# Transformation Scale

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08-05-2020 06:21 PM
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Occasional Contributor II

Hello,

I have been learning Transformation concepts working with matrix algebra to develop a basic 2d conformal transformation calculator in excel.  The scale is developed as a relationship between line segment lengths between one coordinate system and another.  But my question is concerning the concept of scale as it relates to a survey perspective that scale in a transformation is used to change between grid and ground.  It is my understanding that the two scales are different; one derived from a line segment length ration, and the other based on the earth radius, resulting in two different scales and two different processes that use these scales.  I wonder if someone can confirm my understanding above, or if a reference could be recommended that may explain the differences between the two scales.

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Occasional Contributor

Hi, I would say you are pretty spot on in your understanding.

Scale in a map projection: relates to the length of a line mapped to the reference ellipsoid vs the length of the same line in the actual projection

Scale in a 2D conformal transformation: ratio of lengths of a line in two different 2D (in your case) orthogonal coordinate systems. Pretty much the same if you develop a 3D conformal transformation for example as seen in transformation between geodetic datums.