Scale (map)

The scale or map scale is the reduction ratio of charts, maps, relief models, terrain profiles and globes. It is defined as the ratio of a length on the map ( map distance ) to its likeness in nature (natural route).

The concrete representation in numerical or graphical form is referred to as scale indication. The scale is usually as a proportion 1: scale number provided so that this reduction ratio is the inverse of the scale number. ( And vice versa. )

• 2.1 length scale
• 2.2 height scale
• 2.3 surface scale
• 2.4 Globus scale
• 2.5 Variable scale

• 3.1 As a numerical scale
• 3.2 As a graphic scale
• 3.3 scale in digital data

• 4.1 Development of the theoretical foundations
• 4.2 Development of the scale information
• 4.3 Determination of the scale at old maps

Definition of the scale

Basis

Prerequisite for a sense of scale cartographic document is a system of measurement and surveying. Reference surface is usually the Erdellipsoid, that is, the natural path is not the shortest path between two points on the earth's surface, but always reduced to sea level range (see geodesic or geodesic ).

Calculation

The scale is usually in the form 1: scale number is specified. The values ​​are calculated as follows:

Course must be in the same unit both lengths for a correct result. For example, if a scale of 1:50,000 (read: one to fifty thousand ) cards track 1 cm long, then the natural range 50,000 cm, ie, 0.5 km long.

As the scale and usually unless otherwise specified refers to the linear reduction ratio, the scale number must be squared for area comparisons. The figure of a square kilometer at 1:50,000 takes a scale of 1:100,000 so only a quarter of the paper surface.

Examples:

Large and small scales

Depending on the content and the wealth of detail in the maps large scales, medium scales and small scales can be distinguished. The adjectives " large" and " small " refer to the size of an object on the card and not on the scale number. These terms are often confused when the difference of scale and the scale number is ignored. In a large-scale map, the scale number, therefore, is small and vice versa. A map is 1:25,000, for example, of large-scale ( ie larger or the content shown in more detail ) as a map of 1:100,000.

What is referred to as a small or large scale, is relative and depends largely on the subject matter and the state. For example, for the engineering geology a map 1:200,000 even as kleinmaßstäbig, for geographers, however, only an outline map from approximately 1:2,000,000. In a large country like Russia can 1:200,000 still widely considered a major scale, while in a small country like Switzerland, this is already seen as a smaller scale.

All standards can be grouped in scale areas that are characterized by equivalent or very similar degrees of fineness of the drawing and of the content. Example: Large standards such as 1:20,000, 1:25,000 and 1:30,000 allow for a comparable level of detail. Therefore maps authorities give their cards works out in scale rows, which resulted standards relate to each other in a simple ratio and thus are easily comparable. In many states, the number on the scale range to 1:5000 to 1:1,000,000 ranges than the smallest scale.

Base maps are kept in the original scale (also scale output or recording scale). This can be greater than or equal to the work scale (also scale processing ). This in turn may be equal to or greater than the Endmaßstab in which the cartographic document eventually appear.

The scale which is at least necessary for the representation of an object perceptible, threshold scale is called.

Scale types

In this chapter, scale types and not their concrete representation of a document ( scale data ) are treated.

Length scale

Normally standards on routes, so are length scales. However, the spherical surface of the earth can not be mapped completely isometrically on flat cards, because a two-dimensional curved surface is not strictly unwound on the map layer (see map web design ). Length of loyalty cards with a constant length scale over the entire face of card are not possible. A certain length scale can be achieved only in certain areas or directions. In large-scale area is this circumstance for the practical use of little relevance. Especially for small-scale maps and atlases, however, in the specified length scale applies ( the equator or a meridian for example) only for the center of the map and possibly for certain isometrically mapped network lines. On world maps are therefore often finds a clarification as equatorial scale or scale the map center.

Height scale

The height scale (also vertical scale ) is a special case of the linear scale, since it also relates to a route. For relief models or terrain profiles the height can be shown in a different scale than horizontal lengths. The ratio of the two scales is referred to as a magnification factor, the effect as an overshoot.

In sections five - or ten-fold elevations occur. In the didactics peaks are rejected by most modern authors and Relief producers, at least in the large-scale area. For medium - or small-scale relief models in which the characteristics of the mountain would make up only a few millimeters or centimeters, an elevation for clarification may well have its meaning. More than two-fold rise is, however, there usually perceived as unnatural.

Surface scale

In contrast to absolute length-preserving maps consistently equal-area images of the Earth's surface on a flat map are possible. These possess a surface scale. Nevertheless, the surface scale is rarely used, as you can imagine proportions of land inferior to length ratios. One known exception is the Peters Atlas.

World scale

Because the globe is the only cartographic document that reproduces the earth without distortion reduced, is known for the scale of a globe, the term world scale.

Variable scale

With Maps, it may be useful on a larger scale map the touristic city center than the equipped with little of interest outside quarters. In this case, for example, be generated with a Hyperboloidprojektion a sliding scale. This will long for the search grid in the city center, formed outside narrowing stitches. In extreme cases, and especially in highly curved grid lines one gets the feeling of looking through a magnifying glass.

Variable standards also result in thematic Kartenanamorphoten, where the size is not proportionally elected to the representation to the actual geometric size, but depending on an arbitrary attribute.

Scale information

In this chapter, scale information will be treated, so the specific labeling of the various scale types on a cartographic document. A synonym is to scale shape.

As a numerical scale

The scale is now expressed as a proportion or more rarely as a fraction. The numeric representation familiar to us today came only at the beginning of the 19th century in use and has spread worldwide since the beginning of the 20th century. Numerical standards are in addition to the map title, the most essential feature of a card and are therefore usually placed prominently, it is immediately adjacent to the map title, be it in large letters at the legend or visible edge of the map.

In cartography round standards are mostly used, because it can be expected better. Sometimes cards are, for example, for reasons of space on the map sheet or non- metric measurement system in noncircular standards published (examples: map of Zurich 1:12.600, 1:63.360 topographic map of Great Britain corresponding to 6 inches to 1 mile ).

At elevations of relief models and profiling the scale indication can be done in two ways:

• Indication of the length and the height scale " length scale of 1:5000, 1:2500 scale height "
• Indication of the length scale and the elevation factor " scale of 1:5000, two times too high "

Surface standards, for example, in the form " 1 square centimeter corresponds to 6000 square kilometers " specified. At Globes, the diameter is often simply stated.

As a graphic scale

Often, in addition to the numerical scale is a graphic scale, called a scale bar indicated on the card edge. In older cards may be present, for example, those for German, geographical and nautical miles, for hours or marker from up to twenty scale bars to different measurement systems.

In conformal world maps, where the scale lawfully enlarged, for example from the equator to the poles, and scale diagrams can be found. These are nothing more than pyramid- shaped arrangement scale bars, which in contrast to the scale bars on old maps, however, are all numbered in the same unit.

As a variant of the graphic standards can be found in atlases occasionally also squares with square footage or at the edge of the map, a comparison cards a known state (eg outline of Switzerland the same on a Asia map scale ).

Benchmark in digital data

The in a digital geographic information system (GIS ) as " columns of numbers " stored points are initially scale -free.

If these vector data such as directly derived from a measurement of the Earth's surface, they can theoretically be used to scale independently. If they have been, however, vectorized from a paper map, ie previously were generalized already, they should be visualized only in a relatively narrow scale range. It is then, for example, does not make sense to glean coordinates to the nearest meter (even if this is technically possible).

When derived from vector data or scanned paper maps raster data (eg top 50 of the German land survey offices on CD- ROM) are the standards usually given in the product documentation to be understood only as an indication of the reference card used as a data source because the maps can be zoomed on the screen, which the scale changed. The output scale and display scale can therefore be different from the scale of the data base or scale digitization. In general, a changing with the zooming numerical or graphical scale on the screen is displayed.

History

Development of the theoretical foundations

The idea of ​​scale and the sense of scale of maps was well known in the 13th century the makers of nautical charts. However, since most mapmakers to the 17th century had no mathematical training, whose cards were equipped with either an exact projection, still with a scale according to current understanding. In addition, the technical requirements for satisfactory position determinations and measurements were missing.

Since time immemorial, however, especially longer distances were estimated and expressed as day trips. Although fortified Also at the wheel measuring devices provided reasonably good data for the route in question. Although, these methods were covered path lengths, but not the " straight line " to be determined. The results were very inaccurate maps. Only in the 17th century sold in Europe after the establishment of observatories precise location measurement, which were connected to each other since the 18th century by triangulations and compacted. This is the first essential for accurate and thus scale maps was given.

However, the myriad vormetrischen measurement systems difficult surveying extraordinary. With the development of the metric system in France around 1800 round, slightly comparable standards have been possible. Therefore it was only in the 19th century, the equation maps route: Natural course = 1: Enforcing scale number. After 1880, the realization that essential for a fair illustration of a section of the spherical earth on a flat map of the scale and map projection are jointly responsible and sensibly should not be chosen independently created.

Simultaneously with the advent of the scale information in cards, the literary work began with the scale. So mentioned Lewis Carroll in 1893 as the first map at a scale of 1:1 as a theoretical thought experiment.

Development of the scale information

Scale data are still lacking on medieval Christian mappae mundi, as they were not intended as scale maps after today's performance.

Even the first Portolankarte, the Pisan map from the last quarter of the 13th century, has a scale indication. Soon developed on portolan the concept of scale bar that looks like a ladder and resulting in, among others, the French term " échelle " derives. Is, however, the distances are not yet quantified, it is not always clear which measurement system has been used. Portolan are very accurate, but the scales of the different maritime basins are (for example Mediterranean and Black Sea ) different sometimes.

The first world map with a graphic scale is the World Map of Andrew Walsperger of 1448th Walsperger completed his card by chronicling also provides guidance on the use of the scale bar. The first map of the modern era with scale bar is the Albertinische plan of Vienna of 1421 / 1422. The first prints of the Geography of Ptolemy (from 1477 ) contained no scale information. Only the Ptolemy edition of 1513 put the concept of the graphic scale to in printed form and made it known to a wider public. Since then, several scale bars are usually indicated on the maps. So, for example, contained the Tabula Hung aria ( printed in 1528 ) of Lazarus Secretarius and Georg Tannstetter a scale bar, a total of 80 German miles long. Every mile ( 7.5 km ) has been dismantled in a second scale bar into four parts. A legend explains to the reader the application.

Such scale bars but sometimes had to do with the scale of the map slightly since measurements were not yet common and less skilled copyists as a purely graphical element misunderstood and consequently their size just changed the scale bar.

As the 18th century came up with the traveling stagecoaches, scale bars were particularly important. Up to twenty scale bars in a variety of measurement systems have been specified. In contrast, were world maps and historical maps that did not serve the travel or trade, also published in the 18th century often without scale information.

From the beginning of the 19th century, slightly delayed the development of the metric system of measurement, numerical standards came into use. First, they were written as a fraction. An early example is a map of the Austrian Empire from 1822 that has a " rejuvenation of the scale of 1/864.000 of nature." Worth to specifying a numeric scale Heinrich Berghaus made ​​off with his magazine Hertha. On the 7th International Congress of Geographers 1899, the fraction notation was internationally recommended.

In the 20th century, then sat the now generally accepted numerical scale indication in the form of a proportion worldwide. In general, numerical and graphical scale data are combined today on official maps works; in tourist maps are often found only scale bars.

Determination of the scale at old maps

Prescribe the most important library of rules, that the scale is to be recognized in the descriptive cataloging of cartographic documents. In modern cards, where the scale is indicated in numeric form, this is not a problem, however, situation is different when only graphics standards ( scale bars ) in length dimensions obsolete or no scale information are available. The attempt at a determination of the scale is only useful if the Altkarte based on a survey. This is for a lot of cards that originated before the 18th century, not the case.

There are currently at least four different ways, as the scale of an old card can be identified:

Often the paper delay is also a factor, that is, the target scale is not identical to the Istmaßstab. Since the default paper (scale difference) is not precisely known, subsequently determined standards should always make sense rounded or the presumed target scale are given. Examples:

• Scale determined by a comparison of several routes on a French map 1:86.617, presumptive and therefore so rounded scale 1:86.400 ( default scale of the French system of measurement before 1800 )
• Using an analysis software determined scale 1:4.208.740, sensible rounded scale indication 1:4.200.000

Because of the difficulty for non-specialist library staff scale calculation is often not taken at all.

Linguistic aspects

The German language has two adjective forms, in addition to scale less frequently maßstäbig. Präzisierend one says a large scale and kleinmaßstäblich (besides fairly uncommon großmaßstäbig and kleinmaßstäbig ). See more in scale (disambiguation).