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NBS TECHNICAL NOTE

491

Gravity Measurements

And the Standards Laboratory

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U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards
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NBS TECHNICAL NOTE 491

ISSUED AUGUST 1969

Nat. Bur. Stand. (U.S.), Tech. Note 491, 10 pages (Aug. 1969)

CODEN: NBTNA

Gravity Measurements and the Standards Laboratory

D. R. Tate

Mechanics Division

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

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Contents

Page

Abstract ------------------------- 1

1. Introduction --------------------- 1

2. Gravity Networks ------------------- 1

3. Absolute Measurements ---------------- 2

4. Survey Measurements ----------------- 3

5. Local Values of Gravity --------------- 4

6. Standard Gravity ------------------- 4

7. The Computation of Forces -------------- 5

8. Summary ---------- _____________ 5

9. References -----_-- _____________ 7

GRAVITY MEASUREMENTS AND THE STANDARDS LABORATORY

D. R. Tate

The local value of the acceleration due to

gravity is a fundamental datum for almost every

standards laboratory as it, together with accurate

standards of mass, is the basis for the standards

involving force. Instruments used as standards in

this area include precise deadweight piston gages,

deadweight calibrators for force transducers, liquid

manometers, and earth field accelerometer calibrators.

The practical realization of the absolute ampere and

the absolute volt require a knowledge of force. This

paper presents the basic information about how gravity

measurements are made and outlines procedures for

obtaining a suitable value for a given location. It

also gives a brief discussion of the background and

meaning of the term "standard gravity", and its

application in the computation of forces in units of

the pound-force and the kilogram-force.

Key words: Absolute gravity, deadweight, force,

geodetic pendulum, gravity, gravity

meter, Potsdam system, standard gravity,

units of force.

1. Introduction

The local value of the acceleration due to gravity is a matter of

considerable importance to almost every standards laboratory as it, together with accurate standards of mass, is the basis of all force

measurements. Instruments for the measurement of acceleration, accelerometers, have also reached a stage where, for earth field calibrations,

the acceleration due to gravity must be known quite accurately. It is

the purpose of this paper to present the basic information about how

gravity measurements are made and to outline the procedures for obtaining a suitable value for a given location.

2. Gravity Networks

Gravity measurements have been made by geodesists for many years

and a well developed science, with instrumentation and technique, has

grown up in the field. Primarily the interest of the geodesist is to

gain a better knowledge of the shape and structure of the earth, and

the work that has been done has resulted in a network of gravity values
covering the greater portion of the habitable parts of the world. This

network, with its excellent coverage in Europe and the Americas, affords

a ready-made basis for obtaining satisfactory values in most laboratories .

It is helpful to understand the methods by which gravity networks

have been established. The direct measurement of the acceleration due

to gravity through the observation of time and distance is a difficult

undertaking and not well adapted to survey methods. Consequently the

principle has been to establish an absolute value at some one point

and to make the survey measurements with instruments that measure the

difference in gravity between two points, starting at the absolute

site and moving out in the closed-loop technique commonly employed in

other types of surveys. The network values in existence today are derived from an absolute measurement made in Potsdam, Germany.

3. Absolute Measurements

Absolute determinations of the acceleration due to gravity, in

addition to being difficult and time consuming, have in the past been

subject to serious systematic errors which were large when compared to

the accuracy of differential measurements made with survey type

instruments. Consequently it has been desirable to make additional

absolute measurements at various points in the world network, even though only one such determination is theoretically necessary. Up to

quite recently, absolute measurements were restricted by practical

considerations to locations in the national standards laboratories of some of the larger nations.

The classic absolute measurement was made at Potsdam by Kuhnen

and Furtwangler and published in 1906L 1.1 "'

. It was made by the use of

reversible pendulums of the Kater type and resulted in a value of

9.81274 m/s 2 for that station. Subsequent absolute determinations made

in Washington by Heyl and CookL2J and a t Teddington, England by ClarkL3J} gave values 15 to 20 parts per million less than the Potsdam result

after consideration of the gravity differences between the sites. In

recent times absolute measurements have been made from observations on freely falling objects in vacuum by several workersL4 ,5 , 6 , 7 , 8 ,9J . A

discussion of absolute determinations is given by A. H. CookL 10J

The conclusion has been reached that the original Potsdam value is

in error by about 14 parts per million, and in October of 1968 the

International Committee on Weights and Measures adopted a resolution

that, for the needs of metrology, the value at Potsdam should be re- garded as 9.81260 m/s 2

.

Figures in brackets refer to references at the end of this paper
Currently the development of stabilized gas laser systems has made

it possible to make absolute determinations in which the falling object

is one reflector of a Michelson interferometer. This technique improves

the accuracy over the older methods by about an order of magnitude.

Measurements by this method are under way by FallerLlU and SakumaL 12J

Faller's apparatus is sufficiently portable that it can be transported

from one laboratory to another and it is expected to prove most useful

in giving precise values for a number of points in the pattern of the

world gravity network.

4. Survey Measurements

As indicated previously, the values of gravity at most points of

interest are determined from the cumulated differences between a series

of stations starting at a point where the absolute value is known or assumed. Usually, values for well known intermediate points have been

established through a number of redundant measurements made over a period of years. An interesting example of this is the well established

gravity tie made between Potsdam and Bad Harzburg. Since Potsdam lies

in East Germany, it was not accessable to geodesists from nations outside of the Soviet Bloc for many years and Bad Harzburg in Western

Germany became the reference point for the western nations.

Instruments used for gravity surveys fall into two basic categories.

Originally, all such measurements were made with instruments of the

pendulum type, known as geodetic pendulums. These pendulums have, in

essence, an unknown but constant length, and the difference in gravity

between two stations is deduced from the changes in period of the

pendulum when it is swung at the two sites. Successful measurements

with pendulums of this type require highly developed techniques,

painstaking care, and considerable time for each determination!- 13 J #

In more recent years, a different type of instrument has been used

for gravity survey work. These instruments, known as gravity meters,

operate on the principle that a mass suspended by a spring will change

its equilibrium position with changes in gravity. Since gravity

differences are small, such instruments are examples of ingenious designLl4J and construction. Usually the mass is attached to an arm

pivoted at the other end with the torque due to the mass being opposed

by a non-linear spring and moment arm arrangement. The arrangement is

usually such that the system is very near to unstable equilibrium so that a small change in the force on the mass tends to produce a large

displacement of the arm. The actual motion is limited by stops and the arm is brought back to its initial position by a fine spring actuated

by a micrometer screw adjustment. These instruments must be calibrated

by measuring gravity differences between points having known differences, such as stations with geodetic pendulum gravity values.
5 . Local Values of Gravity

The principal agency of the United States Government for the

determination of gravity values is the Coast and Geodetic Survey, a part of the Environmental Science Services Administration of the U. S.

Department of Commerce. The Coast and Geodetic Survey has on file

values of gravity measured in many parts of the country and new measurements are constantly being added to the list.

In cases where a standards laboratory is working at an exceptionally high level of accuracy, it may be desirable to have a direct

gravity tie made by means of a gravity meter from the nearest network

site to the point of interest in the laboratory. For many laboratories,

a value of ample accuracy can be obtained by computation from the nearest

established network station. The Coast and Geodetic Survey can provide

assistance with such a computation if they are given the latitude,

longitude, and elevation of the laboratory point where the value is

needed. The latitude and longitude should be furnished to the nearest

0.1 minute of arc, and the elevation above sea level within about five

feet. At most locations of standards laboratories, this type of

information will enable the computation of gravity with a standard

error not exceeding ± 0.00004 m/s . Values furnished by the Coast and

Geodetic Survey are accompanied by an estimate of standard error.

In general, repeat gravity measurements for a particular location

are unnecessary. Diurnal variations, following the luni-solar tidal

cycle, do not exceed ±0.000003 m/s 2

, and secular changes of the order

of 0.00001 m/s have not been confirmed since the advent of precise

gravity measurements

6. Standard Gravity

The term "standard gravity" is so widely encountered and so much

misunderstood that some explanation is desirable. Standard gravity

bears no relationship to any system of gravity measurements, absolute

or otherwise. It is simply an acceleration that has been adopted by

agreement among the nations of the world as the definition of the

engineering units of force. These units of force, taken as the weight

of a unit mass, were objectionable in their original form because they

varied with the location of the mass on the surface of the earth. By

common consent it was agreed that such a definition must be tied to some specific location on the globe, and a value at 45 degrees latitude

and sea level seemed a reasonable compromise. Any other location

would have been equally valid providing everyone agreed to it. In 1901,

five years before the publication of the Potsdam absolute determination,

the International Conference on Weights and Measures adopted a value

of 9.80665 m/s 2 as the definitive valueLl5J. This value had been

obtained by reducing an absolute measurement made at the International

Bureau of Weights and Measures by Monsieur Defforges to 45 degrees and

sea level. Later it was pointed out that, because of the existence of
gravitational anomalies, there was no unique value for that latitude

and elevation. In 1913, the International Conference reviewed the

situation and reaffirmed that the conventional value should be represented by the number 9.80665 m/s 2

. In essence, this meant that the

definition of the practical units of force was not to be based on the

weight at 45 degrees and sea level, but on the arbitrarily adopted

acceleration value

It may be seen from this that the value of 9.80665 m/s is an arbitrary value of acceleration and not the value of gravity at a specific location. It is not expected that this value will be changed

in the future

7. The Computation of Forces

In the standards laboratory it is frequently necessary to calculate

the force exerted by a given mass in air as, for example, in the

operation of a deadweight piston gage pressure standard. The force,

F, is calculated from the relationship

Kmg^l --J

where m is the mass, g is the local value of the acceleration due to

gravity, a is the density of air, and p is the density of the mass.

If m is given in terms of "apparent mass versus brass standards in

normal air", Oi should be assigned the value 1.2 kg/m3

, the adopted

value for the density of normal air, and p should be assigned the

value 8400 kg/m3

, the adopted value for the density of brass.

The quantity K is a numerical factor, the value of which depends

upon the units of F, m, and g. In the SI system of units,

K = 1, for F in newtons, m in kilograms, and

g in meters per second squared.

Other relationships are as follows:

K = 1, for F in dynes, m in grams, and g in

centimeters per second squared,

K = 1, for F in poundals, m in pounds mass, and

g in feet per second squared,

K = 1/32.17405 for F in pounds force, m in

pounds mass, and g in feet per second squared,
K = 1/980.665 for F in pounds force, m in pounds

mass, and g in centimeters per second squared,

K = 1/9.80665 for F in kilograms force (kiloponds),

m in kilograms mass, and g in meters per second

squared

8. Summary

Most laboratories that carry out calibration functions involving

force measurements, such as various forms of pressure measuring

instruments, force transducers, and certain types of accelerometer

calibrations using the earth's field as a reference, need a suitable

value of gravity established within the laboratory. The value need

not be determined by actual gravity measurement except in exceptional

cases. A value within 0.0001 m/s (10 milligals) gives force values

within one part in 100,000 which is adequate for most purposes. For

most locations of standards laboratories, a value well within this

limit can be obtained from the Coast and Geodetic Survey. In any case,

it is advisable to write to them to ascertain if it is available.

The term "standard gravity", e.g. 9.80665 m/s , is in reality an arbitrarily defined acceleration adopted to define units such as the

pound-force and kilogram-force. It is not the value of gravity at any

specific location and is not affected by any corrections to the Potsdam

system.
9 . References

1. F. Kuhnen and P. Furtwangler, Bestimmnung der absoluten Grosze

der Schwerkraft zu Potsdam (Verof fentlichung des K. Preuszichen

geodatischen Institutes, N. F. no. 27) Berlin: P. Stankiewicz

1906.

2. P. R. Heyl and G. S. Cook, The value of gravity at Washington,

J. Res. NBS 17, 805-39( 1936)RP946

3. J. S. Clark, An absolute determination of the acceleration due

to gravity, Phil. Trans. Roy. Soc. London, Ser. A., 238,

65-123(1939).

4. P. N. Agaletskii and K. N. Egorov, Rezul 1 taty absoliutnykh

opredelenii uskoreniia sily tiazhesti v punkte VNIIM (Leningrad),

Izmeritel Tekhn . , Vol for 1956, no. 6, 29-34.

5. A. I. Martsiniak, Opredelenie absoliutnoi velichiny uskoreniia

sily tiazhesti po padeniiu zhezla v vakuume , Izmeritel Tekhn.

Vol for 1956, no. 5, 11-15.

6. H. Preston, Thomas and others, An absolute measurement of the

acceleration due to gravity at Ottawa, Can. J. Phys _38, 824-52

(1960).

O 7. A Thulin, Une determination absolue de g au pavilion de Breteuil,

par la methode de la chute d'une regie divisee, Ann. Geophys

16, 105-27 (1969).

8. A. H. Cook, A new absolute determination of the acceleration due

to gravity at the National Physical Laboratory, England, Phil.

Trans. Roy. Soc. London, Ser. A., 261, 211-252 (1967).

9. D. R. Tate, Acceleration due to gravity at the National Bureau of

Standards, J. Res. NBS, 72C (Engineering and Instrumentation)

No. 1, 1-20 (1968).

10. A. H. Cook, The absolute determination of the acceleration due to

gravity, Metrologia, I, no. 3, 84-114 (July 1965).

11. J. A. Hammond and J. E. Faller, Laser interferometer system for

the determination of the acceleration of gravity, IEEE J. Quantum

Electronics, QE-3 , no. 11, 597-602 (1967).

12. A. Sakuma, Etat actuel de la nouvelle determination absolue de la

pesanteur au Bureau International des Poids et Mesures , International Association of Geodesy, Bulletin Geodesique, n.s.,

no. 69, 249-260 (1 Sept. 1963).
13. C. H. Swick, Pendulum gravity measurements and isostatic

reductions, Coast and Geodetic Survey Special Publication No.

232 (1942) .

14. Gravitation, Encyclopaedia Britannica, 1959 edition, 10 , 663-682.

15. Comite International des Poids et Mesures, Comptes rendus de

V / S ' N la troisieme conference generale des poids et mesures, Quatrieme

Seance, 66-70, (22 Octobre 1901).

16. Comite International des Poids et Mesures, Comptes rendus de la

s * ' * «. cinquieme conference generale des poids et mesures, Troisieme

Seance, 42-44, (14 Octobre 1913).
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