Roughness

It has been suggested that Rugosity be merged into this article or section. ()

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 may cause friction, wear, drag and fatigue, but it is sometimes beneficial, as it (texture) 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

• International Roughness Index (IRI) - a dimensionless quantity used for measuring road roughness and proposed as a world standard by the World Bank. Typically IRI is presented as an average value over 20 m, 100 m, 400 m, 1 mile etc. IRI is not an excellent indicator on ride quality. Consider two 10 cm high and arc-shaped traffic calming speed bumps, one "spinebreaker" being 1 m long and the other being as much as 10 m long and thus too smooth for calming city traffic. Both give an IRI20 of about 8 mm/m. Not being able to distinguish between two bumps that obviously give dramatically different ride quality, one can really question IRI as a pavement performance indicator.
• 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. Gives a value somewhat larger than Ra (varies with surface shape, 11% for sinusoidal surfaces).
• Roughness numbers, as defined by ISO 1302.
• Surface Texture, as defined by ANSI/ASME B46.1-1985 and ANSI Y14.36-1978.
• Manning's n-value - used by geologists to characterise river channels.
• Roughness of the surface finish on bearings or bushings, such as those used for connecting rods in automotive engines

Theory

The mathematician Benoît Mandelbrot has pointed out the connection between surface roughness and fractal dimension. Traverse length and cutoff length play a key role in surface roughness measurement.

References

• "Surface Finish Roughness Terminology" from Michigan Tech
• "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
• Marks' Standard Handbook for Mechanical Engineers, Section 13.5 "Surface Texture Designation, Production, and Control" by Thomas W. Wolf.
• "Relating Road Roughness and Vehicle Speeds to Human Whole Body Vibration and Exposure Limits" by Ahlin & Granlund in International Journal of Pavement Engineering, Volume 3, Issue 4 December 2002 , pages 207 - 216.