In 1963 renaissance man Kenneth Boulding created the theory of Loss Strength Gradient (LSG). LSG states the amount of a country’s military power that could be brought to bear in any part of the world depended on the distance between the said country and the front lines. By definition LSG functions like distance decay by specifically using military force and describing the force's power as decreasing by distance.
Boulding added a temporal element to LSG by stating that a military revolution occurred in the 20th century with the rise of strategic air power, air transport, and intercontinental missiles.
LSG is a good rule of thumb but it ignores a key geographic factor: terrain. The United Kingdom was able to have a worldwide empire because water was so much easier to cross than vast landmasses. The only comparative empires which ruled large landmasses, the Mongols and the Russia, did so because the steppes were so sparsely populated. France could not support operations in Moscow in 1812 while at the same time the United Kingdom was conducting successful military operations in the Americas, India, Africa, and Australia. Around this time almost completely militarized France had 42 million citizens while the United Kingdom, a non-militarized country, only had some 8 million citizens.
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