CHAPTER I.
BASIC CONCEPTS.
§7. DRAWING A STRAIGHT LINE ON THE EARTH'S SURFACE.
For hanging, that is, drawing straight lines on the ground, poles are used.
Milestones are stakes, pointed on one side. Typically, poles are 1 1/2 - 2 m long. For better visibility, poles are painted in two colors (most often red and white).
The word “hanging” was formed from the word “milestone”.
If you need to draw a straight line between two points A and B, the position of which is given, then first milestones are placed at these points; then an intermediate pole C is installed between them so that poles A and C cover pole B (Fig. 31).
If the distance from point A to point B is large, then you have to place more poles between points A and C and between C and B. In general, when hanging a straight line on a flat surface of the earth, it is necessary that the distance between the poles be from 50 to 100 m, and on hilly from 10 to 50 m.
Sometimes it is necessary to hang a straight line, the direction of which is specified by two poles placed at points A and B. In this case, the straight line continues in the desired direction beyond pole B so that the next pole C is covered by poles A and B (Fig. 32).
Then the next milestones are placed so that they are covered by the two previously placed milestones.
It is necessary that all milestones stand vertically. The correct vertical direction is checked using a plumb line. A plumb line is a cord with a small weight at the end (Fig. 33).
Exercises.
1. Draw a segment and divide it using a scale ruler into 2 equal parts (3, 4, 5, 8, 10 equal parts).
2. Draw a segment and approximately divide it using a compass into 2 equal parts (3, 5, 8 equal parts).
3. How many total segments are there in the drawing? 34? 35 on the drawing?
Slide 2
At school we study geometric constructions in some detail using compasses and rulers and solve many problems. How to solve the same problems on the ground? After all, it is impossible to imagine such a huge compass that could outline the circumference of a school stadium or a ruler for marking park paths.
Slide 3
Knowledge of geometry and the ability to apply this knowledge in practice is useful in any profession. Traditionally, construction on the ground is carried out to take a plan of the land plot and to lay the foundations. However, such knowledge is often needed in other areas of activity.
Slide 4
You might think that working on the ground is no different from working with a compass and ruler on ordinary paper. But that's not true. On the ground, the distances between points are quite large and there are no rulers or compasses that could help us. And in general it is difficult to draw any lines on the ground. Thus, constructions on the ground, based on geometric laws, have their own specifics.
Slide 5
Specifics
Firstly, all straight lines are not drawn on the ground, but are laid, that is, a fairly dense network of points is marked on them, for example, with pegs. Typically, laying straight lines on the ground is called hanging straight lines.
Slide 6
Secondly, it is prohibited to draw any arcs during construction. Therefore, we actually do not have a compass. All that remains of the compass is the ability to plot specific distances on given (laid) straight lines, which should be specified not numerically, but using two points, already marked with pegs, somewhere on the ground. The distances themselves will be measured by steps, feet, fingers, or any objects suitable for this purpose.
Slide 7
To ensure that the pole stands straight, use a plumb line (some kind of weight suspended on a thread). A series of stakes driven into the ground marks a straight line segment on the ground. In the chosen direction, place two milestones at a distance from each other, with other milestones between them, so that when looking through one, the others are covered by each other.
Slide 8
Milestone -
a vertical straight pole, which is used to mark a point on the ground, has a length of about 2 m; pointed at one end so that it can be stuck into the ground
The purpose of hanging is to make the segment AB visible on the site. This is done by marking the starting point A and the ending point B using alignment poles. They must be visible from one observer's station. When hanging, a distinction is made between installing intermediate points, lengthening a segment, hanging on both sides, and determining the point of intersection of two straight lines.
SETTING INTERMEDIATE POINTS
is necessary when it is necessary to sufficiently mark long sections or when it is necessary to mark certain points, for example the corners of a building. Installation of intermediate points on a straight line is usually carried out by one observer and one assistant. The observer stands a few steps from the first pole and sets the direction of view to the end pole of the target.
The assistant stands next to the line being hung without entering it. He faces the observer, holding the intermediate pole vertically between his fingers. The approach of the pole to the target is made by short movements according to the words of the observer (for short segments) or according to the signs of the observer (for long segments). After installing the pole, check its verticality using a plumb line or level. Finally, the observer controls the target, and if necessary, the position of the pole can be changed by repeated instructions. When hanging many intermediate points, the poles furthest from the observer should be installed first.
Hanging through a hill that obstructs visibility EXTENDING A LEG AB, for example from Ado C, should be done by no more than half its length, since beyond this, sufficient accuracy can only be ensured with the help of appropriate optical instruments. To do this, one person is enough to stand with pole C on the extension of segment AB and, using self-adjustment, insert the pole, set it vertically and control the work.
DOUBLE HANGING (centre hanging) requires two observers. This method is used when visibility is limited at both ends, such as by construction, or when both ends of a segment are not visible, such as in mountainous areas. In this case, both observers take aim at the target through the auxiliary points. Observer 1 places his pole C outside target AB and directs observer 2 with pole D to target CA. After this, observer 2 directs observer 1 with pole C to target D "B. This double-sided hanging continues until the deviations on both sides disappear and poles C and D stand on straight AB.
To determine the POINT OF INTERSECTION OF TWO STRAIGHTS on the site, as a rule, it is not
two observers and one assistant go around. In this case, both observers take turns directing the assistant standing in the center to the targets of their lines. The intersection point S will be found when it is located on both line AB and line CD.
The video lesson “Setting a straight line on the ground” is a visual aid that makes it easier to explain to students the solution to the problem of drawing a straight line on the ground and develops the ability to make correct constructions when solving graphic problems. This topic is an important stage for the future development of skills in solving problems graphically, as well as for the ability to make constructions using mathematical rules.
Presenting this material in the form of a video tutorial makes it possible to display the process of constructing without distortion, using perfect visual tools. This method is devoid of disadvantages that may appear when constructing on a board - the image is clear, open, and understandable. Accompanying graphics with a story about the rules of construction does not require additional explanations from the teacher - this is a full-fledged teaching aid for the student to develop this skill. With this manual, carrying out a practical solution to a problem does not require additional special tools in order to demonstrate the process of using the method and form the student’s understanding of it. An animated image makes it possible to track the structured process of solving a graphic problem, forming a deep understanding of the subject by the student.
The video lesson begins with the formulation of a problem that often accompanies graphic constructions - it is necessary to construct a segment longer than the existing ruler. What follows is a step-by-step description of the construction process.
- The ruler is located in the leftmost position on the sheet.
- With its help, extreme points A and B are marked, which are part of the required segment.
- Using a ruler, mark a point located between points A and B - point C.
- The ruler moves to the right so that its left end is located under point C.
- Point D is marked, corresponding to the position of the right end of the ruler, while point B lies between points C and D. It is indicated that all constructed points belong to the same straight line.
- Points A and B are connected to each other, forming part of the segment being built.
- The segment AB is supplemented by the construction of the segment BD, which in total will constitute the required solution to the problem.
It is further indicated that the theoretical material studied in the first part of the video lesson is important for solving many practical problems. Thus, this topic emphasizes the practical value of the material being studied. The knowledge gained is extrapolated to solve problems on the ground. With the help of an animated image, the problem of staking out terrain is formulated when it is necessary to draw long straight lines. The figure shows the installation of milestones on the ground in such a way that each next one covers the previous milestones when looking at them in one straight line. The concept of a geometric method for solving problems on the ground is formed. The video lesson ends by introducing students to the areas of application of the acquired knowledge. They will be interested to know that the skills they acquire are used in modern engineering, in the construction of roads, and the laying of power lines.
The video lesson “Setting a straight line on the ground” can be used by a teacher to explain new material on this topic, since it contains a detailed and visual description of the construction method being studied. Also, this video lesson can help a student master the material during distance learning, and will also be useful when studying the material on his own.
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Slide captions:
Hanging a straight line on the ground The presentation was prepared by Petrova Valentina Vladimirovna, teacher of the MBOU "Gorkovskaya Secondary School"
Once upon a time, a long time ago, people were faced with a task: using a ruler to construct a segment longer than the ruler. Think about how you would do this? A C B D Let's see how people solved this question many years ago
One of the techniques for “carrying out” long sections of straight lines on the ground is hanging the straight line. For this purpose, two poles about 2 meters long are used, pointed at one end so that they can be stuck into the ground.
It is necessary that all milestones stand vertically. The correct vertical direction is checked using a plumb line. A plumb line is a cord with a small weight at the end.
For better visibility, the milestones are painted in two colors, most often red and white.
C B A To draw a straight line on the ground, first mark some points A and B. For this, two milestones are used. The third milestone (C) is placed so that the poles standing at points A and B cover it from the observer located at the point A. The next milestone is placed so that it is covered by the milestones standing at points B and C, etc.
The hanging technique is widely used in practice. Cutting forest clearings.
The hanging technique is widely used in practice when laying high-voltage power lines
The hanging technique is widely used in practice when laying roads
The hanging technique is widely used in practice. Firebreak
The hanging technique is widely used in practice Laying railway tracks
The hanging technique is widely used in practice. Runway lights
Internet resources: Milestones http:// oldskola1.narod.ru/Nikitin/030.gif Plumb http:// www.nne.mrsk-cp.ru/images/stories/company_news/raschistka3.jpg Electric line. transmissions http:// e-kazan.ru/upload/redactor/images/2c04794853fb6e39763a91dd855fb654.jpg Road http:// riavrn.ru/upload/preview/1/9/e/19e4d62513a14e1f5337acc6a8e585ee.jpeg Zh.D. https:// tolmachevo.ru/upload/iblock/010/3.JPG Runway
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