Standard guidelines for choosing exact product dimensions within a given set of constraints
In industrial design, preferred numbers (also called preferred values or preferred series) are standard guidelines for choosing exact product dimensions within a given set of constraints. Product developers must choose numerous lengths, distances, diameters, volumes, and other characteristic quantities. While all of these choices are constrained by considerations of functionality, usability, compatibility, safety or cost, there usually remains considerable leeway in the exact choice for many dimensions.
Using them increases the probability of compatibility between objects designed at different times by different people. In other words, it is one tactic among many in standardization, whether within a company or within an industry, and it is usually desirable in industrial contexts (unless the goal is vendor lock-in or planned obsolescence)
They are chosen such that when a product is manufactured in many different sizes, these will end up roughly equally spaced on a logarithmic scale. They therefore help to minimize the number of different sizes that need to be manufactured or kept in stock.
Preferred numbers represent preferences of simple numbers (such as 1, 2, and 5) multiplied by the powers of a convenient basis, usually 10.[1]
In 1870 Charles Renard proposed a set of preferred numbers.[2] His system was adopted in 1952 as international standard ISO 3.[3] Renard's system divides the interval from 1 to 10 into 5, 10, 20, or 40 steps, leading to the R5, R10, R20 and R40 scales, respectively. The factor between two consecutive numbers in a Renard series is approximately constant (before rounding), namely the 5th, 10th, 20th, or 40th root of 10 (approximately 1.58, 1.26, 1.12, and 1.06, respectively), which leads to a geometric sequence. This way, the maximum relative error is minimized if an arbitrary number is replaced by the nearest Renard number multiplied by the appropriate power of 10. Example: 1.0, 1.6, 2.5, 4.0, 6.3
Graph of two decades E12 series resistor values, which gives resistor values from 1 to 82 ohms (Ω).
The E series is another system of preferred numbers. It consists of the E1, E3, E6, E12, E24, E48, E96 and E192 series. Based on some of the existing manufacturing conventions, the International Electrotechnical Commission (IEC) began work on a new international standard in 1948.[4] The first version of this IEC 63 (renamed into IEC 60063 in 2007) was released in 1952.[4]
It works similarly to the Renard series, except that it subdivides the interval from 1 to 10 into 3, 6, 12, 24, 48, 96 or 192 steps. These subdivisions ensure that when some arbitrary value is replaced with the nearest preferred number, the maximum relative error will be on the order of 40%, 20%, 10%, 5%, etc.
Use of the E series is mostly restricted to electronic parts like resistors, capacitors, inductors and Zener diodes. Commonly produced dimensions for other types of electrical components are either chosen from the Renard series instead or are defined in relevant product standards (for example wires).
1–2–5 series
In applications for which the R5 series provides a too fine graduation, the 1–2–5 series is sometimes used as a cruder alternative. It is effectively an E3 series rounded to one significant digit:
… 0.1 0.2 0.5 1 2 5 10 20 50 100 200 500 1000 …
This series covers a decade (1:10 ratio) in three steps. Adjacent values differ by factors 2 or 2.5. Unlike the Renard series, the 1–2–5 series has not been formally adopted as an international standard. However, the Renard series R10 can be used to extend the 1–2–5 series to a finer graduation.
This series is used to define the scales for graphs and for instruments that display in a two-dimensional form with a graticule, such as oscilloscopes.
In the 1970s the National Bureau of Standards (NBS) defined a set of convenient numbers to ease metrication in the United States. This system of metric values was described as 1–2–5 series in reverse, with assigned preferences for those numbers which are multiples of 5, 2, and 1 (plus their powers of 10), excluding linear dimensions above 100mm.[1]
Audio frequencies
ISO 266, Acoustics—Preferred frequencies, defines two different series of audio frequencies for use in acoustical measurements. Both series are referred to the standard reference frequency of 1000Hz, and use the R10 Renard series from ISO 3, with one using powers of 10, and the other related to the definition of the octave as the frequency ratio 1:2.[5]
For example, a set of nominal center frequencies for use in audio tests and audio test equipment is:
Frequencies to be used in one-third octave analyzers in the audible range[6]
Nominal Center Frequency (Hz)
20
25
31.5
40
50
63
80
100
125
160
200
250
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000
5000
6300
8000
10000
12500
16000
20000
Computer engineering
When dimensioning computer components, the powers of two are frequently used as preferred numbers:
1 2 4 8 16 32 64 128 256 512 1024 ...
Where a finer grading is needed, additional preferred numbers are obtained by multiplying a power of two with a small odd integer:
In computer graphics, widths and heights of raster images are preferred to be multiples of 16, as many compression algorithms (JPEG, MPEG) divide color images into square blocks of that size. Black-and-white JPEG images are divided into 8×8 blocks. Screen resolutions often follow the same principle. Preferred aspect ratios have also an important influence here, e.g., 2:1, 3:2, 4:3, 5:3, 5:4, 8:5, 16:9.
Standard metric paper sizes use the square root of two (√2) as factors between neighbouring dimensions rounded to the nearest mm (Lichtenberg series, ISO 216). An A4 sheet for example has an aspect ratio very close to √2 and an area very close to 1/16 square metre. An A5 is almost exactly half an A4, and has the same aspect ratio. The √2 factor also appears between the standard pen thicknesses for technical drawings in ISO 9175-1: 0.13, 0.18, 0.25, 0.35, 0.50, 0.70, 1.00, 1.40, and 2.00mm. This way, the right pen size is available to continue a drawing that has been magnified to a different standard paper size.
Photography
In photography, aperture, exposure, and film speed generally follow powers of 2:
The aperture size controls how much light enters the camera. It is measured in f-stops: f/1.4, f/2, f/2.8, f/4, etc. Full f-stops are a square root of 2 apart. Camera lens settings are often set to gaps of successive thirds, so each f-stop is a sixth root of 2, rounded to two significant digits: 1.0, 1.1, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.5, 2.8, 3.2, 3.5, 4.0, etc. The spacing is referred to as "one-third of a stop".
The film speed is a measure of the film's sensitivity to light. It is expressed as ISO values such as "ISO 100". An earlier standard, occasionally still in use, uses the term "ASA" rather than "ISO", referring to the (former) American Standards Association. Measured film speeds are rounded to the nearest preferred number from a modified Renard series including 100, 125, 160, 200, 250, 320, 400, 500, 640, 800... This is the same as the R10′ rounded Renard series, except for the use of 6.4 instead of 6.3, and for having more aggressive rounding below ISO 16. Film marketed to amateurs, however, uses a restricted series including only powers of two multiples of ISO 100: 25, 50, 100, 200, 400, 800, 1600 and 3200. Some low-end cameras can only reliably read these values from DX encoded film cartridges because they lack the extra electrical contacts that would be needed to read the complete series. Some digital cameras extend this binary series to values like 12800, 25600, etc. instead of the modified Renard values 12500, 25000, etc.
The shutter speed controls how long the camera lens is open to receive light. These are expressed as fractions of a second, roughly but not exactly based on powers of 2: 1 second, 1⁄2, 1⁄4, 1⁄8, 1⁄15, 1⁄30, 1⁄60, 1⁄125, 1⁄250, 1⁄500, 1⁄1000 of a second.
Retail packaging
In some countries, consumer-protection laws restrict the number of different prepackaged sizes in which certain products can be sold, in order to make it easier for consumers to compare prices.
An example of such a regulation is the European Union directive on the volume of certain prepackaged liquids (75/106/EEC[7]). It restricts the list of allowed wine-bottle sizes to 0.1, 0.25 (1⁄4), 0.375 (3⁄8), 0.5 (1⁄2), 0.75 (3⁄4), 1, 1.5, 2, 3, and 5 litres. Similar lists exist for several other types of products. They vary and often deviate significantly from any geometric series in order to accommodate traditional sizes when feasible. Adjacent package sizes in these lists differ typically by factors 2⁄3 or 3⁄4, in some cases even 1⁄2, 4⁄5, or some other ratio of two small integers.
ISO/IEC 8859-1:1998, Information technology — 8-bit single-byte coded graphic character sets — Part 1: Latin alphabet No. 1, is part of the ISO/IEC 8859 series of ASCII-based standard character encodings, first edition published in 1987. ISO/IEC 8859-1 encodes what it refers to as "Latin alphabet no. 1", consisting of 191 characters from the Latin script. This character-encoding scheme is used throughout the Americas, Western Europe, Oceania, and much of Africa. It is the basis for some popular 8-bit character sets and the first two blocks of characters in Unicode.
The International Electrotechnical Commission is an international standards organization that prepares and publishes international standards for all electrical, electronic and related technologies – collectively known as "electrotechnology". IEC standards cover a vast range of technologies from power generation, transmission and distribution to home appliances and office equipment, semiconductors, fibre optics, batteries, solar energy, nanotechnology and marine energy as well as many others. The IEC also manages four global conformity assessment systems that certify whether equipment, system or components conform to its international standards.
A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active elements, and terminate transmission lines, among other uses. High-power resistors that can dissipate many watts of electrical power as heat may be used as part of motor controls, in power distribution systems, or as test loads for generators. Fixed resistors have resistances that only change slightly with temperature, time or operating voltage. Variable resistors can be used to adjust circuit elements, or as sensing devices for heat, light, humidity, force, or chemical activity.
The neper is a logarithmic unit for ratios of measurements of physical field and power quantities, such as gain and loss of electronic signals. The unit's name is derived from the name of John Napier, the inventor of logarithms. As is the case for the decibel and bel, the neper is a unit defined in the international standard ISO 80000. It is not part of the International System of Units (SI), but is accepted for use alongside the SI.
An electronic color code or electronic colour code is used to indicate the values or ratings of electronic components, usually for resistors, but also for capacitors, inductors, diodes and others. A separate code, the 25-pair color code, is used to identify wires in some telecommunications cables. Different codes are used for wire leads on devices such as transformers or in building wiring.
A logarithmic scale is a way of displaying numerical data over a very wide range of values in a compact way—typically the largest numbers in the data are hundreds or even thousands of times larger than the smallest numbers. Such a scale is nonlinear: the numbers 10 and 20, and 60 and 70, are not the same distance apart on a log scale. Rather, the numbers 10 and 100, and 60 and 600 are equally spaced. Thus moving a unit of distance along the scale means the number has been multiplied by 10. Often exponential growth curves are displayed on a log scale, otherwise they would increase too quickly to fit within a small graph. Another way to think about it is that the number of digits of the data grows at a constant rate. For example, the numbers 10, 100, 1000, and 10000 are equally spaced on a log scale, because their numbers of digits is going up by 1 each time: 2, 3, 4, and 5 digits. In this way, adding two digits multiplies the quantity measured on the log scale by a factor of 100.
Paper size standards govern the size of sheets of paper used as writing paper, stationery, cards, and for some printed documents.
ISO/IEC 8859-6:1999, Information technology — 8-bit single-byte coded graphic character sets — Part 6: Latin/Arabic alphabet, is part of the ISO/IEC 8859 series of ASCII-based standard character encodings, first edition published in 1987. It is informally referred to as Latin/Arabic. It was designed to cover Arabic. Only nominal letters are encoded, no preshaped forms of the letters, so shaping processing is required for display. It does not include the extra letters needed to write most Arabic-script languages other than Arabic itself.
ISO 31 is a superseded international standard concerning physical quantities, units of measurement, their interrelationships and their presentation. It was revised and replaced by ISO/IEC 80000.
Renard series are a system of preferred numbers dividing an interval from 1 to 10 into 5, 10, 20, or 40 steps. This set of preferred numbers was proposed in 1877 by French army engineer Colonel Charles Renard. His system was adopted by the ISO in 1949 to form the ISO Recommendation R3, first published in 1953 or 1954, which evolved into the international standard ISO 3. The factor between two consecutive numbers in a Renard series is approximately constant, namely the 5th, 10th, 20th, or 40th root of 10, which leads to a geometric sequence. This way, the maximum relative error is minimized if an arbitrary number is replaced by the nearest Renard number multiplied by the appropriate power of 10. One application of the Renard series of numbers is to current rating of electric fuses. Another common use is the voltage rating of capacitors.
Mesh is a measurement of particle size often used in determining the particle-size distribution of a granular material. For example, a sample from a truckload of peanuts may be placed atop a mesh with 5 mm openings. When the mesh is shaken, small broken pieces and dust pass through the mesh while whole peanuts are retained on the mesh. A commercial peanut buyer might use a test like this to determine if a batch of peanuts has too many broken pieces. This type of test is common in some industries, and, to facilitate uniform testing methods, several standardized mesh series have been established.
The ISO metric screw thread is the most commonly used type of general-purpose screw thread worldwide. They were one of the first international standards agreed when the International Organization for Standardization (ISO) was set up in 1947.
ISO 80000 or IEC 80000 is an international standard introducing the International System of Quantities (ISQ). It was developed and promulgated jointly by the International Organization for Standardization (ISO) and the International Electrotechnical Commission (IEC).
The ISO/IEC 27000-series comprises information security standards published jointly by the International Organization for Standardization (ISO) and the International Electrotechnical Commission (IEC).
The RKM code, also referred to as "letter and numeral code for resistance and capacitance values and tolerances", "letter and digit code for resistance and capacitance values and tolerances", or informally as "R notation" is a notation to specify resistor and capacitor values defined in the international standard IEC 60062 since 1952. It is also adopted by various other standards including DIN 40825 (1973), BS 1852 (1975), IS 8186 (1976) and EN 60062 (1993). The updated IEC 60062:2016, amended in 2019, comprises the most recent release of the standard.
The ISO basic Latin alphabet is an international standard for a Latin-script alphabet that consists of two sets of 26 letters, codified in various national and international standards and used widely in international communication. They are the same letters that comprise the current English alphabet. Since medieval times, they are also the same letters of the modern Latin alphabet. The order is also important for sorting words into alphabetical order.
The Universal Coded Character Set is a standard set of characters defined by the international standard ISO/IEC 10646, Information technology — Universal Coded Character Set (UCS), which is the basis of many character encodings, improving as characters from previously unrepresented typing systems are added.
ISO/IEC 9797-1Information technology – Security techniques – Message Authentication Codes (MACs) – Part 1: Mechanisms using a block cipher is an international standard that defines methods for calculating a message authentication code (MAC) over data.
The E series is a system of preferred numbers derived for use in electronic components. It consists of the E3, E6, E12, E24, E48, E96 and E192 series, where the number after the 'E' designates the quantity of logarithmic value "steps" per decade. Although it is theoretically possible to produce components of any value, in practice the need for inventory simplification has led the industry to settle on the E series for resistors, capacitors, inductors, and zener diodes. Other types of electrical components are either specified by the Renard series or are defined in relevant product standards.
Preferred metric sizes are a set of international standards and de facto standards that are designed to make using the metric system easier and simpler, especially in engineering and construction practices. One of the methods used to arrive at these preferred sizes is the use of preferred numbers and convenient numbers such as the Renard series, the 1-2-5 series to limit the number of different sizes of components needed.
Buttner, Harold H.; Kohlhaas, H. T., eds. (1943). Reference Data for Radio Engineers (1ed.). Federal Telephone and Radio Corporation (FTR). pp.37–38. Retrieved 2020-01-03. (NB. This 1943 publication already shows a list of new "preferred values of resistance" following what was adopted by the IEC for standardization since 1948 and standardized as the E series of preferred numbers in IEC63:1952. For comparison, it also lists "old standard resistance values" as follows: 50, 75, 100, 150, 200, 250, 300, 350, 400, 450, 500, 600, 750, 1000, 1200, 1500, 2000, 2500, 3000, 3500, 4000, 5000, 7500, 10000, 12000, 15000, 20000, 25000, 30000, 40000, 50000, 60000, 75000, 100000, 120000, 150000, 200000, 250000, 300000, 400000, 500000, 600000, 750000, 1Meg, 1.5Meg, 2.0Meg, 3.0Meg, 4.0Meg, 5.0Meg, 6.0Meg, 7.0Meg, 8.0Meg, 9.0Meg, 10.00Meg.)
Van Dyck, Arthur F. (March 1951) [February 1951]. "Preferred Numbers". Proceedings of the Institute of Radio Engineers. Institute of Radio Engineers (IRE). 39 (2): 115. doi:10.1109/JRPROC.1951.230759. ISSN0096-8390. […] For example, some years ago, the Radio-Television Manufacturers Association found it desirable to standardize the values of resistors. The ASA Preferred Numbers Standard was considered, but judged not to suit the manufacturing conditions and the buying practices of the resistor field at the moment, whereas a special series of numbers suited better. The special series was adopted and, since it was an official RTMA list, it has been utilized by later RTMA committees for other applications than resistors, although adopted originally because of seeming advantages for resistors. Ironically, the original advantages have largely disappeared through changes in resistor manufacturing conditions. But the irregular standard remains… […]
ANSI Z17.1-1973 - American National Standard for Preferred Numbers. American National Standards Institute (ANSI). 1973-09-05. (9 pages) (Replaced: ASA Z17.1-1958 - American National Standard for Preferred Numbers. 1958. Reaffirmed as USASI Z17.1-1958 in 1966 and named ANSI Z17.1-1958 since 1969.)
Kienzle, Otto Helmut[in German] (2013-10-04) [1950]. Written at Hannover, Germany. Normungszahlen[Preferred numbers]. Wissenschaftliche Normung (in German). Vol.2 (reprint of 1sted.). Berlin / Göttingen / Heidelberg, Germany: Springer-Verlag OHG. ISBN978-3-642-99831-7. Retrieved 2017-11-01. (340 pages)
Bergtold, Fritz (1965). Mathematik für Radiotechniker und Elektroniker[Mathematics for Radio and Electronics Technicians] (in German) (3ed.). München, Germany: Franzis-Verlag.
Ries, Clemens (1962). Normung nach Normzahlen[Standardization by preferred numbers] (in German) (1ed.). Berlin, Germany: Duncker & Humblot Verlag[de]. ISBN3-42801242-9. (135 pages)
Berg, Siegfried (1949). Angewandte Normzahl - Gesammelte Aufsätze[Applied preferred number - Collected papers] (in German). Berlin / Köln, Germany: Beuth-Vertrieb GmbH. Retrieved 2017-11-01. (191 pages)
Tuffentsammer, Karl; Schumacher, P. (1953). "Normzahlen – die einstellige Logarithmentafel des Ingenieurs" [Preferred numbers - the engineer's single-digit logarithm table]. Werkstattechnik und Maschinenbau (in German). 43 (4): 156.
Tuffentsammer, Karl (1956). "Das Dezilog, eine Brücke zwischen Logarithmen, Dezibel, Neper und Normzahlen" [The decilog, a bridge between logarithms, decibel, neper and preferred numbers]. VDI-Zeitschrift (in German). 98: 267–274.
Strahringer, Wilhelm (1952). Zauberwelt der Normzahlen[Magic world of preferred numbers] (in German). Frankfurt a. Main, Germany: Verlags- und Wirtschaftsgesellschaft der Elektrizitätswerke m.b.H. (VWEW). (95 pages)
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