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Mapua Institute of Technology Intramuros, Manila

School of Civil, Environmental and Geological Engineering Surveying Department CE121F/B2

FIELDWORK 2 LAYING OF A SIMPLE CURVE BY TRANSIT AND TAPE (THE INCREMENTAL CHORDS AND DEFLECTION ANGLE METHOD) Submitted by: Pascual, Ma. Nadine Stephanie D. GROUP NO. 9 Geramie A.

Chief of Party: Quitain,

Date of Fieldwork: August 14, 2014 Date of Submission: August 29, 2014 Submitted to: Engr. Bienvenido Cervantes Data: STATION

CENTRAL

DEFLECTION

OBSERVED

INCREMENTA L CHORD

INCREMENTA L ANGLE

ANGLE FROM BACK TANGENT

PC:20+782. 06

20+800

17.94m

1.79˚

00˚53’

PC:20+782. 06

20+820

20m

2˚

01˚53’

PC:20+782. 06

20+840

20m

2˚

02˚53’

PC:20+782. 06

20+860

20m

2˚

03˚53’

PC:20+782. 06

20+880

20m

2˚

04˚53’

PC:20+782. 06

20+900

20m

2˚

05˚53’

PC:20+782. 06

20+920

20m

2˚

06˚53’

PC:20+782. 06

20+940

20m

2˚

07˚53’

PC:20+782. 06

20+960

20m

2˚

08˚53’

PC:20+782. 06

20+980

20m

2˚

09˚53’

PC:20+782. 06

21+000

20m

2˚

10˚53’

PC:20+782. 06

21+020

20m

2˚

11˚53’

OCCUPIED

PC:20+782. 06

21+040

20m

2˚

12˚53’

PC:20+782. 06

21+060

20m

2˚

13˚53’

PC:20+782. 06

21+080

20m

2˚

14˚53’

PC:20+782. 06

21+100

20m

2˚

15˚53’

PC:20+782. 06

21+120

20m

2˚

16˚53’

PC:20+782. 06

21+140

20m

2˚

17˚53’

PC:20+782. 06

21+160

20m

2˚

18˚53’

PC:20+782. 06

21+180

20m

2˚

19˚53’

PC:20+782. 06

21+200

20m

2˚

20˚53’

PC:20+782. 06

PT:21+202.0 6

2.06m

0.206˚

20˚59’

R = 572.958m Backward Tangent direction: N50˚E Forward Tangent direction: S78˚E T = 219.938m PC = 20+782.06 LC = 420m PT = 21+202.06 d1 = 1.79˚ C1 = 17.938m

d2 = 0.206˚ C2 = 2.06m Station of the Vertex: 21+002

Discussion: Same as the first fieldwork, we have gathered our data given that the field where we work in is also in the Intramuros Walls, which was still, good enough as the place to do this fieldwork. In this field work, it is about laying out a simple curve by theodolite and tape with the use of incremental chord and deflection angle method. We did it properly because we follow the proper steps in doing this fieldwork. First we assemble the instrument and then level it so the data that can be gathered will be accurate and correct and because we really had team work. Theodolite was used to help us to determine the direction so we can get an accurate angle.

We make sure that the compass will be directed to north. Then we adjust the angle to 0˚ then move it to east with an angle of 50˚. Then the one who was holding the range pole and the one who was holding the tape measure went to the place where the telescope was heading so that we can mark the right place where the vertex was. For the forward tangent, we did the same thing except for the angle which is S78˚E. After determining the place where PC and PT were, we mark and measure the longest chord by measuring the distance of PC and PT. Then we lay the curve by simply following the incremental chord and deflection angle method. Honestly, at first I got confused in doing this fieldwork because it is my first time to encounter this kind of work and it is really confusing. But then, by the help of my professor, we finished this fieldwork properly. I got confused in getting the deflection angle. But then I discovered that is not that difficult because you just have to add 2˚ to the first deflection angle. And the last deflection angle should be less than or equal to 2˚ that if you add all deflection angle, it should be equal to the intersection angle which in this fieldwork is 42˚. And the first incremental chord can be computed and the rest will be constant which is 20 except for the last incremental chord. I knew that incremental angle should be twice its central incremental angle. In laying a simple curve, you can also just stay at your first station, and just add the previous deflection angle to the next one and so are the incremental chord so that it would not be that hassle to the worker. Because it would just be the same if you do the station by station. But I think, it would still depend to the user because for the one I have said, there is a possibility that you will forgot to add the previous measurement to the next one. But, it you will be vigilant enough in what you are doing, you will not commit any error. For me, it would took you a long time in leveling

the instrument because in every station, you have to level the bubble of the instrument to make sure that all the data will be correct and accurate. Also, what I have discovered, you can do this work easily if you are good in leveling an instrument and in moving the instrument to the proper angle and also, if your group has teamwork because you cannot do this easily in a short span of time if you are alone. Having some skills in theodolite, gathering our data was somewhat easy for me since I listened to some of the tips that Engr. Cervantes have told us on how to read the instrument, how to plot the station points onto the field, and other related items that were needed to be done in order to succeed in the fieldwork. As said in the discussion, a simple curve is an arc of a circle, wherein the point of intersection (PI), is the point in which the two tangents, the forward and the back tangent intersects; it is also marked as V. Then, the Intersection Angle (I) is obtained through subtracting the bearing of the two tangents to 180˚. The radius is then given, in which it connects the center of the arc into the PC and PT which was to be explained later. The length of the curve (LC) is the distance between the PC and PT; and is measured along the curve. PC is the point of curvature where the cure begins. Then the Point of Tangency (PT) is where the simple curve ends.

Photos:

Plotting of the curve on the pavement ground using chalk.

Sighting of the deflection angles using the theodolite.

Computation of the data.

Research Works: LAYING OF A HORIZONTAL CURVE In this method, curves are staked out by use of deflection angles turned at the point of curvature from the tangent to points along the curve. The curve is set out by driving pegs at regular interval equal to the length of the normal chord. Usually, the subchords are provided at the beginning and end of the curve to adjust the actual length of the curve. The method is based on the assumption that there is no difference between length of the arcs and their corresponding chords of normal length or less. The underlying principle of this method is that the deflection angle to any point on the circular curve is measured by the one-half the angle subtended at the center of the circle by the arc from the P.C. to that point.

Let points a, b, c, d, e are to be identified in the field to layout a curve between T1 and T2 to change direction from the straight alignment AV to VB as in Figure 38.1(a). To decide about the points, chords ab, bc, cd, de are being considered having nominal length of 30m. To adjust the actual length of the curve

two sub-chords have been provided one at the beginning, T1 and other, eT2 at the end of the curve. The amount of deflection angles that are to be set from the tangent line at the P.C. are computed before setting out the points. The steps for computations are as follows:

Referring to Figure 38.1(b), let the tangential angles for points a, b, c,… be Δ1, Δ,…, Δ, Δ n and their deflection angles (from the tangent at P.C.) be Δ a, Δ b, ….. , Δn. Now, for the first tangential angle 1, from the property of a circle Arc T1 a = R x 21 radians Assuming the length of the arc is same as that of its chord, if C 1 is the length of the first chord i.e., chord T 1 a, then

(Note: the units of measurement of chord and that of the radius of the curve should be same). Similarly, tangential angles for chords of nominal length, say C,

And for last chord of length, say Cn

The deflection angles for the different points a, b, c, etc. can be obtained from the tangential angles. For the first point a, the deflection angle a is equal to the tangential angle of the chord to this point i.e.,1. Thus, a = 1.

The deflection angle to the next point i.e., b is b for which the chord length is T1 b. Thus, the deflection angle

Thus, the deflection angle for any point on the curve is the deflection angle up to previous point plus the tangential angle at the previous point.

Conclusion: We can say that our data gathered is accurate by our error in measuring the length of the chord, followed the procedure properly, and correct computation.

I can conclude that the data that we gathered on this fieldwork is accurate to say. One of the reason is we have just only less than one meter of error in the measurement of the chord compared to the actual and the computed length of the chord. Another reason is that we follow the steps and we successfully did the fieldwork and lay down a simple curve in the Intramuros wall which has the evident of the photos that I have presented to the proceeding part of this fieldwork paper. Another reason to prove that the data is accurate is the computation. In the computation, we have followed and double check the data and the given so that we can get the missing data. We have also used the formulas and the equation given by the book and by our Prof. Cervantes in doing the computation. For what we have done, I can say that it is accurate and precise. As we all know, errors are inevitable to us students because we are just a first timers and we need more experiences to do an almost perfect job. As what our professor said, it is still acceptable if we commit less than 1.5% error because at least we achieve a good work. But still, we cannot just say that we’re just first timers so we cannot do something better than anyone else because through passion and hard work, you can do a better job even you did not experience that work before. In the process of the fieldwork, I would say that because the group knows the tactics in using the theodolite, we got the data accurately and efficiently. We have also succeeded because we have followed the things needed to be done in which have made the work easier for us. The objectives of this fieldwork were also achieved because we are able to lay the simple curve by deflection angle and we are aware of the parts of the curve we are working on.

Regarding the mastery of the skill in leveling, it is somewhat easy for us because we got our teamwork and an ample amount of knowledge in leveling. Then, with the usage of the theodolite, we have succeeded effectively as explained a while ago.

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School of Civil, Environmental and Geological Engineering Surveying Department CE121F/B2

FIELDWORK 2 LAYING OF A SIMPLE CURVE BY TRANSIT AND TAPE (THE INCREMENTAL CHORDS AND DEFLECTION ANGLE METHOD) Submitted by: Pascual, Ma. Nadine Stephanie D. GROUP NO. 9 Geramie A.

Chief of Party: Quitain,

Date of Fieldwork: August 14, 2014 Date of Submission: August 29, 2014 Submitted to: Engr. Bienvenido Cervantes Data: STATION

CENTRAL

DEFLECTION

OBSERVED

INCREMENTA L CHORD

INCREMENTA L ANGLE

ANGLE FROM BACK TANGENT

PC:20+782. 06

20+800

17.94m

1.79˚

00˚53’

PC:20+782. 06

20+820

20m

2˚

01˚53’

PC:20+782. 06

20+840

20m

2˚

02˚53’

PC:20+782. 06

20+860

20m

2˚

03˚53’

PC:20+782. 06

20+880

20m

2˚

04˚53’

PC:20+782. 06

20+900

20m

2˚

05˚53’

PC:20+782. 06

20+920

20m

2˚

06˚53’

PC:20+782. 06

20+940

20m

2˚

07˚53’

PC:20+782. 06

20+960

20m

2˚

08˚53’

PC:20+782. 06

20+980

20m

2˚

09˚53’

PC:20+782. 06

21+000

20m

2˚

10˚53’

PC:20+782. 06

21+020

20m

2˚

11˚53’

OCCUPIED

PC:20+782. 06

21+040

20m

2˚

12˚53’

PC:20+782. 06

21+060

20m

2˚

13˚53’

PC:20+782. 06

21+080

20m

2˚

14˚53’

PC:20+782. 06

21+100

20m

2˚

15˚53’

PC:20+782. 06

21+120

20m

2˚

16˚53’

PC:20+782. 06

21+140

20m

2˚

17˚53’

PC:20+782. 06

21+160

20m

2˚

18˚53’

PC:20+782. 06

21+180

20m

2˚

19˚53’

PC:20+782. 06

21+200

20m

2˚

20˚53’

PC:20+782. 06

PT:21+202.0 6

2.06m

0.206˚

20˚59’

R = 572.958m Backward Tangent direction: N50˚E Forward Tangent direction: S78˚E T = 219.938m PC = 20+782.06 LC = 420m PT = 21+202.06 d1 = 1.79˚ C1 = 17.938m

d2 = 0.206˚ C2 = 2.06m Station of the Vertex: 21+002

Discussion: Same as the first fieldwork, we have gathered our data given that the field where we work in is also in the Intramuros Walls, which was still, good enough as the place to do this fieldwork. In this field work, it is about laying out a simple curve by theodolite and tape with the use of incremental chord and deflection angle method. We did it properly because we follow the proper steps in doing this fieldwork. First we assemble the instrument and then level it so the data that can be gathered will be accurate and correct and because we really had team work. Theodolite was used to help us to determine the direction so we can get an accurate angle.

We make sure that the compass will be directed to north. Then we adjust the angle to 0˚ then move it to east with an angle of 50˚. Then the one who was holding the range pole and the one who was holding the tape measure went to the place where the telescope was heading so that we can mark the right place where the vertex was. For the forward tangent, we did the same thing except for the angle which is S78˚E. After determining the place where PC and PT were, we mark and measure the longest chord by measuring the distance of PC and PT. Then we lay the curve by simply following the incremental chord and deflection angle method. Honestly, at first I got confused in doing this fieldwork because it is my first time to encounter this kind of work and it is really confusing. But then, by the help of my professor, we finished this fieldwork properly. I got confused in getting the deflection angle. But then I discovered that is not that difficult because you just have to add 2˚ to the first deflection angle. And the last deflection angle should be less than or equal to 2˚ that if you add all deflection angle, it should be equal to the intersection angle which in this fieldwork is 42˚. And the first incremental chord can be computed and the rest will be constant which is 20 except for the last incremental chord. I knew that incremental angle should be twice its central incremental angle. In laying a simple curve, you can also just stay at your first station, and just add the previous deflection angle to the next one and so are the incremental chord so that it would not be that hassle to the worker. Because it would just be the same if you do the station by station. But I think, it would still depend to the user because for the one I have said, there is a possibility that you will forgot to add the previous measurement to the next one. But, it you will be vigilant enough in what you are doing, you will not commit any error. For me, it would took you a long time in leveling

the instrument because in every station, you have to level the bubble of the instrument to make sure that all the data will be correct and accurate. Also, what I have discovered, you can do this work easily if you are good in leveling an instrument and in moving the instrument to the proper angle and also, if your group has teamwork because you cannot do this easily in a short span of time if you are alone. Having some skills in theodolite, gathering our data was somewhat easy for me since I listened to some of the tips that Engr. Cervantes have told us on how to read the instrument, how to plot the station points onto the field, and other related items that were needed to be done in order to succeed in the fieldwork. As said in the discussion, a simple curve is an arc of a circle, wherein the point of intersection (PI), is the point in which the two tangents, the forward and the back tangent intersects; it is also marked as V. Then, the Intersection Angle (I) is obtained through subtracting the bearing of the two tangents to 180˚. The radius is then given, in which it connects the center of the arc into the PC and PT which was to be explained later. The length of the curve (LC) is the distance between the PC and PT; and is measured along the curve. PC is the point of curvature where the cure begins. Then the Point of Tangency (PT) is where the simple curve ends.

Photos:

Plotting of the curve on the pavement ground using chalk.

Sighting of the deflection angles using the theodolite.

Computation of the data.

Research Works: LAYING OF A HORIZONTAL CURVE In this method, curves are staked out by use of deflection angles turned at the point of curvature from the tangent to points along the curve. The curve is set out by driving pegs at regular interval equal to the length of the normal chord. Usually, the subchords are provided at the beginning and end of the curve to adjust the actual length of the curve. The method is based on the assumption that there is no difference between length of the arcs and their corresponding chords of normal length or less. The underlying principle of this method is that the deflection angle to any point on the circular curve is measured by the one-half the angle subtended at the center of the circle by the arc from the P.C. to that point.

Let points a, b, c, d, e are to be identified in the field to layout a curve between T1 and T2 to change direction from the straight alignment AV to VB as in Figure 38.1(a). To decide about the points, chords ab, bc, cd, de are being considered having nominal length of 30m. To adjust the actual length of the curve

two sub-chords have been provided one at the beginning, T1 and other, eT2 at the end of the curve. The amount of deflection angles that are to be set from the tangent line at the P.C. are computed before setting out the points. The steps for computations are as follows:

Referring to Figure 38.1(b), let the tangential angles for points a, b, c,… be Δ1, Δ,…, Δ, Δ n and their deflection angles (from the tangent at P.C.) be Δ a, Δ b, ….. , Δn. Now, for the first tangential angle 1, from the property of a circle Arc T1 a = R x 21 radians Assuming the length of the arc is same as that of its chord, if C 1 is the length of the first chord i.e., chord T 1 a, then

(Note: the units of measurement of chord and that of the radius of the curve should be same). Similarly, tangential angles for chords of nominal length, say C,

And for last chord of length, say Cn

The deflection angles for the different points a, b, c, etc. can be obtained from the tangential angles. For the first point a, the deflection angle a is equal to the tangential angle of the chord to this point i.e.,1. Thus, a = 1.

The deflection angle to the next point i.e., b is b for which the chord length is T1 b. Thus, the deflection angle

Thus, the deflection angle for any point on the curve is the deflection angle up to previous point plus the tangential angle at the previous point.

Conclusion: We can say that our data gathered is accurate by our error in measuring the length of the chord, followed the procedure properly, and correct computation.

I can conclude that the data that we gathered on this fieldwork is accurate to say. One of the reason is we have just only less than one meter of error in the measurement of the chord compared to the actual and the computed length of the chord. Another reason is that we follow the steps and we successfully did the fieldwork and lay down a simple curve in the Intramuros wall which has the evident of the photos that I have presented to the proceeding part of this fieldwork paper. Another reason to prove that the data is accurate is the computation. In the computation, we have followed and double check the data and the given so that we can get the missing data. We have also used the formulas and the equation given by the book and by our Prof. Cervantes in doing the computation. For what we have done, I can say that it is accurate and precise. As we all know, errors are inevitable to us students because we are just a first timers and we need more experiences to do an almost perfect job. As what our professor said, it is still acceptable if we commit less than 1.5% error because at least we achieve a good work. But still, we cannot just say that we’re just first timers so we cannot do something better than anyone else because through passion and hard work, you can do a better job even you did not experience that work before. In the process of the fieldwork, I would say that because the group knows the tactics in using the theodolite, we got the data accurately and efficiently. We have also succeeded because we have followed the things needed to be done in which have made the work easier for us. The objectives of this fieldwork were also achieved because we are able to lay the simple curve by deflection angle and we are aware of the parts of the curve we are working on.

Regarding the mastery of the skill in leveling, it is somewhat easy for us because we got our teamwork and an ample amount of knowledge in leveling. Then, with the usage of the theodolite, we have succeeded effectively as explained a while ago.

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