## Engineer's Book

————— PHYSICS – SPACE – ALGORITHMICS ——-

## Survey 01 – Survey and Topography

Written By: Jean-Paul Cipria - Sep• 06•17

Topographical Survey by a Theodolite

How Do we Measure Position, Altitude, Range or Distance, Angle, Surface with the Right Accuracy ? How do we Plot it on Earth Plan ? How do we represent object situation on 3D Earth ?

It is Topography !

Complicated but Not Difficult – Bachelord Level

Expériences En Construction

Created :2017-09-06 18:32:12. – Modified : 2018-12-01 18:00:57.

First we have made remarks on Earth form. It is around an ellipsoid. Then we remarked also that Earth have oceans with some ellipsoid form but it exists also mountains.

When we try to know altitude we use local gravitation to determine it. But altitudes with a local Gravitation Measurements are different from a geometrical Ellipsoid concept. We determine the called Geoid with all Altitudes determined by gravitation as we can « see » locally.

Several maps are used by everybody but how to project « real » 3D measurements with Geoid coordinates or geometrical Ellipsoid coordinates on 2D maps ? After those jobs we have to project one or other points on local map with … local horizontal distances and angles !

We can use GIS (Geographic Information System) or SIG (Système d’Information Géographique) for informatic gestion with some différents data bases whose are complex BUT also we need to do the difficult transformations and calculations.

What a difficult job ! Surveyor-Topographer do it !

How does he do ?

# Survey On Site

## Alignements – How do we Implant Transversal Line Marks on House ?

### How to construct a Thales Equivalent Triangle with Landmarks ?

Problem is to made two external holes through a house to insert a line hose. But we need to be aligned by an external reference line. How to mark with 5 centimeters precision two marks on house ?

Marques de Traversée de Bâtiment-2

### How to made Calculation ?

Marques de Traversée de Bâtiment-1

With only landmarks and chain meters, without theodolite, we determinated marks with about 4 cm precision on 10 meters lenght. With 10 positions marks, 15 length measurements with 10 mm standard deviation it is a good measurements. Nth Standard Deviation for 25 measurement with same standard deviation : $\sigma_N=\sqrt{25*(10)^2}=50 mm$. « Nous sommes dans les clous ! » as said French Surveyors (we are still on the tracks !).

But we made measurements in very bad condition, without correct nail, and crossing lines with one finger on the floor.

In other conditions global standard deviation for those measurements must be 5 mm by hands and about 1 mm by a theodolite.

## Nivelling – How do we Measure Altitude ?

Following 17/09/2017.

# Why do we use a Geoid determined by Gravitation ?

## What is a Geoid ?

### Is it a terrestrial Reference Surface ?

A geoid is a closed surface where it is defined by equipotential gravitation. Then this surface is very close to the ocean surfaces but not around abyssal or mountains.

### Raving Rabbids Earth ?

Raving Rabbids Earth ?

😉

## How do we consider Zero Altitude Reference ?

In abyssal matter and mass average are less important than mountains then gravitation is smaller at the same position. The isosurface tends to go down in earth. In mountains there are a greater mass then gravitation is more important and isosurface go upper in earth. « You are more heavy » then surface with a smaller gravitation seems to be up to you. You are smaller in altitude in relation to ocean altitude !

Altitudes Geoid – ©Jean-Paul Cipria 2017

First it is a great surprise that altitude is smaller in mountains than in ocean. But also you have ensured that verticality is correct even if we must correct it with corriolis acceleration if object are mobile or applicate local gravitation deviation in relation to rotation rate acceleration.

We can mesure and follow changes on gravitation potential as what we want and then we can calculate the right geoid surface which follow the real field. It is not so as proportional as a spherical surface but we can calculate after measurement the right surface and the right altitude « connected » by Newton law to quantity of matter. Quantity of matter is fondamental concept in science, physics and then in survey-topography.

It is what a scientist want and also a professional survey-topographer to have a correct reference surface calculated by average real measurements.

Yes, it do. Geoid is a Terrestrial Reference for Altitude.

## What about Precision if we use GPS Height instead of Reference Altitudes ?

As we can discovered it by the Geoid definition … Altitudes are defined in Geoid terrestrial reference then … the « Height » calculated by GPS is not a terrestrial altitude. We keeps this word « Height » for GPS which is different for some meters than referenced Geoid word « Altitude ». Survey-Topographers don’t use GPS height for levelling but they use Geoid Altitude.

If we use GPS « Height » without making correct topographer measurements then we have got a standard deviation about 0.07 m or 7 cm. We can then rectify « Height » to « Altitude » by a calculation translation « Référence Altimétrique Française 2009 (RAF09) » for local fields in France but we remains with … 7 cm standard deviation. If we made professional measurements we got about 0.006 m or 6 mm or less to 1 mm with high accuracy equipments.. Then we have more than ten times precision with geometrical angles differences and Altitude References than one shot GPS measurements.

## What about True Altimetry Definition ?

Altimetry is the measurement of the height above ground or above mean sea level of a geographical feature ? False or true ? This definition is False !

Correct definition :

Altimetry is the measurement of the height above gravitationnal iso-level on local position on earth.

In local France surface the Geodesic System Reference is : « Réseaux Géodésique Français 1993 » or RGF-1993 or « French Geodesic Network » traducted in English.

We defined Earth (X,Y,Z) coordinates near from Earth Mass Center. The coordinates (X, Y) are situated in Equator plane. coordinate Z is near by the Earth rotate axe (South-North).

## Example of Levelling Reference in France

### IGN Data Sheet for Chapelle Sainte Hélène – Draveil France.

Levelling Reference – Repère de Nivellement. IGN Reference.

We can see « 57.984 m Altitude Normale » as different from the old ocean average from 1969 measurements. Then this « Normal Altitude » is a reference with Gravitation measurement and not with ocean altitude variations since 1969. The 0 m reference Normal Altitude is situated « Marégraphe de Marseille – France » upper the « old » 1969 « Mediterranean Average Level ».

### Levelling Marks

Repère de Nivellement – D.K3-218-326106 – Macaron – Seen 15/09/2017

# Why do we use an Ellipsoid determinated by Geometry ?

## What is a Celest Reference ?

Following 06/09/2017

## What is a Ellipsoid ?

Following 06/09/2017

# How do we construct Plane surface From Earth ?

## Why we use horizontal distance on map ?

We need for a lot of practical applications to use plane plans or maps. But all coordinates are in three dimensions on differents 2D surfaces expanded on … 3D dimensions Space : « C’est là que le bât blesse ! » Aye, there’s the rub! Then plans and maps can’t display correctly objets relations as Positions, Distances, Angles, Altitudes, Surfaces, on a 2D plane surface. But we reduce errors on it and we succeed to do it with some special « Projections ». Each projection have advantages and disadvantages. As professionnal we can use technical and mathematical algorithmes to change Projection types and contexts to reduce errors under accepted tolerances. Then our work is with under control when all errors are under accepted tolerances.

Règles Kutch to read directly distances on maps.

Following 17/09/2017.

## How are Distances on Plans or Map ?

Following 13/09/2017.

# References

## Scientifics

• [CIPRIA-Survey-2017] : Jean-Paul Cipria – « Etudes et Pratiques de Géomètre-Topographe. » 09/2017.
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## Technologies

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Jean-Paul Cipria
06/09/2017

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