Radio Horizon (line of sight)
Maximum line-of-sight range to the radio horizon for a VHF antenna, driven by antenna height and the curvature of the Earth.
Formula
Variables
Example
Antenna at 900 ft: d ≈ 1.23×√900 = 1.23×30 ≈ 37 nm
How it works
This formula estimates how far a VHF antenna can "see" before the Earth's curvature blocks the signal path. As the antenna height increases, the horizon moves outward, so the range grows with the square root of height rather than in a straight line. The constant 1.23 converts the geometric result into nautical miles for height in feet under standard atmospheric conditions.
When to use it
Use this when estimating the maximum line-of-sight distance for VHF communications, such as aircraft-to-aircraft, aircraft-to-ground, or antenna placement planning. It is a quick range check when terrain and buildings are not the limiting factor.
Worked example, step by step
A VHF antenna is mounted 1,600 ft above the ground. Step 1: Write the formula d ≈ 1.23√h Step 2: Substitute the height d ≈ 1.23√1600 Step 3: Find the square root √1600 = 40 Step 4: Multiply d ≈ 1.23 × 40 = 49.2 Final answer: The radio horizon is about 49 nm.
Common mistakes to avoid
- Using metres instead of feet for h without converting first
- Treating this as guaranteed communication range instead of a geometric horizon estimate
- Forgetting that terrain, aircraft attitude, and atmospheric refraction can change the real-world range
Did You Know?
VHF radios (VOR, ILS, comms) work only line-of-sight, which is why an aircraft at altitude can talk to a station hundreds of miles away while it vanishes the moment you land.
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