43:
caused by the difference between the intended and actual directions in which a measurement is taken. Depending on the type of measurement, it either multiplies or divides the true value by the
448:
452:
Although multiplying and dividing by the cosine give slightly different error sizes, the difference is too small to affect the rounded percentages in the table. For example, multiplying by
407:
205:
The longer the length of the instrument, the easier it is to control cosine error. If the instrument is very small, then optical alignment techniques can be used to reduce cosine error.
364:
321:
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590:
156:). Thus the user might measure a block of metal and come away with a width of 208.92 mm when the true width is 208.91 mm, a difference that matters to the subsequent
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but failing to realize that the line of measurement is not quite parallel with the edges, being slightly
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Calculated directly from the values of the cosines of these angles, which are approximately:
54:, since an angle needs to be relatively large for its cosine to depart significantly from 1.
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Some practical examples in which the potential for cosine error must be considered include:
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as if they were equal; the cosine of the angle between them is the ratio of their lengths.
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of this triangle correlates to how much error exists in the measurement (hence the name
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The error is equivalent to treating the hypotenuse and one of the other sides of a
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Strictly, the smaller ratio: the shorter length divided by the longer one.
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of a triangle in which the desired vector is in fact one of the legs. The
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A simple example of cosine error is taking a measurement across a
566:
Introduction to
Precision Machine Design and Error Assessment
140:. Rather than measuring the desired vector (in this case,
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The use of an indicator (distance amplifying instrument)
57:
Approximate error sizes for a few example angles are:
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65 when dividing by the cosine; 66 when multiplying.
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subtracts 1.519%, while dividing by it adds 1.543%.
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50:For small angles the resulting error is typically
516:Carosell, Philip J.; Coombs, William C. (1955).
443:{\displaystyle \cos 0.01^{\circ }=0.9999999848.}
542:Cosine Error Demonstrated and Challenged !
402:{\displaystyle \cos 0.1^{\circ }=0.99999848,}
8:
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359:{\displaystyle \cos 1^{\circ }=0.999848,}
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225:Coordinate Measuring Machines and Systems
47:of the angle between the two directions.
316:{\displaystyle \cos 10^{\circ }=0.9848,}
144:width), the instrument is measuring the
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539:Pieczynski, Joe (17 January 2018).
25:
478:{\displaystyle \cos 10^{\circ }}
625:Error detection and correction
591:"ProLaser 4 OPERATOR'S MANUAL"
518:"Radar Evidence in the Courts"
1:
222:Bosch, John A. (1995-04-10).
563:Mekid, Samir (2008-12-23).
641:
29:
193:Radar traffic enforcement
188:Lidar traffic enforcement
27:Type of measurement error
183:Speed limit enforcement
114:= 1 part in 66,000,000
598:www.whatdotheyknow.com
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122:right-angled triangle
81:= 1 part in 65 or 66
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178:Laser interferometry
103:= 1 part in 660,000
18:Cosine error effect
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92:= 1 part in 6,600
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235:978-0-8247-9581-8
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41:measurement error
16:(Redirected from
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39:is a type of
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32:Solar tracker
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603:25 September
601:. Retrieved
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548:25 September
546:. Retrieved
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264:. Retrieved
261:Dover Motion
260:
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154:cosine error
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131:
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68:
63:
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37:Cosine error
36:
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394:0.99999848
266:2021-09-25
209:References
201:Mitigation
146:hypotenuse
142:orthogonal
111:0.0000015%
52:very small
30:See also:
471:∘
463:
430:∘
422:
386:∘
378:
343:∘
335:
300:∘
292:
158:machining
134:rectangle
619:Category
351:0.999848
164:Examples
138:diagonal
100:0.00015%
128:Concept
573:
528:: 323.
308:0.9848
232:
150:cosine
89:0.015%
45:cosine
594:(PDF)
522:Dicta
108:0.01°
69:Error
64:Angle
605:2021
571:ISBN
550:2021
426:0.01
230:ISBN
97:0.1°
78:1.5%
460:cos
419:cos
409:and
382:0.1
375:cos
332:cos
289:cos
75:10°
621::
596:.
526:32
524:.
520:.
508:^
467:10
296:10
259:.
244:^
160:.
86:1°
607:.
579:.
552:.
435:=
397:,
391:=
354:,
348:=
339:1
311:,
305:=
269:.
238:.
20:)
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