Refractive Index

Value to Enter:

• K=4/3 is the most common value to use to represent the RF refraction (degree of bending) in the earth's atmosphere
• Surveyors often use K=6/3 and this results in what is commonly called the "Visual Line-of-Sight"
• For elevations greater than 5000 over Mean Sea Level use the Low Density, K=2/3 value (ie: Denver, Colorado)
• Use K=Infinity for "flat earth" calculations. These are slant-range designs where one antenna essentially looks "up" at the other, whether it's up to the top of a very tall building or from an earth station to a satellite.
• Use K=1 to solve distance-to-the-horizon calculations as if the earth were a perfect, geometric sphere, with no refraction effects considered.

Significance of This Value:

The Refractive Index or "K" value is used by RF designers, radio operators, astronomers, surveyors, and others to adjust measurements to compensate for the "bending" (refracting) of signals as they pass through the atmosphere. The value K=4/3 is the most commonly used but will result in the most optimistic measurements. It means that a signal can travel 4/3 further than the physical horizon. A value of K=1 is unrealistically small and results in the measurements being made as if the earth were a geometric sphere. Surveyors often use 6/5 as a reasonable estimate of atmospheric refraction but, at the highest elevations (over 5000 feet MSL) values as low as K=2/3 are used.

Background and Technical Perspective:

When performing computations or analyzing data related to spatial relationships it's necessary to understand the differences in measurements for distances on the earth's surface. Data obtained from, or applied to, the real earth (surrounded by a real atmosphere) typically differs from that which would be obtained based on the assumption of a spherical earth and derived using Euclidean or planar metrics. The geometric calculations that could be performed are based on distances being assumed to be a length of an arc of a great circle on a sphere. This geometric result is called a geodetic line, and it is the distance between two points (an antenna and the horizon, for example) that would be experienced by a person walking along a road between the two points. On the other hand, the changes in atmospheric density caused by altitude (density decreases as altitude increases), temperature (hot air is less dense than colder air), and water vapor (moist air is less dense than dry air.. a fact that may seem 'backwards' but it's true.)

When an wave moves from a region of lesser density into an area of greater density it bends towards the denser medium in accordance with several well established principles of physics. The pencil (right) appears to bend as it enters the water because the water is denser than air. The degree to which a propagating wave bends is represented by the refractive index for the medium through which the wave is passing. The refractive index is often represented by the capital letter "K".