lotia sau of Standards

MAY li i9go

NBS MONOGRAPH 15

Calibration of Line Standards of

Length and Measuring Tapes at

The National Bureau of Standards

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

Functions and Activities

The functions of the National Bureau of Standards are set forth in the Act of Congress, March

3, 1901, as amended by Congress in Public Law 619, 1950. These include the development and

maintenance of the national standards of measurement and the provision of means and methods for making measurements consistent with these standards; the determination of physical constants and

properties of materials; the development of methods and instruments for testing materials, devices,

and structures; advisory services to government agencies on scientific and technical problems; in- vention and development of devices to serve special needs of the Government; and the development

of standard practices, codes, and specifications. The work includes basic and applied research,

development, engineering, instrumentation, testing, evaluation, calibration services, and various

consultation and information services. Research projects are also performed for other government

agencies when the work relates to and supplements the basic program of the Bureau or when the

Bureau's unique competence is required. The scope of activities is suggested by the listing of divisions

and sections on the inside of the back cover.

Publications

The results of the Bureau's work take the form of either actual equipment and devices or published papers. These papers appear either in the Bureau's own series of publications or in the journals

of professional and scientific societies. The Bureau itself publishes three periodicals available from

the Government Printing Office: The Journal of Research, published in four separate sections,

presents complete scientific and technical papers; the Technical News Bulletin presents summary

and preliminary reports on work in progress; and Basic Radio Propagation Predictions provides data

for determining the best frequencies to use for radio communications throughout the world. There

are also five series of nonperiodical publications: Monographs, Applied Mathematics Series, Handbooks, Miscellaneous Publications, and Technical Notes. Information on the Bureau's publications can be found in NBS Circular 460, Publications of the

National Bureau of Standards ($1.25) and its Supplement ($1.50), available from the Superintendent

of Documents, Government Printing Office, Washington 25, D.C.
UNITED STATES DEPARTMENT OF COMMERCE • Frederick H. Mueller, Secretary NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

Calibration of Line Standards of

Length and Measuring Tapes at

The National Bureau of Standards

Lewis V. Judson

National Bureau of Standards Monograph 15

Issued May 20, 1960

Supersedes Circular 572

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington 25, D.C. - Price 15 cents

Contents

Page

1. Introduction 1 2. Line standards of length at NBS 1 3. Facilities for calibrating line standards of length 1 4. Facilities for calibrating measuring tapes 3

4.1. Steel-tape bench 3

4.2. Geodetic tape comparator 3

5. Calibration of line standards of length 3

5.1. Reference standards 4

5.2. Working standards 4

5.3. Commercial standards 5

6. Calibration of measuring tapes 5

6.1. Specification for standard steel tapes 6

6.2. Certification of tapes 6

6.3. Standard procedures in steel-tape calibrations 6

6.4. Corrections applicable to steel tapes 7

6.5. Base-line tapes 7

7. Certificates and reports 7

8. Cooperation with officials and others 8

9. General instructions to applicants for calibrations 8

9.1. Apparatus accepted for calibration 8

9.2. Application for calibration 8

9.3. Nature of calibration 8

9.4. Special calibrations 8

9.5. Condition of apparatus 8

9.6. Identification of apparatus + 8

9.7. Shipping instructions 8

9.8. Schedule of test fees 9

9.9. Address 9

10. Appendix—Use of steel tapes 9

in
t

i
Calibration of Line Standards of Length and Measuring Tapes at

the National Bureau of Standards

Lewis V. Judson

The methods used at the National Bureau of Standards in calibrating line standards of length and measuring tapes submitted for standardization are outlined. The equipment

used is described briefly. There is a discussion of some considerations that should be given

as to whether or not a standard should be submitted to the Bureau. Instructions are given

for submitting items to the Bureau for calibration. The appendix contains useful infor- mation on the use of steel tapes.

1. Introduction

The Bureau receives many requests from scientists, industry, and governmental agencies to

calibrate line standards of length and measuring

tapes. This Monograph is issued as a guide for

anyone contemplating the submission of such items

to the Bureau for standardization. It replaces

Circular 332, Testing of line standards of length;

Circular 328, Testing of measuring tapes at the

National Bureau of Standards; and Circular 572,

Calibration of line standards of length and measur-

. ing tapes at the National Bureau of Standards.

2. Line Standards of Length at NBS

The primary standard of length in the United

States is the National Prototype Meter 27 (fig. 1), which is identical in form and material with the

International Prototype Meter deposited at the

International Bureau of Weights and Measures at

Sevres, near Paris, and also with the other national

prototype meters distributed in 1889 in accordance

with the treaty known as the Convention of the

Meter, dated May 20, 1875. Except for expressing

data in feet derived from and published as a result

of geodetic surveys within the United States, for

which the relation 1 foot= 1200/3937 meter

coi tinues to be used, the yard in the United States

is defined in terms of the meter by the relation

1 yard =0.9144 meter. At the Bureau there are secondary and laboratory length standards of various materials, sizes,

and degrees of precision. Their lengths are known

in terms of the prototype meter. These secondary

and laboratory standards are used in the calibration work done by the Bureau.

Proposals have been made to adopt, as the defi- nition of the meter, a specified number of wavelengths of a suitable isotope of an element such

as mercury (for example, the 5461 -A wavelength

of mercury 198). Interferometric calibrations of

end standards of length have been made for many

years. Such calibrations of line standards of

length have been made in Germany, and the

method is being followed with considerable in- terest at the Bureau.

3. Facilities for Calibrating Line

Standards of Length

For the calibration of line standards of length

the most precise measurements now being made

at the Bureau are on its 1-m longitudinal comparator (fig. 2). This has been briefly described

by Page. 1 It is especially suited for the calibration of the subintervals of a bar, using any one of

the several methods that have been developed.

Although this comparator is nominally a 1-m comparator, it is readily adaptable for standardizing

48-in. bars, and can be used for calibrating even

longer bars. For comparing two bars with an accuracy not

better than 1 micron (0.001 mm or 0.00004 in.) a

simple transverse comparator with no thermal

insulation is commonly used. In this instrument

the bars are mounted parallel to each other, and

the carriage supporting the two bars moves back

1 B. L. Page, Calibration of meter line standards of length at the National Bureau of Standards, J. Research NBS 54,1 (1955) RP2559.

Figure 1. U. S. National Prototype Meter 27.

.544725—60

and forth in a direction perpendicular to a line

parallel to the axis of each of the two bars. The

micrometer microscopes are not moved during a comparison with this transverse comparator.

Short bars and small scales are often more conveniently calibrated by means of a linear dividing

engine having two microscopes conveniently

mounted so that they can be focused on the bars

mounted on the longitudinally moving carriage.

The instrument is then, in effect, a longitudinal

comparator.

Micrometer microscopes having a pair of parallel "cross hairs" moving in the focus of a positive-type ocular are probably the most important

parts of any instrument for comparing line standards of length. The movement of the cross wires

is measured by a precision screw and a graduated

drum. In the comparators in the length section

at the Bureau the axes of the microscopes are

vertical.

4. Facilities for Calibrating Measuring

Tapes

At the Bureau there is a temperature-controlled

laboratory about 212 ft long (fig. 3) . Two distinct

installations have been made in this laboratory.

One is a 200-ft steel bench for calibrating steel tapes used in general surveying and engineering

practice, as shown at the right in figure 3. The

other is a geodetic comparator designed especially

for calibrating the 50-m invar base-line tapes, such

as are used by the U. S. Coast and Geodetic Survey. Its use is not limited, however, to a 50-m

length. It is shown at the left in figure 3.

4.1. Steel-Tape Bench

The steel-tape bench has an over-all length of

200 ft 1 in., a width of 2% in., and a thickness of

% in., and is constructed of stainless-steel bars

approximately 12 ft long, with individually lapped

and fitted ends. Stainless-steel conical dowel pins

I having threaded lower ends for locking nuts

securely hold adjoining bars in the correct position.

The supports for the bench are attached firmly to

the wall, but can be adjusted whenever necessary.

The bench is graduated at intervals ordinarily

required for testing tapes graduated in the metric

or in the United States customary system. The

equipment is furnished with the necessary supports

for the tape when it is to be supported at specified

points, with apparatus for applying the tension,

thermometers for observing the temperature, and

the necessary clamps and other auxiliary equipment.

Comparisons of a tape with the bench standard

are ordinarily made with a low-power microscope

and a precision steel scale graduated either to

Xoo in. or to % mm. When unusually high accuracy

is required and the character of the graduation

lines warrants, comparisons with the bench can be

made with a micrometer microscope.

4.2. Geodetic Tape Comparator

A 5-m bar, packed in melting ice when measure- ments are being taken, is the working standard

used as the basis of measurements in the geodetic

tape comparator. Piers bearing microscopes are spaced 5 m apart for a total length of 50 m.

Auxiliary piers 1 m apart, also bearing microscopes, are placed between the 20-m and the 25-m

piers. These provide intervals so that the 5-m

bar can be standardized by means of a calibrated

1-m bar. By use of a special bracket at the 15-m

pier, a double pier at the 30-m location, and an

additional pier near the 45-m pier, it is possible to mount microscopes at the 50-, 100-, and 150-ft

points. In figure 4 are shown the 15-m and 50-ft microscopes at the extreme left, then the covered

trough and carriages for the 5-m bar, immediately

beyond that the six piers with their microscopes

spaced 1-m apart, and other piers beyond them.

In addition to the basic equipment of this comparator, there is the necessary auxiliary equipment, such as tape clamps, thermometers, etc. Most of the work done with this comparator is with the 50-m interval, and the use of this interval

will be assumed for the remainder of this section.

After the 50-m interval is established by moving

the 5-m bar to measure the distance between each

of the 10 possible 5-m intervals between microscopes, and the positions of the 0- and 50-m points

are transferred from the focuses of the microscopes to centers of two hemispheres in piers at

floor level, the 5-m bar is moved outside the 50-m

interval. An invar tape to be calibrated is then

mounted in the comparator, supported on ball- bearing wheels, and proper tension is applied to the

tape by means of a calibrated weight.

The difference between the interval on the tape

and the established 50-m interval is obtained by

the micrometer microscopes.

5. Calibration of Line Standards of

Length

The measurement of line standards of length

undertaken by the Bureau is classified under the

several headings that follow. A complete cal- ibration of this type of length standard includes

the determination of the length at a known temperature and also of the expansivity usually

expressed by the average coefficient of linear

thermal expansion over a small range of temperature that embraces the temperatures at which

the standard is likely to be used. For most work

with any standard except one of the highest

grade it is sufficient to assume a coefficient of

expansion derived from a knowledge of the composition of the materials of which it is made. If the standard is subdivided, a calibration of the

subdivisions may also be necessary. The number

of intervals that it is advisable to compare will depend on the character of the standard and on

the use to which it is to be put. In many cases

3
it is unnecessary to determine the correction for the subdivisions; a proportionate part of the errors

for the total length may be assumed. Where

it is necessary to measure a greater or less distance

than the full length of the standard it is only

necessary, in many cases, to test a few subdivisions; for example, any distance in even feet

may be accurately measured with a 100-ft tape

if the corrections are known for the entire length

of the tape, for each 10-ft subdivision, and for

each foot of the first 10 ft. It should be noted that while platinum-iridium

may be the best material for fundamental length

standards, other materials are better suited to the needs of manufacture and industry; for ex- ample, steel rules and tapes are better for determining the sizes of steel and iron machine parts

and structural members, because changes in

length with changes in temperature are practically

the same in the steel rule or tape as in the steel or iron part being measured.

Metric standards should be graduated to be

correct at either 0° or 20° C, the latter temperature

being preferred for everyday use because it eliminates to a great extent the question of differ- ences in expansion. In this country, standards

in the customary units of yards, feet, and inches

are made to be correct at 68° F (20° C).

Requests for calibrations to be made by the

Bureau should state the use to which the results are to be applied and also the accuracy desired,

in order that the tests may be adequate for the

end in view, avoiding unnecessary labor and

expense. Where the highest attainable accuracy

is needed, it is sometimes advisable to have the

standard verified immediately before and again

immediately after the important measurements

in order to guard against possible changes due to undetected injury or structural alteration.

5.1. Reference Standards

This class includes standards of the highest

type suitable for reference standards for makers

of precision apparatus and for use in the most

exact scientific investigations. One of the best

constructions is that conforming to the specifications adopted for the prototype meters by the

International Committee on Weights and Measures; but less expensive constructions are suffi- cient for all but exceptional purposes. The

ba,rs should be of the X-shaped or of the H -shaped

cross section with all rulings in the plane of the

neutral axis. The graduations should be ac- curately perpendicular to the longitudinal axis

of the standard and lines must be fine, with

sharp, smooth edges, and ruled on plane surfaces

that have been given a faultless mirror or dull

polish, depending upon the type of illumination

used.

The lines on the prototype meters are about

0.006 mm wide. Since the time of the construction of these meters there has been a very marked

tendency toward narrower lines and the use oi microscopes of higher magnification than those

used in the latter part of the last century. But,

whatever may be the width of the line, it is most

important that the line be symmetrical, that is. that the bottom of the groove made by the tracing

mechanism be symmetrical with the edges of the groove line. The portion of the graduations tc be used should be defined by two parallel longitudinal lines about 0.2 mm apart. A material

should be used that does not oxidize or otherwise tarnish on exposure to ah or moisture

The graduations must not be covered by varnish

or other protective covering.

A very useful alloy is one made of approximately

36 percent of nickel and 64 percent of iron, knowr

as invar. Invar possesses a coefficient of expansion that is almost negligible at ordinary temperatures; in addition, it does not rust or tarnish readilj on exposure to the atmosphere. It is important tc remember that most materials, aUoys in particular

undergo slight changes in the course of time, especially if subjected to considerable changes of tem- perature or to mechanical disturbances. Hence

whenever the highest accuracy is desired, standards should occasionally be verified. Standards oi pure nickel and 42 percent of nickel have been

found to be sufficiently stable for use as standards

where verifications of the length of such bars can be made at suitable intervals of time.

The owner of a length standard of the reference

class is usually justified in having a calibration

made by the Bureau.

5.2. Working Standards

This class includes standards suitable for all ordi- nary precision work and suitable for the needs oi college laboratories, manufacturers of the bettei

grades of scientific apparatus, State superintendents of weights and measures, and most scientific work. Either an H -shaped cross section or a rec- tangular cross section with provision for supports

at definite positions should be used. Short bars,

such as decimeter bars, may be of rectangular cross section with the graduations on the upper surface

and with the bars supported directly on a flat sur- face. The lines of the graduations should be sharp

and less than 0.03 mm wide, and they should be

ruled on a plane, well-polished surface that will not

tarnish readily on exposure to the atmosphere. Nc

varnish or other protective covering should be used.

If the metal of the bar tarnishes readily, the lines should be ruled on plugs or strips of nontarnishing

metal. Some such means as a pair of parallel

longitudinal lines about 0.2 mm apart should be provided for defining the portion of the graduations to be used, and to facilitate the alinement oi the bar. The graduation lines should be accurately

perpendicular to the longitudinal axis of the standard. Standards of this class are compared with

working standards of the Bureau and are certified to 0.001 mm if their quality justifies it.

-I
\ 1 T> \ x.\^\...v.\..,x\...x.-\..x\.-v.\

Figure 5. Line standard of length with contact pieces.

In the case of new working standards for State

.. superintendents of weights and measures, it is recommended that these be graduated in milli- meters for a distance of 1,010 mm or in %z in. for

37 in. In addition to the graduation, contact

stops (fig. 5) are a convenience in some routine

work, and a satisfactory arrangement is to have a

.. contact extending across the standard at the zero

line with a contact extending not over halfway

7 across at the yard or meter point , this latter contact

J being so placed as not to interfere with or cover any part of the graduations. The meter standard

. should be accurate to 0.01 mm or better at a tem-

. perature 2 of 20° C. The vard standard should be

accurate to 0.0005 in. at 68° F. The owner of a working standard is sometimes

1 justified in having a calibration made at the

: Bureau, but he may find that a calibration made

by the maker or by himself is sufficient if a refer-

; ence standard is available with which to make the

comparison.

5.3. Commercial Standards

This class includes flat metal bars graduated

along the center of the surface or along one or more edges, with lines less than 0.06 mm (0.0024

in.) wide. They should be of sufficiently good

| grade to meet the requirements for drafting,

i machine work, etc., and to meet the needs of

local sealers of weights and measures. It is

i recommended that those for the use of sealers

be graduated in millimeters for a distance of 1,010

mm or in %2 in. for 37 in. 3 New meter standards

( should be accurate to 0.1 mm or better at a temperature of 20° C, and new yard standards

should be accurate to 0.005 in. at 68° F. Commercial standards seldom require calibration by the Bureau. Local sealers of weights and

measures will usually have their standards cali- brated by State officials, and most other users

will be justified in relying upon the reputation of

the manufacturers, especially if purchase specifications have prescribed the accuracy of the

standards.

6. Calibration of Measuring Tapes

Steel and invar tapes used in surveying, engineering, manufacturing, and construction work

are calibrated at the Bureau. Tapes intended for geodetic base-line work require a very accurate

' Some bars have been made which were accurate at 0° C, and these will

also be considered as meeting the requirements.

3 Contact stops as described for working standards may also be used on

commercial standards for use by local sealers of weights and measures.

calibration; steel tapes used for more routine

work can be calibrated to sufficient accuracy,

using simpler apparatus and procedures.

For the most accurate work, such as primary

triangulation or extensive surveys, tapes of the

ahW of nickel and steel, known as invar, when

properly made, have been found to be the most

satisfactory because of their low coefficient of

expansion and the slowness with which they tar- nish from exposure to the atmosphere. However,

they require very careful handling in the field to present twists and kinks. Standardization

before and after field measurements of first-order

bases for triangulation is usually desirable. The

width of the graduations should be uniform and

not more than 0.04 mm. The graduations should

extend to one edge of the tape but not to the other,

and all measurements should be made at the

graduated edge.

Steel tapes have also been used for precise

geodetic work, but require many precautions in

their use to avoid errors caused by uncertainties

as to the temperature of the tape. The coefficient

of thermal expansion of both invar and steel tapes should be determined when they are used

for work of the highest precision.

Ordinary 100-ft steel tapes to be used for engineering or construction work where an accuracy

not better than 0.001 ft is required may consist

of a steel ribbon with the graduations directly on

the tape, or the intervals may be indicated by

grooves or notches cut in sleeves securely fastened

to the tape. Tapes having the intervals marked

by rivets are not suitable for accurate work.

Tapes having the zero mark at the edge of a ring

and those having the terminal mark on a tension

handle are not recommended for accurate work.

Tapes are compared with the steel-tape bench

at the Bureau when supported throughout their

entire length or when supported at specified

points. These comparisons are accurate to the

nearest 0.001 ft or 0.2 mm. When an accuracy

greater than this is necessary, the Bureau is pre- pared to compare tapes of suitable length on its geodetic-tape comparator.

The standardization of a tape includes the

comparison of the total length and of specially

designated intervals. For most work it is suffi- cient to determine the total length only, and unless

specifically requested to verify intermediate in- tervals, the Bureau calibrates the total length

only. If, however, it is desired to have a tape

for measuring accurately any integral number of

feet, it is usually sufficient to have measurements

5
at every 10-ft point and at each foot of the first or of the last 10 ft. As a basis for issuing a certificate and for placing

its seal on a steel tape the Bureau has adopted the

following specification and procedure.

6.1. Specification for Standard Steel Tapes

A steel tape is considered as standard when it has been calibrated by the Bureau and found to conform to the following specification: It shall be

made of a single piece of metal ribbon, and none

of the graduations shall be on pieces of solder or on sleeves attached to the tape or wire loops,

spring balances, tension handles, or other attachments liable to be detached or changed in shape.

The error in the total length of the tape, when

supported horizontally throughout its length at the standard temperature of 68° F (20° C) and at standard tension, shall not be more than 0.1 in. per 100 ft (2 mm per 25 m). The standard tension is 10 lb (4.5 kg) for tapes 25 to 100 ft or from

10 to 30 m in length and 20 lb (9 kg) for tapes

longer than 100 ft or 30 m.

6.2. Certification of Tapes

Tapes conforming to the specification will be

certified by the Bureau and a precision seal showing year of standardization will be placed on each

tape so certified. For tapes not conforming to the specification, a report will be issued, but the

tapes will not be sealed. The Bureau's serial number on a tape simply signifies that it has been

tested by the Bureau and either a certificate or a report issued.

Ordinarily the length of a steel tape is certified or reported by the Bureau to the nearest 0.001 ft or 0.0002 m (0.2 mm).

The specification given in section 6.1 is intended

to cover steel tapes of highest precision and should

not be taken to imply that only tapes conforming

to it are suitable for use. For instance, tapes

having a terminal graduation at the end of a ring are very desirable for certain purposes, where con- venience is of more importance than high accuracy,

and the Bureau will make the necessary observations and report on such tapes if satisfactory in

other respects.

6.3. Standard Procedures in Steel-Tape

Calibrations

Unless otherwise stated, the comparisons of the

tape with the bench standard are made at the

center of the lines on the edge to which the shortest

graduations are ruled. If all the graduations ex- tend entirely across the tape, the ends farthest

from the observer when the zero of the tape is at

his left hand are used. On tapes that have been

cut off at the zero mark, the extreme end of the

steel ribbon is taken as the zero point and not the

center of any line that may be at that point. On

tapes that have the zero point on a loop attached

to the steel ribbon at the end, the zero is taken at the outside of this loop, unless noted to the

contrary.

Measurements for the calibration of a tape at the Bureau are made only at points at which the

tape is supported.

The standard tension given in the specification

is for a tape when supported on a horizontal flat surface. No standard tension has been officially

adopted for a tape when supported in any other manner. The Bureau is sometimes requested to calibrate a tape supported throughout and supported at ends only under "standard tension."

In such cases the Bureau uses the same tension

for the tape supported at the ends as is used as standard tension when supported throughout.

Many surveyors and engineers use a tension some- what greater than this standard tension when they

are using a tape supported at the ends only. The

correction for sag for a given tension increases

directly as the square of the increase of the weight

per unit length of the tape. In the case of very

heavy tapes the standard tensions of 10 and 20

lb (4.5 and 9 kg) may be found to be inadequate

for tapes supported at the ends only. It is suggested that, dependent on the length of the tape

and its weight per unit length, tensions in the

range of 20 to 40 lb (9 to 18 kg) be used for tapes

used in single catenary type of suspension. Tapes

weighing 0.018 lb/ft or more may be considered as heavy tapes. Tapes weighing 0.009 to 0.011

lb/ft may be considered as light tapes.

In the standardization of invar tapes the following tensions are used, unless otherwise specified:

20 lb for 50-, 100-, and 150-ft tapes, and 15 kg

for 30- and 50-m tapes.

When the lengths of intervals are desired on a

tape supported at points that are more than 200

ft or 50 m apart, these lengths must be computed

from quantities directly observed, using the

mathematical expression for the sag as given in

the appendix.

Since the present tape testing laboratory has

been in use the observations have usually been

made at a temperature very close to 68° F (20° C).

Occasionally this may not be possible. The coefficient of expansion of the bench standard has

been determined, and the difference between this

value and the coefficient of expansion of steel tapes is taken into account whenever necessary.

A value for the coefficient of expansion of

0.00000645 per deg F (0.0000116 per deg C) is assumed for steel tapes. This coefficient may be

considered as correct for all except the most

precise geodetic tapes. Determinations of the

coefficients of expansion of both ordinary steel tapes and stainless-steel tapes give the value stated

above within the limits of all ordinary measure- ments ever made with these tapes. The Bureau

determines the coefficient of expansion of steel tapes only when sufficient need for such a determination is clearly indicated and when the value

of the coefficient usually assumed for steel tapes

may lead to difficulty.

grade

| Hence

idter

I reouir

6
Tapes made by the manufacturers that supply

the surveying and engineering trade with highgrade steel tapes are almost universally correct for

total length at standard tension and temperature

within 0.01 ft, and ordinarily within 0.006 ft. Hence, for most work not requiring an accuracy

better than 0.01 ft, where a certified tape is riot required by law or by the terms of a contract, it is not necessary to submit the tape to the Bureau

for a calibration. As high-grade tapes are ordinarily uniformly graduated within a few thousandths of a foot, the calibration of subintervals

of a tape is not required except when rather precise

measurements are to be made with the tape, that

is, measurements to a few thousandths of a foot. The owner of a tape can often check the uniformity

of division of the tape by measuring, for example,

J a 25-ft distance by using the intervals from 0 to

j 25 ft, 25 to 50 ft, 50 to 75 ft, and 75 to 100 ft on

the tape.

6.4. Corrections Applicable to Steel Tapes

When a tape has been calibrated under one set

I of conditions and it is desired to use it under

another set of conditions, it is often possible to

calculate with sufficient accuracy the difference in

the length of the tape under the two conditions.

I Information on this subject useful to surveyors

has been included in the appendix.

6.5. Base-Line Tapes

When an invar base-line tape is submitted the

first time for calibration on the geodetic comparator, the normal procedure is to determine its coefficient of thermal expansion and its weight per

unit length before undertaking the standardization of its length. At one time it was thought

necessary to check the stability of invar tapes by

"whipping" them rhythmically and determining

the changes in length caused by each group of

' whippings. Tapes received in recent years have

( been found to be sufficiently stable, and the whipping test has been discontinued. For the determination of its coefficient of expansion the elec- trical-resistance method described by Peter Hidj nert and Richard K. Kirby 4 is used.

Calibrations are usually made on the geodetic

comparator under conditions similar to those used

in the field. The standard calibrations now made

1 for the U. S. Coast and Geodetic Survey on their

base-line tapes are those to determine the length

at 25° C of the interval 0 to 50 m with the tape

under a horizontal tension of 15 kg when supported

at the 0-, 25-, and 50-m points, and then when

supported at the 0-, 12. 5-, 37.5-, and 50-m points,

with the 12.5- and 37.5-m points 6 in. above the

place of the 0- and 50-m supports. This second

condition of supports is to duplicate conditions

used in the field when surveying along railroad

* P. Hidnert and R. K. Kirby, A new method for determining linear thermal expansion of invar geodetic surveying tapes, J. Research NBS

50, 179 (1953) RP2407.

rails. For these field conditions the tapes are supported at the 12.5- and 37.5-m points on

rollers, with the tops 6 in. above the rails. The

height of 6 in. was chosen because all invar tapes

possessed by the U. S. Coast and Geodetic Survey

would then be lifted off the rail at the 25-m point.

All measurements are made in the laboratory and

in the field with thermometers weighing 45 g each

attached at points 1 m inside the terminal graduations. For first-order work the values for the

lengths of the intervals are certified not to be in error by more than 1 part in 500,000. Although

all measurements are made on a new tape with

the same care and just as accurately as in subsequent calibrations, the Bureau has made it a

practice not to certify any base-line tape to

first-order accuracy until further calibrations indi- cate that it is a stable tape so that first-order

accuracy has a meaning. The terms "first-order"

and "second-order" are those adopted in geodetic

field surveying. Tapes certified to second-order

accuracy have a certified accuracy of 1 part in

250,000.

When base-line tapes are submitted to the

Bureau rather frequently it is recommended that,

in calibrations after the initial, and one or more

subsequent standardizations, the work be abbreviated. Measurements sufficient to show that

values of the length have not changed more than

the limit of error claimed in the previous calibration are made more easily than those required for a new certification. A statement that the previous

certificate may continue to be used is issued when

the abbreviated test shows that the values in the

previous certificates are still valid.

If thermometers having a weight other than

45 g are used with base-line tapes in the field, that

fact should be stated when the tapes are submitted

for calibration. The thermometers may be submitted so that they can be placed at the proper

positions on the tapes during the calibration.

7. Certificates and Reports

If apparatus submitted for calibration fulfills the requirements for certification, a certificate is issued. Values given in certificates or reports are applicable at the time of the calibration; there is no guarantee of the continued applicability of these

values.

A National Bureau of Standards serial identification number similar to that shown below

NBS No. 2147

is usually engraved, stamped, or etched on apparatus, tapes, and standards that have been cali- brated by the Bureau and for which a certificate or report has been issued. An identification

number is not ordinarily placed on any precise

standard when there is any danger of possible

injury or of minute changes of length being caused, nor in certain other cases where there is already

adequate identification.

7
Tapes and other articles for which definite toler- ances have been prescribed are marked with a seal by the Bureau if the article is found to conform to the specifications. If a certificate or report is issued for such an article, a serial identification

number, referred to above, is also placed on the

article in addition to the seal.

8. Cooperation with Officials

and Others

The Bureau will be pleased to assist investigators, manufacturers, and others by furnishing any

information at its disposal concerning methods of

measurement. It is also the desire of the Bureau to cooperate with manufacturers, scientists, weights

and measures officials, and others in bringing about more satisfactory conditions relating to standards,

physical constants, measuring instruments, and

methods involved in length measurements. It is always desirous of receiving samples or descriptions of new apparatus or improvements on any

type of apparatus mentioned in this Circular.

Persons interested are invited to visit the laboratories of the Bureau, examine the apparatus and

methods, and confer with those in charge regarding

any problems they may have.

9. General Instructions to Applicants

for Calibrations

9.1. Apparatus Accepted for Calibration

The Bureau will accept for calibration only a standard or an apparatus that is well made and

not likely to change excessively. An adequate

degree of quality is insisted upon as a prerequisite

to acceptance for calibration. Line standards of length should be made of suitable material, such

as iron alloy, brass, bronze, platinum alloy, or

glass, and should be of a construction and workmanship suitable for the intended accuracy.

Poorly divided scales on metal, and scales graduated on wood, plastics, or paper will not be ac- cepted. In general, a linear scale of a grade

better than the best machinist's scales will be

required for a calibration by the Bureau.

9.2. Application for Calibration

All articles submitted for calibration should be

accompanied by a written request. This request

should enumerate the articles, giving the identifi- cation marks of each, and should state explicitly

the nature of the calibration desired and an approximate valuation of the articles should be

stated for use in insuring the return shipment.

9.3. Nature of Calibration

The application should state clearly the nature

of the calibration desired, namely, the points at which measurements are to be made and the temperature, especially if other than standard, or any

ir

other conditions. The most accurate results can

be obtained and delays are avoided only when;

such full information is given. It is also desirable Ik a that the Bureau be informed as to the conditions

under which the apparatus is used and the character of the work for which it is employed.

9.4. Special Calibrations

The Bureau will gladly cooperate with scientific investigators, manufacturers of apparatus, and

others who need higher precision than is provided

in the regular schedules by undertaking special

calibrations as far as the regular work of the

Bureau will permit. Kinds of calibrations not at present provided for may be undertaken if the

work is important and the facilities and time are

available. Approved calibrations not provided for

in the regular schedules are considered special,

and a special fee is charged for them. These |( should be arranged for by correspondence before

shipment of the apparatus. The application

should state fully the purpose for which the apparatus has been used or is to be used in the future,

the need for the calibration, and the precision

desired. The special fee charged depends chiefly

upon the time consumed and the amount of alteration required in the Bureau's regular calibrating

apparatus. It is ordinarily possible to give an

estimate of the fee when so requested.

9.5. Condition of Apparatus

Before submitting apparatus for calibration,

the applicant should ascertain that it fully satisfies the requirements for the calibration desired. It must be in good working condition. No repair

work is done at the Bureau. If repairs are needed,

either they should be made by the applicant, or the item should be sent to the maker before it is submitted for calibration. When defects, found

after observations have been begun, exclude any

apparatus from receiving the usual certificate, a

report is rendered giving such information as has

been found. In such cases a fee is charged,

depending upon the time consumed. All possible care is taken in handling apparatus, but the risk

of injury or breakage in shipment or at the Bureau

must be borne by the applicant.

9.6. Identification of Apparatus

All packages should be plainly marked with the

shipper's name and address and should contain a

list of the contents. Each separate piece of

apparatus or sample of material should be provided

with an identification mark or number. The

identification mark should be given in the 1 application.

9.7. Shipping Instructions

Apparatus should be securely packed in cases or packages that will not be broken in transportation and that may be used in returning them to the

if

illi hiih

8
owner. The shipment in both directions is at

!the applicant's risk. Great care should be taken

in packing. Clean, dry excelsior is a suitable

packing material in most cases. Metal parts

should be well protected from corrosion by oil or

grease. Each instrument should also be wrapped

I in strong, waxed paper or other suitable covering

to exclude dust and excelsior. The tops of boxes

should be put on with screws, as any shock due

to nailing and the subsequent opening is likely to cause damage. The tops of the shipping boxes

?hould have the return or forwarding address on

the underside. Transportation charges are payable by the party making the request. The

(barges for shipment to the Bureau must be

prepaid, and, unless otherwise arranged, articles are usually returned or forwarded by express

"collect." Information regarding the disposition

of apparatus after completion of the measurements, including a statement as to the address to which shipment should be made and as to choice

' of carrier, should be supplied. In case such

information is not given, it is understood that the

calibrated apparatus is to be returned to the

shipper.

9.8. Schedules of Test Fees

Schedules of test fees for the calibration of line standards of length and for steel tapes and invar

base-line tapes have been established. Copies

of these schedules may be obtained on application.

9.9. Address

Apparatus submitted for calibrations described

• in this Circular, as well as correspondence relating

thereto, should be addressed: National Bureau of

Standards, "Washington 25, D. C, Attention:

• Division 2.4.

The author expresses his appreciation to B. L.

1 Page, R. F. Ackermann, and J. S. Beers for their

; suggestions during the final revision of the

; manuscript.

10. Appendix—Use of Steel Tapes

In the use of steel tapes for precision work, attention should be paid to the temperature of the tape and to the

j tension applied to the tape. Corrections are sometimes

I necessary to take account of variations between the condij tions of field measurement from those of the laboratory

calibration as shown in the certificate or report. The

accuracy of the balance or tension handle employed for applying tension should be checked by comparison with a

calibrated balance or by the use of calibrated weights used

with a pulley wheel so that the balance is being calibrated

in a horizontal position.

Young's Modulus of Elasticity. A value for Young's

modulus of elasticity is sometimes required in computing

the length of a tape as used in the field under conditions

differing from those used in the calibration laboratory. In a series of measurements made several years ago at

, the Xational Bureau of Standards on a group of 45 steel

tapes, the value for Young's modulus of elasticity was

determined to be 28.0X 106 (that is 28,000,000) lb/in*. Variations in the material in the different tapes cause an

uncertainty of 0.2 or 0.3X106 (200,000 or 300,000) lb/in2

. A tape having the customary black finish has a smaller modulus of elasticity than has the original steel ribbon

from which it is made, because there is included in the

cross-sectional area of the finished tape not only the steel but also the protective coating which has a lower modulus.

A value of 28.0 X106 lb/in2

, may for all practical purposes be assumed for any steel tape, because the maximum error introduced by this assumption in using a 200-ft tape with a change in tension of 15 lb would be about 0.001 ft. Correction for Sag. 5 The difference in the length of a

tape when supported throughout and when supported at equidistant points at the same height, the tension remaining constant, is equal to L /wd\2 24 VP J

'

where L is the length of the tape, w is the weight of the tape per unit length, d the distance between points of support, and P the tension on the tape. These must be in consistent units; usually L and d in feet, w in pounds per

foot and Pin pounds. In a study of a group of 45 tapes, previously mentioned,

t was found that, using tensions between 10 and 25 lb, the difference between the observed value and that ob- tained from the formula for the correction for sag did not

exceed 0.001 ft when the interval between the supports was 25 or 50 ft. Furthermore, when supported at the 0 and 100-ft points at 10 lb tension, the difference between

the observed value and the computed value for the correc- tion for sag did not exceed 0.002 ft, provided the correction

for sag was not larger than 0.060 ft. When the tension was increased to 15, 20, or 25 lb, under the same conditions

of support, the difference between the observed values and

the computed value for the correction for sag, with the exception of a few tapes, did not exceed 0.001 ft. Moreover, there may be an agreement between the observed

value and the computed value to 0.001 ft for individual tapes of relatively heavy weight when under a tension less than 15 lb. The formula was shown to be applicable to

100-ft tapes of nonuniform density, provided sufficient tension was used, e. g., 15 lb or more. As an example of the use of the formula expressing the

correction for sag one may consider a tape weighing

0.0080 lb per linear foot that has a length of 200.004 ft when supported horizontally throughout at a tension of 20

lb and that is to be used supported at the 0- and 200-ft points at that tension. The length may be readily computed to be

200.004-^Q

(

0- OQ8

2

°

Q

X200

)

2 =200.004-0.053 = 199.951ft.

It will be noted that nominal values for L and d are used.

If the tape is to be used at a tension of 25 lb, then the length of the tape supported throughout at 25 lb should be

determined.

Tension of Accuracy. If the length of a tape is known

when supported throughout its length at standard tension and standard temperature, this information, together with

a knowledge of certain constants concerning the physical

properties of the tapes will enable one to determine the

tension (tension of accuracy) to apply to the tape when

supported at equidistant points at any known temperature

to obtain the nominal length. These constants should be

accurately determined. The case in which the observed temperature is the same as the standard temperature is given in text books on serveying, and the tension to be used

in this case is often termed the normal tension. It is found by equating the correction for tension to the cor5 Lewis V.-Judson, Effect of concentrated loads on the length of measuring

tapes, BS Sci. Pap. 31, 390 (1926) S534.

9
0 0.2 0.4 0.6 0.8 1.0 0.8 0.6 0.4 0.2 (

1 1 1 1I i i i 1 1 1i 1 1 1 1 1 1i 1 1 11 1 1 1i 1 1 1i 1 1i 1

1

i 1 11 1 1 1 1 1 1 1 1

1

1 1 1 1 1 1i i 1 1 1 1

i 1 1 1 1 1 1 1 1 1 i 1 1 1 1 1 i i 1 1 1 1

1

1 i M 1 1 1 1 1 1 1 1 1 1 1

Below 68°F AEOC Above 68°F

Constant

u

10I

AEa(t,-to)

Figure 6. Nomogram for steel tapes.
rection for sag. The general case is an extension of this specified case. The equation is AEw2 cP P3

1 -lP0 -AEa (k-t0)]Pi-~^-=Q,

where Pi = Tension to be applied to the tape, when used at the observed temperature, t\, and supported

at equidistant points at a distance, d, apart,

in order that the tape will have its nominal

length.

P0 = Tension at which tape has its nominal length

when supported throughout at standard

temperature, t0 . A — Cross-sectional area of the tape. E=Young's modulus of elasticity.

a= Coefficient of thermal expansion.

<i = Observed temperature. <o= Standard temperature.

w= Weight of the tape per unit length.

d= Distance between the equidistant points of support. As it is difficult to determine A directly with sufficient accuracy, it is usually advisable to determine the product

AE, which is equal to (P2 — Pi)L/AL, where L is the nominal length of the tape supported throughout, and AL is the change in length when the tension is changed from Pi

to P2 . Nomogram for Tension of Accuracy. The solution of the

cubic equation to determine the tension of accuracy of a

tape supported in a catenary can be carried out rapidly

by graphical means, using a nomographic chart, the equation being in Soreau's 6 canonical form IVo. Figure 6 is such a chart, the value of a being 0.00000645

per deg F, and t0 is 68° F. To use this chart to find the

tension of accuracy, Pi, for a tape, place a straightedge on the point representing the constant AEa, axis A, and

on the point representing the observed temperature t u

inclined scale B. The intersection of the straightedge

with the dummy axis C is noted. The straightedge is then placed on this point and on the point representing the value P0, axis D. The point where the straightedge

intersects axis E is determined. Place the straightedge

e Soreau, Nomographic, pages 172, 174, 184, and 192 (Chiron, Paris, 1921).

on this point and the point representing the constant {AEvrd2

) /24, axis G. The point where the straightedge

intersects curve F determines the tension to apply to the tape under the given method of support and at the observed temperature t\. It should be noted that the constants AEa, P0 , and

{AEw2 d

2)j2i are constants of the tape, independent of the

conditions of its use and can be permanently marked on

the chart for each tape, in the office, in preparation for use of the chart in the field. It should be noted that for short lengths of tapes the value of the constant K=(AEw2 d

2 )/24: will be small. The

point of intersection of the straightedge with axis F will then often be somewhat indefinite on the chart, although

the calculated value of the intersection is of course definite. This, however, is not serious as the length of a short

interval of a tape changes very little for a 1 or 2 lb change

in tension. For example, a 25-ft length of tape weighing

0.010 lb/ft will change in length only approximately 0.002

in. when the tension is changed from 10 to 12 lb when

supported at the 0 and 25-ft intervals. For 100-ft tapes, using the 100-ft interval, the change in length is very apparent for a 0.5-lb change in tension. In

this case the chart and formula have been found to be in agreement with the observed values determined by actual

test for various tapes tested at the Bureau. Although

fewer tests have been made for tapes longer than 100 ft, it

is believed that the chart and formula will apply equally

as well. Other nomograms may be drawn whose constants do not come within the scales on the nomogram shown in figure 6, of if conditions are such that a greater accuracy can be used than can be obtained on this chart, a new one can be drawn on suitable paper, with axes E and G further apart. Attention is also called to the fact that the value Po deter- mined for the total length or for one specified interval of a

tape does not necessarily apply to all intervals on the tape. This may be due to one or more of the following conditions: A slight nonuniformity of graduation, a lack of homogeneity, or a lack of uniformity in cross section of the tape. For example, for one tape weighing 0.010 lb/ft, the value PQ was found to vary from 0.5 to 1 lb for the intervals 0

to 25 ft 0 to 50 ft, 0 to 75 ft, and 0 to 100 ft.

Washington, D.C., February 16, 1960

U.S. GOVERNMENT PRINTING OFFICE : I960

11
SELECTED WEIGHTS AND MEASURES

PUBLICATIONS OF THE

NATIONAL BUREAU OF STANDARDS

NBS Handbook 44 2d Edition —1955 Specifications, Tolerances, and

Regulations for Commercial Weighing and

Measuring Devices. Loose Leaf (does not

include binder) $1. 00

NBS Handbook 45 Testing of Measuring Equipment 1. 50

NBS Handbook 67 Checking Prepackaged Commodities . 35

NBS Circular 501 Federal and State Weights and Measures Laws_ _ 6.50

NBS Circular 540 Weights and Measures Case Reference Book 1. 25

NBS Circular 547 Precision Laboratory Standards of Mass and

Laboratory Weights—Section 1 .35

NBS Circular 593 The Federal Basis for Weights and Measures . 30

AVAILABLE REPORTS OF THE

NATIONAL CONFERENCE ON WEIGHTS AND MEASURES

1947 Miscellaneous Publication 189 40^

1953 Miscellaneous Publication 209 40^

1954 Miscellaneous Publication 212 50^

1955 Miscellaneous Publication 216 70^

1956 Miscellaneous Publication 219 70^

1957 Miscellaneous Publication 222 55^

1958 Miscellaneous Publication 225 65^

1959 Miscellaneous Publication 228 65^

Index to the Reports of the National Conference on Weights

and Measures from the First to the Thirty-sixth, 1905 to 1951, Miscellaneous Publication 203 20j?f

ORDER ALL PUBLICATIONS, WITH REMITTANCE, FROM THE SUPERINTENDENT OF DOCUMENTS, GOVERNMENT PRINTING OFFICE, WASHINGTON 25, D.C.
THE NATIONAL BUREAU OF STANDARDS

The scope of activities of the National Bureau of Standards at its major laboratories in Washington,

D.C., and Boulder, Colorado, is suggested in the following listing of the divisions and sections engaged

in technical work. In general, each section carries out specialized research, development, and engineering in the field indicated by its title. A brief description of the activities, and of the resultant

publications, appears on the inside of the front cover. WASHINGTON, D.C.

Electricity and Electronics. Resistance and Reactance. Electron Devices. Electrical Instru- ments. Magnetic Measurement. Dielectrics. Engineering Electronics. Electronic Instrumentation. Electrochemistry.

Optics and Metrology. Photometry and colorimetry. Optical Instruments. Photographic Technology. Length. Engineering Metrology.

Heat. Temperature Physics. Thermodynamics. Cryogenic Physics. Rheology. Molecular Kinetics. Free Radicals Research.

Atomic Physics. Spectroscopy. Radiometry. Mass Spectrometry. Solid State Physics. Elec- tron Physics. Atomic Physics.

Radiation Physics. Neutron Physics. Radiation Theory. Radioactivity. X-ray. High Energy

Radiation. Nucleonic Instrumentation. Radiological Equipment.

Chemistry. Organic Coatings. Surface Chemistry. Organic Chemistry. Analytical Chemistry.

Inorganic Chemistry. Electrodeposition. Molecular Structure and Properties of Gases. Physical

Chemistry. Thermochemistry. Spectrochemistry. Pure Substances.

Mechanics. Sound. Mechanical Instruments. Fluid Mechanics. Engineering Mechanics. Mass

and Scale. Capacity, Density, and Fluid Meters. Combustion Controls.

Organic and Fibrous Materials. Rubber. Textiles. Paper. Leather. Testing and Specifications. Polymer Structure. Plastics. Dental Research.

Metallurgy. Thermal Metallurgy. Chemical Metallurgy. Mechanical Metallurgy. Corrosion.

Metal Physcis.

Mineral Products. Engineering Ceramics. Glass. Refractories. Enameled Metals. Constitution and Microstructure.

Building Technology. Structural Engineering. Fire Protection. Air Conditioning, Heating, and

Refrigeration. Floor, Roof, and Wall Coverings. Codes and Safety Standards. Heat Transfer.

Concreting Materials.

Applied Mathematics. Numerical Analysis. Computation. Statistical Engineering. Mathematical Physics.

Data Processing Systems. SEAC Engineering Group. Components and Techniques. Digital

Circuitry. Digital Systems. Analog Systems. Applications Engineering.

• Office of Basic Instrumentation. • Office of Weights and Measures.

BOULDER, COLORADO

Cryogenic Engineering. Cryogenic Equipment. Cryogenic Processes. Properties of Materials.

Gas Liquefaction.

Radio Propagation Physics. Upper Atmosphere Research. Ionosphere Research. Regular Prediction Services. Sun-Earth Relationships. VHF Research. Radio Warning Services. Airglow

and Aurora. Radio Astronomy and Arctic Propagation.

Radio Propagation Engineering. Data Reduction Instrumentation. Radio Noise. Tropospheric Measurements. Tropospheric Analysis. Propagation-Terrain Effects. Radio-Meteorology.

Lower Atmospheric Physics.

Radio Standards. High-Frequency Electrical Standards. Radio Broadcast Service. Radio and

Microwave Materials. Atomic Frequency and Time Standards. Electronic Calibration Center. Microwave Circuit Standards.

Radio Communication and Systems. Low Frequency and Very Low Frequency Research.

High Frequency and Very High Frequency Research. Modulation Systems. Antenna Research.

Navigation Systems. Systems Analysis. Field Operations.