Renard series

	DIN 323
Area	mathematics
title	Norm numbers and norm number series; Part 1: main values, exact values, round values; Part 2: Introduction
Latest edition	1974-08; 1974-11
ISO	3

The standard numbers or Renard series are preferred numbers specified in the ISO 3 and DIN 323 standards based on geometric sequences . Mathematically, these series are described by the multiplier . It is an integer greater than 1, which denotes the number of stages per decimal. The standard values ​​are rounded for use in practice. Thus z. For example, in the standardization of screws, it is easy to achieve that with larger screw diameters there is a larger arithmetic distance between one screw and the next larger, while smaller screw dimensions are more finely graduated. ${\displaystyle R_{m}={\sqrt[{m}]{10}}}$ ${\displaystyle m}$

The rated currents of fuses , miniature circuit breakers and thus also of connectors and cables are based on the sequence of numbers in the R series.

The values ​​of passive electrical components such as electrical resistors , capacitors and inductors are graded in E series .

General

The Renard series go back to the French military engineer Charles Renard , who in 1877 determined the strength of the cables used for tethered balloons on the geometric sequence

${\displaystyle a_{n}=a_{n-1}\cdot {\sqrt[{5}]{10}}\approx a_{n-1}\cdot 1{,}585}$

standardized and thus reduced the number of variants from 425 to 17. The choice of base 10 goes well with the decimal prefixes for units of measurement , since the sequence in the distance of m terms only differs in the decimal place.

In many cases, standards that are based on such a series are mistakenly considered to be inch-based, as the crooked numbers seem unfamiliar to someone who is used to the metric system and the most common 25 corresponds to the rounded millimeter value of an inch (25.4 mm) .

For suitable values, it is possible to multiply by 10 ⁿ and, if necessary, only a section of a series can be used; the start and end values ​​are given in brackets after the name of the series. If the step size is to be changed, it is attached to the name with a slash . For example, "R10 / 3 (10..315)": 10, 20, 40, 80, 160, 315, since only every third value from the R10 series is used.

values

slightly rounded R5 R10 R20 R40 1.00 1.00 1.00 1.00 1.06 1.12 1.12 1.18 1.25 1.25 1.25 1.32 1.40 1.40 1.50 1.60 1.60 1.60 1.60 1.70 1.80 1.80 1.90 2.00 2.00 2.00 2.12 2.24 2.24 2.36 2.50 2.50 2.50 2.50 2.65 2.80 2.80 3.00 3.15 3.15 3.15 3.35 3.55 3.55 3.75 4.00 4.00 4.00 4.00 4.25 4.50 4.50 4.75 5.00 5.00 5.00 5.30 5.60 5.60 6.00 6.30 6.30 6.30 6.30 6.70 7.10 7.10 7.50 8.00 8.00 8.00 8.50 9.00 9.00 9.50 10.0 10.0 10.0 10.0

rounded R'10 R'20 R'40 1.00 1.00 1.00 1.05 1.12 1.12 1.20 1.25 1.25 1.25 1.30 1.40 1.40 1.50 1.60 1.60 1.60 1.70 1.80 1.80 1.90 2.00 2.00 2.00 2.10 2.20 2.20 2.40 2.50 2.50 2.50 2.60 2.80 2.80 3.00 3.20 3.20 3.20 3.40 3.60 3.60 3.80 4.00 4.00 4.00 4.20 4.50 4.50 4.80 5.00 5.00 5.00 5.30 5.60 5.60 6.00 6.30 6.30 6.30 6.70 7.10 7.10 7.50 8.00 8.00 8.00 8.50 9.00 9.00 9.50 10.0 10.0 10.0

strongly rounded R′′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 ---

example

Ventilation pipes

The series values ​​can be multiplied by any whole number of powers of ten. This results in standard dimensions in millimeters.

1. Ventilation technology

The diameters of pipes and fittings for ventilation technology are graded according to the R20 series. In this way you get meaningful proportions to each other. If you consider a pipe with any diameter and surface cross-section (e.g.  ), then the third following value in the series (here  ) has exactly twice the surface cross-section and can transport twice the amount of air at the same air speed. ${\displaystyle d}$ ${\displaystyle A}$ ${\displaystyle d=160\,\mathrm {mm} ,A\approx 0{,}02\,\mathrm {m} ^{2}}$ ${\displaystyle d=224\,\mathrm {mm} ,A\approx 0{,}04\mathrm {m} ^{2}}$

2. Screw lengths

An assortment of screws is to be produced, which covers the lengths between and . With the help of the standard numbers, the following lengths for the screws result when the series values ​​are multiplied by: ${\displaystyle 30\,\mathrm {mm} }$ ${\displaystyle 100\,\mathrm {mm} }$ ${\displaystyle 10}$

Screw lengths according to the respective Renard series

R5	R10
	${\displaystyle 31{,}5\,\mathrm {mm} }$
${\displaystyle 40\,\mathrm {mm} }$	${\displaystyle 40\,\mathrm {mm} }$
	${\displaystyle 50\,\mathrm {mm} }$
${\displaystyle 63\,\mathrm {mm} }$	${\displaystyle 63\,\mathrm {mm} }$
	${\displaystyle 80\,\mathrm {mm} }$
${\displaystyle 100\,\mathrm {mm} }$	${\displaystyle 100\,\mathrm {mm} }$

Others

Also, fuses are graded according to preferred number.

Relevant ISO standards

• ISO 3: 1973, Preferred Numbers - Series of Preferred Numbers .
• ISO 17: 1973, Guide to the Use of Preferred Numbers and of Series of Preferred Numbers .
• ISO 497: 1973, Guide to the Choice of Series of Preferred Numbers and of Series Containing More Rounded Values ​​of Preferred Numbers .

With one of the forms (with , i.e. m = 3, 6, 12, 24, ...) one obtains the values ​​on which the E series for electronic components are based. ${\displaystyle m}$ ${\displaystyle m=3\cdot 2^{n}}$ ${\displaystyle n\in \mathbb {N} }$

The DIN paper formats are also laid out as a geometric sequence , but on the basis of doubling and not tenfold.

Web links

• http://www.sizes.com/numbers/preferred_numbers.htm