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# Propagation

## •Functions and parameters contained in this package:

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### •Package functions and their basic documentation along with simple examples

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#### •DivergenceFactor

Usage message for DivergenceFactor

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To determine the gradient of the index of refraction we will need to differentiate it.  Here is the index of refraction as a function of height for the 1976 US standard atmosphere

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To differentiate this we will first need to load the Mathematica standard package NumericalMath`NLimit`

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This package containd a function to perform numerical differentiation

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Numerical differentiation is needed here since the expression for ior1976 does not have an explicit analytic form (Temperature1976[h], Pressure1976[h], and WaterVaporDensityMidLatitudeMean[h]).

Here is the value of the gradient of the index of refraction near sea level:

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This value is close to the conventionally quoted 4/3 effective earth radius factor:

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However, at a higher altitude the 4/3 effective earth factor is not appropriate.  For example at a height of 10 kilomenters:

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#### •HeightGainSphericalDiffraction

Usage message for HeightGainSphericalDiffraction

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#### •KnifeEdgeDiffractionFourRay

Implementation not yet complete for this function.

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In Db:

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#### •Multipath

For Loamy Soil:

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Determine when the transmitter and target are within line-of-sight of each other (HorizonDistance is contained in the package "Radar`RadarGeometry`"):

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So the target is within line-of-sight once it is approximately a meter above the ground at this 20 Km distance.

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A contour plot that includes a free space propagation factor using a different color function:

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Transmitter at 100 feet, target at 200 feet, frequency 3 GHz; plot for one-way propagation loss as a function transmitter to target distance. The geometrical horizon for this system is at (in nautical miles):

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Here is an example using the UseRoughnessFactor Option.

RoughnessFactorGaussian:

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RoughnessFactorGeneralized:

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Here is an example using the UseDivergenceFactor Option.

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And with a roughness factor and a divergence factor:

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#### •OutOfLineOfSightDefault

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#### •ReflectionCoefficient

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Absolute value of the reflection coefficient for vertical polarization over sea water at 20° Celsius for frequencies of 100 MHz, 500 MHz, and 1 GHz.

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Absolute value of the reflection coefficient for vertical polarization over sea water at 20° Celsius for frequencies of 100 MHz, 500 MHz, and 1 GHz.

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#### •SphericalDiffraction

This propagation model is of specific interest for so-called "surface wave" radar systems.

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#### •UseDivergenceFactor

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#### •UseRoughnessFactor

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