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Journal of Physics: Conference Series
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Research on Improving Artillery Firing Accuracy by Using Meteorological
Data along Ballistic Trajectory for Artillery Firing
To cite this article: Zhiyuan Zhang et al 2019 J. Phys.: Conf. Ser. 1325 012129
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ICAITA 2019
Journal of Physics: Conference Series 1325 (2019) 012129
IOP Publishing
doi:10.1088/1742-6596/1325/1/012129
1
Research on Improving Artillery Firing Accuracy by Using
Meteorological Data along Ballistic Trajectory for Artillery
Firing
Zhiyuan Zhang, Yuwen Liu, Jun Li* and Ming Jiang
Teaching and Research Section of Fire Command and Control Engineering, PLA
Army Academy of Artillery and Air Defense, Hefei, Anhui, 230031, China
*Corresponding author’s e-mail: 459729129@qq.com
Abstract. In traditional artillery shooting, meteorological information is provided by
meteorological unit, but because of the inconsistency between meteorological observation sites
and shooting sites, there are errors in meteorological data, which affects shooting accuracy. In
order to reduce the influence of meteorological data errors on firing accuracy, it is proposed to
acquire multi-meteorological data along the ballistic trajectory by using the dropsonde carried
by the UAV, and calculate the meteorological data along the ballistic trajectory for artillery
firing. Through simulation calculation, using meteorological data along the ballistic for
artillery firing can effectively improve firing accuracy.
1. Introduction
In traditional artillery firing, meteorological stations or meteorological units are used to provide
meteorological information for artillery firing. Because meteorological stations can only detect
meteorological elements in one place, there must be some errors in replacing meteorological elements
in the whole ballistic trajectory with meteorological elements in this place. Even in the case of stable
weather conditions, this error will cause a deviation of 5% to 10% between the actual range and the
range on the fire table. Especially in artillery long-range strike, the errors caused by meteorological
elements will increase with the increase of range, and because of the larger range, the meteorology
between artillery position and target point may change greatly. The errors caused by replacing
meteorological elements of the whole ballistic trajectory with meteorological elements of one location
will be greater. Therefore, the use of meteorological data along the trajectory for artillery firing is
proposed to reduce the errors caused by the inconsistency of time and place in meteorological
preparation and improve the firing accuracy.
2. Acquisition of meteorological data along trajectory
The acquisition of meteorological data along the trajectory can be detected by UAV. Firstly, UAV
drops several dropsondes along the trajectory. During the falling process, the sounder can detect the
temperature, humidity, air pressure and wind data at different altitudes in the vertical direction, as
shown in Figure 1. Then, the multi-meteorological data are calculated by fitting polynomial method,
and the meteorological data along the trajectory are obtained.
ICAITA 2019
Journal of Physics: Conference Series 1325 (2019) 012129
IOP Publishing
doi:10.1088/1742-6596/1325/1/012129
2
2.1. Detection of meteorological data of dropsonde
2.1.1. Principle of Warm and Wet Pressure. Using GPS digital electronic dropsonde, the sounding
instrument can complete a series of tasks of meteorological data acquisition, processing and
transmission. The temperature sensor adopts thermistor, which can effectively avoid the influence of
long wave radiation on temperature measurement. Humidity sensor adopts humidity sensitive resistor,
which can ensure good measurement accuracy, long-term stability and relatively small lag. The
pressure is measured directly by a silicon single crystal empty cell pressure sensor.
2.1.2. Principle of wind measurement by GPS dropsonde. During the descent of the GPS sounder, the
speed of the sounder descends approximately uniformly under the action of a parachute. When there
are more than four effective satellites, the GPS system measures the distance between the satellite and
the GPS receiver of the sounder by spread spectrum communication technology, and then calculates
the three-dimensional coordinates of the sounder and the time at this moment.
Then the actual wind speed and direction can be calculated by the following formula through the
coordinates
1 1 1
( , , )x y z
and
2 2 2
( , , )x y z
of the two adjacent points of the sounder relative to the
base station during the descent process:
( ) ( )
1212 /arctan xxyy −−=
（1）
( ) ( )
tyyxxv 2
12
2
12 −+−=
（2）
2.2. Acquisition of meteorological data along ballistic trajectory by fitting method
2.2.1. Least square fitting. With
1+n
pairs of tabular data
),,2,1,0)(,( njyx jj =
, the following
equations are established using these data.
m
mxaxaxaax ++++=
2
210
)(
(3)
It is used to fit the given table function. When order
m
is determined, the polynomial can be
determined by only finding
m
aaaa ,,,, 210
.
m
aaaa ,,,, 210
is obtained by minimizing the
sum of squares of residuals as the optimal criterion. According to the principle of finding the
minimum value of multivariate function, the normal equation fitted by the least square method is
finally obtained as follows.
2
0 0 0 0 0
0
12
0 0 0 0 0
1
n n n n n
m
j j j j
j j j j j
n n n n n
m m m m m m
m
j j j j j j
j j j j j
x x x y
a
a
x x x x x y
= = = = =
+ + +
= = = = =
=
(4)
By solving the above formula,
1+m
polynomial coefficients
m
aaaa ,,,, 210
can be obtained.
2.2.2. Acquisition of air temperature and pressure. Firstly, according to the temperature information
measured by each dropsonde, the coefficient of fitting polynomial is calculated from the normalization
equation (4), and the temperature fitting polynomial of each dropsonde detection point is obtained.
Then the coordinates of any point on the ballistic trajectory are substituted into the temperature fitting
polynomial to calculate the temperature of each point on the ballistic trajectory.
Because quadratic polynomial has the advantages of high fitting accuracy and moderate calculation,
we use quadratic polynomial to fit temperature polynomial. Firstly, the temperature data measured by
ICAITA 2019
Journal of Physics: Conference Series 1325 (2019) 012129
IOP Publishing
doi:10.1088/1742-6596/1325/1/012129
3
each dropsonde are fitted with
N
curves according to equation (6). The expression of the curve is as
follows:
2
1 10 11 12
2
2 20 21 22
2
0 1 2
T ( )
()
()
N N N N
y a a y a y
T y a a y a y
T y a a y a y
= + +
= + +
= + +
（5）
In formula:
T
represents temperature and
N
is the number of dropsondes.
By substituting the Y-axis coordinate of the arbitrary point
00
( , )R x y
of ballistic trajectory into
equation (5), a series of corresponding relations between
x
and
T
are obtained. Then the series of
data are fitted into quadratic polynomials, and the expression of temperature curve at
0
y
altitude is
obtained.
2
0 1 2 0
T( ) ( )x a a x a x y y= + + =
（6）
Then the X-axis coordinate of the arbitrary point
00
( , )R x y
of the trajectory is substituted into (6),
and the temperature of the arbitrary point
R
is calculated.
2
0 1 0 2 0 0
T ( )
Ra a x a x y y= + + =
（7）
The acquisition of air pressure is similar to that of temperature, so there is no further discussion
here.
2.2.3. Wind Acquisition. Unlike the acquisition of temperature, wind is a vector unit, which has both
size and direction. Therefore, it is necessary to decompose the vector of wind into scalars on X-axis
and Z-axis. If the angle between wind and X-axis is
, then the wind on X-axis and Z-axis is
respectively:
cos
sin
X
Z
WW
WW
=
=
（8）
Secondly, the quadratic polynomial fitting of the wind on X-axis and Y-axis is carried out, and the
results are as follows:
2
1 10 11 12
2
2 20 21 22
2
0 1 2
()
()
()
X
X
XN N N N
W y a a y a y
W y a a y a y
W y a a y a y
= + +
= + +
= + +
（9）
2
1 10 11 12
2
2 20 21 22
2
0 1 2
()
()
()
Z
Z
ZN N N N
W y a a y a y
W y a a y a y
W y a a y a y
= + +
= + +
= + +
（10）
In formula:
X
W
means vertical wind,
Z
W
means crosswind and
N
means the number of
dropsondes.
By substituting Y-axis coordinates of arbitrary point
00
( , )R x y
of ballistic trajectory into equation
(9) and equation (10), a series of corresponding relations between
x
and
X
W
and
Z
W
are obtained.
ICAITA 2019
Journal of Physics: Conference Series 1325 (2019) 012129
IOP Publishing
doi:10.1088/1742-6596/1325/1/012129
4
Then the series of points are fitted into quadratic polynomials, and the expressions of longitudinal and
cross-wind curves of arbitrary point
R
of ballistic trajectory are obtained:
2
0 1 2 0
2
0 1 2 0
W ( ) ( )
W ( ) ( )
X
Y
x a a x a x y y
x a a x a x y y
= + + =
= + + =
（11）
By substituting the X-axis coordinate of arbitrary point
00
( , )R x y
into formula (11), the
longitudinal
),( 00 yxWX
and cross wind
),( 00 yxWZ
of arbitrary point
R
in ballistic trajectory
are calculated. Finally, the wind speed of arbitrary point
R
is obtained according to the formula of
synthesis operation.
),(),( 00
2
00
2yxWyxWW ZR X+=
（12）
Since the wind direction at any point in the trajectory can come from any direction, different
quadrants of the wind speed
),( RzRx WWR
at any point in the plane coordinate system can be
obtained according to different formulas. If
),( RzRx WWR
is in the first quadrant, as shown in Figure
2, then it is calculated by formula (13) and other analogies.
O
x
y
Z
1
2
3
…… ……
n
X
Z
θ
Rx
W
Rz
W
R
0
Figure 1. Diagram of meteorological data detection. Figure 2. Diagram of wind direction.
R
Rz
W
W
arcsin=
（13）
If
),( RzRx WWR
is in the second and third quadrants, it is calculated according to formula (14).
R
Rz
W
W
arcsin180 −=
（14）
If
),( RzRx WWR
is in the fourth quadrant, it is calculated by formula (15).
R
Rz
W
W
arcsin360 +=
（15）
3. Calculating Ballistic Elements by Using Meteorological Data along Ballistic Trajectory
Taking a certain type of artillery as the research object, the firing accuracy of artillery firing using
meteorological bulletin and meteorological data along ballistic trajectory is analyzed. The results of
shooting distance and sideslip are calculated at different angles of fire and different charge numbers.
Midpoint meteorological bulletin is omitted due to confidentiality. The meteorological data along
the trajectory are shown in Table 1.
ICAITA 2019
Journal of Physics: Conference Series 1325 (2019) 012129
IOP Publishing
doi:10.1088/1742-6596/1325/1/012129
5
Table 1. Along-trajectory meteorological data.
Meteorological data in ascending phase
Meteorological data in downward section
Height
（m）
air
temperat
ure
（℃）
pressure
（hPa）
wind
speed
（m/s）
wind
direction
（°）
Height
（m）
air
temperat
ure
（℃）
pressure
（hPa）
wind
speed
（m/s）
wind
direction
（°）
107
24.7
1033.4
13.0
295.8
4950
-34.4
1028.4
11.6
91.7
235
22.9
1026.8
12.3
225.4
4742
-31.2
1022.5
11.0
81.6
378
20.7
1018.9
11.4
164.4
4535
-28.3
1015.8
10.5
71.8
532
18.2
1010.0
9.7
115.9
4357
-26.2
1006.8
10.1
65.0
695
15.6
1000.4
8.2
80.1
4180
-24.2
999.0
9.9
70.3
857
12.9
991.1
9.0
56.9
3910
-21.4
990.8
8.9
82.7
1010
10.5
982.5
9.9
43.7
3746
-19.8
982.0
9.8
87.7
1185
7.9
973.1
10.8
36.2
3590
-18.3
973.9
8.9
92.5
1305
6.2
967.0
11.9
45.7
3437
-16.8
966.5
7.9
82.1
1478
3.8
958.5
11.0
54.5
3285
-15.4
958.5
9.0
71.2
1610
2.1
952.4
9.8
38.5
3127
-13.9
952.0
10.1
79.8
1775
0.1
945.2
10.2
43.5
2965
-12.4
944.8
9.2
67.8
1937
-1.9
938.5
10.5
59.1
2770
-10.5
938.0
10.3
74.4
2090
-3.6
932.5
11.4
54.6
2615
-9.0
930.4
10.4
70.9
2245
-5.3
926.7
10.8
60.0
2464
-7.5
925.0
11.4
66.9
2416
-7.0
920.5
11.2
75.5
2290
-5.8
918.8
10.5
61.5
2580
-8.7
914.8
10.5
90.1
2145
-4.2
913.6
9.5
56.6
2765
-10.5
908.6
9.9
74.3
1950
-2.5
908.4
10.5
49.6
2974
-12.5
901.8
10.1
77.9
1784
-0.1
902.4
9.7
43.7
3155
-14.2
896.0
10.5
82.1
1620
1.9
896.9
8.5
38.8
3327
-15.8
890.6
11.5
71.5
1479
3.8
891.9
9.0
35.7
3510
-17.5
884.9
10.8
75.3
1315
6.0
887.1
9.7
34.5
3705
-19.4
878.9
11.4
80.7
1170
8.1
882.4
11.5
36.6
3884
-21.1
873.5
11.1
92.7
1020
10.4
877.7
10.6
43.0
4010
-22.4
869.8
10.4
98.5
862
12.9
872.7
11.9
56.4
4273
-25.2
862.1
9.4
85.1
720
15.2
864.8
12.2
75.8
4450
-27.3
857.1
10.4
87.8
586
17.3
859.7
12.9
102.4
4648
-29.8
851.6
9.4
81.6
432
19.8
854.7
10.5
145.5
4820
-32.3
847.0
10.8
93.6
314
21.7
849.0
13.0
189.6
5010
-35.5
842.0
11.7
85.8
206
23.3
843.6
13.5
240.0
Surface temperature:299.6K Ground Pressure:1039.3mm Ground Wind Direction:320.5°
Ground Wind Speed:13.5m/s altitude of Meteorological Station:54m
In theory, the meteorological data along the trajectory can more truly reflect the real meteorological
conditions of the whole trajectory. Therefore, the shooting distance and sideslip calculated by the
meteorological data along the trajectory are taken as accurate values, and the deviation of shooting
distance and sideslip calculated by the meteorological bulletin at the midpoint of the trajectory is
analyzed. Through the trajectory element calculation software, the calculation results of shooting
distance and sideslip at different charge numbers and angles are shown in Table 2-Table 7 (Table
4-Table 7 is outlined).
Table 2. Contrast of shooting distance and deviation of full charge under various meter scales.
Firing
angle
()
cmil
Range of fire
()
c
Xm
Side deviation
()
c
Zm
Meteorological
Bulletin
1c
X
Along-trajectory
meteorological
data
2c
X
Absolute
deviation
21cc
XX−
Meteorological
Bulletin
1c
X
Along-trajectory
meteorological
data
2c
X
Absolute
deviation
21cc
XX−
417
14163
14094
69
152
138
14
583
16052
15922
130
218
208
10
750
16806
16606
200
277
263
14
ICAITA 2019
Journal of Physics: Conference Series 1325 (2019) 012129
IOP Publishing
doi:10.1088/1742-6596/1325/1/012129
6
Table 3. Contrast of shooting distance and deviation of No.1 charge under various meter scales.
Firing
angle
()
cmil
Range of fire
()
c
Xm
Side deviation
()
c
Zm
Meteorological
Bulletin
1c
X
Along-trajectory
meteorological
data
2c
X
Absolute
deviation
21cc
XX−
Meteorological
Bulletin
1c
X
Along-trajectory
meteorological
data
2c
X
Absolute
deviation
21cc
XX−
417
12994
12954
40
113
114
1
583
14835
14751
84
178
176
2
750
15585
15398
187
231
237
6
It can be seen from tables 2 and 3 that:
(1) There are deviations in shooting distance and sideslip calculated by means of midpoint
meteorological bulletin and meteorological data along the trajectory, and the deviation is large,
reaching 200 meters at the maximum. Especially when the range is large and the trajectory is high, the
high-altitude wind varies greatly and the deviation is large. It shows that it is necessary to use
meteorological data along ballistic to ensure artillery firing.
(2) The deviation of shooting distance and sideslip calculated by means of midpoint meteorological
bulletin and meteorological data along the trajectory fluctuates greatly, which indicates that the
meteorological conditions in ballistic airspace vary greatly with the increase of shooting distance. The
meteorological data along the trajectory detected by UAV can reflect the changes of meteorological
conditions along the trajectory more truthfully.
(3) The overall trend of the deviation of shooting distance and sideslip calculated by ballistic
midpoint meteorological bulletin and along ballistic meteorological data increases with the increase of
shooting range. However, even when shooting distance is small, there are still large deviations, which
indicates that the approximate calculation and adjustment error of meteorological data in the process
of compiling meteorological bulletin is large and can not be neglected.
4. Conclusion
Based on the analysis of the influence of meteorological data on artillery firing accuracy, a method of
acquiring meteorological data along ballistic trajectory by UAV is proposed, and the firing accuracy of
artillery firing using meteorological bulletin and meteorological data along ballistic trajectory is
analyzed. It is concluded that the use of meteorological data along the trajectory for artillery firing can
improve firing accuracy and has good military benefits.
References
[1] Wang R., Lv T. (2008) Reflections on the timeliness and regionality of artillery meteorological
support. Equipment and Technology, 5: 119-120.
[2] Dong H.Z. (2008) The Application of GPS Positioning System in Artillery Air Defense Weather
Detection Equipment. Meteorological and Hydrological Equipment, 1: 49-50.
[3] Wu Z.L. (2007) Decisive Shooting Elements Theory. Military Academy Press, Hefei. pp. 85-86.
[4] Liu Y.X., Liu Y.W. External Ballistics. Haichao Press, Beijing. pp. 45-48.
