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Curvature Corrections in Electronic Distance Measurements

  • Martin Hotine

Abstract

It can be shown (Hotine 1960) that if F is a continuous, differentiable scalar, the expansion
$$(\bar{F} - F) = \frac{1}{2}s(F\prime + \bar{F}\prime ) + \frac{1}{{12}}{{s}^{2}}(F\prime \prime - \bar{F}\prime \prime )$$
(1)
along a line of arc length s, is correct to a fourth order. The superscripts refer to successive derivatives of F with respect to s and over-bars indicate values at the far end of the line, while the absence of over-bars indicates values at the near end of the line. It is further assumed that the ordinary Taylor expansion of F along the line exists and is convergent, and that this condition is met, or justified by results, in practical cases.

Keywords

Curvature Correction Velocity Correction Successive Derivative Basic Physical Principle Frenet Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

References to Paper 2

  1. Hdpcke W (1964) On the curvature of electromagnetic waves and its effect on measurement of distance. Vermessungswesen 89:183–200. Translated in Survey Review 141:298–312Google Scholar
  2. Hotine M (1960) The third dimension in geodesy. I.A.G. HelsinkiGoogle Scholar
  3. Saastamoinen J (1964) Curvature correction in electronic distance measurement. Bull Geod 73:265–269CrossRefGoogle Scholar

References to Editorial Commentary

  1. Brunner FK (ed) (1984) Geodetic refraction — effects of electromagnetic wave propagation through the atmosphere. Springer, Berlin Heidelberg New York TokyoGoogle Scholar
  2. Iribane JV, Goodson WL (1981) Atmospheric thermodynamics. 2nd edn. Reidel, DordrechtCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Martin Hotine

There are no affiliations available

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