Good Evening,
Conditions were so so. Moderate, slow QSB with a steady hiss. On
twenty meters the signals were all down a bit, but my reach was better.
Forty meters was noisier with deeper QSB.
I rewrote some antenna modelling code I created a long time ago.
Unwrapping the dipole algorithm was not too difficult. Then I got to
the 1/4 wave vertical algorithm. The electric field equation has an
exponential raised to an imaginary power. Euler's identity unwraps that
into real and an imaginary parts. Normally you ignore the imaginary
part. The resulting function creates its own problems by generating
some unreal lobes. I'm trying to figure out how space can have a volume
with less than no electric field. Hence the guards on my output.
However, this code creates the electric field pattern of a 1/4 wave
dipole antenna which matches standard antenna modeling images.
On 14050.5 kHz at 2200z:
W0CZ - Ken - ND
NO8V - John - MI
K4JPN - Steve - GA
K6XK - Roy - IA
On 7047.5 kHz at 0000z:
K0DTJ - Brian - CA
WM5F - Dwight - ID
K6PJV - Dale - CA
Until next week 73,
Kevin. KD5ONS
-
// vertical.c
// K. J. Rock
// August 27, 2023
// g++ -o vert vertical.c
#include <stdio.h>
#include <math.h>
#define ETA 376.991118308 // characteristic impedance of
free space
#define RAD 0.017453293 // radian to degree
#define PI 3.1415926535 // cherry, of course
#define TWOPI 6.28318530718 // Katzenjammer feast
struct pt // 4 space vector
{
float w, x, y, z;
} arc[20], vert[1300]; // buffers for template and
pattern
int main( void )
{
int i=0; // template index
float f = 100; // frequency in MHz
float lambda = 300 / f; // wavelength in meters
float l = lambda / 4; // length of antenna in meters
float k = TWOPI / lambda; // save some space
float h = 1.0; // height of antenna in
wavelengths
float I0 = 2; // maximum current in
amperes
float r = 1000; // distance from antenna
to observer in meters
float dTheta = 5.0; // azimuth step size
float dPhi = 5.0; // elevation step size
float scale = 1.0; // fudge factor for
display purposes
float radius; // E(θ,φ) in
Volt/meter or Newton/Coulomb
// create one set of points in the X,Y plane at θ = 0
for (float phi=0; phi<90; phi += dPhi) // elevation NOT azimuth
{
radius = scale * cos(k * r)
* (k * l * ETA * I0 * cos(phi * RAD) * cos(h * k *
sin(phi * RAD)))
/ (TWOPI * r);
// store X,Y in arc[] of struct pt
if (radius > 0) // remove negative lobes
{
printf("%7.4f ", radius ); // E(θ,φ) where θ = 0
arc[i].x = radius*cos(phi*RAD); // store phi, radius in X,Y
coordinates
arc[i].y = radius*sin(phi*RAD);
arc[i++].z = 0.0; // at Z = 0
}
radius = scale * sin(k * r)
* (k * l * ETA * I0 * cos(phi * RAD) * cos(h * k *
sin(phi * RAD)))
/ (TWOPI * r);
if (radius > 0) // remove negative lobes
{
printf("%7.4f ", radius ); // E(θ,φ) where θ = 0
arc[i].x = radius*cos(phi*RAD); // store radius in X,Y
coordinates with Z = 0
arc[i].y = radius*sin(phi*RAD);
arc[i++].z = 0.0; // count vertices
per slice
}
}
printf("\n%3d points in the template\n", i);
// sweep the X,Y arc[] template around the Y axis
// vert[] is indexed serially, there are no delimiters between slices
int m = 0; // count vertices
for (int j=0; j<i; j++) // step from the bottom to
the top (0 to 90 degrees)
{
for (float theta=0; theta<360; theta += dTheta)
{
vert[m].x = arc[j].x * cos(theta*RAD);
vert[m].y = arc[j].y;
vert[m++].z = arc[j].x * sin(theta*RAD);
}
}
printf("%4d vertices in radiation pattern\n", m); // vertex count
return m;
}
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