By William Frederick Durand
Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer ebook information mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
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Extra info for Aerodynamic Theory: A General Review of Progress Under a Grant of the Guggenheim Fund for the Promotion of Aeronautics
In contradistinction to the term vector, the term scalar is used to imply a number, or geometrically, a length, without reference to direction. The scalar value of a vector is simply its length measured in any convenient unit. Thus in Fig. 10 if the length of OP is 10 units, then as a scalar, OP is a line 10 units long and that is all; while as a vector, OP is a line 10 units long and inclined at an angle () with the XX direction. It may also be noted that the specification direction implies something more than line of action.
Kinematic Similitude. The most important application of the theory of dimensions to the problems of aeronautics is found in the development of the theory of kinematic similitude. Of this we shall give here only a brief outline. We must first note the characteristics of a dimensionless quantity. Algebraically, when the expression of the dimensions reduces to unity, the quantity is dimensionless. Thus Length -:- Length = L -:- L Volume-:- Statical Moment of Area= £3-:- £3 Moment of force -:- Energy = M L 2 T-2 -:- M £2 T-2 Thus a ratio is always dimensionless and generally the quotient of two quantities each of which has the same dimensions.
Addition of Vectors. Taking. form (1) in Fig. 13 we have AB = x1 + i y1 BC = x2 + i Y2 We now apply the usual rules of algebra to the addition of these two vectors. We may evidently do this under the condition that we are able to interpret our results in a manner consistent with the geometry of the diagram. We shall then have: y AB + BC = (x1 + x 2) + i (Yt + Y2) On the right the interpretation is clear. It directs us, starting from A to go a distance (x1 + x2) in the X direction and X then a distance (y1 + y 2 ) in the Y direction.