Gravity Tolerance Application Help

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Table of Contents

Purpose of the Gravity Calculator

The purpose of this program is to determine the potential error in weighment that will occur if a Non automatic weighing device is calibrated in one geographic location in Canada, and then moved to another.

Note: This phenomenon occurs with scales operating on force measurement principles (such as electronic loadcell and spring scales) and does not affect those which operate on lever principles.

The Weights and Measures inspection can proceed if this error is less than one half the in-service limit of error allowed by the Specifications for Non automatic weighing devices.

Theory of Operation

The scale inspection location and final destination can be identified by using a postal code, or a latitude and longitude.

The postal code method uses gravity measurements made by Natural Resources Canada (NRCan) for a 50 km radius around a "centroid" location for the postal code. A postal code may have several "centroid" locations, if it is discontinuous, has more than one enumeration area etc. If there is more than one "centroid" location, gravity measurements for a 50 km radius around each are used. The calculator examines minimum and maximum gravity values in both locations, and identifes a "worst case" scenario for a potential error due to a change in location.

If the latitude and longitude method is chosen, NRCan measurements are used to predict gravity values for the specified location. The uncertainty for this predicted value is used to establish minimum and maximum gravity values. Again, the calculator examines minimum and maximum gravity values in both locations to determine a "worst case" scenario for a potential error due to a change in location. The latitude and longitude method is the more precise since the consideration is for a selected location, and not for a 50 km radius.

Operating Instructions

Note: All white shaded boxes require information input. All grey shaded boxes display information and will not accept input information.

  1. Select the scale class from the "Class" drop down selection box.
  2. Enter the scale capacity in the text box marked "Scale Capacity".
  3. Select the unit of measure for the scale capacity in the drop down selection box.
  4. Enter the verification interval by typing in a positive number in the text box.
  5. Select the unit of measure for the verification interval.
  6. There are two methods to select the location of the scale inspection. Choose a postal code entry, or a latitude and longitude entry with your mouse.
    1. Postal code entries require the postal code for the location of the scale inspection. Do not put a space or dash anywhere in the entry.
    2. Latitude and longitude entries for the scale inspection location may be in decimal format, or degree, minute, second. Do not enter a decimal point or comma.
  7. Select the location of the final destination for the scale, using the same method as in (6.) above.
  8. Click the button marked "Calculate" to calculate the most restrictive tolerance for the scale, and the percentage of error due to the change in location.
  9. Click the icon under the "Action" header to display the limits of error for the scale, and other information about the calculations.
  10. The percent of error caused by the difference in acceleration due to gravity at both locations is displayed. If this value is greater than the most restrictive tolerance, then the inspection should not proceed.
  11. The final result is displayed under the "Status" header.

Data Entry Problems

The "Operating instructions" may be of some help.

  1. The location calculator must have entries in all data "drop down" boxes. Mouse click on the arrow at the side of the box to display a drop down list, and mouse click on your selection.

    The unit of measure entries must not conflict ie: If the scale capacity unit of measure is metric, then the e Verification unit of measure must also be metric.

  2. The location calculator must have positive numbers (entered from the computer keyboard) in all text boxes.

    The “verification interval” must divide evenly into the "scale capacity".

Scale Class

Non automatic weighing devices must be configured so that the scale capacity and the verification interval produce the appropriate number of graduations (see column IV in the table below) for the scale class. The size of the verification interval must also conform to Column III in the same table.

The classes of Non automatic weighing devices are as set out in column I of the table to this section on the basis of the device's accuracy, verification scale interval and number of scale intervals as set out in columns II, III and IV, respectively, of that table.

Column I Column II Column III Column IV
Class Accuracy Verification scale interval (e) Number of verification scale intervals
International Units Canadian Units Minumum Maximum
I Special e e 50 000  
II High e ≤ 0.05 g e ≤ 0.002 oz. 100 100 000
0.1 g ≤ e 0.005 oz. ≤ e 5 000 100 000
III Medium 0.1 g ≤ e ≤ 2 g 0.0002 lb. (0.005 oz.) ≤ e ≤ 0.005 lb. (0.1 oz.) 100 10 000
5 g ≤ e 0.01 lb. (0.2. oz) ≤ e 500 10 000
IIIHD Medium (high capacity devices) 2 kg ≤ e 5 lb. ≤ e 2 000  
IIII Ordinary 5 g ≤ e 0.01 lb. (0.2 oz.) ≤ e 100 1 200

Scale Capacity

"maximum capacity" or "Max" means the maximum weighing capacity of a Non automatic weighing device and, in the case of a multiple range device, the maximum weighing capacity of the relevant range.

Verification Interval

The "verification scale interval" or "e" means a value, specified by the manufacturer and expressed in units of mass, that is used for the classification and inspection of a Non automatic weighing device. "e" may be different than the actual scale interval, or "d".

The verification scale interval for Class I and II weighing devices that are not equipped with auxiliary indicating elements, for Class III, IIIHD and IIII weighing devices, for multiple range devices and for multi-interval devices is equal to the actual scale interval, or "d".

Example when "e" is not equal to "d":

A Class II, precious metal scale may have the actual scale interval "d" equal to 1 mg. The scale is inspected, and the limits of error are determined using "e", the verification interval which might be 10 mg. This feature must be mentioned in the "Notice of Approval" for the scale.

Actual scale interval

The "actual scale interval" or "d" means the value, expressed in units of mass

  1. with respect to analogue indications, of the difference between the values corresponding to two consecutive scale marks; and
  2. with respect to digital indications, the difference between two consecutively indicated values.

Note: "d" may be different than the verification scale interval "e".

Scale Limits of Error

Note: This calculator uses acceptance limits of error for all calculations.

Acceptance Limits of Error

The acceptance limits of error applicable for each class of Non automatic weighing device are one-half the in-service limits of error for a specified load.

In-service Limits of Error

The in-service limits of error set out in column I of the table below apply, in respect of each class of Non automatic weighing device set out in column II of that table, according to the specified load.

(2) In the table to this section, "m" means the weight of the load placed on the weighing device, and is expressed in the number of verification scale intervals.

(3) The in-service limits of error that apply to a Class IIIHD weighing device are ±1 e where the load is not less than zero and not more than 500 verification scale intervals, and where the load exceeds 500 verification scale intervals, calculated by adding ±1 e for each additional 800 verification scale intervals or less, to a maximum of ±22 e.

Column I Column II
Limits of error Class I Class II Class III Class IIII
± 1 e 0 ≤ m ≤ 50 000 0 ≤ m ≤ 5 000 0 ≤ m ≤ 500 0 ≤ m ≤ 50
± 2 e 50 000 ≤ m ≤ 200 000 5 000 ≤ m ≤ 20 000 500 ≤ m ≤ 2 000 50 ≤ m ≤ 200
± 3 e m > 200 000 20 000 ≤ m ≤ 100 000 2 000 ≤ m ≤ 4 000 200 ≤ m ≤ 400
± 5 e     4 000 ≤ m ≤ 10 000 400 ≤ m ≤ 1 200

Most Restrictive Step Tolerance

Non automatic weighing devices are subject to limits of error consisting of a series of tolerance "steps", dependant upon the load placed upon the scale platter. The most restrictive tolerance, is the smallest limit of error allowance, determined as a percent ( Limit of error / Load on scale platter X 100).

Inspection Site

The location where the "non automatic weighing device" is inspected and certified by a Canadian Weights and Measures inspector.

Final Destination

The location where the "non automatic weighing device" is used in trade, after having been moved from the inspection location.

Postal Code Entry

The "location of inspection" and the "final destination" of the scale can be identified by entering a Postal Code.

The postal code is used to identify latitude and longitude co-ordinates from a Statistics Canada database. Some postal codes may be discontinuous, and may have more than one set of co-ordinates.

These co-ordinates are 'centroid', in that they are located at a central point in the postal code area. Gravity measurements for a 50 km radius around each co-ordinate are then sampled to determine maximum and minimum gravity values for each area, and for overall minimum and maximum values.

Latitude and Longitude Entry

Latitude and longitude co-ordinates can be entered directly to identify the "location of inspection" and the "final destination" of the scale.

This can be done when the 50 km radius of gravity measurements from a "postal code entry" produces a large difference between the minimum and maximum gravity values.

Latitude and longitude can be entered in decimal format, or by degree, minute and second. All longitudes must be negative values between -46 and -142 degrees. Latitude values must be positive, between +41 and +84 degrees.

Non Automatic Weighing Devices

Most scales in Canada fall into one of two categories:

  1. "Non-automatic weighing devices" (by far the largest category), includes weighing machines that weigh discrete loads and that require an operator's intervention during the weighing process, such as to deposit the load to be measured on the weighing and load-receiving element and to remove it therefrom or to obtain weight results.
  2. "Automatic weighing devices"

Specifications Relating to Non-automatic Weighing Devices

Application:

  1. Subject to subsection (2), these Specifications apply to any non-automatic weighing device and to any equipment or accessory that is attached to the device or used in conjunction with it.
  2. A non-automatic weighing device that, before the date on which these Specifications come into force (February 4, 1998), has been approved pursuant to subsection 3(1) of the Weights and Measures Act or inspected under the terms of a previous enactment, or the class, type or design in respect of which was so approved
    1. is subject to the performance requirements set out in these Specifications; and
    2. is not subject to any of the provisions of these Specifications relating to design, composition, construction or marking where the non-automatic weighing device meets the requirements that applied when its class, type or design was approved or, failing which, that applied to the device on its approval or inspection.

Automatic Weighing Devices

"Automatic weighing device" means a weighing device that weighs without the intervention of an operator and that follows a predetermined program of automatic processes that are characteristic of the device and that may include

  1. the automatic weighing of bulk commodities in interrupted and successive drafts of predetermined amounts, the values of which are summed to derive a total net weight,
  2. the automatic and dynamic weighing of preassembled discrete loads, and
  3. the automatic classification of articles or loads into several subgroups according to their mass.

Website location of the Non Automatic Weighing Device Specifications

Gravity Database Information

The Canadian Gravity Database has been accumulated since the 1950s, and is maintained by the Geodetic Survey Division of Geomatics Canada (Natural Resources Canada).

General information about acceleration due to gravity:

According to the 1980 convention, g = 978.0327 ( 1 + 0.0052790414 Sin2( L ) + 0.0000232718 Sin4( L ) + 0.0000001262 Sin6( L ) ) where L is the latitude in radians of the point of observation, the terms "Sin2", "Sin4", "Sin6", are the function Sine squared (2), Sine to the fourth power (4) and Sine to the sixth power (6) respectively.

The units are in gals (or cm/s*s). This equation is said to be accurate to one part per billion (1/1,000,000,000).

Gravity will decrease also with elevation above the mean sea level at the rate of -0.0003086 gal/m.

Finally, tides play some role in the observed gravity values but the range in Canada is around +/- 0.0002 gal/day (or less). This effect decreases with latitude since the tides are at their strongest at the equator.

Canada also has local gravity anomalies that range from -0.2 to +0.14 gal and these anomalies are mainly due to crustal deformations (subduction zones and post glacial rebound) and different rock densities underground.

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