Laying of a simple curve ON UNEVEN GROUND USING TRANSIT AND THEODOLITE(DOUBLE-DEFLECTION ANGLE method) Table of contents Introduction --------------------------------------------------------------2 Objectives and instruments ---------------------------------------------- 3 Procedure and Computation --------------------------------------------4 Preliminary data sheet ----------------------------------------------------6 Final data sheet -------------------------------------------------------------8 Pictures ----------------------------------------------------------------------10 Research and discussions ------------------------------------------------11 Conclusion -------------------------------------------------------------------14 Introduction 1 This method involves setting up theodolite on station PC and also at station PT where the point at which the two instruments will meet with the same deflection angle would be the location of the points along the curve.Laying of a simple curve ON UNEVEN GROUND USING TRANSIT AND THEODOLITE (DOUBLE-DEFLECTION ANGLE method) Another method in to lay out a simple curve is the use of two theodolites using double-deflection angle. Objectives: 2 . Like field work 1. we are going to use double-deflection angle method with almost the same procedure to lay-out the curve but we are going to measure the incremental chord and compare it to the computed value and get the percent error. The convenient deflection-angle method of locating points on a simple curve is based on the fact that in geometry. the deflection angle to any point on the curve is equal to the sum of the incremental deflection angles for each subdivision of the arc. both inscribed angle and an angle formed by a tangent and a chord are measured by one-half the intercepted arc. we used incremental chord and deflection angle method to locate the points along the curve but this time. Therefore. They are made of wood or metal. 3 to 4 cm thick and about 2 m long. 2. 50m or 100m in length. To be able to lay a simple curve in uneven ground. They are used to mark areas and to set out straight lines on the field. Usually in 30m. 3. Instruments: A theodolite is a precision instrument used for measuring angles both horizontally and vertically. Marking pins 2 range poles Straight round stalks. The professor gives the following datas: d1= 3 . To be able to lay a simple curve using double-deflection angle method.Laying of a simple curve ON UNEVEN GROUND USING TRANSIT AND THEODOLITE (DOUBLE-DEFLECTION ANGLE method) 1. in which case a flag may be attached to improve the visibility. Procedures: 1. To master the use of transit and theodolite in laying a simple curve. Theodolites can rotate along their horizontal axis as well as their vertical axis. Tape Used to measure horizontal distances as well as slopes. They are also used to mark points which must be seen from a distance. 5.1.6. 3. Set up the transit at PC. The students: 2. 2. (Note that the first isntrument’s reading is referred 2 ( ) 4 . Along this line and with a distance equal the length of the long chord from PC locate the location of PT. To locate the first intermediate point A in the curve mark on the ground the intersection of the line of sight in both instruments with a reading equal to d1° . With the lower clamp still loosened. direct telescope again along the tangent.3. Half D D/2 = 2. Turn the telescope in the direction of the backward tangent and mark its direction with a range pole. 2. Level the theodolite and set the horizontal vernier to zero while sighting PC. Half d1 d1/2 = e. Set the position on the exact location of PT. 2. Half d2 d2/2 = f.2. Loosen the upper clamp and turn the telescope until the reading on the vernier equals the magnitude of the total deflection angle of the curve. 2. Total Deflection Angle I/2 = c. Level and prient the transit at the magnetic south. Length of the Long chord C = d. VERY IMPORTANT: Before going to the field the student must compute: a. Set the horizontal vernier reading to zero. 2.Laying of a simple curve ON UNEVEN GROUND USING TRANSIT AND THEODOLITE (DOUBLE-DEFLECTION ANGLE method) D= d2= Location of PC on the site (Note: Location and not station is given since d1 and d2 are given) Azimuth of the back tangent (PC to V)= Adopt Full Chord Length= (preferably 2m to 5m) GIVEN I= d1 + 8D +d2 = (simple curve with 8 intermediate points) NOTE: Be very careful in assigning the location of PC and the direction of the backward tangent so that the curve may not be obstructed by any structure. Angle of Intersection I = b.4. but now use a reading in the horizontal vernier equal to ( d ° +22 D ) . The next intermediate point B may be located on the ground using the same procedure as in step 8. The third intermediate point C may also be found following the same process. 2 ) 5. 1 6.Laying of a simple curve ON UNEVEN GROUND USING TRANSIT AND THEODOLITE (DOUBLE-DEFLECTION ANGLE method) from the back tangent while the second instrument reading is referred from the long chord. Continue the process to locate other intermediate points on the curve with a gradual increase in the deflection angle up to the last intermediate point. Compute the % of error using the formula: length−measured chord length |computed chord |x 100 computed chord length Error= 5 . 7. but this time use a reading equal to ( d 1 ° +2 D .) 4. Laying of a simple curve ON UNEVEN GROUND USING TRANSIT AND THEODOLITE (DOUBLE-DEFLECTION ANGLE method) 6 . Laying of a simple curve ON UNEVEN GROUND USING TRANSIT AND THEODOLITE (DOUBLE-DEFLECTION ANGLE method) 7 . Laying of a simple curve ON UNEVEN GROUND USING TRANSIT AND THEODOLITE (DOUBLE-DEFLECTION ANGLE method) 8 . d. Ira Balmoris Data Supplied: d1= 3. b.85 2 1.15 2 1.1 2 2.21 0.1 2 2.75m Half d1 d1/2 = 1.61° 13. BY 1ST Inst.5% 7. D PT A PT B PT C PT D PT E PT F PT G PT H PT I PT PT PC CHORD COMPUTE ACTUAL D 1.84 2 2. c. OCC.61° 7.61° 4.5% 8% 10.07 1.: 4 Time: 12pm-4:30pm Weather: Sunny Location: Rizal Park Professor: Engr.85 2 2.61° 28.61° Half d2 d2/2 = 0.73 2 1.61° 16. e.78° Location of PC on the site (Note location and not station is now given since d 1 and d2 are given) Adopt Full chord length of 2m (Preferably 2m to 5m) Given: a.61° 19.22° D= 6° d2= 0.61° 10.61° 25.39° Half D D/2 = 3° STATION OCC. PC PC PC PC PC PC PC PC PC PC I= d1 + 8D + d2 = 52° (simple curve with 8 intermediate points) Angle of intersection I = 52° Total deflection angle I/2 = 26° Length of the long chord C = 16.26 0. 2015 Group No.34 DEFLECTIO N ANGLE % ERROR 1.61° 22.61° 61% 45% 5% 10% 7. BY OBSERVE 2nd Inst.Laying of a simple curve ON UNEVEN GROUND USING TRANSIT AND THEODOLITE (DOUBLE-DEFLECTION ANGLE method) Final Data Sheet Field Work 3 (Double- Laying of Simple Curve on Uneven Ground Using Transit and Theodolite Deflection Angle Method) Date: Oct 22.5% 30% 9 .5% 7.2 2 1. f. 61 ° 2 d 1+8 D =25.11 m sin 3 ° 52 C=2 (19.61 ° 2 d 1+7 D =22.78=52° 1 R= =19.222 )=1.61 ° 2 d 1+ 9 D =28.61 ° 2 d 1+6 D =19.61 ° 2 10 .61 ° 2 2 d 1+ D =4.07 m 0.78 c =2 ( 19.11 ) sin 2 Deflection Angles: d 1 3.75 m 2 ( ) ( 3.11 ) sin =16.26 m 2 ) c 1=2 ( 19.11 ) sin ( =0.61° 2 d 1+3 D =10.Laying of a simple curve ON UNEVEN GROUND USING TRANSIT AND THEODOLITE (DOUBLE-DEFLECTION ANGLE method) Computation: I =3.22+ ( 8∗6 ) +0.61° 2 d 1+5 D =16.61° 2 d 1+2 D =7.22° = =1.61 ° 2 d 1+ 4 D =13. 21| error H ¿ I = x 100 =10.15| error F ¿ G= x 100 =7.84| error G ¿ H = x 100 =8 2 |2−2.07 |2−1.26 Pictures: .5 2 |2−2. Percentage Error error PT ¿ A= |1.26−0.73| x 100 =61 1.85| error D ¿ E= x 100 =7.5 2 |2−1.5 2 |0.07−1.85| error E ¿ F= x 100 =7.1| error A ¿ B= x 100 =45 2 |2−2.34| error I ¿ PT = x 100 =30 0.1| error B ¿C= x 100 =5 2 |2−2.5 2 |2−1.2| error C ¿ D= x 100 =10 2 |2−1. Locating point A on the curve through the intersection of the two instruments.Setting the instruments at stations PC and PT. . Measuring the incremental chords. Measuring the long chord. 2. Inaccessible PI Under certain conditions. these will be PI. I angle. however. and degree of curve. so that line AB will clear obstruction. Measure angles a and b by setting up at both A and B. Measure the distance AB. Normally. Sometimes. 3. the terrain features limit the size of various elements of the curve. If this happens. In this case. 4. Mark two intervisible points A and B. it may be impossible or impractical to occupy the PI.1 AV = AB sin b sin K BV = AB sin b sin K PI = Sta A +AV .Research and Discussions TERRAIN RESTRICTIONS To solve a simple curve. the surveyor must determine the degree of curve from the limiting factor. one on each tangents. the surveyor locates the elements by using the following steps: 1. the surveyor must know three parts. Compute inaccessible distances AV and BV as follows : I=a+b K = 180° . 4. Measure and record the length of ine VW along the tangent. Proceed with the curve computation and layout. parallel to AV. Set an offset PC at point Y by measuring from point Q toward point P a distance equal to the station of the PC minus station S. 6.5. along this line of sight a distance QS equals PW. will clear the obstacle at the PC. parallel to the tangent line AV. Determine the tangent distance from the PI to the PC on the basis of the degree of curve or other given limiting factor. 7. so that a line PQ. the surveyor must establish the location of an offset station at PC. Note that the station number of point S = PI. 1. Establish point W on the tangent line by setting the instrument at the PI and laying off angle V (V = 180° . 6. and lay off a 90-degree angle to sight along line QS. 2. Inaccessible PC When the PC is inaccessible and both PI and PT are set and readily accessible. Set point Q. Swing a tape using the computed length of line PW and the line of sight to set point W. Back sight point W and lay off a 90degree angle to sight along the line PQ. 8. 3. Measure. and set point S. 7. backsight P. Place the instrument on the PT and back the curve in as far as possible. Compute and record the length of line PW so that point W is on the tangent line AV and line PW is perpendicular to the tangent. 9. Place the instrument at point Q. 5. and record the distance PQ. to set the PC . where dp is that portion of the central angle subtended by AP and equal to two times the deflection angle P. The length of line PW = R (1 – cos D).I). Measure along this line of sight to a point Q beyond the obstacle. Locate the PC at a distance T minus AV from the point A and the PT at distance T minus BV from point B. Place the instrument at point P. Select one of the stations on the curve. This sights the instrument along the tangent AV. Inaccessible PT When the PT is inaccessible and both the PI and PC are readily accessible. lay off a 90-degree angle and a distance from Y to PC equal to line PW and QS. is the angle at the center of the curve between point P and PT.after the obstacle has been removed. which is equal to two times the difference between the deflection at P and one half of I. 2. Angle d. the surveyor must establish an offset station at the PT using the method for inaccessible PC with the following exceptions: 1. Carefully set reference points for points Q. 4. . and W to insure points are available to set the PC after clearing and construction have begun. Lay the curve in as far as possible from the PC instead of the PT. S. Note that the station at point S equals the computed station value of PT plus YQ. 3. Y. Letter the curve so that the point A is at the PT instead of the PC. Use station S to number the stations of the alignment ahead. back sight point Q. place the instrument at point Y. follow the steps for inaccessible PC to set line PQ and QS. Conclusion: This method consists in setting up a theodolite at each tangent point and working out the deflection angles from the tangents. after we have laid out the curve. the shorter the incremental chord you would get from the computed distance and the shorter the distance of PC to PT from the computed distance. we double checked the distance of PC to PT and we noticed that we have laid out station PT 0.5 meters shorter than the computed and that is the source of our error. In our case. The distance from PC to PT that was computed from the given should at least be laid out precisely because the distances of the incremental chord would be affected by the reading of the angles form both stations. . Other than that. Their sight of intersection would be the locations of the points along the curve. it more accurate because you will rely on the intersection of the sights of the two instruments which is based on the principle that the angle between the tangent and the chord is equal to the angle subtended by the chord in the opposite segment. This method is most convenient when the ground is undulating. Hence. rough and not suitable for linear measurements compared on the first two methods we have used in laying out the curve. there would be huge source of error like we have done in our field work. The longer the distances of error the PT was laid out from PC. The theodolites are then set to read corresponding deflection angles and points set out to lie on both lines of sight. Setting up station PT should be accurate because if not. other measurements were closed enough from the computed distances. there would be less errors in terms of using tape because all the angles are calculated. the longer the distance of incremental chord you would get. Since this method is good to use for inaccessible or uneven grounds.