Validation of local gravity

1. Validation of local gravity Mr. Neville Tayler South African National Accreditation System

2. Validation of Local Gravity Introduction The accurate measurement of Force by means of the application of mass is dependent on the knowledge of the value of the local gravity. An example of this principle is the pressure balance or dead weight tester, where the pressure is proportional to the application of Force over a known area.

3. Validation of Local Gravity Introduction • Gravity is known to vary by as much as 0,5% across the surface of the Earth, and to change by up to 0,003% per 100 meter change in altitude. • This variation is due to • latitude; • altitude; • topography; • geology.

4. Validation of Local Gravity Introduction • This variation is due to • latitude; • There is greater outward centrifugal force at latitudes closer to the equator resulting slightly lower gravitational acceleration at the equator that at the poles. • altitude; • topography; • geology.

5. Validation of Local Gravity Introduction • This variation is due to • latitude; • altitude; • Gravity decreases with altitude due to the greater distance from the centre of the earth; • topography; • geology.

6. Validation of Local Gravity Introduction • This variation is due to • latitude; • altitude; • local topography; • Variations in the local topography such as mountains can influence local gravity; • geology.

7. Validation of Local Gravity Introduction • This variation is due to • latitude; • altitude; • local topography; • geology. • differences in the substrata, and the density of the underlying rock. Denser rocks resulting in higher than normal gravitational fields.

8. Validation of Local Gravity Introduction • This variation is due to • latitude; • altitude; • local topography; • geology. • In addition to the above gravity can be affected by the tides typically ± 2 µm/s² or (due to the gravitational effects of the sun and the moon)

9. Validation of Local Gravity Standard Gravity This may be somewhat of a misnomer as gravity is anything but standard. The value of Standard Gravity is defined to be precisely 9,806 65 m/s² at the third CGPM meeting held in 1901.

10. Validation of Local Gravity Standard Gravity The purpose on defining this value was to establish a convenient reference for defining the now obsolete unit kilogram force. Standard of nominal gravity and is denoted by g0 or gn

11. Validation of Local Gravity Why use Local Gravity as opposed to Standard Gravity Laboratory A located in Johannesburg has had their local g measured as it was determined as being 9,7855 m/s². Should they choose to ignore this value and simply use the defined standard gravity of 9,80665 m/s² this would result in an error of measurement of + 0,2157%.

12. Validation of Local Gravity Why use Local Gravity as opposed to Standard Gravity Would an error of + 0,2157% be acceptable? Consider the specifications of this piston balance of Perhaps this is a no brainer?

13. Validation of Local Gravity Measurement of Gravity Measurement of gravity is achieved by using an instrument known either as a gravimeter of gravitometer. In it’s simplest form the gravimeter is a device which measures the differences in the force resulting from the local gravity and an accurately known mass.

14. Validation of Local Gravity Measurement of Gravity Sets of measurements are performed using the 3 gravimeters, first at the reference site, then at the test site, and again at the reference site. The linear drift is determined, corrections are applied for the tidal drift.

15. Validation of Local Gravity Measurement of Gravity As the gravity at the reference site is known, and the measurements are relative in nature it is possible to calculate the effective local gravity at the test site.

16. Validation of Local Gravity Calculation of Gravity In instances where the highest accuracy is not necessary, or where measurements are performed ‘on-site’, it is possible to make use of the a calculated value for local g.

17. Validation of Local Gravity Calculation of Gravity The NPL have provided the following formula which allows for the approximation of local g to a stated uncertainty of ± 5 in 105 (0,005%)

18. Validation of Local Gravity Calculation of Gravity Where

19. Validation of Local Gravity Calculation of Gravity On the basis of the claims made by the NPL it was decided to test the hypothesis that the calculated value for local gravity would be within the claimed 0,005%. A request was made for data from the accredited SANAS calibration laboratories who had their local gravity measured by the Council for Geoscience.

20. Validation of Local Gravity Calculation of Gravity • Data was provided by three SANAS accredited calibration laboratories • Wika Instruments; • Denel aviation; • SAA Avionics. • A spreadsheet was prepared to perform the calculation of the local gravity using the formula provided by the NPL.

21. Validation of Local Gravity Case Study 1 From the issued report Absolute gravity 9.7855000 m/s² ± 0,000 000 5 m/s² Latitude 26,20863º Longitude 28,09028º Altitude 1700 m Calculated local gravity 9.7851601 m/s² Difference - 0,00034 m/s² or - 0,0035 %

22. Validation of Local Gravity Case Study 1 An attempt was made to validate the positional information provided in the report. Latitude 26,20863º Longitude 28,09028º Altitude 1700 m

23. Validation of Local Gravity Case Study 2 From the issued report Absolute gravity 9.7853794 m/s² ± 0,000 000 3 m/s² Latitude 26º 08’ 51” Longitude 28º 15’ 42” Altitude 1678 m Calculated local gravity 9.785184343 m/s² Difference - 0,00020 m/s² or - 0,0020 %

24. Validation of Local Gravity Case Study 3 From the issued report Absolute gravity 9.7853471 m/s² Latitude 26º 08’ 35,5” Longitude 28º 13’ 32,1” Altitude 1747 m Calculated local gravity 9.784967541 m/s² Difference - 0,00038 m/s² or - 0,0039 %

25. Validation of Local Gravity Case Study 3 Validation of altitude data from case studies 2 & 3. Altitude 2 1 678 m Altitude 3 1 747 m The altitude reported along the runway are as follows 1679 m, 1688 m, 1693 m (laboratory 3 is located ± 30 m above the ground level)

26. Validation of Local Gravity Conclusions • In all 3 case studies the calculated local • gravity read lower that the measured value; • The mean error was determined as being • approximately – 0,00031 m/s² • or – 0,0031 %. • The calculated values are all within the • stated uncertainty of ± 0,005 % as • suggested by the NPL.

27. Validation of Local Gravity Conclusions • Unfortunately the sample size is to small to • made other inferences and draw other • conclusions, it is however assumed that • since in all cases the calculated value is • lower than the measured value may be due • to the underlying strata.

28. Validation of Local Gravity Acknowledgements • Mr Dewald Vermeulen - SAA; • Mr Tjaart Labuschagne – Denel Aviation; • Mr Paresh Wellcome – WIKA Instruments SA • Google Maps • The NPL

29. The End Thank you nevillet@sanas.co.za Tel: 012 394 3780 Fax: 012 394 4780