Scale factor

As μ scale factor is used in Geodetic the aspect ratio of two versions of a survey network or an entire earth model referred.
The cartography knows correction factors for different maps and their projections, as well as noticeable paper arrears .

In geodesy

Since surveying networks have only very little distortion and the earth's dimensions are well known, the possible scale factors are always close to the value  1 . It is therefore also written in the form

µ = 1 + m

and calls the small size  m the scale correction. In modern route networks,  m is at most a few ppm (millimeters per km), so the scale factor is almost always within the limits

0.99999 <µ <1.00001.

Newer networks - even if they are based on terrestrial measurements - are often controlled and reinforced with data derived from satellite geodetic systems . A 7-parameter transformation with 3 shifts and 3 small angles of rotation is often used ; the 7th parameter is the scale factor. It means that the routes in network model A best match those in network B if they are lengthened or shortened by the factor µ.

The fact that µ is not exactly 1 even with modern network measurements can be due to several factors. The two most important are:

Historically, the scale factor appeared in several ways from around 1800:

In cartography

Cartography also speaks of the scale factor when z. B. an area is shown in different map projections or if the map scale changes noticeably within a map sheet or system for mathematical reasons. Usually the nominal scale only applies in the center of the map or (in the case of cone projections ) in the two reference parallels , whereas µ <1 in between.

Changes in scale can also occur through the entry of the paper - especially as a result of changing humidity . Here, empirical values ​​for the scale correction m are sometimes  given.