THE STAFF READING ACCURACY AT LASER LEVEL
DIRECT LEVELING
Georgy Viktorovich Zemskiys
1and Natalia Sergeevna Kopylova
2 1The Department of Mine-Surveying, Ural State Mining University, Yekaterinburg, Russia
2The Department of Geodesy, Saint-Petersburg Mining University, Saint-Petersburg, Russia
E-Mail: [email protected]
ABSTRACT
The aim of the study is plane laser system precision detection as direct leveling means. Two goals have been put forward in order to achieve the aim of the study: to detect the staff reading precision by naked eye using laser level horizontal light trail and reveal reading error type of the dependence from the distance to the rod. The research has been done using optical tilting level Н-05, laser levels: Condtrol Xliner combo and ADA 6D Servo Liner. The distance between devices and the levelling staff have been measured every 1-3 m, maximum distance is 25 m. The staff has been put in vertical position by a circular bubble. The staff readings have been taken with 1 mm precision. Rod’s height has been randomly changed 10 times at every distance. The research results have demonstrated that the dependence of rod reading mean squared error (MSE) from the distance between the device and the rod does not follow theoretically established linear law, but possesses wavelike properties. The smallest error values have been recorded at the distance of 13 - 15 m, local maximums have made 4-5 m and 22-25 m from the device to the rod.
Keywords: precision of the levelling staff reading, laser level, mean squared error, dependence from the distance.
INTRODUCTION
Mine survey current condition is characterized by general usage of new devices, Laser Levels (LL) or Plane Laser Systems (PLS) are the most wide-spread among them. In particular (Kiselev V.A., Frolov P.M., 2018) offered the technique of transmitting plane coordinates and position angle to sub-level mining gallery level using PLS, thus, substituting the vertical method of projecting level making for creating PLS laser level. The number of authors proposed to use PLS for drift size surveying by photo planimetry (Kiselev V.A., Porshukov D.V., 2018). Besides, the type of devices mentioned is more often being used for surface layout (Shiv Kumar Lohan, et al. 2014 and Chhavi Bansal et al., 2014) construction (L. S. Blake, 1994), irrigation (Yongsheng Si, et al., 2009), etc. In the latter, PLS is basically used as the device for direct leveling. In mine survey practice the appearance of visible horizontal (and/or vertical) light plane, produced by laser emitter under the low light conditions at underground working, allows solving a set of mine survey tasks, for instance, the task of height working directing, in more favorable conditions. In this connection the usage of PLS in mine working can be more than appropriate. Though, the question may arise - what is the direct leveling precision when applying this type of device? Such kind of research has not been done in works mentioned above, which determines the topicality of this study and allows formulation its main aim as the precision determination of PLS as direct leveling device.
In technical publications (Ogloblin D.N. et al., 1981and Ushakov I.N., 1989) it is demonstrated that RMS elevation error in direct leveling is determined by rod reading sampling RMS error
m
2z
2
m
o2, which, in its2 2
m
m
m
o
v
, (1)Wheremv is error in rod reading because of the
sighting error:
l
v
m
v
10
0
, (2)Wherev is field glass optical magnification; L is the distance from the device to the rod. Under the conditions of laser level application the value of v = 1.
48
000
,
0
1
5
20626
0
10
l
m
v ;Т is rod reading error because of level tube axis missetting in horizontal position.
l
m
1
,
0
, (3)
Where is sensitiveness of the level tube per one division, which axis is set with average error 0.1.
For leveling devices with self-adjustment leveling axis, those include laser levels
l
m
0
,
1
.By using obtained values mvand т in formula
(1), one can get
l
l
l
coefficient at l t is not established. In this connection, the basic task is to study the precision of rod reading sampling at PLS laser trail. In such a case, main emphasis is placed on studying the precision of sampling by naked eye and revealing reading error dependence type form the distance to the rod.
MATERIALS AND METHODS
The following devices (Table-1) have been used for solving the tasks put forward and the below given measurement taking scheme has been adopted.
Table-1. Technical parameters of the device.
Basic parameters
Type of device Condtrol Xliner
combo (laser level)
ADA 6D ServoLiner (laser level)
Н-05 (optical leveling device) RMS error in elevation measurement per 1
km of double run procedure, mm 0.5
field glass optical magnification, power 42
Min. leveling distance, m 1б5
Mass, kg 11
Sensitiveness of the level tube per one
division, sec 10
Distance measuring М 50 25
Precision, mm/m 0.1 0.1
Way of putting the observing line into horizontal position
Pendular
compensator Servo drives Tubular bubble
The devices have been placed on tripods in one line, transversely to rod setting line. Leveling rod, manufactured by Carl Zeiss AG, was 30 cm in length with centimetric graduation line. The rod has been placed on the tripod by theodolite stand with circular level. The distance between the devices and the rod made up (in round numbers): 2, 3, 4, 5, 6, 10, 11, 14, 17, 19, 22, 25 m. Further increasing in distance has not been possible due to the complexity of obtaining reliable results at rod reading sampling by PLS application.
The samples have been taken with 1 mm precision at each rod setting: by leveling device - using direct leveling methodology (samples taken by leveling device were accepted as error-free), by laser level - at upper and lower horizontal light trail directly on the rod. In the latter, the distance from the observer to the rod made up 0.3 - 0.5 m. Before sampling the rod has been put in vertical position by a circular level in order to eliminate the error of rod incline
The height of rod stand position has been changed 10 times at every interval. The rod’s position height has been randomly changed by putting random thickness wooden plaques (plaque thickness varied from 0.5 to 2-3 cm) under the rod stand. In general, 8-10 plaques have been used.
Sampling results have been recorded into a field note book, where differences in sampling obtained by leveling device and every laser level have been calculated for the control. The control manifested itself in determination of differences for different rod stand position heights.
RESULTS
Table-2. Rod reading sampling RMS error for different Plane Laser Systems.
N L, m mXliner, mm mServoLiner, mm
1 2.17 0.58 0.47
2 3.02 0.58 0.47
3 3.02 0.61 0.57
4 5.00 0.74 0.74
5 5.04 0.55 0.61
6 5.00 0.62 0.74
7 6.11 0.48 0.54
8 6.10 0.86 0.94
9 8.07 0.58 0.63
10 8.18 0.35 0.44
11 10.06 0.39 0.47
12 11.37 0.68 0.66
13 11.43 0.49 0.41
14 11.46 0.28 0.50
15 14.17 0.28 0.35
16 16.80 0.66 0.61
17 16.85 0.54 0.39
18 19.43 0.37 0.94
19 22.09 0.61 0.95
20 22.17 0.71 0.77
21 25.22 0.71 1.00
22 25.27 0.85 0.44
Figure-1. The graph of rod reading sampling RMS error dependence from the distance between the device and the rod.
Repeated rod reading sampling at the same distances between the devices and the rod are determined by the necessity of obtaining reliable results.
RESULTS’ DISCUSSIONS
The research results have demonstrated that the dependence of rod reading sampling root mean square error from the distance between the device and the rod does not follow theoretically established linear law (Figure-1). Though, there have been an attempt to build the trend as a linear dependence(Figure-2). However, in this case determination coefficient is extremely low, that
demonstrates the invalidity of the obtained data approximation by linear dependence. Certainly, the approximation by fourth power polynomial also does not provide high values for determination coefficient, but it has allowed reflecting the changeable nature of the root mean square error dependence from the distance between the device and the rod in more accurate way. Wavelike dependence property can be observed in the graph (Figure 1), where the lowest error values have been recorded at the distance of 13 - 15 m from the devices to the rod. At the same time the local maximums have been recorded in the area of 4-5 m and 22-25 m.
y = -4E-05x4 + 0,0023x3 - 0,0437x2 + 0,2953x R² = 0,3142
y = -6E-05x4 + 0,003x3 - 0,0525x2 + 0,3297x R² = 0,4746
0,00 0,20 0,40 0,60 0,80 1,00 1,20
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
M
ean
sq
u
ar
ed
e
rr
or
,
m
m
Figure-2. The graph of rod reading sampling RMS error dependence from the distance between the device and the rod.
The research results have demonstrated that the dependence of rod reading sampling root mean square error from the distance between the device and the rod does not follow theoretically established linear law. It calls for all-rounded analysis and detection of reasons leading to such RMS error properties. Besides, the results obtained allow making certain changes into the direct leveling operating methodology, as well as all the working, based on it, e.g. to set precise limitations on the distance between the device and the rods to 15 m in order to obtain more accurate results.
REFERENCES
L. S. Blake. 1994. Civil Engineer's Reference Book 4th Edition Taylor & Francis. p. 1246.
Chhavi Bansal, Gurmohan Singh, D. K. Jain, Manjit Kaur. 2014. Laser land leveling prototype development.
Kiselev V. A., Frolov P. M. 2018. A method of transferring the azimuth and coordinates to the sub-level through a vertical mine working using a laser level. The XIth Russian-German raw materials conference, Potsdam, Germany, 7-8 November 2018. ISBN: 978-036707726-6. - CRC Press Taylor & Francis Group. pp. 205-212.
Kiselev V. A., Porshukov D. V. 2018. Justification of parameters of photoplanimetric method for determining the cross section area of horizontal opening. XIV International forum-contest of young researchers Nopical issues of rational use of natural resources - CRC Press Taylor & Francis Group. pp. 173-179.
Markshei`derskoe delo: Uchebnikdliavuzov [Mine surveying: a textbook for high schools], Ogloblin D.N., Gerasimenko G. I., Akimov A. G. and others, 3rd ed. rev. and enl., Moscow, Nedra, 1981, p. 704.
y = 0,0032x + 0,5318 R² = 0,0213 y = 0,0082x + 0,5234
R² = 0,0948
0,00 0,20 0,40 0,60 0,80 1,00 1,20
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Me
an
sq
u
ar
e e
rr
or
,
m
m
Shiv Kumar Lohan, Harminder Singh Sidhu, Manpreet Singh. 2014. Laser Guided Land Leveling and Grading for Precision Farming. Precision Farming: A New Approach, Edition: First, Chapter: Laser Guided Land Leveling and Grading for Precision Farming. Publisher: Astral International Pvt Ltd. New Delhi., Editors: Tulasa Ram, Shiv Kumar Lohan, Ranveer Singh, Purshotam Singh. pp. 148-158.
