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effearthradius

Effective earth radius

Since R2021a

Description

Re = effearthradius returns the effective radius Re of a spherical earth computed from the gradient of the index of refraction of the atmosphere. The radius is in meters. This syntax uses the default value of -39e-9 for the gradient, making the effective radius approximately 4/3 of the actual earth radius. For more information about the computation, see Effective Earth Radius from Refractivity Gradient.

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Re = effearthradius(refgrad) computes the effective radius from the specified gradient of the refractivity, refgrad, of the atmosphere.

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Re = effearthradius(R,ha,ht) returns the effective Earth radius, Re, using the average radius of curvature method (see [1]). R is the line-of-sight range to the target. ha is the radar altitude above mean sea level (MSL). ht is the target altitude above MSL. See Effective Earth Radius from Average Radius of Curvature.

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Re = effearthradius(R,ha,ht,'SurfaceRefractivity',ns) also specifies the scalar surface refractivity, ns for the average radius of curvature method. See Effective Earth Radius from Average Radius of Curvature.

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Re = effearthradius(R,ha,ht,___,'BreakPointAltitude',altbp) also specifies the altitude of the convergence point, altbp, for the average radius of curvature method.

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Re = effearthradius(R,ha,ht,___,'BreakPointRefractivity',npb) also specifies the refractivity at the convergence point, npb, for the average radius of curvature method.

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[Re,k] = effearthradius(___) also outputs the effective radius factor, k. Use this option with any of the syntaxes described above. See Effective Earth Radius.

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Examples

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Return the default effective earth radius due to atmospheric refraction.

re = effearthradius
re = 
8.4774e+06

Compute the ratio of the effective earth radius to the actual earth radius.

r = physconst('EarthRadius');
disp(re/r)
    1.3306

Compute the effective earth radius from a specified refractivity gradient, -40e-9.

rgrad = -40e-9;
re = effearthradius(rgrad)
re = 
8.5498e+06

Calculate the effective Earth radii for a radar positioned at sea level aimed at two targets. The first target is at 8000 meters above sea level at a range of 100 km. The second target is at 9000 meters altitude at a range of 200 km.

rng = [100e3,200e3];
ha = [0];
ht = [8.0e3, 9.0e3];
re = effearthradius(rng,ha,ht)
re = 1×2
106 ×

    7.4342    7.3525

Calculate the effective Earth radii for a radar positioned at sea level and aimed at two targets. The first target is at 8000 meters above sea level at a range of 100 km. The second target is at 9000 meters altitude at a range of 200 km. Specify the surface refractivity as 100.0 N-units.

rng = [100e3,200e3];
ha = [0,0];
ht = [8.0e3,9.0e3];
re = effearthradius(rng,ha,ht,'SurfaceRefractivity',100)
re = 1×2
106 ×

    6.3582    6.3582

Calculate the effective Earth radii for a radar positioned at sea level aimed at two targets. The first target is at 8000 meters above sea level at a range of 100 km. The second target is at 9000 meters altitude at a range of 200 km. The breakpoint altitude is 10000.0 meters and the surface refractivity is 350 N-units.

rng = [100e3,200e3];
ha = [0,0];
ht = [8.0e3,9.0e3];
re = effearthradius(rng,ha,ht,'SurfaceRefractivity',350.0, ...
    'BreakPointAltitude',10000.0)
re = 1×2
106 ×

    7.5877    7.4917

Calculate the effective Earth radii for a radar positioned at sea level and aimed at two targets. The first target is at 8000 meters above sea level at a range of 100 km. The second target is at 9000 meters altitude at a range of 200 km. The breakpoint altitude is 10000.0 meters, the breakpoint refractivity is 300 N-units, and the surface refractivity is 375 N-units.

rng = [100e3,200e3];
ha = 0;
ht = [8.0e3, 9.0e3];
re = effearthradius(rng,ha,ht,'SurfaceRefractivity',375, ...
    'BreakPointAltitude',10e3,'BreakPointRefractivity',300)
re = 1×2
106 ×

    6.6962    6.6930

Calculate the effective Earth radius factors for a radar positioned at sea level aimed at two targets. The first target is at 8000 meters above sea level at a range of 100 km. The second target is at 9000 meters altitude at a range of 200 km. The break point altitude is one kilometer, the breakpoint refractivity is 300.0 N-units, and the surface refractivity is 350.0 N-units.

rng = [100e3,200e3];
ha = [0,0];
ht = [8.0e3,9.0e3];
[re,k] = effearthradius(rng,ha,ht,'SurfaceRefractivity',350.0, ...
    'BreakPointAltitude',1000.0,'BreakPointRefractivity',300.0)
re = 1×2
106 ×

    7.7113    7.5724

k = 1×2

    1.2104    1.1886

Input Arguments

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Refractivity gradient, specified as a scalar. Units are in N-units/meter.

Data Types: double

Line-of-sight range to the target from the radar, specified as a positive scalar or a 1-by-M vector of positive values. M must be the same for R, ha, and ht. However, if one of R, ha, and ht is a scalar and another is a 1-by-M vector, the scalar is expanded into a 1-by-M vector. Units are in meters.

Data Types: double

Radar altitude above mean sea level, specified as a scalar or a 1-by-M vector. M must be the same for R, ha, and ht. However, if one of R, ha, and ht is a scalar and another is a 1-by-M vector, the scalar is expanded into a 1-by-M vector. Units are in meters.

Data Types: double

Target altitude above mean sea level, specified as a scalar or an M-length vector. M must be the same R, ha, and ht. However, if one of R, ha, and ht is a scalar and another is a 1-by-M vector, the scalar is expanded into a 1-by-M vector. Units are in meters.

Data Types: double

Scalar surface refractivity, specified as a positive scalar. Units are N-units.

Dependencies

To enable this argument, use the syntax specifying 'SurfaceRefractivity'.

Data Types: double

Convergence point altitude, specified as a scalar. The convergence point altitude defaults to 12192 meters when any of the input altitudes specified in ha or ht are greater than 9144 meters. Otherwise, it defaults to 9144 meters. Setting the 'BreakPointAltitude' and 'BreakPointRefractivity' values can be used to tune the output to measured refraction values. For more information, see Effective Earth Radius from Average Radius of Curvature. Units are in meters.

Dependencies

To enable this argument, use the syntax specifying 'BreakPointAltitude'.

Data Types: double

Convergence point refractivity, specified as a scalar. The refractivity defaults to 66.65 N-units when any of the input altitudes specified in ha or ht are greater than 9144 meters. Otherwise, the default is 102.9. Setting the 'BreakPointAltitude' and 'BreakPointRefractivity' values can be used to tune the output to measured refraction values. For more information, see Effective Earth Radius from Average Radius of Curvature. Units are N-units.

Dependencies

To enable this argument, use the syntax specifying 'BreakPointRefractivity'.

Data Types: double

Output Arguments

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Effective earth radius, returned as a positive scalar. Units are in meters.

Effective earth radius factor, returned as a positive scalar. The effective earth radius factor is the ratio of the effective earth radius to the physical earth radius. Units are dimensionless.

Data Types: double

More About

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References

[1] Doerry, Armin. W. "Earth Curvature and Atmospheric Refraction Effects on Radar Signal Propagation", Sandia National Laboratories, SAND2012-10690, January 2013.

[2] Long, Maurice W. Radar Reflectivity of Land and Sea, 2nd Ed. Artech House, 2001.

[3] Mahafza, Bassem R. Radar Signal Analysis and Processing Using MATLAB, CRC Press, 2009.

[4] Skolnik, Merrill I. Introduction to Radar Systems, Third edition, McGraw-Hill, 2001.

[5] Ward, James. "Space-Time Adaptive Processing for Airborne Radar", Lincoln Lab Technical Report, 1994.

Extended Capabilities

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Version History

Introduced in R2021a