49 50 Ver6.09.hp Geodesic distance & Earth Euclidean distance calculator, bearing

[Gil]

For HP49-HP50, programs basically to calculate exact distances (error less than 0.5 mm) on the Earth surface at theorical sea level

Present Version 3.2 "corrects" my previous reasoning for approximated real distance above sea level (altitudes h1 & h2).

Explanation
From the two points P1 & P2, I calculate a first "possible" angle (mean.thets) between them, then a mean radius (=s/mean.theta), considering the ellipsoid to be a sphere.

I calculate also radii R.1 & R.2 from Earth centre to point P1 and to P2 (with program lat—>R), then I build a second mean radius.2= (R1+R2)/2.

From those two mean radii (meanR12), I have to consider a new, mean, greater radius at altitude (h1+h2)/2.

In other words,
s.h (distance between points P1 & P2 at altitude h1 & h2) =s (original distance at sea level)
× [meanR12+ (h1+h2)/2]/meanR12.

The new code for that latter program:
h—>s.h
\<< "Before, run

P1P2\->D
 or 
P1\->P2
.

2 methods \-> 2 Results
as a complex#" DROP "Rough 
approximation!
" UNROT 'h2' STO 'h1' STO STD RAD \pi 2 / lat1 D\->RAD - SIN \pi 2 / lat2 D\->RAD - SIN * lon1 D\->RAD lon2 D\->RAD - COS * \pi 2 / lat1 D\->RAD - COS \pi 2 / lat2 D\->RAD - COS * + \->NUM ACOS s SWAP / lat1 lat\->R DROP lat2 lat\->R DROP + 2 / 2 \->LIST '\GmR12' STO 1 2
FOR i \GmR12 i GET DUP h1 h2 + 2 / + SWAP / s *
NEXT R\->C DUP 's.h' STO "s(" h1 + "/" + h2 + ")" + \->TAG s "s(0,0)" \->TAG SWAP s.h s s R\->C - DUP '\GDs.h' STO "\GDs.h[m]" \->TAG
\>>

Copy the file-directory ending by .doc.

Inside are the five user programs :
A) Four very accurate programs
1) C.abh (to calibrate first your ellipsoid)
2) P1P2—> (indirect method/problem, to find the distance)
3) P1—>P2 (direct method/problem, to find point P2) )
4) lat—>
(gives
- distance from Earth centre to latitude at sea level
- & Earth circumference along that latitude)

B) Essay to give an "idea" of the "real", effective distance above sea level.
No real maths or geodesic, scentifical consideration.
Just a possible approximation to give a rough idea of the difference when calculating very "accurately", but only at Earth sea level.
5) h—>s.h.

Observations or commentaries welcome.

Regards,
Gil