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/* refract.cpp: functions & test code for low-precision refraction
Copyright (C) 2010, Project Pluto
This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301, USA. */
#include <math.h>
#include "watdefs.h"
#include "afuncs.h"
#define PI 3.1415926535897932384626433832795028841971693993751058209749445923
/*
REFRACT.CPP contains functions to convert an observed altitude
(one affected by refraction) to a true altitude (one that would be
seen on an airless planet), or vice versa. The first case is
handled using the method of G G Bennett, 'The Calculation of
Astronomical Refraction in Marine Navigation', _Journal of the
Institute for Navigation_, Vol 35, p 255-259 (1982), as explained
in Meeus' _Astronomical Algorithms_, p 102. The maximum error of
this is stated to be .9 arcsecond, for the range 0-90 degrees.
For the inverse problem, handled in the function reverse_refraction(),
we first get a "pretty good" answer using the formula of Saemundsson,
_Sky & Telescope_, p 70, July 1986, again as explained in _AA_.
The only problem is that this formula is accurate to within about 4".
One iteration using the refraction( ) function repairs this problem.
All inputs and outputs from these functions are in radians.
*/
double DLL_FUNC refraction( const double observed_alt)
{
double rval, ang = observed_alt;
ang += (7.31 * PI / 180.) / (ang * 180. / PI + 4.4);
rval = cos( ang) / sin( ang); /* from Meeus, _AA_, p 102 */
rval -= .06 * sin( (14.7 * rval + 13.) * PI / 180.);
return( rval * (PI / 180.) / 60.); /* cvt to radians */
}
double DLL_FUNC reverse_refraction( const double true_alt)
{
double rval, delta = 1.;
const double tolerance = .01 * (PI / 180.) / 3600.;
int n_iter = 10;
rval = true_alt + (10.3 * PI / 180.) / (true_alt * 180. / PI + 5.11);
rval = cos( rval) / sin( rval); /* from Meeus, _AA_, p 102 */
rval *= 1.02 * (PI / 180.) / 60.; /* cvt to radians */
/* The above gives a good first approximation */
/* Now improve that answer as follows: */
while( n_iter-- && (delta > tolerance || delta < -tolerance))
{
delta = rval;
rval = refraction( true_alt + rval);
delta -= rval;
}
return( rval);
}
double DLL_FUNC saasta_refraction( const double observed_alt,
const double pressure_mb, const double temp_kelvin,
const double relative_humidity)
{
double xi;
const double tan_z0 = cos( observed_alt) / sin( observed_alt);
const double tan_z0_2 = tan_z0 * tan_z0;
const double delta = 18.36;
const double pw0 =
relative_humidity * exp( delta * log( temp_kelvin / 247.1));
const double q = (pressure_mb - .156 * pw0) / temp_kelvin;
xi = 16.271 * q * tan_z0 * (1. + .0000394 * q * tan_z0_2) -
.0000749 * pressure_mb * tan_z0 * (1. + tan_z0_2);
/* The above refraction is in _arcseconds_... */
return( xi * (PI / 180.) / 3600.); /* cvt to radians */
}
double DLL_FUNC reverse_saasta_refraction( const double true_alt,
const double pressure_mb, const double temp_kelvin,
const double relative_humidity)
{
double rval;
rval = true_alt + (10.3 * PI / 180.) / (true_alt * 180. / PI + 5.11);
rval = cos( rval) / sin( rval); /* from Meeus, _AA_, p 102 */
rval *= 1.02 * (PI / 180.) / 60.; /* cvt to radians */
/* The above gives a good first approximation */
/* Now improve that answer as follows: */
rval = saasta_refraction( true_alt + rval,
pressure_mb, temp_kelvin, relative_humidity);
return( rval);
}
#ifdef TEST_PROGRAM
#include <stdio.h>
#include <stdlib.h>
int main( const int argc, const char **argv)
{
int i;
double ang, ref, scale = 1.;
if( argc == 3)
scale = atof( argv[2]);
for( i = 1; i <= 90; i++)
{
ang = (double)i * PI / 180;
printf( "%2d:%9.5lf %9.5lf %9.5lf %9.5lf\n", i,
refraction( ang) * 60. * 180. / PI,
reverse_refraction( ang) * 60. * 180. / PI,
saasta_refraction( ang, 1013., 293., .20 ) * 60. * 180. / PI,
reverse_saasta_refraction( ang, 1013., 293., .20) * 60. * 180. / PI);
}
printf( "Polar refraction: %.4lf arcsec\n",
refraction( PI / 2) * 3600. * 180. / PI);
if( argc > 1)
{
ang = atof( argv[1]) * PI / 180.;
ref = refraction( ang);
printf( "M: %9.5lf %9.5lf %9.5lf\n", ref * 60. * 180. / PI,
reverse_refraction( ang - ref) * 60. * 180. / PI,
reverse_refraction( ang) * 60. * 180. / PI);
ref = saasta_refraction( ang, 1013., 293., .20);
printf( "S: %9.5lf %9.5lf %9.5lf\n", ref * 60. * 180. / PI,
reverse_saasta_refraction( ang - ref, 1013., 293., .20)
* 60. * 180. / PI,
reverse_saasta_refraction( ang, 1013., 293., .20)
* 60. * 180. / PI);
ref = 0.;
for( i = 0; i < 9; i++)
{
ref = refraction( ang + ref) * scale;
printf( " %9.5lf %9.5lf\n", ref * 60. * 180. / PI,
ref * 180. / PI);
}
}
return( 0);
}
#endif
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