Accelerating the pace of engineering and science

# blakechart

Range-angle-height (Blake) chart

## Syntax

• blakechart(vcp,vcpangles) example
• blakechart(vcp,vcpangles,rmax,hmax) example
• blakechart(___,'Name','Value') example

## Description

example

blakechart(vcp,vcpangles) creates a range-angle-height plot (also called a Blake chart) for a narrowband radar antenna. This chart shows the maximum radar range as a function of target elevation. In addition, the Blake chart displays lines of constant range and lines of constant height. The input consist of the vertical coverage pattern, vcp, and vertical coverage pattern angles, vcpangles, produced by radarvcd.

example

blakechart(vcp,vcpangles,rmax,hmax), in addition, specifies the maximum range and height of the Blake chart. You can specify range and height units separately in the Name-Value pairs, RangeUnit and HeightUnit. This syntax can use any of the input arguments in the previous syntax.

example

blakechart(___,'Name','Value') allows you to specify additional input parameters in the form of Name-Value pairs. You can specify additional name-value pair arguments in any order as (Name1,Value1,...,NameN,ValueN). This syntax can use any of the input arguments in the previous syntaxes.

## Examples

expand all

### Display Vertical Coverage Diagram

Display the vertical coverage diagram of an antenna transmitting at 100 MHz and placed 20 meters above the ground. Set the free-space range to 100 km. Use default plotting parameters.

```freq = 100e6;
ant_height = 20;
rng_fs = 100;
blakechart(vcp, vcpangles);
```

### Display Vertical Coverage Diagram Specifying Maximum Range and Height

Display the vertical coverage diagram of an antenna transmitting at 100 MHz and placed 20 meters above the ground. Set the free-space range to 100 km. Set the maximum plotting range to 300 km and the maximum plotting height to 250 km.

```freq = 100e6;
ant_height = 20;
rng_fs = 100;
rmax = 300;
hmax = 250;
blakechart(vcp,vcpangles,rmax,hmax);
```

### Display Vertical Coverage Diagram of Sinc Pattern Antenna

Plot the range-height-angle curve of a radar having a sinc-function antenna pattern.

Specify antenna pattern

Specify the antenna pattern as a sinc function.

```pat_angles = linspace(-90,90,361)';
pat_u = 1.39157/sind(90/2)*sind(pat_angles);
pat = sinc(pat_u/pi);
```

Set the transmitting frequency to 100 MHz, the free-space range to 100 km, the antenna tilt angle to 0 degrees, and place the antenna 20 meters above the ground. Assume a surface roughness of one meter.

```freq = 100e6;
ant_height = 10;
rng_fs = 100;
tilt_ang = 0;
surf_roughness = 1;
```

```[vcp, vcpangles] = radarvcd(freq,rng_fs,ant_height,...
'RangeUnit','km','HeightUnit','m',...
'AntennaPattern',pat,...
'PatternAngles',pat_angles,'TiltAngle',tilt_ang,...
'SurfaceRoughness',surf_roughness);
```

Set the maximum plotting range to 300 km and the maximum plotting height to 250,000 m. Choose the range units as kilometers, 'km', and the height units as meters, 'm'. Set the range and height axes scale powers to 1/2.

```rmax = 300;
hmax = 250e3;
blakechart(vcp, vcpangles, rmax, hmax, 'RangeUnit','km',...
'ScalePower',1/2,'HeightUnit','m');
```

## Input Arguments

expand all

### vcp — Vertical coverage patternreal-valued vector

Vertical coverage pattern specified as a K-by-1 column vector. The vertical coverage pattern is the actual maximum range of the radar. Each entry of the vertical coverage pattern corresponds to one of the angles specified in vcpangles. Values are expressed in kilometers unless you change the unit of measure using the 'RangeUnit' Name-Value pair.

Example: [282.3831; 291.0502; 299.4252]

Data Types: double

### vcpangles — Vertical coverage pattern anglesreal-valued vector

Vertical coverage pattern angles specified as a K-by-1 column vector. The set of angles range from –90° to 90°.

Example: [2.1480; 2.2340; 2.3199]

Data Types: double

### rmax — Maximum range of plotreal-valued scalar

Maximum range of plot specified as a real-valued scalar. Range units are specified by the RangeUnit Name-Value pair.

Example: 200

Data Types: double

### hmax — Maximum height of plotreal-valued scalar

Maximum height of plot specified as a real-valued scalar. Height units are specified by the HeightUnit Name-Value pair.

Example: 100000

Data Types: double

### Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: ‘RangeUnit','m'

### 'RangeUnit' — Radar range units'km' (default) | 'nmi' | 'mi' | 'ft' | 'm'

Range units denoting nautical miles, miles, kilometers, feet or meters. This Name-Value pair specifies the units for the vertical coverage pattern input argument, vcp, and the maximum range input argument, rmax.

Example: 'mi'

Data Types: char

### 'HeightUnit' — Height units'km' (default) | 'nmi' | 'mi' | 'ft' | 'm'

Height units specified as one of 'nmi' | 'mi' | 'km' | 'ft' |'m' denoting nautical miles, miles, kilometers, feet or meters. This Name-Value pair specifies the units for the maximum height, hmax.

Example: 'm'

Data Types: char

### 'ScalePower' — Scale power0.25 (default) | real-valued scalar

Scale power, specified as a scalar between 0 and 1. This parameter specifies the range and height axis scale power.

Example: 0.5

Data Types: double

### 'SurfaceRefractivity' — Surface refractivity313 (default) | real-valued scalar

Surface refractivity, specified as a non-negative real-valued scalar. The surface refractivity is a parameter of the CRPL Exponential Reference Atmosphere Model used in this function.

Example: 314

Data Types: double

### 'RefractionExponent' — Refraction exponent0.143859 (default) | real-valued scalar

Refraction exponent specified as a non-negative, real-valued scalar. The refraction exponent is a parameter of the CRPL Exponential Reference Atmosphere Model used in this function.

Example: 0.15

Data Types: double

expand all

### CRPL Exponential Reference Atmosphere Model

The blakechart function uses the CRPL Exponential Reference Atmosphere to model refraction effects. The index of refraction is a function of height

$n\left(h\right)=1.0+\left({N}_{s}\text{\hspace{0.17em}}×\text{\hspace{0.17em}}{10}^{-6}\right){e}^{-{R}_{exp}h}$

where Ns is the atmospheric refractivity value (in units of 10–6) at the surface of the earth, Rexp is a decay constant, and h is the height above the surface in kilometers. The default value of Ns is 313 and can be modified using the 'SurfaceRefractivity' Name-Value pair. The default value of Rexp is 0.143859 and can be modified using the 'RefractionExponent' Name-Value pair.

## References

[1] Blake, L.V. Machine Plotting of Radar Vertical-Plane Coverage Diagrams. Naval Research Laboratory Report 7098, 1970.