Since we really know nothing about Mr OConnor's interest and background because he has chosen not to introduce himself, excuse me for making some assumptions.

It seems to me that he is seeking a formula for success on the battlefield based on establishing metrics for unit engagement areas. As the posts from both Wilf and RTK point out, it is not quite that simple. Back in the near Dark Ages (I'd have to defer to Ken White for the real Dark Ages), FM 100-5 discussed areas of interest and areas of influence in terms of both time and distance, by level of command. Areas of influence were essential limited by the range of fire support systems. However, these times and distances are best treated as rules of thumb. It ought to be readily apparent that one cannot be expected to defend against a mechanized battalion size force with a dismounted rifle platoon on a frontage of 5 kilometers . However, it is not quite so clear that a dismounted rifle platoon will be more successful in attacking an entrenched infantry force on a 300 meter frontage than on a 500 meter frontage, regardless of terrrain type. There are far too many variables to try to get a simplistic analysis that is as fine-grained as that. Successful tactics are not a matter of applying data into "plug and chug" formulas; there is at least as much art as science to the matter.