Line of sight and the radio horizon

What it is

Above about 30 MHz, signals mostly travel in straight lines. Two stations can talk when their antennas can effectively "see" each other, with a little help from the atmosphere that carries the path somewhat past the horizon you can see. This is the normal way VHF, UHF and microwave signals work, and it is why antenna height matters more than power.

The radio horizon

The Earth curves away beneath a straight line, so an antenna only sees as far as the ground allows: the geometric horizon is about 1.22 × √h miles with h in feet. Radio goes a bit further because the air thins with height, which bends a wave slightly downward and lets it follow the curve. The usual allowance is to pretend the Earth is one third bigger (4/3 of its radius), which turns 1.22 into 1.41.

The square root means height pays off slowly: four times the height only doubles the range.

Antenna height	Radio horizon
6 ft (a handheld at head height)	about 3.5 miles
30 ft	about 7.7 miles
100 ft	about 14 miles
500 ft	about 32 miles
1,000 ft	about 45 miles
10,000 ft (an aircraft)	about 140 miles

Two antennas

Each antenna has its own horizon, and the two stations can connect when those horizons meet or overlap. The maximum distance between them is the sum of the two: a station at 50 ft and one at 200 ft reach about 1.41 × (7.1 + 14.1) = 30 miles. Try the sliders: each extra foot added to the lower antenna gains more distance than a foot added to the higher one.

These distances are the optimistic limit. They assume a smooth Earth; hills, buildings and trees cut them short, and they ignore signal strength: a path can be clear yet too weak to copy.

In practice

• Height beats power. Doubling antenna height extends the horizon by about 41%, while doubling power buys only 3 dB and cannot help a blocked path. Repeaters sit on towers and mountaintops for this reason.
• Clear the path. Obstacles near the line, not just on it, weaken the signal. Practical links try to keep a zone around the line clear, not merely the line itself.
• Short waves cast sharper shadows. UHF and microwaves are blocked and absorbed by walls, hills and foliage more than VHF, while longer waves bend around obstacles more readily. See Frequency and wavelength.
• Taller means more cable. A higher antenna gains range but needs a longer feed line, which has loss; see Feed line loss and velocity factor.
• Beyond the horizon happens. Weather, the ionosphere and even meteor trails sometimes carry VHF signals far past line of sight; see Tropospheric ducting and scatter and Sporadic E.

Related

• Tropospheric ducting and scatterWeather that bends VHF and UHF well past the horizon.
• Sporadic EShort-lived patches of ionization that open VHF over long distances.
• Ground wave and surface waveLow-frequency signals that follow the curve of the Earth.
• Frequency and wavelengthTwo ways to describe the same wave, tied together by the speed of light.
• Feed line loss and velocity factorAttenuation by frequency and electrical length.
• Towers and mastsChoosing and installing supports.