Dynamical Systems MAT 5932. The Lanchester Equations of Warfare Explained Larry L. Southard. Friday, June 6, 2014. Agenda. History of the Lanchester Equation Models Lanchester Attrition Model Deficiencies of the equations. History.
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The Lanchester Equations of Warfare Explained
Larry L. Southard
Friday, June 6, 2014
The solution to these equations as functions of x(t) and y(t) provide insights about battle outcome.
Mathematically it looks simple:
Integrating the equations which describe modern warfare
we get the following state equation, called Lanchester's "Square Law":
After extensive derivation, the following expression for the X force level is derived as a function of time (the Y force level is equivalent):
x(t) becomes zero at about t = 14 hours.
Surviving Y force is about y(14) = 50.
How do kill rates affect outcome?
Now y(t) becomes zero at about t =24 hrs.
Surviving X force is about x(24) = 20.
Can Y overcome this disadvantage by adding forces?
Not by adding 30 (the initial size of X's whole force).
What will it do to add a little more to Y?
This is enough to turn the tide decidedly in Y's favor.
How many survivors are there when X wins a fight-to-the-finish?
When X wins, how long does it take?
How long does it take if X wins?
(Assume battle termination at x(t) = xBP or y(t) = yBP)
In what case does X win? If and only if: