Date: Sat, 24 Nov 2007 13:34:55 -0500
From: Frank Ghigo <fghigo@nrao.edu>
To: Rick Fisher <rfisher@nrao.edu>
Cc: rnorrod@nrao.edu, fghigo <fghigo@nrao.edu>
Subject: Re: 20-meter pointing corrections

Rick,

This is how it goes:

DAZ = az' - az
DEL = el' - el

az' and el'  are the values you send to the encoder;
az and el are the calculated astronomical az/el

The full model, which you can ignore, because not
all these terms are used:
DAZ = P1 - P2*cos(phi)*sin(az)*sec(el) + P3*tan(el)
   - P4*sec(el) + P5*sin(az)*tan(el) - P6*cos(az)*tan(el)
   + P12*az + P13*cos(az) + P14*sin(az)

DEL = P5*cos(az) + P6*sin(az) + P7
   - P8*(cos(phi)*cos(az)*sin(el)-sin(phi)*cos(el))
   + P9*el + P10*cos(el) + P11*sin(el)
   +P15*cos(2az) + P16*sin(2az)

This form is used for antennas of different types of axes;
the "phi" term is 90 deg for an az/el telescope, so
some terms drop out; and
not all the coefficients are used, so
it simplifies to:

DAZ = P1 + P3*tan(el) - P4*sec(el) + p5*sin(az)*tan(el)
   - P6*cos(az)*tan(el)

DEL = P5*cos(az) + P6*sin(az) + P7
   - P8*cos(el)+ P9*el + P15*cos(2az) + P16*sin(2az)

The coefficient values, in degrees:
P1 = -0.614458
P3 = +0.002687
P4 = -0.020850
P5 = +0.007284
P6 = +0.003707
P7 = -0.127830
P8 = -0.071832
P9 = +0.027348
P15= -0.001024
P16= -0.004177

There is also a refraction correction,
but probably you can ignore it.
The form of it looks  complicated,
but I can send it to you if you want.

-- frank

Date: Sat, 24 Nov 2007 13:45:13 -0500
From: Frank Ghigo <fghigo@nrao.edu>
To: Rick Fisher <rfisher@nrao.edu>
Cc: Frank Ghigo <fghigo@nrao.edu>, rnorrod@nrao.edu
Subject: Re: 20-meter pointing corrections

Rick,

Oops, I got a sign wrong -- the DEL equation is actually:
(the P8 term is subtracted, not added)

DEL = P5*cos(az) + P6*sin(az) + P7
  - P8*cos(el)+ P9*el + P15*cos(2az) + P16*sin(2az)
====================================================================
/* refrw

   Compute refraction correction given surface weather input.
   Copied from FORTRAN.
*/

#include <math.h>
#include <stdio.h>
#include "../include/dpi.h"

#define MAX(a,b) ((a > b) ? a : b)

static double p[5]={0.458675e1,
                    0.322009e0,
                    0.103452e-1,
                    0.274777e-3,
                    0.157115e-5};
static double cvt = 1.33289;
static double a = 40;
static double b = 2.7;
static double c = 4.0;
static double d = 42.5;
static double e = 0.4;
static double f = 2.64;
static double g = .57295787e-4;

double refrw(delin,tempc,humi,pres)
double delin;
float tempc,humi,pres;

{
  double el,rhumi,dewpt,x,pp,tempk,sn;
  double aphi,ang,dele,bphi,ref;
  int i;

  el = MAX(1.0,delin*RAD2DEG);
/*
  fprintf(stderr,"REFRW: el=%f\n",el);
*/

/* Compute SN (surface refractivity)
*/
  rhumi = (100.0-humi)*0.9;
  dewpt = tempc-rhumi*(-.136667+rhumi*1.33333e-3+tempc*1.5e-3);
/*
  fprintf(stderr,"REFRW: dewpt=%f\n",dewpt);
*/
  x = dewpt;
  pp = p[0];
  for (i=1; i<5; i++) {
    pp += x*p[i];
    x += dewpt;
  }
/*
  fprintf(stderr,"REFRW: tempk,cvt,pp,sn=%f %f %f %f\n",tempk,cvt,pp,sn);
*/
  tempk = tempc + 273.0;
  sn = 77.6*(pres+(4810.0*cvt*pp)/tempk)/tempk;

/* Compute refraction at elevation
*/
/*
  fprintf(stderr,"REFRW: el,b,c= %f %f %f\n",el,b,c);
*/
  aphi = a/pow((el+b),c);
  ang = (90-el)*DEG2RAD;
  dele = -d/pow((el+e),f);
  bphi = g*(sin(ang)/cos(ang)+dele);
  if (el < 0.01) bphi = g*(1.0+dele);
  return (bphi*sn-aphi)*DEG2RAD;

}