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I am a student pilot and I am learning about radio signals/communication.

I am studying for a test and a practice questions states:

You are flying circuits at a small airport and are flying at 1800ft ASL in the circuit (1000ft AGL) when you hear a radio call from a commercial jet at an airport 123 nautical miles to the south. Roughly how high does this jet need to be so that you can hear his radio call?

The only reference I can think of is that VHF signals can be heard by using a formula of: Nautical miles = 1.23 * √ height above ground level. The answer would be 10000 ft (AGL)?, but I am not sure if that is the right formula to use or how to figure it out.

Please help.

Ralph J
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Speed2772
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1 Answers1

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The formula you're using is correct, but don't forget your own altitude.

$$d = 1,23 × (\sqrt{h_1} + \sqrt{h_2})$$

So in your case:

$$123 = 1.23 × (\sqrt x + \sqrt{1000})$$ $$100 = \sqrt x + 31.623$$ $$\sqrt x = 68.377$$ $$x = 4675\ \mathrm{ft}$$

Jan Hudec
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Sami
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    Your answer looks right once I stop thinking you're an idiot because you used commas where decimals go ;) – Greg Taylor Nov 16 '15 at 00:06
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    Culture differences.. We use comma as decimal marker in Finland. – Sami Nov 16 '15 at 04:25
  • @Sami Then note that this is language-dependent, not culture-dependent ;-) – yo' Nov 16 '15 at 15:24
  • I just want to clarify that I didn't actually think you were an idiot. The commas did confuse me at first though. Was just trying to be funny, but upon re reading my own comment, it wasn't 100% clear I was joking. – Greg Taylor Nov 16 '15 at 16:25
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    @Greg Taylor No worries, I assumed you were :) – Sami Nov 16 '15 at 18:15
  • @yo' Bad choise of term on my behalf. Regarding computer user-interfaces and programming 'culture' is a set of rules for decimal markers, date formats, currency symbols etc. – Sami Nov 17 '15 at 08:58