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Soil Science Society of America Journal Abstract -

The Colding Equation for Soil Drainage: Its Origin, Evolution, and Use


This article in SSSAJ

  1. Vol. 63 No. 1, p. 33-39
    Received: Feb 24, 1998

    * Corresponding author(s): volkmann@ifgb.uni-hannover.de
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  1. R. R. van der Ploeg ,
  2. Maria Marquardt and
  3. M. B. Kirkham
  1. Inst. of Soil Science, Univ. of Hannover, Herrenhaeuser Str.2, 30419 Hannover, Fed. Rep. Germany
    Dep. of Agronomy, Kansas State Univ., Manhattan, KS 66506-5501



The derivation of the ellipse equation by the Danish engineer Colding in 1872 marked the beginning of a new epoch in the field of soil drainage. Little is known about the circumstances that led to the derivation of this equation or about the evolution of the Colding equation in later years. Therefore, we decided to survey the early European literature on these subjects. The survey revealed that Colding's derivation was based mainly on research published by the French engineer Delacroix in 1859 and by the Danish engineer Hannemann in 1870. Although Colding used soil water flow concepts as developed earlier by Darcy and Dupuit, it is possible he was not familiar with the work of these French engineers. After Colding's equation had been widely used for drainage design purposes in Denmark, his equation appeared in the German literature around the turn of the century. From Germany, the Colding equation spread to other European countries and to the USA. In the 1930s and the 1940s, the Colding equation was modified by Hooghoudt in the Netherlands and by Aronovici and Donnan in the USA. The Hooghoudt equation is used today as a drainage design standard in various parts of the world.

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