The next 50 years of the SI: a review of the opportunities for the e-Science age

Foster, Marcus P.

doi:10.1088/0026-1394/47/6/r01

Cited by 29 publications

(9 citation statements)

References 69 publications

(73 reference statements)

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“…One of the most important aspects of formulating physical equations in a dimensionally consistent manner relates to the construction of quantity-calculation software that is able to handle angle (and solid angle) correctly [26,43]. By including rad (as a constant of Nature) explicitly wherever it should occur, 'appropriate' units for angles (and solid angles)-and all other physical quantities-appear automatically, without any need for post-calculation 'adjustment' according to ad hoc 'rules' requiring human 'insight' for their application.…”

Section: Proposal For Treating Angle and Solid Angle Correctlymentioning

confidence: 99%

Proposal for the dimensionally consistent treatment of angle and solid angle by the International System of Units (SI)

Leonard

2021

Metrologia

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Because of continued confusion caused by the SI's interpretation of angle and solid angle as dimensionless quantities (and the radian and steradian as dimensionless derived units), it is time for the SI to treat these dimensional physical quantities correctly. Building on previous authors' foundations, starting from Euclid's Elements, I argue that angle should be recognized as a base quantity with an independent dimension: angle, A. A dimensionally consistent analysis of rotational geometry and mechanics results in the appearance of a constant of Nature equal to the central angle of a plane circular sector whose arc length is equal to that of its radius. This is the common (but not current SI) concept of the radian, rad, appropriately chosen as the base unit for angle. What the SI calls 'angle' is actually a nondimensionalized angle: the physical angle (dimension A) divided by one radian. Using a coordinate-system-independent definition of solid angle, I show that this is a derived quantity with dimension A 2 and appropriate unit radian-squared. The steradian is retained as a coherent derived unit: sr = rad 2 . Clarification of terminology is needed in distinguishing between 'geometrical' and 'mathematical' trigonometric functions and in related topics, including the distinction between frequency and angular velocity, and between phase and phase angle, among other things.

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Section: Proposal For Treating Angle and Solid Angle Correctlymentioning

confidence: 99%

Proposal for the dimensionally consistent treatment of angle and solid angle by the International System of Units (SI)

Leonard

2021

Metrologia

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“…The case for treating angle as a base quantity has been made many times over a long period, for example by Brinsmade (1936), Romain (1962), Eder (1982), Torrens (1986), Brownstein (1997), Foster (2010) and Mohr and Phillips (2015).…”

Section: The Case For Making Angle a Base Quantitymentioning

confidence: 99%

Implications of adopting plane angle as a base quantity in the SI

Quincey

Brown

2016

Metrologia

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The treatment of angles within the SI is anomalous compared with other quantities, and there is a case for removing this anomaly by declaring plane angle to be an additional base quantity within the system. It is shown that this could bring several benefits in terms of treating angle on an equal basis with other metrics, removing potentially harmful ambiguities, and bringing SI units more in line with concepts in basic physics, but at the expense of significant upheaval to familiar equations within mathematics and physics. This paper sets out the most important of these changes so that an alternative unit system containing angle as a base quantity can be seen in the round, irrespective of whether it is ever widely adopted. The alternative formulas and units can be treated as the underlying, more general equations of mathematical physics, independent of the units used for angle, which are conventionally simplified by implicitly assuming that the unit used for angle is the radian.

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“…They are significant also in the context of the documented conflict between the SI and the requirements of many data systems and informatics particularly evident in sensor and instrumentation technologies [6].…”

Section: An Application To Measurement: Stipulation Of Measurement Unitsmentioning

confidence: 99%

Rounding, stipulation and notation issues in measurement

Pavese¹

2013

Int. J. Metrol. Qual. Eng.

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The next 50 years of the SI: a review of the opportunities for the e-Science age

Cited by 29 publications

References 69 publications

Proposal for the dimensionally consistent treatment of angle and solid angle by the International System of Units (SI)

Proposal for the dimensionally consistent treatment of angle and solid angle by the International System of Units (SI)

Implications of adopting plane angle as a base quantity in the SI

Rounding, stipulation and notation issues in measurement

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