Weight is a gravitational acceleration force, which influences an object. In our case it may be a weighed object which is influenced by Earth gravitational acceleration force. Two objects are attracted by each other with force that is directly proportional to product of their masses and inversely proportional to the squared distance between them. Thus, the same object weighs a bit more if placed on poles than on equator. This is a result of Earth being oblate, with distance from the middle of Earth to equator being longer than from the pole. The same refers to weighing. Mass of a weighed object if weighed on a top of high mountain is lower compared to the same object weighed on mountain foot.

Fig. 1. Schema of lever scale

Concluding from above, a weight is thus a force. In order to determine a weight, the gravitational acceleration force which attracts the object must be specified. Actually, in case of traditional lever scale, the difference between gravitational force of a measured object and a weight is compared. The reliability of this measurement depends on the accuracy of standard mass used for comparison of the two objects.

Mass is a measure of inertia, i.e. a tendency of an object to remain at rest or in motion with a given speed. Popularly, it is comprehended as quantity of matter and energy cumulated in a physical object. The higher the mass of an object, the more difficult it is to put it into motion or acceleration. Thus, mass is a constant value independent on location, and weight does depend on location (latitude and altitude above sea level).

In case of standard instruments, that is lever scales, measuring process is a comparison of the weighed object with standard mass. As it is a direct comparison, the weighing result does not bear error arising from change of gravitational acceleration force. Hence the basic practical aspect – the possibility of weighing in every place in the world regardless of changes in ‘g’.

In case measuring instruments of electronic weighing instruments, during weighing process there is no direct comparison with standard mass. In order to obtain a measuring result, indirect values are measured. The indirect values are current (in case of measuring instruments with electromagnetic conversion) or change of bridge resistance (in case of load cell based measuring instruments). The indirect values, are than processed by electronic circuits into a measuring result expressed in grams or kilograms. Generally, there are many more weighing methods, but in most of them, in order to obtain a result, it is necessary to measure terrestrial force which attracts the object: F = m × g

Scaling of measuring instruments in specific units requires consideration of gravitational acceleration value “g” on instrument calibration location. If a measuring instrument is relocated from its original place of calibration, it requires taking into consideration change of „g” value and correcting instrument’s characteristics for the new location (as result of “g” value change). The “g” factor correction can be processed in various ways, depending on functional possibilities of a measuring instrument.

In order to be aware of the problem range, it is necessary to do practical calculation of changes in gravitational acceleration force in relation to altitude and altitude above sea level. Than refer its result to errors which occur on a weighing instrument. A detailed approach to this matter is presented in Directive 90/384/EEC, which specifies a formula for calculation of changes in "g". Additionally, it describes acceptance criterion for a weighing instrument: a weighing instrument can be verified if its error does not exceed 1/3 of maximal permissible error as specified by the Directive.

[1-A]. The formula for calculating the value of gravitational acceleration, taking into account
latitude and altitude above sea level, where:

g - gravitational acceleration value
- latitude [st]
a - altitude above sea level [m]

[1-B]. The condition for the size of the errors resulting from changes in "g"

where:
n       - quantity of measuring instrument verifying units

  - deviation arising from latitude change
  - deviation arising from altitude above sea level change

gR     - nominal value of gravitational acceleration force for specific zone

BGD  - maximal permissible error (MPE)

Error size of a weighing instrument arising from change of „g” value, depends on resolution of a weighing instrument, that is quantity of verifying units (n). Significance should also focus on the distance of relocation, specifically:
- change of latitude
- change of altitude above sea level

Fig. 3. Poland with division into latitude zones

Fig. 4. Poland with division into altitude above sea level.

"For the purpose of calculation, it has been assumed, that weighing instruments have been calibrated at one end of Poland, e.g. in Gdansk 54,5°; 100m above sea level, and than relocated to the opposite side of Poland (e.g. to Zakopane 49,5°; 1000m).

On weighing instrument relocation it has not been calibrated. Error size which occur in typical weighing instruments is presented on below table:

One of the basic means to eliminate such errors is calibration of a weighing instrument on its operation location. For weighing instruments class I, and most of those in class II, the problem of errors caused by “g” change, was solved by introduction of a system of internal automatic calibration, realized through application of a weight installed inside the weighing instrument casing. In addition, this system eliminates temperature errors, due to constant monitoring of working temperature of an instrument, and detection of changes which may influence the operation of the instrument.

A build-in mechanism of automatic internal calibration eliminates the long-lasting changes of weighing instrument characteristics, i.e. its components, and provides stability of measurement. The question of operation of automatic internal calibration system depends on:
- whether the weighing instrument is offered as verified
- if it is a non-verified device, (than the user may decide on calibration system initiation).

There are, however, weighing instruments class II, which are covered by so called 2-stage verification process. The procedure requires calibration of a weighing instrument with external weight on location. This way the errors arising from “g” change are eliminated. Such procedure can also refer to weighing instruments class III, if it is recognized as necessary. Due to fact, calibration of a weighing instrument with external weight is blocked in case of verified weighing instruments, the procedure is only accessible to authorized personnel.
(PN-EN 45501 – Metrological aspects of non-automatic weighing instruments, point 4.1.2.5. point 4.1.2.6)

The second way to eliminate errors arising from change of “g” value is insertion of a correction factor during production stage of a weighing instrument. The inserted factor recognizes the difference in „g” between assembly place and place of instrument operation. It is the best solution from the economic point of view, but it requires very precise determination of location of instrument utilization.

The solutions presented above are used during assembly and control stages of RADWAG weighing instruments. The method of errors arising from “g” change, depends on resolution and design of a weighing instrument. Due to ISO 9001:2000 system implemented in RADWAG, it is obliged to keep the records from control of weighing instruments, including mechanisms responsible for compensation of errors caused by change of “g” value. Hence, documents attached to a purchased weighing instrument include a datasheet specifying the area for proper operation of this instrument:
The specific weighing instrument can be operated without additional calibration procedure in the geographical area: 51 - 53 : 100 - 300

The above statement relates to verified weighing instruments in III class with system of external calibration.

Apart from the obvious phrase, that errors should be corrected, there remains a technical aspect referring to this matter. Modern world, as rightly suggested, has become a global village, which facilitates the movement of both the population and equipment. In case of electronic weighing instruments, it is an easy, simple and sometimes justified economically - the opportunity to use the same weighing instrument in different locations. But what about accuracy of the instrument?

In case of weighing instruments equipped with system of automatic internal calibration, or external calibration with standard mass being accessible, the problem does not exist. If the instrument is relocated, than the calibration process is performed, and errors resulting from instrument relocation are eliminated. What about weighing instrument class III with external calibration blocked for the operator? Relocation of such instrument will cause appearance of errors, which may not be noticed. Thus, such weighing instrument, if relocated, have to be recalibrated, which is mostly the same as verification performed for the second time. The matters discussed above should be clear specially to personnel who supervises control over weighing instruments in a company.