0:04

Hello, welcome to this part of geometric leveling

where we will address a certain number of definitions,

what is an altitude,

and see the principle of measuring with a level and a rod.

The first definition that we will address is the true altitude;

what is an altitude?

We have seen in the part that deals with Geodesy

the definition of a geoid;

I remind you, the geoid is the reference surface for altitudes,

its a physical surface that depends on the gravitational field.

Then I can draw a topographic surface

and the altitude is the distance measured by the vertical;

if I consider her the point <i>A</i>,

I have my distance here along the vertical

is the altitude of point <i>A</i>, so the orthometric height

or true altitude, is this distance.

If I consider here a point <i>B</i>, I do the same exercise

I have my distance here <i>HB</i> that is the true altitude at this point.

What you should know is that the gravitational field will vary

so we will have here at point <i>A</i> a vector of gravity with its orientation

and at point <i>B</i> I have another vector with its orientation

and the other orientations of these two vectors are not necessarily parallel,

there may be variations in the gravitational field,

thus these variations must be taken into account

to have a rigorous model of the altitudes.

2:05

In the definition of the altimeter system

we have to go back to what we call a fundamental point,

in this case to define this mean sea level

we will use a tide gauge that will be placed on the coastline,

particularly, in this case, in Marseille,

and then we will use a method of measurement,

in this case leveling,

in order to propagate this horizontal reference to the country.

This is what we did for Switzerland, where we went from Marseille,

on a route along the Rhône valley

to finally arrive here in Geneva

4:43

Therefore the first assumption to make our lives simpler,

and this is often the case on construction site operations,

or of the work across a neighborhood or a city,

is that the two surfaces here passing through point <i>A</i> and point <i>B</i>,

so these surface levels, are parallel

because we made an assumption that the gravitational field here is uniform

and that we are on the same vertical.

We speak in this case of usual altitude,

it is what we will use in most topometric work.

The usual altitude, is based on a fundamental point, as we have seen,

it is the point that is attached to the mean sea level,

we have here materialized in Geneva at "Pierre du Niton".

a base point, as a reference, for our Swiss altitude system.

The altitude system consist of, as seen on this map,

this is not the roads but in fact it is the leveling paths

that have been made across the country on the federal level,

so we have here a series of paths with points which are documented

where we find information about the altitude.

We talk here of an altimetric network.

6:04

The reference frame was defined early in the twentieth century, in 1902,

and it is called the Federal leveling, NF02,

and it is effectively connected to this "Pierre du Niton"

as a horizontal reference for our country.

I will remind you that it is a non rigorous system,

the gravitational field influence the leveling measurement.

We will stop now for a small quiz

where we will look at two different paths across Switzerland.

We will leave here in Lausanne

7:19

or across the Alps,

is this <i>ΔH</i> equal?

That is the question that is posed in this quiz.

In 1995 Switzerland upgraded its national Geodesy,

in particular a rigorous system was defined for altitudes,

namely the system <i>RAN95</i> which is the new national altimetric network.

It is a rigorous orthometric system,

so the altitude measurements according to the theory of potential gravitational field.

We apply to the raw leveling measurements

the orthometric corrections

and we have now a perfect model for our altitude in Switzerland.

If we now compare the model defined in 1902, <i>NF02</i>,

with this new model,

we have the following map which shows these differences.

We can note in the plateau region,

so here in this area,

I see that the altimetry differences are near zero

or a few centimeters;

in contrast if I go to the Alp region

where the geoid is more disturbed by steeper slopes,

and well, in this case, I see that I may have these differences

between the two models up to 40-50 cm.

So these elements are now documented

and we have a rigorous network of altitudes for Switzerland.

When talking about documentation,

each of the points along the federal and cantonal leveling,

is documented in the records in which

we will find a certain number of information,

namely, identification of the point,

we have its region, we have a number corresponding to the national map,

then you will obviously have the approximate coordinates

to situate the point on a map;

associated with this, you have a photo that can identify this point in the landscape

in this case here, at the foot of a building,

we have an indication of the materialization,

in this case a pin

that was realized by the Federal Office of Topography

and we obviously have the value of the altitude here in the system <i>NF02</i>

with an estimated precision here of 3 millimeters.

We also see in this record

that there are regular updates and the controls here

of these altitude points, which are made by the Federal Office of Topography.

The measuring principle:

to be able to measure with the level,

it is necessary that the line of sight is horizontal.

We remind you here that the spirit level used to calibrate the level,

we have here the guideline;

once the bubble is in the upper portion of the tube,

the tangent in this upper portion here gives the guideline.

If the level is adjusted, this guideline will be parallel to the line of sight

and thus enable us to make measurements on an horizontal plane.

The measures is done on the staff;

the graduations of the staff are as following:

you have first the meters, the decimeters

and then the centimeters that are given here by the small black and white markers.

The millimeter will be estimated by eye with a precision of plus or minus one millimeter.

In this example here, we can say that we have one meter,

we have two decimeters

and we can count the number of centimeters starting from here to here

and we have seven centimeters,

and the estimation of millimeters we give here is about eight millimeters,

so that the height reading is 1,278 meters.

12:02

The measurement principle is as following:

you have the level that is placed here in the middle of the range,

between point <i>A</i> and point <i>B</i>,

on point <i>A</i> we place a vertical rod

we will make a so-called back reading,

then this rod will move with its operator to point <i>B</i>

and we will make a front reading;

here we define a direction of measurement and direction of travel,

that will give an indication of the height difference

+ if we ascend, - if we descend

and height difference is, as we have already shown,

the difference between the back reading and the front reading.

Now if we place it in the context of a path,

we will move on to a known point in altimetry, for example,

and make a series of spans here until reaching the point <i>B</i>

and the sum of these height differences

will give us the difference in elevation between <i>A</i> and <i>B</i> ;

so we have here in the first section a <i>Δh1</i>,

in the second section you have a <i>Δh2</i>, etc.,

to finish at <i>Δhn</i> and terminate at the point <i>B</i>,

and the sum of these differences of level or vertical drops

give the height between point <i>A</i> and point <i>B</i>.

For the field operations of a geometric leveling routing

we generally use the following formula

where we see the different points

with the back readings and the front readings,

that we have here in a first span,

and we will directly calculate the difference in level with its sign,

it helps the along a path

to sum these differences of level positive and negative

and finally have the height difference along this section of the path.

To summarize this part dedicated to geometric leveling

we have seen a certain number of definitions of altitudes:

the usual altitudes, orthometric altitudes,

so an update of our system

that takes into account the gravitational field,

and we have seen the principles with the description of the level,

the description of the staff on which we make a reading

and the principle of the path.

I invite you to see

the different videos shot on location

that illustrate and complete these theoretical principles.