Keep in mind that this is not pure engineering, as you're not just trying to solve a problem, you're trying to solve a problem against a living, reacting adversary. So strategy ("game theory") enters into the picture.
Edward Luttwak's book "Strategy: The logic of war and peace" (http://www.amazon.com/Strategy-Logic-Peace-Revised-Enlarged/...) has a lengthy dioscussion of the strategic back-and-forth in the Battle of Britain. Besides the beams, both sides were also experimenting with new kinds of bombers, bombs, fighter planes, ways of finding and fighting fighter planes, countermeasures for preventing the enemy from finding your fighter planes, etc. Very interesting read.
Edward Luttwak's book "Strategy: The logic of war and peace" (http://www.amazon.com/Strategy-Logic-Peace-Revised-Enlarged/...) has a lengthy dioscussion of the strategic back-and-forth in the Battle of Britain. Besides the beams, both sides were also experimenting with new kinds of bombers, bombs, fighter planes, ways of finding and fighting fighter planes, countermeasures for preventing the enemy from finding your fighter planes, etc. Very interesting read.