Validation of local gravity
Mr. Neville Tayler
South African National Accreditation System
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.
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.
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.
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.
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.
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.
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)
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.
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
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%.
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?
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.
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.
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.
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.
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%)
Validation of Local Gravity
Calculation of Gravity
Where
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.
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.
Validation of Local Gravity
Case Study 1
From the issued report
Absolute gravity
9.7855000 m/s² ± 0,000 000 5 m/s²
Latitude
Longitude
Altitude
26,20863º
28,09028º
1700 m
Calculated local gravity
9.7851601 m/s²
Difference
- 0,00034 m/s² or - 0,0035 %
Validation of Local Gravity
Case Study 1
An attempt was made to validate the positional
information provided in the report.
Latitude
Longitude
Altitude
26,20863º
28,09028º
1700 m
Validation of Local Gravity
Case Study 2
From the issued report
Absolute gravity
9.7853794 m/s² ± 0,000 000 3 m/s²
Latitude
Longitude
Altitude
26º 08’ 51”
28º 15’ 42”
1678 m
Calculated local gravity
9.785184343 m/s²
Difference
- 0,00020 m/s² or - 0,0020 %
Validation of Local Gravity
Case Study 3
From the issued report
Absolute gravity
9.7853471 m/s²
Latitude
Longitude
Altitude
26º 08’ 35,5”
28º 13’ 32,1”
1747 m
Calculated local gravity
9.784967541 m/s²
Difference
- 0,00038 m/s² or - 0,0039 %
Validation of Local Gravity
Case Study 3
Validation of altitude data from
case studies 2 & 3.
Altitude 2
Altitude 3
1 678 m
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)
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.
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.
Validation of Local Gravity
Acknowledgements
•
•
•
•
•
Mr Dewald Vermeulen - SAA;
Mr Tjaart Labuschagne – Denel Aviation;
Mr Paresh Wellcome – WIKA Instruments SA
Google Maps
The NPL
The End
Thank you
nevillet@sanas.co.za
Tel: 012 394 3780
Fax: 012 394 4780