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Other lengths may be used—such as 100 metres (330 ft) where SI is favoured or a shorter length for sharper curves. Where degree of curvature is based on 100 units of arc length, the conversion between degree of curvature and radius is Dr = 18000/π ≈ 5729.57795, where D is degree and r is radius.
The angle θ is taken in the positive sense and must lie in the interval 0 < θ ≤ π (radian measure). The chord function can be related to the modern sine function, by taking one of the points to be (1,0), and the other point to be (cos θ, sin θ), and then using the Pythagorean theorem to calculate the chord length: [2]
S is the Sommerfeld Number or bearing characteristic number r is the shaft radius c is the radial clearance μ is the absolute viscosity of the lubricant N is the speed of the rotating shaft in rev/s P is the load per unit of projected bearing area. The second part of the equation is seen to be the Hersey number.
A standard example is the Reuleaux triangle, the intersection of three circles, each centered where the other two circles cross. [2] Its boundary curve consists of three arcs of these circles, meeting at 120° angles, so it is not smooth, and in fact these angles are the sharpest possible for any curve of constant width. [3]
Engineering fits are generally used as part of geometric dimensioning and tolerancing when a part or assembly is designed. In engineering terms, the "fit" is the clearance between two mating parts, and the size of this clearance determines whether the parts can, at one end of the spectrum, move or rotate independently from each other or, at the other end, are temporarily or permanently joined.
A bearing compass, is a nautical instrument used to determine the bearing of observed objects. (Bearing: angle formed by the north and the visual to a certain object in the sea or ashore). Used in navigation to determine the angle between the direction of an object and the magnetic north or, indirectly relative to another reference point.
A standard Brunton compass, used commonly by geologists and surveyors to obtain a bearing in the field. In navigation, bearing or azimuth is the horizontal angle between the direction of an object and north or another object. The angle value can be specified in various angular units, such as degrees, mils, or grad. More specifically:
The angular diameter, angular size, apparent diameter, or apparent size is an angular separation (in units of angle) describing how large a sphere or circle appears from a given point of view. In the vision sciences , it is called the visual angle , and in optics , it is the angular aperture (of a lens ).