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The American YDS (or 'Yosemite Decimal System') was developed independently by climbers at Tahquitz Peak who adapted the class 5 rating of Sierra Club Class 1–5 system in the 1950s. [4] The class 5 portion of the class scale is a rock climbing classification system, while classes 1–4 are used for hiking and scrambling. [4]
The Yosemite Decimal System (YDS) is a five-part grading system used for rating the difficulty of rock climbing routes in the United States and Canada. [1] It was first devised by members of the Sierra Club in Southern California in the 1950s as a refinement of earlier systems from the 1930s, [ 2 ] and quickly spread throughout North America.
If using the imperial units yards for distance and inches for target size, one has to multiply by a factor of 1000 ⁄ 36 ≈ 27.78, since there are 36 inches in one yard. distance in yards = target in inches angle in mrad × 27.78 {\displaystyle {\text{distance in yards}}={\frac {\text{target in inches}}{\text{angle in mrad}}}\times 27.78}
The vertical exaggeration is given by: = where VS is the vertical scale and HS is the horizontal scale, both given as representative fractions.. For example, if 1 centimetre (0.39 in) vertically represents 200 metres (660 ft) and 1 centimetre (0.39 in) horizontally represents 4,000 metres (13,000 ft), the vertical exaggeration, 20×, is given by:
1 Sq. Karam or Sarsahi 2.777777 Sq. yds. 9 Sarsahies or 1 Marla 24.999999 Sq. yards say 25 Sq.yards. 20 Marlas or 1 Kanal 499.9999 Sq. yards say 500 Sq.yards; 193.60 Marlas (9 Kanals1 Acre or 4840 Sq.yds 13 Marlas 5 Sarsahis)
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The scaling is uniform if and only if the scaling factors are equal (v x = v y = v z). If all except one of the scale factors are equal to 1, we have directional scaling. In the case where v x = v y = v z = k, scaling increases the area of any surface by a factor of k 2 and the volume of any solid object by a factor of k 3.
The Reynolds and Womersley Numbers are also used to calculate the thicknesses of the boundary layers that can form from the fluid flow’s viscous effects. The Reynolds number is used to calculate the convective inertial boundary layer thickness that can form, and the Womersley number is used to calculate the transient inertial boundary thickness that can form.