/dt = -delta d
9. dd/dt = -alpha a

And introduce a new variable, mu:

10. delta/alpha = mu*mu

mu is then the relative advantage of the two sides. If mu>1, the defender survives when the attacker is eliminated, and if mu<1, the attacker survives.

Define V = ln(mu). V is positive when the defender has the advantage, and V is negative if the attacker has the advantage. This is termed the defender's advantage parameter.

Define lambda = sqrt(alpha*delta) = sqrt(A*D)

lambda is the intensity of the battle. Let T be the length of the battle and epsilon = lambda*T. epsilon is termed the bitterness of the battle.

The following statistical fits are known:

11. ln(D/A) = 0.230 + 1.266 ln(x(0)/y(0))

12. ln(epsilon) is approximately normal with mean -2.16 and standard deviation 0.83

These fits seem to hold for land combat. For air combat (Battle of Britain, single days of operations), the following fits are known:

13. ln(D/A) = 0.242 + 1.544 ln(x(0)/y(0)) (x and y measured in sorties)

14. ln(epsilon) is approximately normal with mean -3.65 and standard deviation 0.30.

[JWE]

And yes, I know it's very OT, and I hope it doesn't go any farther, but I thought Herwin would get a kick out of this; and, after all, one good 'techie' deserves another.

Physicists at Lawrence Livermore National Laboratories and Stanford University SLAC Project jointly announced that they recently isolated the heaviest element yet known to science.

The new element, Governmentium (Gv), has one neutron, 25 assistant neutrons, 88 deputy neutrons, and 198 assistant deputy neutrons, giving it an atomic mass of 312. These 312 neuronic particles are held together by marginally attractive particles called morons, which are, in turn, surrounded and bonded together by vast quantities of lepton-like particles called peons.

http://www.daveramsey.com/etc/cms/heavi ... 1004.htmlc

Ciao. John

[RevRick]

And I thought that dealing with the plethora of theological doctrines, dogmas, heresies, and saints was difficult. Could you please tell me, sir, which language you are speaking? OY!

[JWE]

Ok, back to the topic. Sorry for the OT shift.

The interesting part of the analysis is that it assumes a mathematical relationship between the parameters.

One of the real nastinesses of operational modeling is that relative fractional strengths are often unknown to the decision engine. Thus 6 and 7 become indeterminate. 8 and 9 become invalidated by the indeterminate nature of ‘a’ and ‘d’.

Mu is a mathematical expression of relative advantage and takes no account of non-mathematical factors, such as commander will, unit cohesion, instantiated morale, environment, and some poor dork with more heart than sense doing an impossible deed. These non-mathematical factors are the fundamentals of randomization in a combat algorithm.

btw, lets pull this discussion somewhere else. It's not AE related, so maybe the main forum would be a better place.
Ciao. J