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What is the maximum distance the voice messages sent by the tower on a radio channel can be received by an aircraft?

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VHF transmissions are limited by line of sight. So, assuming the transmitter is at the tower location, and assuming the aircraft is at cruise altitude (say F300, or 30,000 feet or more), the maximum range is perhaps 200 to 300 km before the curvature of the earth eliminates the line of sight. This also depends on weather conditions and the transmitter power.

In practice, VHF coverage may be extended using additional transceiver sites on the same (or different) frequency. This is particularly important in mountainous terrain.

For oceanic flights where there is no place to put additional transceiver sites, HF (shortwave) radio can be used which has a much greater range (thousands of km), especially at night. Some aircraft are also equipped with satellite phones so controllers can simply call them. However, this wouldn't be the tower controllers talking to the pilots over the ocean, as tower controllers aren't responsible for en route control.

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Depends on how the antenna, radios, terrain, etc are configured. I have experience some places that you needed to be very close < 10 miles. And some places where you could hear ATIS at 60 miles.

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