This lesson is about the method of how to change the scale in AutoCAD using the quick calculator utilities.

This method is universal and allows you to determine and change the scale in AutoCAD of any objects, even without knowing their size. This is useful when pasting bitmaps or other underlays.

We will also consider the standard ways to change the scale in AutoCAD and one of the sub-options is the "Reference line".

Suppose we have some kind of drawing of a building reconstruction plan and a scanned image that shows a summary network plan and needs to be inserted into AutoCAD. Next, we need to scale our picture so that the dimensions become true and combine the building in the drawing with the building in the image. Go to the Insert tab, then Attach, in the window that appears, find our picture, click Open and OK. We indicate the insertion point away from our drawing, indicate the scale 1 and press Enter. Done, the picture is inserted, but as we can see it is not the size it should be, so first we will visually enlarge it so that it is convenient to work. Now we need to scale the loaded image in such a way that the building in the picture matches the size of the building in our drawing. To begin with, using the example of an arbitrary object, let's consider how the Scale tool works. Go to the Home tab and in the Editing tools select Scale. Next, select our object, press Enter and select the base point. The base point is the point about which the object will change. Next, on the command line, specify the scale factor, i.e. if we want to increase our object three times, we set 3 accordingly. To reduce the object, let's say ten times, you must specify 0.1 and note that fractional numbers on the command line are entered through a dot , not separated by commas. This is how the Default Scale tool works. Now, in order to find out the scale factor, we need to measure one and the same side of the object in the picture and in the drawing, then divide one size by another. But we will do otherwise. Select the Scale tool, select the image you want to scale and press Enter. For the base point, select absolutely any angle, then click on the right mouse button and select Quick Calculator. And now we can determine the scale factor in a quick calculator. To do this, we select the Distance between two points utility, specify the distance between two points of the source object, then click on the Divide button on the calculator, again select the Distance between two points utility and indicate the distance in the picture corresponding to that indicated in the drawing. Now pressing Enter, we get the scale factor, then Apply and again Enter, ready. And the last thing left to do is to position the building from the drawing to the picture with the correct angle of rotation. So, select the object that we will position, then on the Home tab, on the Edit panel, find and select the Alignment tool. Now, with the left mouse button, we indicate a point on the object that we are positioning and a point on the figure, in the place where we position our object. It will suffice for us to point to three points. Everything is ready, but our object is under the substrate. To send the matte to the back, we need to select it, on the Home tab, on the Editing panel, click the icon and select Send to Back. This is how we scaled our picture and positioned our object on the master plan of networks.

Betuganov Astemir

Project Manager:

Shopagova Alla Sergeevna

Institution:

MKOU "Secondary School No. 27", Nalchik

In the presented research work in mathematics on the topic "Scale and its application" I will try to find out at what scale it will be convenient to place objects on A4 sheet. Working on a research project on scale will help me consolidate my knowledge of mathematics.

In my research project in mathematics "Scale and its application", I will need to refine and compare mathematical calculations with the data obtained.

In the course of my research work in mathematics on the scale and its application, I hope that the scales that I will set will allow me to arrange objects on an A4 landscape sheet.

Also, in the practical part of my work, I will consider and mathematically solve interesting problems for distance and scale.

Introduction
Main part
1. Definition of scale.
2. Solving interesting problems on scale.
findings
Applications.

Introduction

In mathematics lessons in the 6th grade, we went through this interesting topic, from which we learned how, using a scale, you can find the distance on the ground, knowing the length of the segment on the map corresponding to this distance on the ground, and vice versa.

When drawing an image of objects on paper, we are most often forced to change their actual dimensions: large objects have to be depicted in a reduced form, and small objects must be enlarged.

Areas of the earth's surface are depicted on paper in a reduced form. An example of such an image is any map, plan. And small details are depicted in the drawings in an enlarged form.

But a drawing, map or plan should give an idea of ​​the real dimensions of objects. Therefore, a special entry is made on the drawings and maps, showing the ratio of the length of the segment on the map or drawing to its real length.

The topic of my research project in mathematics is “ Scale and its application».

Objective of the project: find out at what scale it will be convenient to place objects on A4 sheet.

Project objectives:

1. consolidate school knowledge in mathematics;
2. clarify whether the mathematical calculations are comparable with the data obtained.

Hypothesis: patterns most effectively draw 1:10, apartment layout 1:100; house passport 1:1000; city ​​map 1:10000; area map 1:100000.

Expected Result: the scales I set will allow you to place objects on the landscape sheet.

Equipment:
ruler, pencil, compass, calculator, map.
sheet A 4, ruler, pencil.

Scale definition

Scale- this is a fraction, where the numerator is one, and the denominator is the number that shows how many times the distance on the terrain is reduced than on the ground.

For example: 1:1000 (one thousandth) means that all distances on the ground are reduced by a thousand times. The larger the number in the denominator of the fraction, the greater the reduction and the greater the coverage of the territory.

• numerical, expressed in numbers 1:1000;
• named, expressed in words, that is, we translate cm into m: in 1cm 10m, 10m is the scale value;
• linear, knowing the scale value, we can determine the distances.

Let's look at the map. At the top is the scale (1:500,000). The map is said to be drawn to a scale of one five hundred thousandth. This means that 1 cm on the map corresponds to 500,000 cm on the ground. This means that a segment on the map of 1 cm corresponds to a segment on the ground of 5 km.

And if I take a segment 3 cm long on the map, then on the ground it will be a segment 15 km long.

I downloaded a map of the Kabardino-Balkarian Republic from the Internet. Map of the republic with a scale of 1:10000, that is, 1 cm 100 meters, and the scale of the surroundings 1:100000 at 1 cm 1 kilometer. I immediately found my native village on it.

So, the scale (German. Maßstab, lit. " measuring stick»: Mass « measure», Stab « stick”) - in general, the ratio of two linear dimensions.

In many areas of practical application scale is the ratio of the size of the image to the size of the depicted object .

The concept of scale is most common in geodesy, cartography and design - the ratio of the natural size of an object to the size of its image.

A person is not able to depict large objects, such as a house, in full size, and therefore, when depicting a large object in a drawing, drawing, layout, and so on, a person reduces the size of the object several times: two, five, ten, one hundred, one thousand, and so on times. The number showing how many times the depicted object is reduced is the scale.

The scale is also used when depicting the microworld. A person cannot depict a living cell, which he examines through a microscope, in full size and therefore increases the size of its image by several times.

The number showing how many times the increase or decrease in a real phenomenon was made when it is depicted, defined as a scale.

Some photographers measure scale as the ratio of the size of an object to the size of its image on paper, screen, or other media.

The correct scaling technique depends on the context in which the image is used.

findings

compared their assumptions put forward in my hypothesis with inscriptions on patterns, maps and technical plans of the house and apartment. It turned out that in some places I was wrong 10 and even 100 times.

• patterns most effectively draw 1:10;
• layout of the apartment 1:100;
• house passport 1:1000;
• city ​​map 1:10000;
• area map 1:100000.

In fact, the plan of the apartment is usually taken on a scale of 1:200; the scale of the maps turned out to be exactly the same as in the original, but they are already located on 6 landscape sheets!

So once again, I am convinced that before assuming, you need to recalculate several times.

Thus, we formed the concept of scale, map, drawing, worked out solving problems for calculating the length of a segment on the ground and on the map.

Solving problems on a scale

Task 1. The distance between the two cities is 400 km. Find the length of the segment connecting these cities on a map drawn at a scale of 1:5000000.

Decision:
400km = 400000m = 40000000cm
40000000: 5000000 = 40: 5 = 8 (cm)

Task 2. Distance from Moscow to St. Petersburg in a straight line is approximately 635 km from center to center. On the highway, the length of the route is 700 km.
By how many times should this distance be reduced so that it can be depicted on a slide as a segment 14 cm long?

Decision:
700km = 700000m = 70000000cm
70000000cm: 14cm=5000000(times)

When going to the forest or hiking, we always take a map with us. It is with its help that tourists determine their location on the ground and pave the route. Naturally, the distances on the maps are not shown in real terms, but on a certain scale.

Step by step instructions on how to determine the scale

Usually the compiler indicates the linear or numerical scale of the drawing or map, with the help of which the distance between objects on the ground is determined. But sometimes the topographic map does not contain this information, and you have to determine the scale yourself. Some knowledge in geography will be useful for this (Figure 1).

In fact, calculating the scale is a simple task if you know how to proceed correctly. Of the tools you will need the card itself and a ruler.

The easiest way to determine the scale is to use a kilometer grid. It is affixed to any map, and the sides of each square correspond to a certain number of kilometers.

Figure 1. Ability to determine the scale - a useful skill for a tourist

You can find out this distance from the captions at the exit of the grid lines to the edges of the map. For example, the caption indicates that the distance between two grid lines is 1 km. Now measure this distance with a ruler. Suppose you got an indicator of 2 cm. Accordingly, each centimeter of the map corresponds to 500 meters on the ground, and the scale of the drawing itself is 1:50000.

The concept and types of scales

To learn how to correctly calculate the scale, it would be useful to familiarize yourself with the very definition of this concept. So, from a scientific point of view, the scale is a certain indicator according to which the length of a segment on a map, plan or topographic survey corresponds to the actual length of the same segment on the ground (Figure 2).

There are several types of scale:

1. Numerical: scale, made in the form of a fraction. In it, the numerator is always one, and the denominator is a number that shows how many times the distance on the map is reduced.
2. Linear: scale for easier orientation. It is a special measuring ruler that is applied to maps to facilitate the calculation of distances on the ground.
3. Cross scale: used for the most accurate measurements. Usually it is engraved on metal rulers, which are called scale rulers.

Figure 2. Mapping usually uses numerical or linear varieties

The simplest is the named or verbal scale. In this case, the map image simply indicates what distance corresponds to 1 cm of the plan (for example, 1 cm 5 km).

Scale Accuracy Options

The scale accuracy in the drawing is limited to a distance of 0.01 cm. The number of meters corresponding to this indicator on the ground is called the definition of “graphic accuracy”.

To find out this indicator, you need to use the degree grid and do some calculations. It is best to use a numerical scale. We take its denominator and divide by 10,000, since 1 cm of the plan contains 10 thousand segments of 0.01 cm each. The resulting number will correspond to the size of the accuracy.

For example, if the map has a scale of 1:25,000, its accuracy on the ground will be 2.5 meters, and for a 1:100,000 scheme, it will be 10 meters, and so on.

Scaling method

At the beginning of the article, we already described how you can determine the scale of the image using a kilometer grid and a ruler. But there are other ways to set the degree of reduction and scaling on a specific terrain plan (Figure 3).

Tourists usually use the following methods:

1. Map nomenclature: To use this method, you need to carefully consider the details of the card. In fact, the nomenclature is the alphanumeric name of the sheet. Each scale series has its own designation. For example, M-35 corresponds to a scale of 1:1000000, and M-35-18-A-6-1 to 1:10000. Of course, to determine in this way, you need to know the nomenclature designations by heart.
2. Known distances: in this case, on the map you need to find images of kilometer posts, which are usually installed on the highway. Directly on the map you need to measure the distance between them. In this case, the number of centimeters on the map will correspond to one kilometer on the ground.
3. Meridian arc: one minute along the meridian corresponds to 1.85 km, although this figure is usually rounded up to 2 km. On the side frame of any card there are inscriptions of minutes and degrees, and a checker is used to highlight each minute. If the length of one minute is 3.7 cm, then the scale will be 1:5000, that is, one centimeter on the map will correspond to 0.5 km on the ground.

Figure 3. You can determine the degree of reduction of objects on the map by simple calculations

Maps with a scale of 1:2000000 usually indicate the distance between certain settlements in kilometers. In this case, to determine the scale, you need to measure the distance on the map with a ruler. Then the distance indicated in kilometers should be divided by the resulting number in centimeters. As a result, you will get a number that will correspond to the number of kilometers in one centimeter.

Design rules

If the topographic map of the area was made correctly, the scale must be indicated on it. An exception can only be home-made maps or hand-drawn terrain plans. In all other cases, the scale must be drawn up in accordance with GOST.

If the map has been compiled correctly, finding even smaller objects will not be difficult, because all measurements correspond exactly to the location on the ground.

The procedure for determining the scale on the finished drawing

Scale is needed not only to determine the distance on the map. It is also used in drawing up drawings (Figure 4).

It is important to choose the right scale for the part drawing. For example, small or prefabricated elements are best done in full size, that is, on a 1:1 scale. But sometimes, for ease of reading, an object drawn on paper is reduced or enlarged.

It is not difficult to find out the scale of the drawing, since it is determined in much the same way as the geographical one. First of all, you need to carefully study the drawing. According to GOST, the scale should be indicated in the lower right corner. At the same time, in mechanical engineering and instrument making, an increase is usually used, and in construction drawings, a decrease.

Scale is the ratio of 2 linear dimensions, which is used when creating drawings and models and allows you to show large objects in a reduced form, and small objects in an enlarged one. In other words, this is the ratio of the length of the segment on the map to the true length on the ground. Different practical situations may require you to know how to find the scale.

When does scaling become necessary? It mostly happens in the following situations:

• when using the card;
• when making a drawing;
• in the manufacture of models of various objects.

Scale types

Under the numerical scale it is necessary to understand the scale expressed as a fraction. Its numerator is one, and the denominator is a number showing how many times the image is smaller than the real object.

A linear scale is a ruler that you can see on maps. This segment is divided into equal parts, signed by the values ​​of their respective distances on the real terrain. A linear scale is convenient in that it provides the ability to measure and build distances on plans and maps.

A named scale is a verbal description of what distance in reality corresponds to one centimeter on the map. For example, there are 100,000 centimeters in one kilometer. In this case, the numerical scale would look like this: 1:100000.

How to find the map scale?

Take, for example, a school atlas and look at any of its pages. At the bottom, you can see a ruler that indicates how much distance in the real area corresponds to one centimeter on your map.

The scale in atlases is usually indicated in centimeters, which will need to be converted to kilometers. For example, when you see the inscription 1:9 500 000, you will understand that 95 kilometers of real terrain corresponds to only 1 cm of the map.

If, for example, you know that the distance between your city and the neighboring one is 40 km, then you can simply measure the gap between them on the map with a ruler and determine the ratio. So, if by measuring you got a distance of 2 cm, then you get a scale of 2:40=2:4000000=1:2000000. As you can see, finding the scale is not difficult at all.

Other Uses for Scale

When making models of aircraft, tanks, ships, cars and other objects, certain scaling standards are used. For example, it can be a scale of 1:24, 1:48, 1:144. At the same time, the manufactured models must be smaller than their prototypes exactly by the specified number of times.

Scaling may be needed, for example, when enlarging a picture. In this case, the image is divided into cells of a certain size, for example, 0.5 cm. A sheet of paper will also need to be drawn into cells, but already enlarged by the required number of times (for example, the lengths of their sides can be one and a half centimeters, if the picture needs to be enlarged 3 times) . By applying the contours of the original drawing to the lined sheet, it will be possible to obtain an image that is very close to the original.

On any geographical map, you can see approximately the following inscription: "Scale 1: 100,000." Traditionally, the first number is 1, and the second can vary. If there is no inscription, then there is certainly a tiny ruler, divided into equal segments, or a nomogram. These signs indicate the ratio of the size of an object on a map or plan to its actual size.

You will need

• Roulette or compasses
• Ruler

Instruction

1. If you have a plan on which different objects are fairly accurately plotted, and you need to find out at what scale this plan was made, start with measurements. Select an object, one that is nearby. Measure it on the plan and write down the results.

2. Measure the actual object. Use a tape measure for this. In order to avoid mistakes, make a peg and hook a tape measure loop on it. Drive a peg into the ground so that the zero mark of the tape measure is on the tier of the starting point of the length or width of the object.

3. Determine the scale. It is more convenient for everyone to write it down in numbers. Write down the size of the object on the plan, after that - the one that turned out when measured on the territory. Let's say you have a barn 5 meters long on the plan occupies 2.5 cm. Convert meters to centimeters. That is, it turns out that you have 500 cm in 2.5 cm. Calculate how many centimeters of territory are contained in 1 cm on the plan. To do this, divide the larger number by the smaller one. It turns out 2.5:500 = 1:200, that is, 1 cm on the plan corresponds to 2 m on the territory.

4. In order to determine the scale more correctly, take several measurements. Let's say measure the barn on the site and the distance from the gate to the pond. The plans are different, and the dimensions of one or another object can be applied unsatisfactorily correctly. If there are discrepancies, make another frosted. The image of the object, the one that does not correspond to the other two, correct on the plan.

Scale is a numerical designation of parameters related to real objects that are unthinkable to depict in natural size. The figure applies their layouts.

Instruction

1. The scale is written in several ways, say, numerically - 1: 1000000. The size ratio can also be indicated in this form: 1 cm 10 km is a named scale. The linear display method is shown by a ticked line.

2. When considering scale in relation to cartography, the appearance of a particular map will depend on the ratios used. The larger it is, the more detailed the area will be depicted. The detail is also influenced by the nature of the territory, which is sparsely inhabited, say, easier to depict. Maps are large, medium and small scale. Large-scale maps are when 1 cm is from 100 to 2000 meters, medium-scale maps are 1 cm to 10 km, small-scale maps are 1 cm more than 10 km.

3. Scale matters in photography as well. With the help of lenses, photographers change the size from hefty small to hefty large. The methodology of the metamorphosis of scale depends on the specifics of the surveys. If these are small objects, say, insects, the scale increases, if they are huge, it decreases.

4. The representation is also used in many sciences. In mathematics it is the ratio of numbers, in programming it is the scale of time, in astronomy it is the scale of the universe. The meaning of the word is also used in the construction industry.

5. Firms are distinguished by the scale of their activities. There are, say, territorial organizations, but there are also federal tiers. Different in scale and people. True, not from a physical point of view, there is a psychological representation of the “scale of the figure”. This refers to human qualities, goals and results of activities.

Related videos

Note!
The size of a reduced object is relative to its natural size. The distance between objects can be changed by several centimeters, meters, kilometers. The scale of reality changes a lot, but all parameters must remain proportional. If proportions are not observed, it will be unthinkable to analyze the distances and sizes of objects.

With the need to present the real dimensions of the object depicted in the drawing, a person is faced more closely at school. In a drawing lesson, it may be necessary to draw a detail on a scale of 1:2 or 1:4, in a geography lesson - to calculate the exact distance between two cities. In order to cope with the task, you need to know how the scale is translated.

You will need

• - geographic map;
• – detail drawing;
• - calculator;
• - drawing accessories.

Instruction

1. If you need to draw details on a 1:1 scale, this means that 1 cm of the surface will correspond to 1 cm in the drawing. Measure the surface you want to depict and draw it on paper at natural size.

2. Other scales are also used in drawing. 1:2 means that the detail in the drawing should be half as large as in reality. If the scale is 1; 4, this means that 1 cm in the drawing is equal to 4 cm of the part. It also happens the other way around. It is possible to draw a completely small object, say, on a scale of 4:1, 10:1, etc. If you see a similar designation in front of you, it means that the object in the picture is four or ten times larger than it really is.

3. In geography, scale conversion is also required. Look at the geographic map. In one of the lower corners, you will see either a ruler with numbers, or primitive numbers - say, 1:50,000. The numbers, finally, are larger than in the drawing, but the rule for translating them is exactly the same, that is, in the above example, per 1 cm of the map 50,000 cm of the earth's surface is brought, that is, 500 m. This is a map of a relatively huge scale. Looking at the atlas of the world, you will see much more impressive figures.

4. Quite often it is necessary to scale not a linear measure, but a square one, that is, to determine how many square centimeters. To do this, measure the area you need by any comfortable method. Say, with palette support. In order to find out the real area of ​​the territory, you need to convert the linear scale into a square one, that is, build the number of centimeters contained in 1 cm of the map into a square. Multiply the resulting number by the area of ​​the plot shown on the map. This way you will find out how many square meters the territory that concerns you occupies.

5. Occasionally there is a need to translate the scale of a three-dimensional object. For example, at a labor lesson, a teacher can give the task to make a part depicted in a technical drawing on a certain scale. You need to find out how much material this will require. The translation thesis will be the same. First, find out how many real centimeters this or that line in the drawing corresponds to. Determine the volume of the part from the drawing. This is a simple mathematical problem, the method of solving it depends on the shape of a particular part. The number that indicates the scale, cube, and then multiply by the volume of the part, calculated according to the drawing.

Helpful advice
You can try to draw a simple plan on your own, setting yourself a certain scale. Let's say a 1:10 scale for a room plan would absolutely fit. Measure the length of the walls and large objects, determine their relative position and draw a plan in strict accordance with the data received.

Note!
The scale is the larger, the smaller the denominator of the fraction with which it is written. 1:100 is larger than 1:2,000. It is more comfortable to measure an object with an assistant. If there is no assistant, and there was no peg at hand, firmly press the tape measure against the wall of the object. It is more comfortable to measure everyone on the ground - say, on the bottom of the wall.