## Example 1,Page No:162¶

In [1]:
import math

#variable declaration
print'mathematically ellipsoid is represented by \n((x/a)**2)+((y/b)**2)+((z/c)**2) = 1\n ';
print'\nThe approximate expression for ellipsoid backscattered RCS is given by\n ';
print'\nσ =(π*a**2 b**2 c**2)/[ a**2 (sinθ)**2 (cosɸ)**+ b**2 (sinθ)**2 (sinɸ)^2+c**2 (cosθ)**2 ]**2\n';
print'\nif a = b ,the ellipsoid becomes Roll symmetric,above eqn becomes\n';
print'\nσ = (π* b**4 c**2)/[ a**2 (sinθ)**2 + c**2 (cosθ)**2 ]**2\n';

mathematically ellipsoid is represented by
((x/a)**2)+((y/b)**2)+((z/c)**2) = 1

The approximate expression for ellipsoid backscattered RCS is given by

σ =(π*a**2 b**2 c**2)/[ a**2 (sinθ)**2 (cosɸ)**+ b**2 (sinθ)**2 (sinɸ)^2+c**2 (cosθ)**2 ]**2

if a = b ,the ellipsoid becomes Roll symmetric,above eqn becomes

σ = (π* b**4 c**2)/[ a**2 (sinθ)**2 + c**2 (cosθ)**2 ]**2



## Example 2,Page No:162¶

In [2]:
import math

#variable declaration
print'mathematically ellipsoid is represented by \n((x/a)**2)+((y/b)**2)+((z/c)**2) = 1\n ';
print'\nThe approximate expression for ellipsoid backscattered RCS is given by\n ';
print'\nσ =(π*a**2 b**2 c**2)/[ a**2 (sinθ)**2 (cosɸ)**2+ b**2 (sinθ)**2 (sinɸ)**+c**2 (cosθ)**2 ]**2\n';
print'\nif a = b = c ,the ellipsoid becomes a sphere,above eqn becomes\n';
print'\nσ = (π* a**6)/[ a**2 (sinθ)**2 + a**2 (cosθ)**2 ]**2\n';
print'\nσ = (π* a**6)/[ a**4]\n';
print'\nσ of sphere is π*a**2 ' ;

mathematically ellipsoid is represented by
((x/a)**2)+((y/b)**2)+((z/c)**2) = 1

The approximate expression for ellipsoid backscattered RCS is given by

σ =(π*a**2 b**2 c**2)/[ a**2 (sinθ)**2 (cosɸ)**2+ b**2 (sinθ)**2 (sinɸ)**+c**2 (cosθ)**2 ]**2

if a = b = c ,the ellipsoid becomes a sphere,above eqn becomes

σ = (π* a**6)/[ a**2 (sinθ)**2 + a**2 (cosθ)**2 ]**2

σ = (π* a**6)/[ a**4]

σ of sphere is π*a**2


## Example 3,Page No:163¶

In [3]:
import math

#variable declaration
print'As it has Circular symmetry ,RCS of circular flat plate is independent \n of ɸ ,RCS depends on aspect angle.\n';
print'\nFor normal incidence θ = 0,then\n';
print'\nσ = (4*π**3*r**4)/(λ**2)\n';
print'\nif r = 1 m  then\n';
print'σ = (4*π**3)/(λ**2)' ;

As it has Circular symmetry ,RCS of circular flat plate is independent
of ɸ ,RCS depends on aspect angle.

For normal incidence θ = 0,then

σ = (4*π**3*r**4)/(λ**2)

if r = 1 m  then

σ = (4*π**3)/(λ**2)


## Example 4, Page No:163¶

In [6]:
import math

# Variable Declaration

lamda  = 0.03;                # wavelength in m
Pt     = 250*10**3;            # transmitter power
G      = 2000;                # antenna gain
R      = 50*10**3;             # maximum range
Pr     = 10*10**-12;           # minimum detectable power

# Calculations
Ae     = (lamda*lamda*G)/(4*math.pi);       # effective aperture area
RCS    = (Pr*(4*math.pi*R*R)**2)/(Pt*G*Ae);  # Radar cross section of the target

# Output
print 'Radar cross section of the target is %3.2f'%RCS,'m^2';

Radar cross section of the target is 137.81 m^2