[Singollo]

I think the engines would be represented as horses, wagons or whatever transportation you're using.

I dunno...I'm probably being needlessly nitpicky here, but this just doesn't capture the idea well. If adding engines is like adding, say, wagons, then the only way that this would speed the army is if all of the army rode in these wagons, or on the horses, which is obviously unrealistic and kind of silly. Just throwing some wagons into the army doesn't speed up poor Joe Legionnaire, who still has to walk and determines the speed of the entire army. Obviously, there could be specialized armies consisting only of cavalry and the like, in which adding better engines could be like adding higher-quality horses, but these would be the exception.

I guess the engines = wagons/horses would work for terrain (non-combat) movement, in a limited way. If you have 1000 soldiers and 333 wagons, then a third of the soldiers could be cycled in and out of the wagons, resting while the army moved, in order to retain overall stamina and freshness. Even this is of limited effectiveness, though, and it's still pretty unrealistic, historically speaking. Regardless, combat speed would have to be handled separately, using this concept.

I like the idea of each component having its own movement rate much better. That solves things right there. I would do away with engines altogether, and give each component a movement speed, with the lowest speed determing the overall speed of the army.