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Daniel wrote: Maybe they’re using a considerably lower level of power with a high gain directional antenna?
A 9-element Yagi-Uda (for example) has a linearly-polarized peak gain of about 10 dBd, which is a power gain of 10 X. The antenna input power needed to produce a maximum radiated power of 29,000 watts then will be 29,000 watts/10 = 2,900 watts.
And if they were using a transmitter rated for 35 milliwatts, then ignoring coax attenuation and matching losses, a directional antenna would need a gain of 828,571 times, or 59.2 dBd to radiate a maximum power of 29,000 watts. And the main lobe of that radiation pattern would be extremely narrow.
Such an antenna is highly impractical in the band 88-108 MHz.