How did German radio beams reach distant English cities during WWII? [closed]

During WWII, the Germans were using radio beacons (the "Knickebein" system) to guide their bombers into English territory. They set up two beacons, one in Kleve, a city in West Germany, and one at Stollberg Hill (North Frisia). The two radio beams intersected over Derby.

The Knickebein system supposedly relied on line-of-sight propagation, but the distance between these locations is simply too great to allow for LOS. According to William CY Lee (page 350, equation 11.3.1), the radio horizon (i.e. the service range of the beacons) can be calculated as $$R= \sqrt{2h_a} + \sqrt{2h_b}$$ where $$R$$ is the distance in miles, $$h_a$$ is the aircraft altitude and $$h_b$$ is the ground-station antenna height in feet. If we plug in the numbers (say, the height of the beacon in Kleve (239ft) and the flight height of the German bombers (19,200ft)), we get a maximum beam range of 217,8 miles. However, Derby and Kleve are far away from each other, about 330 miles. So how could the Knickebein beams reach Derby?

closed as off-topic by The Photon, stafusa, Jon Custer, Kyle Kanos, Cosmas ZachosAug 23 at 19:41

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• Check the frequency and propagation characteristics of that frequency. Remember you receive radio broadcasts when you can’t see the antenna. – Jon Custer Aug 18 at 16:23
• The frequency was 30-33MHz. – Hepper Aug 18 at 16:37