Development of the concentric reticle Baum for optical surveying instruments

Transcription

1 Development of the concentric reticle Baum for optical surveying instruments Kazuhide Nakaniwa Kansai Construction Survey Co., Ltd., Japan, Nobuyoshi Yabuki Division of Sustainable Energy and Environmental Engineering, Osaka University, Japan Takashi Kitayama Nishio Rent All Co., Ltd., Japan Tatsunori Makizumi Kyushu Kyoritsu University, Japan Abstract Total Station (TS) is an instrument to measure a distance and angle. The measurement has been originally conducted by two persons. Nowadays, the measurement can be conducted by one person thanks to the non-prismatic function. However, the conventional cross-hair reticle does not allow us to measure a cylindrical structure. This is because it is difficult to set the intersection of the cross-hairs to the target without a visible mark such as a dot or angle. Especially, if the target is a cylindrical object such as a pole, pile, etc., it would be impossible to identify its center line. Moreover, if the place of the target is a tip or an acute angle, laser beam would pass through and the distance cannot be measured In this research, in order to solve these problems, we developed a new reticle named Baum., which has concentric circle scale marks. The Baum owes its name to the similarity between the concentric circles and tree (Baum in German) rings. The space of the Baum s marks can be measured as 1/1,000 of the distance between the TS and the target object. The center of the reticle indicates the center line of the structure when one circle of the Baum is set to both ends of a cylindrical structure. Then, the radius and coordinates can be easily measured by measuring the distance. Such a simple operation has enabled us to measure what we had not been able to do with optical surveying instruments. We firmly believe that this technology has improved the capability of nonprismatic optical surveying instruments and that it will hopefully be applied to various surveying and measurement. We also hope it will eventually improve the operation efficiency and reduce cost. Keywords: Measure cylindrical structures, concentric circle, reticle, non-prismatic total station. 1 The background of the development Driving Piles is one of the common processes of foundation construction in building a structure. A pile is necessary to be driven with measuring the slippage and adjusting it, which is done by two transits setting to the alignment of the pile. However, this method requires much time and effort because every time the pile is hit and its position changes, those two transits have to be moved to the

2 next datum lines. This problem is caused by the fact that it is impossible to measure the center line of a cylindrical structure such as a prestressed concrete pile. Also, there are more than 30 million utility poles (Nippon Telegraph and Telephone West Corporation, 01; The Federation of Electric Power Companies of Japan, 01) and their degradation is getting a problem. Many tilting poles are often seen (Figure 1). The poles sag under their own weight and consequently they can break, which expose our lives to dangerousness and insecurity. That is why it is important to know their condition when considering the maintenance of these structures. However, measuring their condition requires much time and effort. Figure 1. A tilted utility pole. There are two ways to measure a condition of a cylindrical body such as pile and utility pole; using 3D laser scanner and total station (TS). In the method using a 3D laser scanner, the center line has to be calculated from point cloud data after the measurement. The calculation is too laborious to be done immediately on site. In the method using a TS (JECC Co., Ltd., 000), the user has to measure the angles of both edges and calculate their half angle as a center of the width and measure the distance to the center, then calculate the radius and coordinates from the measured distance and angles. However, unless the cylindrical structure stands vertically, the radius must be known to measure the cylindrical structure. This troublesome in measuring makes it complicated and difficult to calculate the lower shape of truncated cone like a Japanese utility pole. On the other hand, TS is a most popular surveying instrument in the construction industry. TS has been used for about 30 years. During this period, its measurable distance and function have been significantly improved and even computing capability has been equipped in TS because of the embedded computer inside. Moreover, most of TS have a non-prismatic function nowadays, that is, a prism reflector is not necessary. When conducting a measurement with a prismatic TS, one person holds the pin-pole with a prism reflector straight on the point to be measured. Then, the other person sets the intersection of cross-hairs of the TS to the prism reflector in order to measure the distance and angle. On the other hand, with a non-prismatic TS, the measurement can be done by only a person because a prism reflector is not necessary. However, the measurement with a non-prismatic TS is not often conducted but a non-prismatic TS is used as an assisting method to the measurement with a

3 prismatic TS. This is because the TS s reticle is cross- hairs. It is difficult to set their intersection to targets without a visible mark such as a dot and angle on the measurement object. Also, the point or corner of the structure cannot be measured because the laser beam passes through. As it stands now, the advantage of non-prismatic TS has not tapped to the maximum. Therefore, this research suggests a method to efficiently measure the center line and radius of cylindrical structures and their usage examples, which is enabled by the Baum, concentric circles reticle built in a non-prismatic TS instead of the conventional cross-hair reticle. A TS with the built-in Baum The Baum is the new reticle for a TS. The reticle has concentric circle scale marks in addition to the traditional cross-hairs. These circle scale marks are equally spaced. The ratio of the width between each circle to the distance is 1 to Since this width of the circles appears 1mm (0.001m) at a distance of 1m away, it is possible to calculate the radius from the indicated gauge number of the Baum and the distance to the center on the structure surface. For example, as Figure 3 shows, when the gauge number of the Baum indicated by the both edges of the structure is 4 and the distance is 50m, the radius is calculated by this formula; /1000=0.(m). Also, the gauge with circles enables to measure tilted cylindrical structures. All to be done to get the Baum available is to replace the cross-hairs reticle with the Baum, which costs very little. Figure. A TS with the Baum. Figure 3. Measuring a cylindrical structure. 3 The calculation of the width of the Baum s gauge and the accuracy Figure 4 shows the relation among the gauge s width, the distance to the object L and the actual width D. The width of the gauge is 0.6mm so that the ratio of D to L is 1 to However, D and L are slightly not in proportion because of the lens s warp and distance. When L is 10m and D appears to be the same as one scale of the Baum, D is 10.03mm. When L is 100m, D is 99.60mm. That is, there is an error of 0.03mm when the target is measured from 10m away. However, the viewed width and actual width are slightly different depending on TS manufacturer. In this research, the TS from Leica was used.

4 Figure 4. The width viewed through the Baum. Figure 5. The relation between the radius and the viewed width. 4 The range of application When a cylindrical object is seen through the Baum built into a TS, the distance to the object L is the distance to the surface of the object. As Figure 5 shows, the calculated radius based on the Baum s gauge is shorter than the actual radius. Then, the relation among the cylinder s radius r, the viewed width of the gauge a and the distance to the cylinder s surface L can be expressed in a formula below from Figure 5. L L + r = L + ( a ) r (1) or

5 ( a ) r L = () r ( a ) The merging of error is small enough when the difference between the actual radius and viewed radius is less than 1%. Therefore, if the distance is not less than a/ = 99r/100, the actual radius and the viewed width are equal. For example, when the radius is 100mm (r=0.1m), the distance which causes the difference is a 99 = r = 0.099( m) (3) 100 Consequently, we obtain L = 9.85( m) (4) More specifically, when the actual radius of 100mm is seen from 9.85m or more away, it is almost parallel with the viewed radius. This is why they are considered to be equal. 5 The experiment for the margin of error of presumptive reading Each gauge is disposed in every 0.6mm. That is, when the target indicates somewhere between two scale lines, the operator have to presume the number. We had an experiment how much operators ability of the presumptive reading influenced the measurement accuracy. In this experiment, a TS was placed a TS with the Baum at heights of 1.5m, a 1m ruler was placed at the point 8.009m horizontal away from the TS and the center of the Baum lay over 500mm scale of the ruler as Figure 6 shows, then the ruler was set in two ways; vertically and horizontally. Ten people who have the 0 to 10 years of experience in surveying read the scale of the ruler indicated by the scale number of the Baum. Figure 6. Experiment subject The reason why the experiment subject was a 1m ruler is to avoid the error which could be caused by other element but presumptive reading. If the experiment subject was a cylindrical structure, it could raise the possibility that the calculation of a theoretical value would include much error because of the relation between the subject and instrument.

6 Table 1 and shows the result of the experiment for presumptive reading. Table 1 shows the experiment result in which the ruler was set vertically and the ruler s vertical width was supposed to be the pile s width. Table shows the experiment result in which the ruler was set horizontally and the ruler s horizontal width was supposed to be the pile s width. Based on the calculated width 3.36, these tables show the error between it and the actual width which was calculated with the read value. These results show that people could presumptively read the scale every less than 1/10 though the results vary. It is equivalent to the Baum s presumptive reading accuracy of 1mm at 10m away. Table 1. The actual width and measured width (A ruler placed vertically) Operator Read value (mm) Pile s width(mm) Reading error(mm) Upside Downside (Up-Down) (Actual width-calculated width) A B C D E F G H I J Average absolute value Table. The actual width and measured width (A ruler placed horizontally) Read value (mm) Pile s width(mm) Reading error(mm) Operator Left side Right side (Right-Left) (Actual width-calculated width) A B C D E F G H I J Average absolute value Applications 6.1 Measuring the verticality in driving a foundation pile In the piling construction, it is common to use two transits to measure the tilt of the pile. Every time the pile is hit and its position changes, those two transits have to be moved to the next datum lines. On the other hand, if a TS has the Baum, it can measure the tilt by itself from any angle (Figure 7). Moreover, the TS can record the piling process. The efficiency of construction management will be improved.

7 Figure 7. Measuring verticality 6. Measuring the corner or point of a structure Until now, if the target is the corner or point of a structure, it has been impossible to measure the location of the target with a non-prismatic TS because the laser beam passes through. However, as Figures 8 and 9 show, it is possible to measure them with the TS with the Baum by setting the intersection of a cross-hairs and circle of the Baum to the corner or point to measure and offsetting the value according to gauge width from the measured coordinates. Figure 8. Measuring a corner Figure 9. Measuring a point 7 Result This research proved the Baum which is a reticle with concentric circles added to cross-hairs enabled to measure the radius and central coordinates of a cylindrical structure which was difficult to measure. Also, some usage examples are suggested in this research. It is expectable that equipping a TS with the Baum makes the utilization of a non-prismatic TS more effective. It is necessary to estimate error further through various measurement experiments. Another issue is to get available by other manufacturers TS as well as the Leica. We also aim to extend the range of application of the Baum to measuring the canter of other shaped structures such as a square pole by applying this research.

8 Acknowledgements The authors would like to thank Mr. Akihiko Miyamoto from Kansai Construction Survey Co., Ltd. for his efforts in the experiments and data analysis in this research. The authors also would like to thank Leica Geosystems, Inc. for their cooperation in developing the instrument and providing the data. References JECC CO., LTD., 000.The measuring method of cylindrical features in surveying, JP-A NIPPON TELEGRAPH AND TELEPHONE WEST CORPORATION, 01. The situation of the communication equipments installation, Available online: www. ntt-west.co.jp/info/databook/pdf/044.pdf, Last accessed: February 01. THE FEDERATION OF ELECTRIC POWER COMPANIES OF JAPAN, 01. Electric power statistics information, Available online: www. fepc.or.jp/library/data/tokei/index.html, Last accessed: February 01.