Article: Line of Sight Radio Range & Antenna Heights

Background

What is Line-of-Sight (LOS) Propagation?

In radio communication, LOS propagation refers to the direct path between a transmitting antenna and a receiving antenna. High-frequency radio waves (like VHF, UHF, 900MHz, FM radio, TV broadcasting, Wi-Fi, and more) travel in relatively straight lines, similar to light. Obstacles like buildings, hills, and the curvature of the Earth itself can block these signals.

The Radio Horizon Concept

While we often think of LOS as a perfectly straight line limited only by physical obstructions, the Earth’s curvature is the ultimate limiter for terrestrial communications.

  • Geometric Horizon: This is the horizon you would see visually, limited purely by the geometric shape of the Earth.
  • Radio Horizon: Radio waves traveling through the atmosphere tend to bend slightly downwards due to refraction caused by changes in atmospheric density and water vapor content with altitude. This bending allows radio waves to travel slightly beyond the geometric horizon.
  • Effective Earth Radius (4/3 Model): To simplify calculations, this atmospheric bending effect is commonly modeled by assuming the radio waves travel in straight lines but over an Earth with a larger radius. The standard model uses an “effective Earth radius” that is 4/3 times the actual Earth radius (approximately 3959 miles or 6371 km). This model works well for “standard” atmospheric conditions.

Calculating the Radio Horizon Distance

A widely used practical formula to estimate the distance to the radio horizon (d) in miles, given the antenna height (h) in feet, and incorporating the 4/3 effective Earth radius model is:

d (miles) ≈ sqrt(2 * h (feet))

This formula gives the distance from a single antenna to its radio horizon point on the Earth’s surface.

Calculating Total LOS Communication Range

For communication between two antennas with heights h1 and h2 (in feet), the maximum theoretical LOS distance (D_total) is the sum of their individual radio horizon distances:

D_total (miles) ≈ d1 + d2 ≈ sqrt(2 * h1) + sqrt(2 * h2)

Example Calculations

Radio Horizon Distance (from one antenna)

Antenna Height: 10 ft -> Radio Horizon: 4.47 miles

Antenna Height: 25 ft -> Radio Horizon: 7.07 miles

Antenna Height: 50 ft -> Radio Horizon: 10.00 miles

Total LOS Communication Range (between two identical antennas)

Two Antennas at 10 ft each -> Total LOS Range: 8.94 miles (4.47 mi *2)

Two Antennas at 25 ft each -> Total LOS Range: 14.14 miles (7.07 mi * 2)

Two Antennas at 50 ft each -> Total LOS Range: 20.00 miles (10.00 mi * 2)

Total LOS Range (between two different height antennas)

Antenna 1 at 10 ft, Antenna 2 at 50 ft -> Total LOS Range: 14.47 miles (4.47 mi + 10.00 mi)

Practical Implications

  • Height is Key: As the calculations show, increasing antenna height significantly increases the distance to the radio horizon and thus the potential communication range. Raising an antenna from 10 ft to 50 ft more than doubles its horizon distance (4.47 miles to 10.00 miles).
  • Range Increases with Height: The total LOS range between two antennas increases substantially as their heights increase. Two antennas at 50 ft can theoretically communicate over twice the distance (20 miles) compared to two antennas at 10 ft (8.94 miles).
  • Non-Linear Relationship: The range increases with the square root of height. Doubling the height does not double the range; it increases it by a factor of sqrt(2) (approximately 1.41).
  • Obstructions Matter: This calculation gives the maximum theoretical range limited only by the Earth’s curvature under standard atmospheric conditions. Any physical obstruction within this path (buildings, hills, dense forests) will block or severely degrade the signal. True LOS requires not just clearing the horizon but also clearing obstacles along the path.
  • Real-World vs. Theory: The 4/3 Earth radius model is an average. Actual atmospheric conditions (temperature inversions, high humidity) can sometimes cause more or less bending (refraction). Unusual conditions like “ducting” can occasionally allow radio waves to travel much farther than the calculated radio horizon.

Additional Relevant Information

  • Fresnel Zone: While not strictly part of the horizon calculation, achieving a good quality LOS link requires not just a direct line but also clearance within a football-shaped region around the direct path called the first Fresnel zone. Obstructions intruding significantly into this zone (even if not blocking the direct path) can cause signal degradation due to reflections and diffraction. Taller antennas help provide better Fresnel zone clearance over the curve of the Earth.