The Process of Measuring Height - Research Paper Example

Surveying How high is that tower? Instructor: Abstract The study was used to find out the various methods and techniques applied in the process of measuring height in relation to electrical transmission tower in the absence of approaching or reaching the base. In order to a gain good results theodolite and measuring tape were used in the process of contraction of horizontal triangle between which between two theodolite stations and the tower. The distance between the stations and the angles which had been measured, made it possible and clear to analysis and get the distance to the tower. Results gains from the distance measured were used to create and form two vertical triangles between the theodolite station, which were identified as the horizontal plane and the top and bottom of the tower. By use the angles plus the distance that had been calculated from the two sites of the tower, tower height the end result were (38.64+/_0.087). The entire procedures and the process diploid within this research highly emphasized on making of assumptions in relation to top and bottom within the surface of the building being vertically in line, This resulted in the (2centimeters) error within the entire outcomes proportional to the horizontal displacement realized within the top and bottom measuring points. 1.0 Introduction The main importance of this research work was to introduce and familiarize ourselves in the field of surveying practices and gain all the required skills in the same practice. We gained great knowledge during the introduction to the principle of geometric, trigonometry and triangulation and incorporation to the use of a theodolite; the surveying field tends to allow the professionals in this field to calculate heights and distances of objects. In most cases estimated heights and distances may be achieved by deploying use of a series of connected triangles connected in an overlapping manner and their corresponding angles reading. Other important aspects used in the procedure are the distance between two stations. The surveying method is supported by the estimation of the objects’ height that could not be easily measured. 2.0 Aim The main goal of this particular research measure and calculate the height of an electrical tower by the aid of recorded angles by the use of theodolite and the distances that were measured within two given stations. The use of Trigonometric functions was applied during the entire process of calculating and height estimations. 3.0 Equipment and Materials Digital theodolite – This is used in the process of measuring of angles from each station to another through several points on any given electrical tower normally to 20 seconds. Tripod – Tripod is applied in the process of holding theodolite in place and insuring that there is steadiness throughout the entire process. Box Tape –It is an instrument used in the process of measuring distances within or in between 2 given stations. Pegs– Normally used in the process of marking the places. Plumb bulb – They are use as supporting of the tripod at the centre of the station pegs. Safety vest – The vest were assisted in the process of assuring there is safety measures or precautions during the entire process. 4.0 Procedure 4.1 Setting up theodolite 1. Identifying and selection of an appropriate site for the process of setting up the required station 1 (left). The peg is supposed to be hammered into the soil and be applied and used as the reference point for station 1. The tripod’s legs are supposed to be extended and allowed to stand directly over the top of Station 1 peg by the support of the plumb bulb doe the purpose of assisting in the process of positioning. 2. Step two theodolite has to be taken out of the box and be placed or attached in to the tripod head using the 5/8ths bolt. Then there must be assurance that the theodolite is properly placed and inserted into the tripod head, the wing nuts have to be tightened by the help of the foot screws within the centre of their run. 3. The length of the tripod’s legs for instance the head of the tripod should be exactly is within the ground. 4. Then Observe via the an optical device/ plummet of the theodolite and thereafter slightly fix and make sure it is a position of the tripod’s leg until when the peg appears to be at a centre point of the optical plummet’s crosshair and make sure that the tripod head is level. Finally comfortably press the tripod’s legs on the ground surface by exerting on the shoe. 5. Then move the length of the tripod legs up to a place whereby the fish eye bubble is seen in the current centre 6. Re observe through the optical plummet to verify that the peg is directly placed on the crosshair. And make sure the foot screw is adjusted accordingly if the peg is not centred. 7. Then make sure that the theodolite is rotated until the bubble tube appears to be is parallel to the two foot screws (1) again make sure that the foot screws is rotated until the bubble on the tube is centred. From position one make sure the rotated via theodolite 90 degrees to position 2 and then make adjustments on the third foot screw only until the bubble is at the centre of its run. Refresh the same procedure until the bubble is central in both place1 and 2. 8. While in the direction of position 1, make sure the theodolite is rotated180oto position 3, confirm whether the bubble is central. If it appears to be out of adjustment, you will be required to bring the bubble half way back by applying the use of the foot screws and half way back by the capstan screw. Then while at position 2 theodolite is supposed to be twisted 180 degrees in order to position 4 and confirm whether the bubble is central. In cases whereby the bubble is not centred, the same process has to be redone. 9. Finally the theodolite has to be rotated to position 1, 2, 3 and 4 so as to make sure that the bubble is placed on the centre and confirm if the optical plummet’s crosshair is placed actually on the top of the peg. The same process has to be repeated until the bubble is seen on the centre and the peg appears on the centre to the optical plummet. 4.2 Measuring 10. Within the I station (left), The 0 point should be set for the theodolite in the left direction of the tower .It has to be rotated aiming the telescope at the top of the tower in order to get the horizontal and vertical angular readings. The telescope has to be aimed at the bottom of the tower and both the horizontal and vertical angle measurements have to be carefully recorder. 11. The height of the theodolite’s horizontal axis should be from the ground by use of the tape measure. 12. Station 2 has to be moved (right) and place a peg on the ground. Use the tape measure to observe and record the distance between Station 1 and Station 2’s pegs. And then position the theodolite and tripod over to Station 2 and make sure the same procedures are done repeatedly. 13. Apply the same measurement process for Station 1 and capture the horizontal and vertical angle readings/ measurements for the top and the bottom of the station’s 2 tower. Then apply the use of measuring tape to capture and record height of the theodolite’s horizontal axis. 14. Then remove the theodolite from the tripod head and equipment and wipe any excess dirt from all instruments that have been used. The process has to be gently and return it back to the in protective covers. 15. Only captured data and information will be used in the process. Finally apply the use of trigonometry to in order to get the height of the tower Clear illustrations in the appendix section 5.0 Results 5.1 Measured angles and distances Station 1 Deg Min Sec Vertical angle V1 (Top of tower) 79˚ 27' 0±10" Vertical angle V2 (Bottom of tower) 90˚ 23' 40±10" Horizontal angle H1 (Tower) 31˚ 58' 40±10" Horizontal angle H2 (Station 2) 76˚ 10' 0±10" Height from ground to the centre of the telescope 1.57 Metres   Station 2 Deg Min Sec Vertical angle V3(Top of tower) 78˚ 03' 40±10" Vertical angle V4(Bottom of tower) 90˚ 28' 20±10" Horizontal angle H3 (Tower) 157˚ 1' 0±10" Horizontal angle H4 (Station 1) 29˚ 01' 40±10" Height from ground to the centre of the telescope 1.595 Metres   Distance between 2 stations 35 Metres 5.2 Horizontal angles 5.3 Vertical angles 6.0 Discussion 6.1 Alternative method In the entire planning process, there was another different method that was to be used as substitute in the process of gaining the height of the tower. The method was to seen to resemble the one that was emphasised and preferred. However the theodolite stations were supposed to be at a 180° angle with the stated tower. The other method was to use a 3rd theodolite station and hence it was sidelined because of the difficult process during the setting up of another or different station which would cause several inconveniencies. More information in relation of the same is found in the Appendices 6.2 Preferred method In this particular method there was recording of vertical and horizontal angles were within the 2 stations together with the distances between the two stations. After doing all the paper work, there was a formation a triangle between the 3 points consisting of the 2 stations and the tower. In this method the use of horizontal angle theodolite readings assisted in the process of determining the three corresponding angles. By applying the use of angles and the captured distances between the two stations, distances recorded from station 1 and station 2 were calculated by use of the sin rule. The results were therefore 199.93 m in relation to station 1 and 176.293 m for station 2 respectively. Vertical angle measurements were relevant during the formation of the triangles bound within stations 1 and 2 as far as the top and bottom of the tower is concerned. The theodolite telescope height was also recorded as a way of making sure there is high level of accuracy within the report and hence appropriate final results. Then the triangle together with the marching angles was therefore separated into half. The use of Cos function was then applied by use Cos function, captured distance which was identified as horizontal measured from the theodolite telescope on level with the tower was identified and calculated. Again the bottom half of the tower’s height was then identified and calculated by deploying the use of the angle which from the bottom triangle and in this case the use of Sine function was applied. The level distance and the angle was use for the top triangle, therefore top half of the tower’s height was reached by the use of Tan function. Then both the top together with the bottom half of the tower’s height was then summed up in order to reach the final height within the tower and it resulted to 38.553 m for station 1 and 38.7267 m for station 2.respectively. 6.3. Errors The concluding results of the tower was found to be 38.553m for Station 1 and 38.727m for station 2, respectively, and the differences within the stated results was identified to be exactly 0.174m.This resulted from the errors that were experienced within the entire process which may be caused by the instruments, human and other random errors that would not be avoided easily. 6.3.1 Instrumental There were three instruments that were used in the process of height the tower, namely; theodolite, measuring tape and calculator) and they have had hand in the process of causing the errors that were encountered. From the results the theodolite displayed the readings within 20 seconds hence the error level has to be within the range of ±10 seconds as far as the readings are concerned. In cases whereby single angle measurement was identified to be out by 10 seconds, then it would have hindered the final outcome by about 10cm. It was assumed that the box tape would produce accurate results of about 5cm. The box tape did not produce electronic readings; this indicated that the readings were to be captured manually from the tape. In this regard the assumption of errors was to base on various factors for instance, stretching, uneven ground, slackness and reading errors. The readings from the tape were identified to be about 1 cm. unfortunately this was not believed to be that accurate as the margin error was seen to be very high. Distance in between the stations was captured and recorded before the peg was placed on the ground; this facilitated accurate readings of exactly 35 m that was in between the two stations. Unfortunately this had no any impact on the as far as accuracy is concerned on the tape, it did not have any influence on the rounding errors during the calculation process and the use of calculator. Texas Instrument Nspire CAS calculator was used during the process of summing up the figures and calculations. This calculator tends to accumulate a round 15 figures. 6.3.2 Human errors and assumptions Human beings make mistakes which are hard to notice especially if they are logical because they will as well give particular results though the results will not be correct. One major known mistake occurs when measuring distances and people make an assumption and believe that two reference points were on a level ground. If the two points are not on a level ground, then it means that the tape measurements are exaggerated since the distance covered by the tape is more than the actual line between the two points due to variations in ground level. This leads to inaccurate results of the calculated distance. For example, distance from a reference point to a tower and also vertical heights of towers. Unless a theodolite is used to measure angles, accuracy of results cannot be verified. In an effort to determine if the ground was level, the height between the theodolite and the ground was noted. Nevertheless, this effort was termed as futile without the angle of elevation between the two. A late adjustment was required to correct the mistake and it was assumed that the angle of elevation of the theodolite from the tower on a level ground was 90°. The theodolite has to be positioned as confirmed in the system but it was found to be hard to set the theodolite exactly over the second peg. This further reduced the distance which had already been measured by 2cm. The theodolite had to be verified for evenness before taking further measurements. Nonetheless, the theodolite level could also vary during the process of computing angles. The rate at which this could have changed the final result is not known. 6.3.3 Random errors and others Other arbitrary factors like temperature and atmospheric conditions might also affect the working of the theodolite and this could also have an effect on the measurements. These factors were not easy to measure the rate at which they affect results thus random errors are included. Random error has been defined by the University of South Australia, Chemistry department as follows: “It is the irreproducibility in creating duplicate measurements and has an impact on the accuracy of a result. Random errors are distributed following a Gaussian-shape ‘bell’ curve” (University of South Australia). This curve shows two characteristics of random errors: 1. The probability of small errors is greater than large. 2. The possibility of overstating is the same as that of understating From these findings, an error may reverse itself whereas other errors just make the final results to vary. If more than one station were laid down more angle readings could be taken then the average of the recorded readings obtained and this ensures more accuracy of the height of the tower. However, this may be limited by time factor and the complications of laying down additional stations. During the surveying process, we suggested a different method of determining the height of the towers but this new method was found to be unrealistic because a minimum of three stations would have been required. Thus, it was thrown away because of the complexities involved. We applied the sine rule and combined it with the chosen method and found out that the distance from station one to the tower was 199.93m and the distance from station two to the same tower was 176.293m. The vertical angles of the theodolite were employed to make a triangle with the top and bottom of the tower which was divided into right angled triangles. The vertical angle together with the distance between the station and the tower were used to determine the heights of the top and bottom parts of the tower using trigonometric ratios. The heights of the two parts were added together and found that the height of the tower was 38.553m for station one and 38.727m for station two. The disparity of the two results (0.174m) was as a result of human, random, and instrument’s errors. These errors had an effect to the distance and angle measurements and this in turn added to the inefficiency of the final results of the tower’s height. Generally, the conclusion was that the objective of the experiment was attained since the difference between the two results was only 0.174m. This was justified by the errors which occurred throughout the surveying process. It is also understood that more accurate results could be attained by laying down additional stations though this was unrealistic because of the complexities involved. 7.0 Conclusion In conclusion, in the surveying process, there was a hypothesis of using another different method of getting the towers height. It was then decided that the other method seemed to be difficult and not applicable. As it would require at least three stations, this rendered to the disqualification of the alternate method. It also had several challenges as compared to the one applied in the report. The inclusion of the sine rule with the method that has been used in the report resulted into outcomes that indicated that the distance to the tower was 199.93m from station one and 176.293m from station two. The use vertical angle and the distance from station to tower, the bottom and the top section of the towers height was calculated by the application of trigonometric functions. After the addition of height of the two sections, it the tower’s height emerged 38.553 m in relation to one and 38.727 m for station 2. a difference of 0.174 metres was recorded within the two results which due to various challenges which would include human, instrumental, and random errors. To sum up it was emphasised that the main objective of the research was achieved as the final results within the state stations tend to display little variance which was calculated to be about 0.174 metres.. 8.0 Reference List University of South Australia. (n.d.). Error. Retrieved April 9, 2011, from University of South Australia, Department of Chemistry: http://www.physics.umd.edu/courses/Phys276/Hill/Information/Notes/ErrorAnalysis html 9.0 Appendices 9.1 Appendices I Alternative method 9.2 Appendices II Derived distances and height of tower Read More