a) 2. Geometric Leveling

The geometric leveling is based on the difference of readings in vertical sights graduates. The precision obtained is quite large, of the order of millimeters in the works of first order, up to only a few centimeters in common topographical. In general, the instruments used in geometric leveling are called levels. They are also used in leveling operations, associated with levels, the sights. The purpose of the levels is to provide a horizontal plane for topographical operations. The center wire of the telescope reticle defines a horizontal reference plane. The levels can be optical, digital and laser (figure 1).

Figure 1

Auto Level        -        Digital Level        -        Laser Transmitter

The optical level is the classic leveling equipment. It basically consists of a telescope mounted on a tripod, with possibility of being leveled with precision, through hot bolts and bubbles. The accuracy of this equipment depends on the leveling system, the sensitivity of the bubbles and the precision of the sights. Some optical levels have an automatic compensator or leveler, which allows the automated horizontal positioning in fractions of a second, provided that the "Coarse" is within the tolerance range.

The working principle of a digital level is one-dimensional processing of images, from a barcode-coded scope. The coded aim reading is made by means of a network of optical sensors, which recognizes the coding of an image correlation process between the image of the sights and a standard image recorded in the instrument memory. In terms of accuracy, electronic levels have accuracies varying from 0.4 mm to 0.9 mm in double leveling and with a view to invar. 

Laser levels consist of a type of equipment designed to horizontal planes, vertical or with a certain inclination. They are composed of two units: the unit, which is an apparatus emitting a laser beam passing through a rotating prism thus defining a horizontal plane materialized by the radiation; and the detecting unit, which can be attached to a beacon and moved up and down, with relation to the previously materialized plan. The laser beam strikes vertically in a prism pentagonal and after two reflections on the faces, emerges in the horizontal direction. The horizontality equipment is a critical condition for proper operation and is usually achieved by one of three methods: usually with three tubular level screwing screws; through an optical compensator based on the effect of gravity on an internal pendulum or an electronic compensator. It has a range of up to 450 m, with a precision of 1 mm for distances of up to 100 m, and 3 mm for longer distances, depending on the brands and models.

The sights are wooden or metal rulers used in leveling for determination vertical distances, measured between the projection of the trace of the horizontal reticle of the dumpy level and the spot where the crosshair is installed. The most commonly used sights are the "talking sights". These have a length of 4 meters, being graded in centimeters. Centimeters are painted alternately in black and white, the numbered decimeters in black and meters marked by circles painted in black or red.

The sights are usually docking. They are made up of three parts, to be placed the first part into the second and these two then finally into the third. A spring device fixes one piece on the other when the sight is completely distended, so that the graduation of one is the continuation of another. There are direct graduation and indirect graduation reading with direct or indirect image bezel instruments, respectively.

Simple Geometric Leveling

Simple Geometric Leveling is one in which from a single station of the level it is possible to aim the sight placed successively on all points of the terrain to level. Thus, considering Fig. 2, wishing to determine the difference in level between points A and B, the level shall be installed in any position on the ground, preferably equidistant from the points to be level. The reading of the crosshairs at A and B is determined. Between A and B will be calculated by the difference between the readings processed at points A and B. In the geometric leveling, the profile of the terrain to be studied is 10 meters or 20 meters in 20 meters, depending on the nature of the work. Then the level is parked at a convenient point, on the line to level or out of it. From this only position of the instrument the readings on the sights can be set, first in a known quota point and then,  successively, in the other points.

Aimed at the first stake, generally of known quota, it is by convention called of "backsight". All visas from the backsight are called "forward visas". In this way, for each leveling station, one has a reverse view and one or more visas forward. For the calculation of the dimensions of the leveled points it is also necessary to carry out the measurement of the height of the instrument, i.e. the height of the optical axis above the reference plane. To determine the height of the instrument, an initial reading is made at a known dimension point.  For the readings of the survey to have meaning, it is necessary that they are referenced to a plane, called a level reference.

Figure 2

When using the mean sea level, the level reference is equal to zero. When the level is arbitrary, a high initial value is assigned, so that in the course of the survey there are no negative shares. Therefore, there are two rules for leveling:

(i) the height of the instrument (Ai) is equal to the sum of the backsight (RE) with the point (C) where it was made:

Ai = C + RE

(ii) the dimension of a point (C), as a function of the height of the instrument (Ai), is the difference between such height and the forward look (VANTE) read at the same point:

C = Ai-VANTE

See also  #PART 1