A theoretical radio-horizon calculation
A fictional technical worksheet explicitly defines maximum geometric radio range in nautical miles as 1.23 times the sum of the square roots of antenna heights in feet. It places the aircraft antenna at 3,600 feet and the ground antenna at sea level. Ignore terrain, interference and other propagation effects for this model. The exercise asks for the numerical result and whether it proves reliable communication at that distance. One learner changes nautical miles to kilometres without conversion; another treats the model as guaranteed coverage for every station. No actual service volume, frequency assignment, equipment standard or operational flight instruction is supplied. A suitable answer must retain the specified units, show the arithmetic and distinguish ideal geometry from usable coverage, message intelligibility and authority to enter an airspace.
1. Calculate the model range.
Read the worked answer
The square roots are 60 and 0. Therefore the range is 1.23 times 60, or 73.8 nautical miles, approximately 74 nautical miles.
2. Does that result prove real coverage or grant a clearance?
Read the worked answer
No. Actual terrain, equipment, interference and service limitations remain relevant, and a geometric range calculation is not an air traffic clearance.