# Chapter 23: Ground Wave Propagation

### Example 23-1.1, Page number: 783

In [1]:
#Variable declaration
f1 = 0.1      #Frequency (MHz)
f2 = 1.0        #Frequency (MHz)
f3 = 10.0       #Frequency (MHz)

#Calculations
d1 = 50/(f1**(1.0/3)) #Distance for f1 (miles)
d2 = 50/(f2**(1.0/3)) #Distance for f2 (miles)
d3 = 50/(f3**(1.0/3)) #Distance for f3 (miles)

#Result
print "The distance for 100kHz is", round(d1,2), "miles"
print "The distance for 1MHz is", d2, "miles"
print "The distance for 10MHz is", round(d3,2), "miles"

The distance for 100kHz is 107.72 miles
The distance for 1MHz is 50.0 miles
The distance for 10MHz is 23.21 miles


### Example 23-2.1, Page number: 786

In [2]:
from math import pi,sin

#Variable declaration
f = 3e6     #Frequency (Hz)
sigma = 0.5     #Standard deviation of surface irregularities (unitless)
theta = 30      #Angle of incidence as measured from normal angle (degrees)
c = 3e8     #Speed of light (m/s)

#Calculations
wave_lt = c/f   #Wavelength (m)
R = 4*pi*sigma*sin(theta*pi/180)/wave_lt
#Roughness factor (unitless)

#Result
print "The roughness factor is", round(R,9)

The roughness factor is 0.031415927


### Example 23-2.2, Page number: 786

In [4]:
from math import pi,sin

#Variable declaration
f = 10e6        #Frequency (Hz)
sigma = 5       #Standard deviation of surface irregularities (unitless)
theta1 = 30      #Angle of incidence as measured from normal angle (degrees)
theta2 = 45      #Angle of incidence as measured from normal angle (degrees)
theta3 = 60      #Angle of incidence as measured from normal angle (degrees)
c = 3e8         #Speed of light (m/s)

#Calculations
wave_lt = c/f       #Wavelength (m)
R1 = 4*pi*sigma*sin(theta1*pi/180)/wave_lt
#Roughness factor for theta1 (unitless)
R2 = 4*pi*sigma*sin(theta2*pi/180)/wave_lt
#Roughness factor for theta2 (unitless)
R3 = 4*pi*sigma*sin(theta3*pi/180)/wave_lt
#Roughness factor for theta3 (unitless)

#Result
print "The roughness factor for 30 degrees is", round(R1,4)
print "The roughness factor for 45 degrees is", round(R2,3)
print "The roughness factor for 60 degrees is", round(R3,4)

The roughness factor for 30 degrees is 1.0472
The roughness factor for 45 degrees is 1.481
The roughness factor for 60 degrees is 1.8138


### Example 23-2.3, Page number: 787

In [13]:
#Variable declaration
f1 = 0.3      #Frequency (MHz)
f2 = 1      #Frequency (MHz)
f3 = 3      #Frequency (MHz)
sigma = 4e-5    #Standard deviation of surface irregularities (unitless)

#Calculations
x1 = (18e3)*sigma/f1    #Parameter x for f1 (unitless)
x2 = (18e3)*sigma/f2    #Parameter x for f2 (unitless)
x3 = (18e3)*sigma/f3    #Parameter x for f3 (unitless)

#Result
print "The parameter x for 0.3MHz is", x1
print "The parameter x for 1MHz is", x2
print "The parameter x for 3MHz is", x3

The parameter x for 0.3MHz is 2.4
The parameter x for 1MHz is 0.72
The parameter x for 3MHz is 0.24


### Example 23-5.1, Page number: 790

In [24]:
from math import pi, sqrt

#Variable declaration
f1 = 5e3        #Frequency (Hz)
f2 = 50e3        #Frequency (Hz)
f3 = 500e3        #Frequency (Hz)
sigma = 5e-5    #Standard deviation of surface irregularities (unitless)
eps_r = 15.0      #Relative permittivity (unitless)
mu = pi*4e-7    #Absolute Permeability (H/m)

#Calculations
w1 = 2*pi*f1    #Angular frequency (rad/s)
w2 = 2*pi*f2    #Angular frequency (rad/s)
w3 = 2*pi*f3    #Angular frequency (rad/s)

Zs1 = sqrt((w1*mu)/sqrt(sigma**2 + (w1**2)*eps_r))
#Surface impedence for f1 (ohm)
Zs2 = sqrt((w2*mu)/sqrt(sigma**2 + (w2**2)*eps_r))
#Surface impedence for f2 (ohm)
Zs3 = sqrt((w3*mu)/sqrt(sigma**2 + (w3**2)*eps_r))
#Surface impedence for f3 (ohm)

#Result
print "The surface impedence for 5kHz is", round(Zs1,5), "ohms"
print "The surface impedence for 50kHz is", round(Zs2,5), "ohms"
print "The surface impedence for 500kHz is", round(Zs3,5), "ohms"

#There has been a numerical mistake in the calculation/substitution of square root of
#(sigma**2 + (w1**2)*eps_r) and in the second case, the mistake in the calculation of
#(w2*mu)/sqrt(sigma**2 + (w2**2)*eps_r)

The surface impedence for 5kHz is 0.00057 ohms
The surface impedence for 50kHz is 0.00057 ohms
The surface impedence for 500kHz is 0.00057 ohms


### Example 23-7.1, Page number: 793

In [25]:
from math import pi, atan, cos

#Variable declaration
f = 2.0       #Frequency (MHz)
sigma = 5e-5    #Standard deviation of surface irregularities (unitless)
eps_r = 15.0      #Relative permittivity (unitless)
d = 20e3        #Distance (m)
eff = 0.5       #Antenna efficiency (unitless)
c = 3e8         #Speed of light (m/s)
E1 = 0.5e-3     #Ground wave electric field strength (V/m)

#Calculations
wave_lt = c/(f*10**6)       #Wavelength (m)
x = (18e3)*sigma/f  #Parameter x (unitless)

b = atan((eps_r + 1)/x)     #Phase constant (unitless)

p = (pi/x)*(d/wave_lt)*cos(b)    #Numerical distance (unitless)

A = (2 + 0.3*p)/(2 + p + 0.6*(p**2))    #Reduction factor (unitless)

E_t = E1 * d/A

#Result
print "The Electric field strength at the transmitted end is", round(E_t,2),"V/m"

The Electric field strength at the transmitted end is 445.72 V/m