Question: Lanchester Model. A fair amount of information can be deduced directly from the form of the Lanchester equations, without actually solving them.
(a) What condition on the sizes of the two forces must be met in order that the fractional loss rate of both sides be equal? [Fractional loss rate = N/N.]
(b) Find a relation of the form F(N1, N2) = c, where c is a constant, which is valid throughout the engagement. [The result should be a simple quadratic expression similar to the answer in (a).]
(c) If N1(0) and N2(0) are known, who will win? (The battle continues until one side is totally depleted.)
(d) As a function of time, the size of either side will have the form
Ni(t) = Ai sinh ωt + Bi cosh ωt
What is the value of ω?