# Applied Geodesy. Self-measurement with tape measure, pegs and wit

## Recommendation points

Undoubtedly, any work must be performed by qualified professionals. The result of their activities will meet all the requirements of the legislation and can be an argument in court when resolving controversial issues. But what if there is no opportunity to attract specialists, but you really want to get high-quality material? Then, armed with the knowledge of previous articles in the Applied Geodesy cycle, devoted to the basic concepts of geodetic work and the equipment used, we will try to independently perform some basic geodetic work.

So, we need to choose a place for the construction of the proposed house, for example, in a summer cottage. To do this, we will make a topographic survey for horizontal planning of the territory in order to level the construction site, after which we will split the axes of the foundation of the future structure. In the absence of specialized equipment, our tools will be things that any more or less caring owner will have in the pantry..

## Site measurements

Ideally, if the plot were rectangular, this would not be difficult, but usually plots in summer cottages can have rather bizarre configurations..

Let’s try to perform our manipulations on the example of the area indicated on the map in green. First of all, we need to imagine what we are dealing with, i.e. we need to get the actual size of the land plot and its area in order to correctly plan the location of the future house. To do this, arm yourself with a tape measure, writing paper, pencil and patience. It is quite obvious that the longer the tape measure, the better, so make sure you buy at least a 20-meter tape beforehand, it will still come in handy for our alignment work..

We sequentially measure all the lengths of the section, entering the obtained values ​​into a previously drawn diagram. Since our site is of an irregular shape, it is advisable to measure at least one diagonal, after pulling a nylon thread between the corners of the site, so as not to go astray when measuring.

## Drawing a parcel to the plan scale

As we can see, the configuration is far from the ideal form, which would simplify our task. We will arm ourselves with graph paper, at worst a piece of paper from a school notebook will do. At this stage, we need to imagine what a “scale” is, and how to use it.

Scale is the ratio of a line on a plan to its dimensions in nature. A scale of 1: 1 (one to one) indicates that, for example, the part is shown in the drawing in full size. To detail small elements, use the magnification scale, for example, a 2: 1 scale value indicates that the image in the drawing is doubled in relation to the original.

Since land plots have a significant length, it is customary to depict them on a scale of reduction, starting from 1: 500. This ratio suggests that one centimeter of the plan corresponds to 500 centimeters or 5 meters on the ground. It is customary to depict plans of quarters on a scale of 1: 2000, a city from 1: 5000, but the map of the region fits well in the glove compartment of a car, depicted on a scale of 1: 1,000,000 and smaller. Accordingly, a scale of 1: 1000 is considered a larger scale than 1:10 000, since the terrain is drawn in more detail on cartographic materials of this scale..

In our case, it makes no sense to bind to the standard values ​​of scales, the main thing is that it is convenient for you to work with the plan. The drawing of the site, which we have taken as an example, fits well on a sheet of graph paper at a scale of 1: 200, so in order to depict a line on the drawing, the length of which on the ground is 64.19 m, we need to put a piece of paper with a length of 32 , 1 cm. If the size of the sheet allows, you can draw an area at a scale of 1: 100, then the same side would have a length of 64.2 cm, which increases the accuracy of subsequent calculations, but does not add convenience in working with the map. So in each specific case, based on the size of the site, select the scale with which it will be convenient for you to work.

Let’s choose the base side, i.e. side, parallel to which construction will be carried out. In general, it is better to take the longest side of the section as the basis, so we will do so, unless, of course, you are an apologist of Feng Shui. To obtain a large-scale site plan, you must perform the following steps:

1. Parallel to the millimeter grid, draw the base line “A-B”.
2. With a compass we draw an arc from the vertex “A”, the radius of which is equal to the length of the front side of the section “A-G”.
3. Similarly, we draw an arc, the radius that corresponds to the length of the back side of the section from the top “B-C”.
4. With a compass we draw an arc equal to the measured diagonal of the section from the vertex “A” to the intersection with the arc No. 3, we get point “B” – the starting point for our last side.
5. From the vertex “B” draw an arc equal to the length of the last side to the intersection with the arc No. 2, we get the point “G”.
6. Connecting points “B”, “C” and “D” by segments, we obtain a large-scale closed polygon “A-B-V-D”, corresponding to the configuration of the site on the ground.

## Plot area calculation

As many remember from the school geometry course, the length of the rectangle multiplied by its width gives us the area of ​​the figure. Since we are dealing with a not quite regular rectangle, we calculate its area using the method of reducing areas to simple geometric shapes – a square and a right-angled triangle.

We have drawn our site to scale, and we know what the area of ​​one square of the millimeter grid is. Therefore, it remains to count the number of whole squares, multiplying them by the area of ​​one square, plus calculate the areas of incomplete squares as the total area of ​​its constituent figures – right triangles and squares.

At the end of our calculations, we get the area of ​​our site. This area includes a number of errors in measurements and graphical measurements from graph paper, therefore, armed with a piece of paper with the calculation of areas, you should not chase with it a neighbor in a cooperative with the words “where is my land?” This piece of paper and the diagram will be useful to us for the following actions, namely for shooting the terrain and breaking down the axes of the future house. Since we were calculating in meters, then we will get the area in square meters. Summer residents use the popular term “weaving”, but for cartographic work, the concept of a hectare is used. One hectare is the area of ​​a square with a side of 100 m. Accordingly, a weaving is a square with a side of 10 meters. Therefore, 1 hectare = 100 ares = 10,000 square meters.

## The simplest do-it-yourself topographic survey

Based on this example, we will try to understand the principle of performing a topographic survey. A point on the terrain is described by three parameters: the spatial position relative to the X, Y coordinate system (where X is the direction to the north, Y is the east direction) and the altitude parameter Z. By connecting the survey points on the plane, we get a plan of the land plot, and the Z coordinate allows us to describe the terrain, which is the ultimate goal of our work.

Relief is a set of land irregularities, which, as we can observe, consists of various elements – mountains, lowlands, flat spaces, the bottom of water bodies, etc. Lines on the map that connect points with the same height are called contour lines. These lines, in combination with elevation marks and special conventional signs, display the terrain on cartographic materials..

To perform this type of work and apply the obtained values ​​to the plan of our site, we need:

• wooden stakes at least 60 mm long
• flat board 4-5 m long
• carpentry level
• hammer, nails, sledgehammer

Having decided on the construction site, we perform the following actions:

• along the perimeter of the proposed construction or in any arbitrary part of the site, we mark the directions along which the work will be carried out;
• visually select the highest shooting point, and hammer the first peg with a sledgehammer so that its height above ground level is at least 20 cm;
• we hammer in the remaining pegs along the planned axes of the shooting, the distance between them should be no more than the length of your board, and the height above ground level should not be less than the height of the first peg. If you drive the pegs at distances equal to the length of the board, you will not have to additionally measure the distances between them;
• We put a wooden board on the ground near the first peg, attach it to the peg with a nail, then make a pencil notch on the second peg at the level. We passed the elevation of the ground from the first peg to the second;
• we repeat the actions on the second peg, only in this case the bottom of the board is attached to the mark that we marked with a pencil, and a notch is made on the third peg. These steps are repeated for all survey points;
• armed with the plan we created, we take measurements between the pegs and measure the distances from the serifs on the pegs to ground level, fixing everything on the diagram to scale.

So, we got the elevation plan relative to the highest point of the site. If we somehow did not guess the highest point, it doesn’t matter, we just get the excess with the opposite sign. For the convenience of calculations, we take “zero” of our site for a whole positive value, for example 10 meters (it is unlikely that you will have large elevation differences on the site). We begin to sequentially subtract (or add) the values ​​of the excess at each of the points, and apply them to the diagram as a numerical value.

From the provided section along the survey axes, it can be seen that not always equal distances between survey points provide an accurate description of the relief. In this case, we may need to additionally apply a couple of points in the characteristic places of the relief to increase the overall accuracy of the work. This is the principle of topography – describe the terrain with the required number of pickets at approximately equal distances, plus add picketage in places that “fall out” of the overall picture.

Now we will draw horizontal lines on our object, for which we begin to look for points on the plan with the same height in order to connect them with a smooth line, and with horror for ourselves we find that we simply do not have such points! Don’t panic, friends, school knowledge will save us again, this time from the field of mathematics. We will use the interpolation method, i.e. we obtain intermediate values ​​from the set of known.

Knowing the values ​​of the heights at the extreme points, we can assume how the height of the terrain will change in proportion to the distance between the survey points..

It is customary to draw the horizontal lines at standard intervals depending on the terrain and the scale of the plan, but in our case we can draw the horizontal lines with any step for clarity. Since the height difference in the section is 10.00 – 9.45 = 0.55 m, it makes sense to draw these lines every 10 centimeters in height.

As a result, we will receive a topographic plan of the area, which will serve as the basis for future construction or site planning. The arrows in the drawing show the directions of water flow..

## Stake out the axes of the house

After determining the location of the future house, we need to fix the construction axes. It is most aesthetically pleasing to build a house parallel to the longest side of the site, unless otherwise stipulated by the building rules in your summer cottage cooperative.

1. On the side parallel to which the construction will be carried out, we sequentially measure the distances 0-1 and 1-2 with a tape measure according to the diagram, fix points “1” and “2” with wooden pegs.
2. Knowing at what distance the wall of our house A-B will be from the base side, we calculate the diagonals of the rectangle 2-A and 1-B, then we lay them on the ground using the method of serifs with a tape measure. The intersection of arcs 1-A and 2-A on the ground will give us point “A” of the first corner of the house, we fix it with a peg.
3. Similarly, we postpone point “B” and as a result we get the line AB, parallel to the base line.
4. With the same serif principle, we fix the remaining points of the corners of the building “B” and “D”.

As a result, we have a fixed rectangle corresponding to the boundaries of our future home. To make sure that you have set out the corners of the house correctly, measure again the sides of the rectangle and any of the diagonals to compare the obtained values ​​with theoretical.

When digging a foundation pit, the pegs fixing the corners of the house may be lost, so they must be “removed” from the boundaries of the earthworks by several meters. Let’s use a similar method of obtaining points on the ground using linear serifs. Having estimated how far it is possible to move the points outside the pit, we calculate the diagonals and get the following picture:

We used points “1” and “2” and additionally set out points 3–8 using the linear serif method using a tape measure. During construction work, the intersection of a stretched nylon thread between points 1-6, 2-7, 3-4 and 5-8 will give us the center lines of the foundation of the future house.

In general, a right angle on the ground can be built as follows:

• measure a 3 m segment on the baseline
• from the end of the segment with a tape measure we make a notch on the ground with a length of 4 m
• from the opposite end of the segment we make a notch 5 m long
• we get a right triangle

Likewise, you can proportionally set aside a right angle on the ground with any side lengths as far as the tape measure will allow. It should be noted that at all stages of measurements, the tape must be kept parallel to the ground without “sagging”, with the maximum tension.

With these simple examples, we examined some of the main types of geodetic work. Any more or less serious construction is not complete without an up-to-date topographic base, and understanding the principle of performing work, you can carry out some of them yourself.

The next article in our series “Applied Geodesy” will be devoted to GPS measurements. In the near future, “space” methods will completely replace “ground” ones, but it is still worth having an idea of ​​the basics of performing elementary operations, because the use of an electronic calculator does not cancel the study of oral counting at school.

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