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Renard series

April 12, 2024

Renard series are a system of preferred numbers dividing an interval from 1 to 10 into 5, 10, 20, or 40 steps.[1] This set of preferred numbers was proposed in 1877 by French army engineer Colonel Charles Renard.[2][3][4] His system was adopted by the ISO in 1949[5] to form the ISO Recommendation R3, first published in 1953[6] or 1954, which evolved into the international standard ISO 3.[1] 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. One application of the Renard series of numbers is the current rating of electric fuses. Another common use is the voltage rating of capacitors (e.g. 100 V, 160 V, 250 V, 400 V, 630 V).

Base series edit

The most basic R5 series consists of these five rounded numbers, which are powers of the fifth root of 10, rounded to two digits. The Renard numbers are not always rounded to the closest three-digit number to the theoretical geometric sequence:

R5: 1.00 1.60 2.50 4.00 6.30

Examples edit

  • If some design constraints were assumed so that two screws in a gadget should be placed between 32 mm and 55 mm apart, the resulting length would be 40 mm, because 4 is in the R5 series of preferred numbers.
  • If a set of nails with lengths between roughly 15 and 300 mm should be produced, then the application of the R5 series would lead to a product repertoire of 16 mm, 25 mm, 40 mm, 63 mm, 100 mm, 160 mm, and 250 mm long nails.
  • If traditional English wine cask sizes had been metricated, the rundlet (18 gallons, ca 68 liters), barrel (31.5 gal., ca 119 liters), tierce (42 gal., ca 159 liters), hogshead (63 gal., ca 239 liters), puncheon (84 gal., ca 318 liters), butt (126 gal., ca 477 liters) and tun (252 gal., ca 954 liters) could have become 63 (or 60 by R″5), 100, 160 (or 150), 250, 400, 630 (or 600) and 1000 liters, respectively.

Alternative series edit

If a finer resolution is needed, another five numbers are added to the series, one after each of the original R5 numbers, and one ends up with the R10 series. These are rounded to a multiple of 0.05. Where an even finer grading is needed, the R20, R40, and R80 series can be applied. The R20 series is usually rounded to a multiple of 0.05, and the R40 and R80 values interpolate between the R20 values, rather than being powers of the 80th root of 10 rounded correctly. In the table below, the additional R80 values are written to the right of the R40 values in the column named "R80 add'l". The R40 numbers 3.00 and 6.00 are higher than they "should" be by interpolation, in order to give rounder numbers.

In some applications more rounded values are desirable, either because the numbers from the normal series would imply an unrealistically high accuracy, or because an integer value is needed (e.g., the number of teeth in a gear). For these needs, more rounded versions of the Renard series have been defined in ISO 3. In the table below, rounded values that differ from their less rounded counterparts are shown in bold.

As the Renard numbers repeat after every 10-fold change of the scale, they are particularly well-suited for use with SI units. It makes no difference whether the Renard numbers are used with metres or millimetres. But one would need to use an appropriate number base to avoid ending up with two incompatible sets of nicely spaced dimensions, if for instance they were applied with both inches and feet. In the case of inches and feet a root of 12 would be desirable, that is, n√12 where n is the desired number of divisions within the major step size of twelve. Similarly, a base of two, eight, or sixteen would fit nicely with the binary units commonly found in computer science.

Each of the Renard sequences can be reduced to a subset by taking every nth value in a series, which is designated by adding the number n after a slash.[4] For example, "R10″/3 (1…1000)" designates a series consisting of every third value in the R″10 series from 1 to 1000, that is, 1, 2, 4, 8, 15, 30, 60, 120, 250, 500, 1000.

Such narrowing of the general original series brings the opposite idea of deepening the series and to redefine it by a strict simple formula. As the beginning of the selected series seen higher, the {1, 2, 4, 8, ...} series can be defined as binary. That means that the R10 series can be formulated as R10 ≈ bR3 = 3√2n, generating just 9 values of R10, just because of the kind of periodicity. This way rounding is eliminated, as the 3 values of the first period are repeated multiplied by 2. The usual cons however is that the thousand product of such multiplication is shifted slightly: Instead of decadic 1000, the binary 1024 appears, as classics in IT. The pro is that the characteristics is now fully valid, that whatever value multiplied by 2 is also member of the series, any rounding effectively eliminated. The multiplication by 2 is possible in R10 too, to get another members, but the long fractioned numbers complicate the R10 accuracy.

See also edit

References edit

  1. ^ a b ISO 3:1973-04 - Preferred Numbers - Series of Preferred Numbers. International Standards Organization (ISO). April 1973. Retrieved 2016-12-18. (Replaced: ISO Recommendation R3-1954 - Preferred Numbers - Series of Preferred Numbers. July 1954. (July 1953))
  2. ^ Kienzle, Otto Helmut [in German] (2013-10-04) [1950]. Written at Hannover, Germany. Normungszahlen [Preferred numbers]. Wissenschaftliche Normung (in German). Vol. 2 (reprint of 1st ed.). Berlin / Göttingen / Heidelberg, Germany: Springer-Verlag OHG. ISBN 978-3-642-99831-7. Retrieved 2017-11-01. (340 pages)
  3. ^ Paulin, Eugen (2007-09-01). Logarithmen, Normzahlen, Dezibel, Neper, Phon - natürlich verwandt! [Logarithms, preferred numbers, decibel, neper, phon - naturally related!] (PDF) (in German). (PDF) from the original on 2016-12-18. Retrieved 2016-12-18.
  4. ^ a b "preferred numbers". Sizes, Inc. 2014-06-10 [2000]. from the original on 2017-11-01. Retrieved 2017-11-01.
  5. ^ ISO 17:1973-04 - Guide to the use of preferred numbers and of series of preferred numbers. International Standards Organization (ISO). April 1973. from the original on 2017-11-02. Retrieved 2017-11-02. […] Preferred numbers were first utilized in France at the end of the nineteenth century. From 1877 to 1879, Captain Charles Renard, an officer in the engineer corps, made a rational study of the elements necessary in the construction of […] aircraft. He computed the specifications […] according to a grading system […]. Recognizing the advantage to be derived from the geometrical progression, he adopted […] a grading system […] that would yield a tenth multiple of the value […] after every fifth step of the series […] Renard's theory was to substitute […] more rounded but […] practical values […] as a power of 10, positive, nil or negative. He thus obtained […] 10 16 25 40 63 100 […] continued in both directions […] by the symbol R5 […] the R10, R20, R40 series were formed, each adopted ratio being the square root of the preceding one […] The first standardization drafts were drawn up on these bases in Germany by the Normenausschuss der Deutschen Industrie on 13 April 1920, and in France by the Commission permanente de standardisation in document X of 19 December 1921. […] the commission of standardization in the Netherlands proposed their unification […] reached in 1931 […] in June 1932, the International Federation of the National Standardizing Associations organized an international meeting in Milan, where the ISA Technical Committee 32, Preferred numbers, was set up and its Secretariat assigned to France. On 19 September 1934, the ISA Technical Committee 32 held a meeting in Stockholm; sixteen nations were represented: Austria, Belgium, Czechoslovakia, Denmark, Finland, France, Germany, Hungary, Italy, Netherlands, Norway, Poland, Spain, Sweden, Switzerland, U.S.S.R. With the exception of the Spanish, Hungarian and Italian […] the other delegations accepted the draft […] Japan communicated […] its approval […] the international recommendation was laid down in ISA Bulletin 11 (December 1935). […] After the Second World War, the work was resumed by ISO. The Technical Committee ISO/TC 19, Preferred numbers, was set up and France again held the Secretariat. This Committee at its first meeting […] in Paris in July 1949 […] recommended […] preferred numbers defined by […] ISA Bulletin 11, […] R5, R10, R20, R40. This meeting was attended by […] 19 […] nations: Austria, Belgium, Czechoslovakia, Denmark, Finland, France, Hungary, India, Israel, Italy, Netherlands, Norway, Poland, Portugal, Sweden, Switzerland, United Kingdom, U.S.A., U.S.S.R. During […] subsequent meetings in New York in 1952 and […] the Hague in 1953, […] attended also by Germany, […] series R80 was added […] The draft thus amended became ISO Recommendation R3. […] (Replaced: ISO Recommendation R17-1956 - Preferred Numbers - Guide to the Use of Preferred Numbers and of Series of Preferred Numbers. 1956. (1955) and ISO R17/A1-1966 - Amendment 1 to ISO Recommendation R17-1955. 1966.)
  6. ^ De Simone, Daniel V. (July 1971). U.S. Metric Study Interim Report - Engineering Standards (PDF). Washington, USA: The National Bureau of Standards (NBS). NBS Special Publication 345-11 (Code: XNBSA). (PDF) from the original on 2017-11-03. Retrieved 2017-11-03. {{cite book}}: |website= ignored (help)

Further reading edit

April 12, 2024
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Renard series are a system of preferred numbers dividing an interval from 1 to 10 into 5 10 20 or 40 steps 1 This set of preferred numbers was proposed in 1877 by French army engineer Colonel Charles Renard 2 3 4 His system was adopted by the ISO in 1949 5 to form the ISO Recommendation R3 first published in 1953 6 or 1954 which evolved into the international standard ISO 3 1 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 One application of the Renard series of numbers is the current rating of electric fuses Another common use is the voltage rating of capacitors e g 100 V 160 V 250 V 400 V 630 V Contents 1 Base series 2 Examples 3 Alternative series 4 See also 5 References 6 Further readingBase series editThe most basic R5 series consists of these five rounded numbers which are powers of the fifth root of 10 rounded to two digits The Renard numbers are not always rounded to the closest three digit number to the theoretical geometric sequence R5 1 00 1 60 2 50 4 00 6 30Examples editIf some design constraints were assumed so that two screws in a gadget should be placed between 32 mm and 55 mm apart the resulting length would be 40 mm because 4 is in the R5 series of preferred numbers If a set of nails with lengths between roughly 15 and 300 mm should be produced then the application of the R5 series would lead to a product repertoire of 16 mm 25 mm 40 mm 63 mm 100 mm 160 mm and 250 mm long nails If traditional English wine cask sizes had been metricated the rundlet 18 gallons ca 68 liters barrel 31 5 gal ca 119 liters tierce 42 gal ca 159 liters hogshead 63 gal ca 239 liters puncheon 84 gal ca 318 liters butt 126 gal ca 477 liters and tun 252 gal ca 954 liters could have become 63 or 60 by R 5 100 160 or 150 250 400 630 or 600 and 1000 liters respectively Alternative series editIf a finer resolution is needed another five numbers are added to the series one after each of the original R5 numbers and one ends up with the R10 series These are rounded to a multiple of 0 05 Where an even finer grading is needed the R20 R40 and R80 series can be applied The R20 series is usually rounded to a multiple of 0 05 and the R40 and R80 values interpolate between the R20 values rather than being powers of the 80th root of 10 rounded correctly In the table below the additional R80 values are written to the right of the R40 values in the column named R80 add l The R40 numbers 3 00 and 6 00 are higher than they should be by interpolation in order to give rounder numbers In some applications more rounded values are desirable either because the numbers from the normal series would imply an unrealistically high accuracy or because an integer value is needed e g the number of teeth in a gear For these needs more rounded versions of the Renard series have been defined in ISO 3 In the table below rounded values that differ from their less rounded counterparts are shown in bold least roundedR5 R10 R20 R40 R80 add l1 00 1 00 1 00 1 00 1 031 06 1 091 12 1 12 1 151 18 1 221 25 1 25 1 25 1 281 32 1 361 40 1 40 1 451 50 1 551 60 1 60 1 60 1 60 1 651 70 1 751 80 1 80 1 851 90 1 952 00 2 00 2 00 2 062 12 2 182 24 2 24 2 302 36 2 432 50 2 50 2 50 2 50 2 582 65 2 722 80 2 80 2 903 00 3 073 15 3 15 3 15 3 253 35 3 453 55 3 55 3 653 75 3 874 00 4 00 4 00 4 00 4 124 25 4 374 50 4 50 4 624 75 4 875 00 5 00 5 00 5 155 30 5 455 60 5 60 5 756 00 6 156 30 6 30 6 30 6 30 6 506 70 6 907 10 7 10 7 307 50 7 758 00 8 00 8 00 8 258 50 8 759 00 9 00 9 259 50 9 7510 0 10 0 10 0 10 0 medium roundedR 10 R 20 R 401 00 1 00 1 001 051 10 1 101 201 25 1 25 1 251 301 40 1 401 501 60 1 60 1 601 701 80 1 801 902 00 2 00 2 002 102 20 2 202 402 50 2 50 2 502 602 80 2 803 003 20 3 20 3 203 403 60 3 603 804 00 4 00 4 004 204 50 4 504 805 00 5 00 5 005 305 60 5 606 006 30 6 30 6 306 707 10 7 107 508 00 8 00 8 008 509 00 9 009 5010 0 10 0 10 0 most roundedR 5 R 10 R 20 1 0 1 0 1 0 1 1 1 2 1 2 1 4 1 5 1 5 1 6 1 8 2 0 2 0 2 2 2 5 2 5 2 5 2 8 3 0 3 0 3 5 4 0 4 0 4 0 4 5 5 0 5 0 5 5 6 0 6 0 6 0 7 0 8 0 8 0 9 0 10 10 10 As the Renard numbers repeat after every 10 fold change of the scale they are particularly well suited for use with SI units It makes no difference whether the Renard numbers are used with metres or millimetres But one would need to use an appropriate number base to avoid ending up with two incompatible sets of nicely spaced dimensions if for instance they were applied with both inches and feet In the case of inches and feet a root of 12 would be desirable that is n 12 where n is the desired number of divisions within the major step size of twelve Similarly a base of two eight or sixteen would fit nicely with the binary units commonly found in computer science Each of the Renard sequences can be reduced to a subset by taking every nth value in a series which is designated by adding the number n after a slash 4 For example R10 3 1 1000 designates a series consisting of every third value in the R 10 series from 1 to 1000 that is 1 2 4 8 15 30 60 120 250 500 1000 Such narrowing of the general original series brings the opposite idea of deepening the series and to redefine it by a strict simple formula As the beginning of the selected series seen higher the 1 2 4 8 series can be defined as binary That means that the R10 series can be formulated as R10 bR3 3 2n generating just 9 values of R10 just because of the kind of periodicity This way rounding is eliminated as the 3 values of the first period are repeated multiplied by 2 The usual cons however is that the thousand product of such multiplication is shifted slightly Instead of decadic 1000 the binary 1024 appears as classics in IT The pro is that the characteristics is now fully valid that whatever value multiplied by 2 is also member of the series any rounding effectively eliminated The multiplication by 2 is possible in R10 too to get another members but the long fractioned numbers complicate the R10 accuracy See also editPreferred numbers Preferred metric sizes 1 2 5 series E series preferred numbers Logarithm Decibel Neper Phon Nominal Pipe Size NPS Geometric progressionReferences edit a b ISO 3 1973 04 Preferred Numbers Series of Preferred Numbers International Standards Organization ISO April 1973 Retrieved 2016 12 18 Replaced ISO Recommendation R3 1954 Preferred Numbers Series of Preferred Numbers July 1954 July 1953 Kienzle Otto Helmut in German 2013 10 04 1950 Written at Hannover Germany Normungszahlen Preferred numbers Wissenschaftliche Normung in German Vol 2 reprint of 1st ed Berlin Gottingen Heidelberg Germany Springer Verlag OHG ISBN 978 3 642 99831 7 Retrieved 2017 11 01 340 pages Paulin Eugen 2007 09 01 Logarithmen Normzahlen Dezibel Neper Phon naturlich verwandt Logarithms preferred numbers decibel neper phon naturally related PDF in German Archived PDF from the original on 2016 12 18 Retrieved 2016 12 18 a b preferred numbers Sizes Inc 2014 06 10 2000 Archived from the original on 2017 11 01 Retrieved 2017 11 01 ISO 17 1973 04 Guide to the use of preferred numbers and of series of preferred numbers International Standards Organization ISO April 1973 Archived from the original on 2017 11 02 Retrieved 2017 11 02 Preferred numbers were first utilized in France at the end of the nineteenth century From 1877 to 1879 Captain Charles Renard an officer in the engineer corps made a rational study of the elements necessary in the construction of aircraft He computed the specifications according to a grading system Recognizing the advantage to be derived from the geometrical progression he adopted a grading system that would yield a tenth multiple of the value after every fifth step of the series Renard s theory was to substitute more rounded but practical values as a power of 10 positive nil or negative He thus obtained 10 16 25 40 63 100 continued in both directions by the symbol R5 the R10 R20 R40 series were formed each adopted ratio being the square root of the preceding one The first standardization drafts were drawn up on these bases in Germany by the Normenausschuss der Deutschen Industrie on 13 April 1920 and in France by the Commission permanente de standardisation in document X of 19 December 1921 the commission of standardization in the Netherlands proposed their unification reached in 1931 in June 1932 the International Federation of the National Standardizing Associations organized an international meeting in Milan where the ISA Technical Committee 32 Preferred numbers was set up and its Secretariat assigned to France On 19 September 1934 the ISA Technical Committee 32 held a meeting in Stockholm sixteen nations were represented Austria Belgium Czechoslovakia Denmark Finland France Germany Hungary Italy Netherlands Norway Poland Spain Sweden Switzerland U S S R With the exception of the Spanish Hungarian and Italian the other delegations accepted the draft Japan communicated its approval the international recommendation was laid down in ISA Bulletin 11 December 1935 After the Second World War the work was resumed by ISO The Technical Committee ISO TC 19 Preferred numbers was set up and France again held the Secretariat This Committee at its first meeting in Paris in July 1949 recommended preferred numbers defined by ISA Bulletin 11 R5 R10 R20 R40 This meeting was attended by 19 nations Austria Belgium Czechoslovakia Denmark Finland France Hungary India Israel Italy Netherlands Norway Poland Portugal Sweden Switzerland United Kingdom U S A U S S R During subsequent meetings in New York in 1952 and the Hague in 1953 attended also by Germany series R80 was added The draft thus amended became ISO Recommendation R3 Replaced ISO Recommendation R17 1956 Preferred Numbers Guide to the Use of Preferred Numbers and of Series of Preferred Numbers 1956 1955 and ISO R17 A1 1966 Amendment 1 to ISO Recommendation R17 1955 1966 De Simone Daniel V July 1971 U S Metric Study Interim Report Engineering Standards PDF Washington USA The National Bureau of Standards NBS NBS Special Publication 345 11 Code XNBSA Archived PDF from the original on 2017 11 03 Retrieved 2017 11 03 a href Template Cite book html title Template Cite book cite book a website ignored help Further reading editHirshfeld Clarence Floyd Berry C H 1922 12 04 Size Standardization by Preferred Numbers Mechanical Engineering 44 12 New York USA The American Society of Mechanical Engineers 791 1 Hazeltine Louis Alan January 1927 December 1926 Preferred Numbers Proceedings of the Institute of Radio Engineers 14 4 Institute of Radio Engineers IRE 785 787 doi 10 1109 JRPROC 1926 221089 ISSN 0731 5996 Van Dyck Arthur F February 1936 Preferred Numbers Proceedings of the Institute of Radio Engineers 24 2 Institute of Radio Engineers IRE 159 179 doi 10 1109 JRPROC 1936 228053 ISSN 0731 5996 S2CID 140107818 Van Dyck Arthur F March 1951 February 1951 Preferred Numbers Proceedings of the IRE 39 2 Institute of Radio Engineers IRE 115 doi 10 1109 JRPROC 1951 230759 ISSN 0096 8390 ISO 497 1973 05 Guide to the choice of series of preferred numbers and of series containing more rounded values of preferred numbers International Standards Organization ISO May 1973 Archived from the original on 2017 11 02 Retrieved 2017 11 02 Replaced ISO Recommendation R497 1966 Preferred Numbers Guide to the Choice of Series of Preferred Numbers and of Series Containing More Rounded Values of Preferred Numbers 1966 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 Brucke zwischen Logarithmen Dezibel Neper und Normzahlen The decilog a bridge between logarithms decibel neper and preferred numbers VDI Zeitschrift in German 98 267 274 Retrieved from https en wikipedia org w index php title Renard series amp oldid 1196429645, wikipedia, wiki, book, books, library,

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