Many computational methods have been suggested for the solution of this theoretical situation, such as Riemann variables, Lax-Wendroff and other finite difference procedures. The basic approach adopted here is to re-examine the fundamental theory of pressure wave motion and adapt it to a mesh method interpolation procedure. At the same time the boundary conditions for inflow and outflow, such as the filling and emptying of engine cylinders, has been resolved for the generality of gas properties and in terms of the unsteady gas flow which controls those processes. The same generality of gas property and composition is traced throughout the pipe system. This change of gas property is very significant in two-stroke engines where the exhaust blowdown is followed by short-circuited scavenge air. Vitally important in this context is the solution for the continual transmission and reflection of pressure waves as they encounter both differing temperature gradients and gas properties, and both gradual and sudden changes of area throughout the engine ducting. Of equal importance is the ability of the calculation to predict the effect of internal heat generation within the duct or of external heat loss from it, and to be able to trace the effect of the ensuing gas temperature change on both the pressure wave system and the nett gas flow.The new theoretical approach is programmed for a computer and the physical dimensions of a Husqvarna 250 motocross engine are used as input data. The correlation of the theory with the measured pressure and performance characteristics is demonstrably good. Extended insight into the behaviour of the actual engine is described.One of the unusual aspects of this new approach to this necessarily very complex theoretical situation is that both the theory, and the computational method for its solution, is relatively easy to comprehend and to apply in practice.