## Improving the Theory of Heights in Geodesy

Transactions of IAA RAS, issue 68, 36–42 (2024)

**DOI**: 10.32876/ApplAstron.68.36-42

**Keywords**:
geoid, systems altitude, normal altitude, altitude above sea level, coordinate line, power line, geoid search method

### Abstract

The problem in geodesy that has not been solved yet is the development of an international elevation system, which is essentially a system of potential differences, the transformation of which gives a linear measure of the elevation system used in high-precision leveling (orthometric, normal or dynamic). Since in practice different countries use different height systems (e. g. orthometric — in Western countries and normal — in CIS countries) when implementing a general elevation system, there is a need to select the most appropriate one. For an informed choice, it is necessary to develop a system of criteria, perform control calculations, and compare their results, and thereby identifying the most suitable system. Such calculations can be carried out by resorting to physical modeling using mathematical tools (MATLAB). The important thing here is to design an adequate physical model, on the example of which the test will be performed. A special role is played by the initial definitions, and a clear separation of the elements of the real and normal fields, since they significantly affect the type of height. The numerical results obtained on the physical model allowed us to prove that normal heights have much more advantages over to the orthometric ones. The most important of them has been known for a long time to be the rigor of calculating the normal height, which the orthometric one is lacking. The normal height can be viewed as a segment of three lines: normal, coordinate and force. Along the way, a method for calculating the normal height as the length of a coordinate line in a spheroidal coordinate system has been obtained. The established advantages of normal heights allow it to be used as a working height system in the international system.

### Citation

`S. S. Rakhmonov, V. V. Popadyev. Improving the Theory of Heights in Geodesy // Transactions of IAA RAS. — 2024. — Issue 68. — P. 36–42.`

```
@article{rakhmonov2024,
abstract = {The problem in geodesy that has not been solved yet is the development of an international elevation system, which is essentially a system of potential differences, the transformation of which gives a linear measure of the elevation system used in high-precision leveling (orthometric, normal or dynamic). Since in practice different countries use different height systems (e. g. orthometric — in Western countries and normal — in CIS countries) when implementing a general elevation system, there is a need to select the most appropriate one. For an informed choice, it is necessary to develop a system of criteria, perform control calculations, and compare their results, and thereby identifying the most suitable system. Such calculations can be carried out by resorting to physical modeling using mathematical tools (MATLAB). The important thing here is to design an adequate physical model, on the example of which the test will be performed. A special role is played by the initial definitions, and a clear separation of the elements of the real and normal fields, since they significantly affect the type of height.
The numerical results obtained on the physical model allowed us to prove that normal heights have much more advantages over to the orthometric ones. The most important of them has been known for a long time to be the rigor of calculating the normal height, which the orthometric one is lacking. The normal height can be viewed as a segment of three lines: normal, coordinate and force. Along the way, a method for calculating the normal height as the length of a coordinate line in a spheroidal coordinate system has been obtained. The established advantages of normal heights allow it to be used as a working height system in the international system.},
author = {S.~S. Rakhmonov and V.~V. Popadyev},
doi = {10.32876/ApplAstron.68.36-42},
issue = {68},
journal = {Transactions of IAA RAS},
keyword = {geoid, systems altitude, normal altitude, altitude above sea level, coordinate line, power line, geoid search method},
pages = {36--42},
title = {Improving the Theory of Heights in Geodesy},
url = {http://iaaras.ru/en/library/paper/2176/},
year = {2024}
}
```

```
TY - JOUR
TI - Improving the Theory of Heights in Geodesy
AU - Rakhmonov, S. S.
AU - Popadyev, V. V.
PY - 2024
T2 - Transactions of IAA RAS
IS - 68
SP - 36
AB - The problem in geodesy that has not been solved yet is the
development of an international elevation system, which is
essentially a system of potential differences, the transformation of
which gives a linear measure of the elevation system used in high-
precision leveling (orthometric, normal or dynamic). Since in
practice different countries use different height systems (e. g.
orthometric — in Western countries and normal — in CIS countries)
when implementing a general elevation system, there is a need to
select the most appropriate one. For an informed choice, it is
necessary to develop a system of criteria, perform control
calculations, and compare their results, and thereby identifying the
most suitable system. Such calculations can be carried out by
resorting to physical modeling using mathematical tools (MATLAB). The
important thing here is to design an adequate physical model, on the
example of which the test will be performed. A special role is played
by the initial definitions, and a clear separation of the elements of
the real and normal fields, since they significantly affect the type
of height. The numerical results obtained on the physical model
allowed us to prove that normal heights have much more advantages
over to the orthometric ones. The most important of them has been
known for a long time to be the rigor of calculating the normal
height, which the orthometric one is lacking. The normal height can
be viewed as a segment of three lines: normal, coordinate and force.
Along the way, a method for calculating the normal height as the
length of a coordinate line in a spheroidal coordinate system has
been obtained. The established advantages of normal heights allow it
to be used as a working height system in the international system.
DO - 10.32876/ApplAstron.68.36-42
UR - http://iaaras.ru/en/library/paper/2176/
ER -
```