An AM antenna is two things working together: a vertical radiator (the tower) and a buried ground system (the radials). The tower’s electrical height sets its radiation resistance and how much ground-wave field it can throw at the horizon. The ground system doesn’t radiate — its job is to keep your transmitter power out of the lossy earth. Efficiency is the fight between the two. Drag any slider — everything updates live.
The blue curve is the best a tower of a given electrical height could do — the ground-wave field per kilowatt radiated, over a perfect ground. It climbs as the tower gets electrically taller, peaks right around 5/8-wave (225°, the most efficient ground-wave radiator), then falls as a high-angle lobe steals power. Your tower’s ideal point rides on that curve (blue dot). The green dot is what you actually get after two losses drag it down: a low radiation resistance when the tower is short, and ground-system loss when the radials are sparse or short. The gap between the blue and green dots is your wasted power. The three red dashed lines are the FCC minimum-efficiency floors a station must clear to be licensed.
Watch the radiation resistance card as you shorten the tower. A quarter-wave sits near 36 Ω; drop to a stubby 30° radiator and it collapses toward 1 Ω. Radiation resistance is the “good” resistance that actually turns current into signal — when it falls to the same order as the ground-loss resistance, half your power or more just heats the dirt. That is the real reason a physically short antenna (or a low-band station forced onto a short tower) is so inefficient: not that it aims poorly, but that it can barely radiate what you feed it. This is also why the low end of the band is so unforgiving — a fixed number of feet is far fewer electrical degrees down at 560 than up at 1600.