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In affine geometry, uniform scaling (or isotropic scaling[1]) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions (isotropically). The result of uniform scaling is similar (in the geometric sense) to the original. A scale factor of 1 is normally allowed, so ...
This implies that the vertical scale factor, h, equals the horizontal scale factor, k. Since k = sec φ, so must h. The graph shows the variation of this scale factor with latitude. Some numerical values are listed below. at latitude 30° the scale factor is k = sec 30° = 1.15, at latitude 45° the scale factor is k = sec 45° = 1.41,
A typical value of the scale factor is k 0 = 0.9996 so that k = 1 when x is approximately 180 km. When x is approximately 255 km and k 0 = 1.0004: the scale factor is within 0.04% of unity over a strip of about 510 km wide.
Scale factor (cosmology) The expansion of the universe is parametrized by a dimensionless scale factor . Also known as the cosmic scale factor or sometimes the Robertson–Walker scale factor, [1] this is a key parameter of the Friedmann equations. In the early stages of the Big Bang, most of the energy was in the form of radiation, and that ...
In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by the construction of a dimensionless quantity, in the general framework of dimensional analysis and in particular applications such as fluid mechanics.
Aspect ratio (aeronautics) An ASH 31 glider with very high aspect ratio (AR=33.5) and lift-to-drag ratio (L/D=56) In aeronautics, the aspect ratio of a wing is the ratio of its span to its mean chord. It is equal to the square of the wingspan divided by the wing area. Thus, a long, narrow wing has a high aspect ratio, whereas a short, wide wing ...
In Euclidean geometry, a plane is a flat two- dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional space . A prototypical example is one of a room's walls, infinitely extended and assumed infinitesimal thin. While a pair of real numbers suffices to describe points on a plane, the ...
Shear mapping. Horizontal shearing of the plane, transforming the blue into the red shape. The black dot is the origin. In fluid dynamics a shear mapping depicts fluid flow between parallel plates in relative motion. In plane geometry, a shear mapping is an affine transformation that displaces each point in a fixed direction by an amount ...