The Line of Sight (LOS) Calculator helps determine the maximum distance between two antennas or towers for reliable radio communication, considering the curvature of the Earth and standard atmospheric refraction.
Line of Sight Calculator
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Maximum Line of Sight Distance: …
Line of Sight Calculator Formula
The maximum line-of-sight distance ($D_{max}$) in kilometers, considering the curvature of the Earth and standard atmospheric refraction (with a K-factor of $4/3$), is calculated as:
$$D_{max} (\text{km}) \approx 4.12 \times (\sqrt{h_1 (\text{m})} + \sqrt{h_2 (\text{m})})$$Where $h_1$ and $h_2$ are the heights of the two antennas/towers in meters.
Formula Source: Wikipedia – Line-of-sight propagation | RF Wireless World
Variables
- Tower Height 1 (H1): The height of the first antenna or tower, measured in meters (m).
- Tower Height 2 (H2): The height of the second antenna or tower, also measured in meters (m).
- Actual Link Distance (D): The measured ground distance between the two points, measured in kilometers (km).
- Maximum LOS Distance ($D_{max}$): The calculated furthest distance in km at which line of sight is theoretically maintained.
Related Calculators
- Fresnel Zone Calculator
- Free Space Path Loss Calculator
- Effective Radiated Power (ERP) Calculator
- Antenna Gain Estimator
What is Line of Sight?
Line of Sight (LOS) propagation is a characteristic of electromagnetic radiation or acoustic wave propagation which means waves travel in a straight line from the source (transmitter) to the receiver. This is the simplest and most direct path for radio waves, commonly used in microwave and satellite communications, as well as terrestrial broadcasting.
In practical terms, achieving line of sight means ensuring there are no physical obstructions—such as hills, buildings, or large trees—blocking the direct path. Crucially, due to the Earth’s curvature, the line of sight is limited even in flat, unobstructed areas. The calculated maximum LOS distance factors in this curvature, often using an effective Earth radius ($K$-factor) to account for atmospheric bending (refraction) of the radio waves.
A successful communication link requires not only the direct path (LOS) but also sufficient clearance around the path, defined by the Fresnel Zone, to avoid signal attenuation and phase cancellation.
How to Calculate Line of Sight (Example)
Let’s find the maximum LOS distance for two towers and check if they can communicate across a 50 km link.
- Identify Heights: Tower 1 Height ($h_1$) = 120 m. Tower 2 Height ($h_2$) = 80 m. Actual Link Distance ($D$) = 50 km.
- Calculate Square Roots: $\sqrt{120} \approx 10.95$ and $\sqrt{80} \approx 8.94$.
- Apply Formula: Add the square roots and multiply by the $4.12$ factor: $D_{max} \approx 4.12 \times (10.95 + 8.94)$
- Determine Maximum LOS Distance: $D_{max} \approx 4.12 \times 19.89 \approx 81.95 \text{ km}$.
- Compare with Actual Distance: Since the maximum distance (81.95 km) is greater than the actual link distance (50 km), **Line of Sight exists** between the two towers.
Frequently Asked Questions (FAQ)
Why does the Earth’s curvature affect Line of Sight? The Earth is a sphere, so as the distance between two points increases, the surface of the Earth curves downward between them. This curvature eventually causes the horizon to block the direct path between the two antennas, requiring taller structures to compensate for the “Earth bulge.”
What is the K-factor in LOS calculations? The K-factor (effective Earth radius factor) is used to account for the phenomenon of atmospheric refraction, where radio waves are bent slightly toward the Earth. A standard atmosphere usually corresponds to a K-factor of 4/3 or 1.333, which is the value embedded in the simplified $4.12$ constant.
Is Line of Sight enough for a stable wireless link? No. While necessary, LOS is not sufficient. You also need to ensure that the primary Fresnel Zone is clear of obstructions. The Fresnel Zone is an elliptical volume around the LOS path where signal energy travels; partial blocking of this zone causes significant signal degradation.
What unit should I use for the heights and distance? The common formula requires antenna heights to be in meters (m) and the distances to be in kilometers (km). Always ensure unit consistency to obtain accurate results.