Roughness or rugosity is a measurement (see surface metrology) of the small-scale variations in the height of a physical surface. This is in contrast to large-scale variations, which may be either part of the geometry of the surface or unwanted 'waviness'. Roughness is sometimes an undesirable property, as it causes friction, wear, drag and fatigue, but it is sometimes beneficial, as it allows surfaces to trap lubricants and prevents them from welding together. It is measured in different ways for different purposes. Here are some examples.

Examples

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• International Roughness Index (IRI) - a dimensionless quantity used for measuring road roughness and proposed as a world standard by the World Bank.
• Average roughness (R_a). The average height of the bumps on a surface, measured in micrometres or microinches.
• Root mean square (RMS) roughness. Less common than average roughness. Measured in the same units.
• Roughness numbers, as defined by ISO 1302.
• Manning's n-value - used by geologists to characterise river channels.

Theory

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The mathematician Benoit Mandelbrot has pointed out the connection between surface roughness and fractal dimension.

References

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• "Surface Finish Roughness Terminology" from Michigan Tech
• "Surface Profile Parameters" at Surface Metrology Guide
• "Surfaces and Profiles" (ibid.)
• "International Roughness Index" at The University of Michigan Transportation Research Institute (UMTRI)
• "Propeller Roughness Definitions" at Phoenix Marine Services
• "Verified Roughness Characteristics of Natural Channels" at USGS.
• "A Theory of Roughness" - interview with Mandelbrot at edge.org

Metrology

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