Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 11, No. 3, 2024 

 

89 

Correction	of	Gravitational	Acceleration	at	High	
Altitude	and	Low	Pressure	and	the	Application	in	
Weighing	
Shuangming Jin, Liang Pang, Heping Shen * 

Measurement and Testing Institute of Xizang Autonomous Region, Lhasa Tibet, 850000, China 

* Corresponding author: Heping Shen 

 

Abstract: Earth gravity field data is the basic data and strategic data of a country. The accurate measurement of Earth gravity 
field is of great scientific significance to the fields of metrology, earthquake prevention and disaster reduction, surveying and 
mapping, geodynamics and so on. It is of great strategic significance to the fields of Marine science, resource exploration and 
national security. China has a vast territory and diverse landforms. From the southeast coast to the Qinghai-Tibet Plateau, the 
elevation difference is more than 5,000 meters, and the elevation difference in a small range is small, and the acceleration of 
gravity can also be ignored. However, when the altitude difference is large, the change of acceleration of gravity will have a great 
impact on high-precision measurement. The effect of gravity acceleration in low altitude area and Lhasa under high altitude and 
low-pressure environment on the weighing instrument is compared and analyzed, and the correction method of altitude on the 
weighing instrument is proposed. 

Keywords: Acceleration of Gravity; Elevation Difference; High Altitude Low Pressure; Weighing. 
 

1. Introduction 
The gravity field of the earth is one of the most important 

physical fields of the earth, which reflects the spatial 
distribution, movement and change of the earth's materials, 
and restricts all physical events occurring on the earth and its 
adjacent space. 

2. Basic Concepts 
(1) Mass: in physics, the amount of matter contained in the 

object is called mass, and the mass does not change with the 
shape, state, and spatial position of the object, which is the 
basic attribute of the object, that is, the same object has the 
same mass all over the earth. Mass is usually denoted. The 
unit of mass in the SI system of units is the kilogram, kg. 

(2) Acceleration of gravity: The acceleration of objects near 
the Earth's surface when only subjected to gravity is called the 
acceleration of gravity, g , also known as the acceleration of 

free fall, which is expressed. The acceleration of gravity 
increases with the increase of latitude and decreases with the 
increase of altitude. Our country has a vast territory and a 
large latitude span, so the variation of the acceleration of 
gravity is larger. It requires us to pay attention to the influence 
of gravity acceleration value when the weighing instrument is 
used and verified across regions g . 

(3) Gravity: due to the attraction of the earth and the force 
of the object, called gravity, life often refers to the size of the 
object by gravity as weight. Mass and weight are completely 
different and should not be confused. The unit of gravity is 

G , represents the symbol bit, the formula is: G mg . It's 

the mass of the object, m  and g is the local acceleration of 

gravity. 

3. The Influence of Gravity 
Acceleration on the Stability of the 
Weighing Instrument 

According to the principle of mechanics, weighing can be 
divided into dynamic effect weighing and static effect 
weighing. 

3.1. Dynamic Effect Weighing 
also known as gravity balance weighing, is the use of 

known objects in the gravitational field of the earth's 
gravitational acceleration and the size of the mass to measure 
the mass of the said object. Such as mechanical lever scale, 
balance is the use of lever balance principle for measurement. 
As shown in the picture: 

 

 
Fig 1. Dynamic effect principle weighing diagram 

 
According to the lever balance principle, 

1 1 1 2 2 2m l g m l g     . Since the distance between the 

measured object and the measured object is very close, the 
difference between the acceleration of gravity is negligible, 

that is, it can be seen that 1 2g g  1 2 2 1m m l l  when 

the lever is balanced, the mass of the measured object is equal 

1l 2l

1m
2m

1g 2g



 

90 

to the product of the lever ratio and the mass of the known 
weight, and the measured result is the mass of the object, and 
the result is independent of the acceleration of gravity. 

3.2. Static Effect Weighing 
Static effect weighing, also known as gravity deformation 

method weighing, is to use the size of the deformation or 
internal stress generated by the elastic body of the object 
under the action of gravity to measure the magnitude of 
gravity, such as electronic scale and spring scale are to use 
gravity deformation method for weighing and measuring, as 
shown in Figure 2 

 

Fig 2. Work diagram of static effect weighing system 
 
The weighing principle of the electronic weighing device 

is to convert the gravity of the object acting on the sensor into 
the number of electrical parameters (voltage, current, 
capacitance or frequency) according to a certain functional 
relationship to show the weight of the object being measured. 
Therefore, the weighing result of the electronic weighing 
device (sensing principle) is not the mass value of the object, 
but the gravity value, which is affected by the change of the 
gravitational acceleration value. 

3.3. Calculation Formula of Gravitational 
Acceleration Changing with Latitude 

The normal gravity formula recommended by the 
International Geophysical and Geodesy Association in 1979:  

  2 2 29.780327 1 0.0053024sin 0.000005sin 2g m s      

 -Latitude of the Earth at the measuring point. 

 

 
Fig 3. Geographical position and gravitational acceleration position 

relationship diagram 

3.4. Calculation Formula of the Change of 
Gravitational Acceleration with Altitude 
Common Approximate Formulas are as 
Follows: 

 

2

0 0

4
0

1 1 2

1 3.14 10

h h
g g g

R R

g h





         
   

  

 

h - Height above ground; 

R - Radius of the earth; 

0g - The acceleration of gravity when an object is on the 

Earth's surface 
This is the approximate formula for the change of 

gravitational acceleration with height. It can be obtained from 
the formula for every increase in elevation 1 km   The 

acceleration of gravity decreases by about 3.1 2mm s . 

The common formulas used in field practice are as follows: 

     2 2
2

2 3
, 1 1 2 sinr h r f m f h h

a a
          

 

2 2a b
m

GM




 

 r   is the normal gravity value of the projection point 

of the point on the ellipsoid; 
f  is the ellipsoid oblateness; 
  is the angular speed of the earth's rotation; 

GM   is the earth's gravitational constant (including 
atmospheric mass) 
  is the geodetic latitude of the point; 

h  is the height of the point from the normal to the elliptic 
surface 

4. Influence of the Change of Gravity 
Acceleration Value on the Weighing 
Result 

When installing and purchasing electronic weighing 
instruments across provinces the variation of the acceleration 
of gravity between provinces is easy to attract attention 
because the variation of the acceleration of gravity is mainly 
affected by geographical latitude and altitude. In this paper, 
the influence of latitude and altitude on the accuracy of 
electronic weighing results is discussed under the 
circumstance that latitude and altitude vary greatly in the 
province. 

Lhasa measuring point: 91.029° E, 29.632° N; 3643 m 
above sea level; 

Beijing measuring point: 115.903° E, 40.227° N; 35 m 
above sea level; 

By adding relevant parameters, the gravitational 
acceleration of Beijing and Lhasa can be obtained as follows: 

 
Table 1. Formula modification and absolute gravimeter 

measurements in Beijing and Lhasa 

Point position Formula correction 
Absolute gravimeter 

measurement
Beijing 9.8014 9.8012
Lhasa 9.7813 9.7810

Test object

Strain gauge load cell

amplifier A/D converter

Single‐chip 
processor

Keyboard

display

printer



 

91 

Choose the same set of grade weights, choose the same 
model, the same manufacturer's electronic balance: 

National Metrology Institute use balance information: 
balance model: 224S; Number: 18562177; Manufacturer: 
Sartourius; Actual indexing value: 0.0001g; Calibration index 
value: 0.001g. Experimental conditions: Temperature 22℃, 
humidity 41.2%. 

Balance information used in Xizang measurement: Balance 
model: 224S; Number: 18561538; Manufacturer: Sartourius; 
Actual indexing value: 0.0001g; Calibration index value: 
0.001g. Temperature 21.6℃, humidity 40.7%. 

Select 100g weight in the same set of grade weights, 
Beijing measuring point, continuous measurement 10 times, 
the average is 100.0002g; Using the same measurement 
method, the average value of continuous measurement in 
Lhasa is 99.7935; 

From the above measurement results, it can be seen that the 
same weight in Beijing and Lhasa, ignoring the influence of 
air density and temperature and humidity, causes the 
measurement error mainly because of the change of gravity 
acceleration caused by the difference in elevation. 

According to the working principle of the electronic 
balance, ignoring the mass changes caused by environmental 
conditions in the two places of the experiment, according to 

Hooke's law: F kx  The process of gravity measurement 
is the change caused by the gravity of the object, resulting in 
the difference of the shape variable, which affects the final 
measurement result. Because G mg  , For convenience, 

the acceleration of gravity in Beijing is 1g  , and the 

acceleration of gravity in Lhasa is 2g  . 1 1G mg  ,

2 2G mg , 1 2

1 2

m m

g g
  

It can be obtained from the above formula: 1 2
2

1

m g
m

g


so we can get 2 99.7941m  . 

5. Conclusion 
By comparing the above experimental results, it can be 

seen that the absolute error value of the experimental result is 
0.0006 and the relative error is as follows when the weighing 
device is modified based on the absolute value of the local 
gravitational acceleration: 0.0006012%, which is about 6 
parts per million, the experimental results have a high 
reliability. In summary, the experimental process is reliable, 
and the weighing error in the weighing process can be 
accurately corrected through the measurement of 
gravitational acceleration at different points. 

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