Gravitational Effects on Balance

“Why do I have to calibrate my balance? Wasn’t it done at the factory?”

Published with permission from Adam Equipment®

This question frequently comes up when a customer receives a balance and is instructed by the operator's manual to calibrate it before use. There are many reasons a balance may need to be calibrated:

  • Disturbances during shipping may cause minor changes to the mechanics
  • Temperature changes can affect calibration
  • Some users may use weights that are slightly different from those used at the factory
  • The location may have a different gravitational force than the factory.

The least understood of these reasons is due to the imperfect shape of our planet. Gravity is not the same everywhere on Earth. This is important because balances do not measure mass, instead, they measure the force of gravity pulling the mass towards the center of the Earth.

During calibration a previously determined weight is used to set the balance's parameters and thus guaranteeing its accuracy. For example, when a 1 kilogram mass (the standard) is placed on a balance, its force will read as 1000g. Then any other weight that is put on the balance will be measured against this standard. If it has half the mass it will have half the force on the balance and it will read half

If this balance is moved to a place where the gravity is different, it will display a different value as the force will be different. This is what happens as you move around the world.

Our Planet is almost a sphere, but not a perfect one. The poles have been squashed down by millions of years of spinning and the equator bulges slightly. If you stand at the poles you are slightly closer to the center of the Earth than if you stand on the equator. As you move closer to the center of the Earth, the force due to gravity will be slightly greater. As you move away from the center it will be less. Likewise, if you climb a mountain you move further from the center and the force is less.

Different balances will react differently to a change in location. A less sensitive balance, say readable to 1.0g, may not be able to measure a change in gravity when it is moved to a different location. More sensitive balances, such as those found in laboratories, will more readily display the difference in gravitational forces. On the most sensitive laboratory balances it is possible that a very small difference in location can cause large changes to the balance's calibration. For example an analytical laboratory balance capable of weighing 100g readable to 0.0001g can detect very small changes in gravity.

If the balance is calibrated with a 100g mass and then moved upstairs in a building say 10 meters, about 3 floors, the change in gravity will cause the balance to measure the 100g mass as 99.9970g, or 0.0030g less because it is further away from the center of the Earth.

If the balance is moved North by 1,000 meters (1km), it will measure the same 100g mass as 100.0007g, an increase of 0.0007g, because it has moved closer to the North Pole. If it is moved South by 1,000 meters, it would be measured 0.0007g less. And if it moved East or West it would stay the same as it is neither further nor closer to the center of the Earth.

See Appendix A for details of how the value for gravity changes over the Planet.

APPENDIX A
Variations in Gravity as the Latitude and Altitude varies

Gravity value versus latitude and altitude

Table 1 - Gravity Variation by Latitude and Altitude

Number of balance intervals (n)

Gravity variation with Latitude change at a constant altitude

Gravity variation with Altitude change at a constant latitude

10 km
~54 minutes

10 m

20 m

50 m

1,000,000 2,000,000 3,000,000 5,000,000

7.5
11.3
22.5
37.5

3
6
9
15

6
12
18
30

15
30
45
75

100.000 200,000 300,000
500,000

0.75
1.13
2.25
3.75

0.3
0.6
0.9
1.5

0.6
1.2
1.8
3.0

1.5
3.0
4.5
7.5

1000 km
~9 degree

1000 m

2000 m

5000 m

10,000 20,000 30,000 50,000

7.5
11.3
22.5
37.5

3
6
9
15

6
12
18
30

15
30
45
75

1000
2000
3000
5000

0.75
1.13
2.25
3.75

0.3
0.6
0.9
1.5

0.6
1.2
1.8
3.0

1.5
3.0
4.5
7.5

Photos courtesy of Adam Equipment.