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Technische Winkelmessungen

Technische Winkelmessungen


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wobei n die Zahl der Beobachtungen ist, und als mittleren Fehler des arithmetischen Mittelwerts die Größe 2 _I V .I 8 F = ± yn = ± n. (n - 1 . Für obiges Beispiel ist 1= ± = ± 2,2' und F= ± V!: = ± 0,35', während der maximale Fehler der einzelnen Beobachtung ± 3' sein würdeI). Meist ist es aber in der Technik nicht möglich, eine für die Gaußsche Fehler- rechnung genügende Zahl von Beobachtungen anzustellen. In der Regel wird es sich sogar darum handeln, vor der Ausführung die Genauigkeit der einzelnen Verfahren zu bestimmen, um daraufhin entscheiden zu können, welches von ihnen für den vorliegenden Zwec, k geeignet bzw. ausreichend ist. Häufig wird sich dies durch einfache Betrachtungen ergeben; schwieriger wird aber die Fehler- berechnung, wenn das Meßergebnis nicht unmittelbar, sondern als Funktion einer Größe auftritt, oder wenn es von mehreren Faktoren abhängt. Am einfachsten führt hier die Anwendung der Differentialrechnung zum Ziele. Es sei z. B. das Ergebnis R eine Funktion der beobachteten Größe x, also R = g;(x). Begeht man bei der Bestimmung von x einen Fehler ± I, so erhält man im Ergebnis R einen Fehler F, der dadurch bestimmt ist, daß R + F = rp (x ± I) sein muß.


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Product Details
  • ISBN-13: 9783709152683
  • Publisher: Springer Verlag GmbH
  • Binding: Paperback
  • Height: 234 mm
  • No of Pages: 77
  • Series Title: Werkstattbücher
  • Weight: 177 gr
  • ISBN-10: 3709152682
  • Publisher Date: 01 Jan 1930
  • Edition: 1930 ed.
  • Language: German
  • Returnable: N
  • Spine Width: 4 mm
  • Width: 156 mm


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