  In 1999 the author suggested an equation to describe the rate and temporal
distribution of battle casualties. This equation was proposed as a replacement
for the Lanchester equation. Unlike Lanchester's equation, the author's
equation is based on a measurement of the spatial distribution of forces
involved in a battle, and incorporates this by use of the concept of the
fractal dimension. In this report, the form of the expected Loss-Exchange-Ratio
function based on this equation is determined. It is shown how this function
can be used as a Metamodel to describe the outcome of some cellular automaton
models. While this is not an exhaustive proof of the validity of the equation,
the match for the case studied is convincing, pointing to the potential of the
equation to be adopted more generally for combat models. This is particularly
so in the context of earlier work studying historical battle data that also
supports an equation of the form of the author's proposal.
