We explain what a graphic scale is, what it is for and various examples. In addition, the differences with a numerical scale.
What is a graphic scale?
A graphic scale is a straight graduated line, divided into equal parts. The units of the scale represent the relationship between the actual length of an object and the equivalent in drawing units.
It is usually used in maps , nautical charts, planes and other forms of spatial representation with unit by unit scale, that is, in which each unit drawn represents a set of real units of measurement. Not to be confused with the numerical scale , although both are cases of scale.
The graphic scale was first used in the Pisan Charter of the late thirteenth century , a document found in Pisa, Italy. It is a map of the seas Mediterranean, Black and part of the Atlantic Ocean. Its graphic scale appears as a circle whose radius is divided into three equal parts, each of which represents (not numerically) a distance from the map to scale.
This design has since changed to the shape of the straight line, generally located on the banks of the maps vertically or horizontally, and maritimely known as Log of leagues.
What is a graphic scale for?
The graphic scales give the person who queries a map information about the scale of his drawing. In other words, it explains how the representation is linked to the actual distances of the segment of the land surface that it describes.
You can do it without the need to resort to numbers or numerical relationships, but through a graphic or visual type convention, as established by the various cartographic sciences.
Graphic scales are used primarily in cartography, engineering, and architecture.
In the case of cartography, we usually speak of 3 types of scales depending on the terrestrial dimensions to be represented. Thus, there were large-scale, medium-scale and small-scale maps.
The small scale refers to planes where large real areas are represented in a very small space. These are essentially from countries or the entire globe.
On the other hand, large-scale ones are used to represent not so large tracts of land on paper. Similarly, maps of the earth can show distortions in terms of their scales. This distortion will vary according to the type of projection and is due to the spherical character of the globe.
The graphic scales used for engineering arose when greater accuracy was necessary in the elaboration of mechanical parts. For this reason, the complexity of civil engineering structures from the Modern and Contemporary Ages made these scales a necessity.
Primarily, engineering scales are given in proportions ranging from 1:10 to 1:60, depending on the actual quantities to be represented.
Additionally, the appearance of the scale for uses related to engineering and architecture has been vital. This instrument is a kind of prismatic ruler and has different scales on each of its faces.
Examples of graphic scale
The graphic scales vary according to the type of use that they want to be given, as well as the magnitude to represent. On a graphical scale a segment could imply a real length of 50 km.
For example, we could have a trunk of leagues with a total length of 5 centimeters equivalent to 500 kilometers. Likewise, this trunk of leagues could be subdivided into 5 subsegments, so that each subsegment would actually be equivalent to 100 km.
This relationship between actual dimensions and dimensions in the drawing can vary from a large scale to a small scale. This is according to the correspondence between the magnitudes.
Graphical scales are an important tool for representing aspects of the real world at the plane level. They allow greater accuracy for navigation, as well as for construction and industry.
Graphic scale and numerical scale
Unlike the graphic scale, which represents the scale by visual proportions, a numerical scale is one that fulfills the same function , that is, to inform us how the proportions of reality have been represented on a plane or document, but Express the proportion through a set of numbers .
For example, a scale of 1:20 means that each unit of the representation equals 20 of real life, depending on the units in which they are expressed. Thus, it is common to see scales of 1 / 50,000 or 5/500, depending on how abstract the drawing is to be able to present huge objects or massive lengths, on a small screen or a paper cutout.
Both the numerical scale and the graphic scale are common in maps, plans, technical drawing works , architectural projections, etc.
Types of graphic scales
Large scale, small or linear scale and What’s the difference?
Imagine that every map is an aerial view over a given space. Thus, to know if a scale is large or small, or if it is larger than another, just understand that the scale is nothing more than the level of approximation of the aerial view of the map. Another way is to observe the numerical scale, remembering that it is a division. Thus, the lower this denominator, the larger the scale.
Example. Consider these two scales: a) 1: 5000; b) 1: 10,000. The first scale is a division of 1 to 5,000 that, when calculated, will certainly give a larger number than a division of 1 to 10,000. Therefore, the first scale is larger than the second.
Thus, it is possible to see that the larger the scale, the smaller the area represented on the map and vice versa, because the larger the scale, the greater the approximation of the aerial view of the represented location. This allows us, in turn, a greater level of detail of the information, because the closer we are to a location, the more details we can see.
The larger the scale, the smaller the area represented and the greater the level of detail
A world map has a very small scale, with a large represented area, and it will certainly present less details than, for example, a map of the state of Bahia, which would have, in this case, a large scale.
The graphical scale method measures the performance of people with already defined and graduated factors. It uses a double entry questionnaire, the horizontal lines represent the performance evaluation factors and the vertical columns, the degrees of variation of those factors. Each factor is defined by a summary, simple and objective description.
Continuous graphic scales. – They are those in which only the two extreme points are defined, and the evaluation is located at any point on the line that joins them.
Semi-continuous graphic scales. – The treatment is identical to the continuous ones only that it includes defined intermediate points to facilitate the evaluation.
Discontinuous graphic scales. – They are scales in which the position of their brands has already been established and described and from which the evaluator will have to choose one to assess performance.
Handling the Method
Nebulous criteria.- It is necessary to use descriptive phrases that precisely define each factor.
Halo effect .- This effect makes the evaluator consider a general impression when evaluating each factor.
Central tendency.- It refers to evaluating all the factors in the same way.
Benevolence in the face of exaggerated rigor.- It implies subjectivity in the evaluation.
Prejudices.- It is the tendency to evaluate individual differences such as age, sex, which affect the evaluation of people.
- Easy to understand and simple to apply
- It allows a comprehensive and summarized view of the evaluation factors
- It simplifies the evaluator’s work and the evaluation record is not very complicated.
- Does not provide flexibility to the evaluator
- It is subject to personal distortion and interference from the evaluators
- Tends to fall into a routine and standardize test results
- You need mathematical and statistical procedures to correct distortions
To calculate the scale, just remember your concept: Scale (E) is the relationship (division) between the area of the map (d) by the real area (D). Thus:
E = d D
So, to calculate a scale of a map in which two points are 5 cm apart from each other, and in the real world, they are separated by 1000 cm, just apply the formula:
E = 5/1000 → E = 1/200
The scale, in this case, is 1: 200 or one to two hundred .
How to calculate the scale of a map?
Before starting to calculate the scale of a map, we must be clear about several concepts that will help us to a great extent to calculate the scale with some ease;
- “D” is the distance on the paper
- “D” is the actual distance
- “1” is the unit of scale
- “U” is the scale itself of the map we are analyzing
With these clear concepts, the time has come to begin to see the steps that we must follow.
How to calculate the scale of a map step by step
Below we show you all the necessary steps to find out the scale of a map through a few simple steps;
- The formula to calculate the scale of any map is;
1 / U = d / D2
- Now look for two points on the map , and if you can mark them in any way do so. You can use significant points on the map to make it easier.
- Use Google to measure the actual distance between these two points. If you have taken two significant points, for example two cities, it will be quite easy to get the data, but you can always measure it quickly using, for example, Google Maps .
- In our case, and to make the calculation with an example, we are going to take the distance between the cities of Gijón and Oviedo, which is 28 kilometers. You should measure that same distance on the map in front of you, measuring as roughly as you can.
- It should be said that to calculate the scale of the map accurately, it would be more convenient to choose significant points of greater depth, such as a geodesic vertex since that distance is known and above all precise. The distance between two cities can change depending on where it is measured from.
- The distance on the map between those two cities, let’s assume it is 10 centimeters.
- Once the initial formula has been transferred, we will find; 1 / U = 10/28, but we would be using different units of measurement (10 that we have measured in centimeters and the data of 28 kilometers). The simplest thing in this case, and for the resulting scale to be logical later, is to change the kilometers to centimeters.
- In this way the formula would remain; 1 / U = 10/2800000, from where we should clear the “U” which is the unknown we are looking for ; U = 2800000 x 1/10. Doing the corresponding operations the U would be equal to 280,000
- This data, transformed into a normal scale format, would be 1: 280,000, which is the scale of the map we are consulting.
- Calculating the scale of a map is a really simple process that can get us out of a lot of trouble, where the scale is not correctly indicated or, for example, is not visible.
Have you been able to calculate the scale of a map without major problems? Tell us if you have any questions or problems in the space reserved for comments on this post, on our social networks or even on our forum.
History of graphic scale
There is a reference that the Pisan Charter was the first time that a graphic scale was used in cartography. This map was found in the city of Pisa in the 13th century, the place from which it takes its name. In essence, this find was intended for navigation.
It has several characteristics. The map shows the Mediterranean Sea, the Black Sea, as well as the Atlantic Ocean as a whole.
To achieve this scale, the map makers appealed to geometric figures. These shapes establish a proportional relationship between the measurements on the chart and the actual measurements of the earth’s surface.
Since ancient times there have been attempts to make navigation charts that express routes, as well as coastlines. In fact, the Pisan Chart is in line with the Portulan charts and gives a detailed description of the coastline, but without details regarding topography.
The portulan charts follow the same spirit of the maps that arrived until the Modern Age for navigation. They also have a grid that accounts for both the navigation directions and the winds. Additionally, they have the so-called trunk of leagues or graphic scale.
This chart format was used by Arab, Portuguese, Majorcan and Italian sailors. Also, with regard to engineering scales, there is knowledge of the so-called scale boxes that were used in the nineteenth century.
Evolution of graphic scales
The representations of the graphical scales evolved from the patterns in the form of geometric figures until they reached a narrow bar. This change occurred from the fourteenth century.
This bar graphically establishes the analogy between the measurements of the plan or chart and the actual measurements. The bar can be arranged both horizontally and vertically and is known as a “trunk of leagues”.
In these first bars the corresponding numerical values were not placed. By then it was virtually a norm that the correspondence between distances was 50 miles in the case of Portulan maps.
In the case of marine charts, the well-known Mercator projection was used . This consists of a cylindrical projection that is made tangential to the equator of the earth. For this reason the Mercator projection has distortions depending on the latitude.
Today the same philosophy of the Portulan maps is still used. Likewise, this type of scale represents an advance with respect to lexical scales, which are subject to confusion due to disused terms.
For example, it usually occurs on lexical correspondence scales between inches and a virtually unused unit, such as the furlong. This unit is known only to people familiar with the culture of the British Empire. what is a graphic scale