Mapua Institute of Technology

School of Civil Engineering and Environmental and Sanitary EngineeringElementary Surveying

ADVANCE FIELD MANUAL

FIELDWORK NO. 1LAYING A SIMPLE CURVE BY TRANSIT AND TAPE

(THE INCREMENTAL CHORDS AND DEFLECTION ANGLE METHOD)

CE121F / B2

Submitted by Cayanan, Jonas I. 2013102552 Group 3 Cayanan, Jonas I. October 8, 2015 October 15, 2015

Submitted to Engr. Valerie Ira Balmoris

GRADE

Table of Contents

Introduction 3Objectives and Instruments 4Procedures 6Computations 9Questions and Problems 8

Preliminary Data Sheet 11Final Data Sheet 13Research and Discussion 16Conclusion 18

Introduction

Straight (tangent) sections of most types of transportation routes, such as highways, railroads, and pipelines, are connected by curves in both the horizontal and vertical planes. An exception is a transmission line, in which a series of straight lines is used with abrupt angular changes at tower locations if needed.

This fieldwork tackles about some properties of circle and taught us on how to survey on a curve path. In this fieldwork we used two methods namely the incremental method and the deflection angle method.

In this fieldwork, students are expected to practice on to verify the known formula in getting a chord by getting the actual length of the chord using the deflection angle of the given data.

Objectives1. To be able to lay a simple curve by deflection

angle.2. To master the skill in leveling, orienting and using

the transit effectively.

InstrumentsRange Poles

Surveying instrument consisting of a straight rod painted in bands of alternate red and white each one foot wide. Used for sighting by surveyors

Chalkis a soft, white, porous sedimentary carbonate rock, a form of limestone

composed of the mineral calcite.

50 meter tape used in surveying for measuring

Horizontal, vertical or slope distances. Tapes are issued in various lengths and widths and graduated in variety of ways.

Marking PinsThese are made either of iron, steel

or brass wire, as preferred. They are about fourteen inches long pointed at

one end to enter the ground, and formed into a ring at the other end for

convenience in handling.

TheodoliteAn instrument similar to an ordinary surveyor's level but capable of finer readings and including a prism arrangement that permits simultaneous observation of the rod and the leveling bubble.

PROCEDURESProcedure:

1. The professor gives the following data:a. R = ___________mb. Backward Tangent Direction = ___________c. Forward Tangent Direction = ___________d. Station of the Vertex = ___________e. Adopt Full Chord Length= ___________m

2. The student compute the elements of the simple curve using the following formulas:

If the azimuths of the backward and forward tangents are given, the intersection angle I can be solved using:I = azimuth of the forward tangent - azimuth of the backward tangent

The tangent distance must be solved using:T = R*tan( I/2)

The middle ordinate distance can be computed using:M = R*( 1 - cos(I/2) )

The length of the curve (Lc) can be computed using (provided that I is in radians)Lc = I * R

The long chord (C) can be solved using:C = 2*R*sin (I/2)

The station of PC can be computed using:Station of PC = Station V - T

The station of PT can be found by:Station of PT = Station PC + Lc

The length of the first sub chord from PC, if PC is not exactly on a full station (otherwise C1 = a full chord length):

C1 = first full station on the curve - Station PC

The length of the last sub chord from PC, if PC is not exactly on a full station (otherwise C2 = a full chord length):

C2 = Station PT - last full station on the curve

The value of the first deflection angle d1:d1 = 2*sin-1 ( C1 / 2R )

The value of the last deflection angle d2:D2 = 2*sin-1 ( C2 / 2R )

3. Set up the transit/theodolite over the vertex V, level the instrument and sight/locate PC and PT using the computed length of the tangent segments. Mark the position of PC and PT by marking pins if on soft ground or chalk if on pavement.

4. Transfer the instrument over PC, level and start locating points of the curve using the following procedures:

a. Initialize the horizontal vernier by setting to zero reading. Tighten the upper clamp and adjust it with the upper tangent screw.

b. Using the telescope, sight the vertex or PI with the vernier still at zero reading.

c. Tighten the lower clamp and focus it using the lower tangent screw.

d. With the lower tangent screw already tight, loosen the upper clamp and start to measure half the first deflection angle. Mark the direction with a range pole. Along this line, using a marking pin/chalk, mark point A measured with a tape the length of the first subchord.

e. Locate the next point B, a full chord length from point A but this time intersecting the line sighted at an angle of half the sum of d1 and the full D of the curve. Note that the transit/theodolite is still positioned over station PC.

f. Proceed in locating other points on the curve following step E until you cover all full chord stations on the entire length of the curve.

g. Measure the distance and from the last full station on the curve and intersecting the line of sight with a deflection angle equal to half the intersection angle, mark the last point as PT.

5. Check the position of PT by determining the length of PC from PT and compare it to the computed total length of the chord of the simple curve.

COMPUTATIONSIf the azimuths of the backward and forward tangents

are given, the intersection angle I can be solved using:I = azimuth of the forward tangent - azimuth of the backward tangent

The tangent distance must be solved using:T = R*tan( I/2)

The middle ordinate distance can be computed using:M = R*( 1 - cos(I/2) )

The length of the curve (Lc) can be computed using (provided that I is in radians)

Lc = I * R

The long chord (C) can be solved using:C = 2*R*sin (I/2)

The station of PC can be computed using:Station of PC = Station V - T

The station of PT can be found by:Station of PT = Station PC + Lc

The length of the first sub chord from PC, if PC is not exactly on a full station (otherwise C1 = a full chord length):

C1 = first full station on the curve - Station PC

The length of the last sub chord from PC, if PC is not exactly on a full station (otherwise C2 = a full chord length):

C2 = Station PT - last full station on the curve

The value of the first deflection angle d1:d1 = 2*sin-1 ( C1 / 2R )

The value of the last deflection angle d2:d2 = 2*sin-1 ( C2 / 2R )

Preliminary data sheetDate: October 08, 2015 Group No. : 1Time: 12:00 Location: Luneta ParkWeather: Sunny Professor: Engr. Ira Balmoris

Data Supplied:R1 = 80m Backward TangentDirection: 48 0 30’ Forward Tangent Direction: 113 o 30 ’Station of the Vertex: 30 + 001Adopt Full Chord Length: 20m

Station Incremental Chord

Central Incremental

Angle

Deflection Angle From

Back TangentOccupied ObservedPC A 10 7o9’43.1’’ 3O34’59.96’’PC B 20 14o19’26.2’’ 1

0o44’43.06’’PC C 20 14o19’26.2’’ 1

7o54’26.16’’PC D 20 14o19’26.2’’ 25o4’9.26’’PC PT 20 14o19’26.2’’ 32o30’

Computed Length of the Chord: 85.9679 mActual Length of the Chord: 81.10 m

ComputationsI = Front Azimuth - Back Azimuth T = R tan (I/2) = 113o30 – 48o30 =80 tan (65o/2 = 65 o =50.9656m

Lc = IR C = 2R sin (I/2) =80 (65pi/180) = 2*80*sin (65/2) =90.7571m =85.9679m

Station PC = Station V - PT Station PT = Station PC + Lc=30+001 - 50.9656 =29+950 + 90=29+950 =30+040

Central Incremental Angle

CIAPC-A =(10/80)(180/pi) = 7 o 9 ’ 43.1 ’’ CIAPC-A =(20/80)(180/pi) = 14 o 19 ’ 26.2 ’’ CIAPC-B =(20/80)(180/pi) = 14 o 19 ’ 26.2 ’’ CIAPC-C =(20/80)(180/pi) = 14 o 19 ’ 26.2 ’’ CIAPC-PT =(20/80)(180/pi) = 14 o 19 ’ 26.2 ’’

d1 =2 sin (1o/2*80) =7 o 9 ’ 59.92 ’’ ’ Deflection Pc-A = d0/2 = 3 O 34 ’ 59.96 ’’ Deflection Pc-B = (d1o + Do)/2 =10 o 44 ’ 43.06 ’’ Deflection Pc-c = (d1o + 2Do)/2 =17 o 54 ’ 26.16 ’’ Deflection Pc-D = (d1o + 3Do)/2 =25 o 4 ’ 9.26 ’’ Deflection Pc-Pt = I/2 =32 o 30 ’

Sketch

Final data sheetDate: October 08, 2015 Group No. : 1Time: 12:00 Location: Luneta ParkWeather: Sunny Professor: Engr. Ira Balmoris

Data Supplied:R1 = 80m Backward TangentDirection: 48 0 30’ Forward Tangent Direction: 113 o 30 ’Station of the Vertex: 30 + 001Adopt Full Chord Length: 20m

Station Incremental Chord

Central Incremental

Angle

Deflection Angle From

Back TangentOccupied ObservedPC A 10 7o9’43.1’’ 3O34’59.96’’PC B 20 14o19’26.2’’ 1

0o44’43.06’’PC C 20 14o19’26.2’’ 1

7o54’26.16’’PC D 20 14o19’26.2’’ 25o4’9.26’’PC PT 20 14o19’26.2’’ 32o30’

Computed Length of the Chord: 20mActual Length of the Chord: 20m

ComputationsI = Front Azimuth - Back Azimuth T = R tan (I/2) = 113o30 – 48o30 =80 tan (65o/2 = 65 o =50.9656m

Lc = IR C = 2R sin (I/2) =80 (65pi/180) = 2*80*sin (65/2) =90.7571m =85.9679m

Station PC = Station V - PT Station PT = Station PC + Lc=30+001 - 50.9656 =29+950 + 90=29+950 =30+040

Central Incremental Angle

CIAPC-A =(10/80)(180/pi) = 7 o 9 ’ 43.1 ’’ CIAPC-A =(20/80)(180/pi) = 14 o 19 ’ 26.2 ’’ CIAPC-B =(20/80)(180/pi) = 14 o 19 ’ 26.2 ’’ CIAPC-C =(20/80)(180/pi) = 14 o 19 ’ 26.2 ’’ CIAPC-PT =(20/80)(180/pi) = 14 o 19 ’ 26.2 ’’

d1 =2 sin (1o/2*80) =7 o 9 ’ 59.92 ’’ ’ Deflection Pc-A = d0/2 = 3 O 34 ’ 59.96 ’’ Deflection Pc-B = (d1o + Do)/2 =10 o 44 ’ 43.06 ’’ Deflection Pc-c = (d1o + 2Do)/2 =17 o 54 ’ 26.16 ’’ Deflection Pc-D = (d1o + 3Do)/2 =25 o 4 ’ 9.26 ’’ Deflection Pc-Pt = I/2 =32 o 30 ’

Sketch

Set-up of the Theodolite on the vertex of the two tangent lines

Finding the point PC by measuring the length of the tangent line.

Setting up point from point PC to point A considering the distance and its deflection angle from point PT

Measuring the chord PC-PT to get our actual chord length to be compared on the computed chord length

The location of the fieldwork

Other pictures, including the location of the points

Research and discussionCurves are regular bends provided in the lines of communication like roads,

railways and canals etc. to bring about gradual change of direction. They enable the vehicle to pass from one path on to another when the two paths meet at an angle. They are also used in the vertical plane at all changes of grade to avoid the abrupt change of grade at the apex.

There are two types of curves, vertical and horizontal curves. Curves provided in the horizontal plane to have the gradual change in direction are known as horizontal curves. Curves provided in the vertical plane to obtain the gradual change in grade are called as vertical curves. Vertical curves may be circular or parabolic and are generally arcs of parabolas. They are laid out on the ground along the center line of the work.

Horizontal Curves used in horizontal planes to connect two straight tangent sections.

Simple Curve: A circular arc connecting two tangents.

Compound Curve: Two or more circular arcs of different radii tangent to each other.

Broken-back Curve: Combination of a short length of tangent connecting two circular arcs that have centers on the same side. Reverse Curve: Two circular arcs tangent to each other, with their centers on opposite side of the alignment. ‘’

PI: Point of intersectionPC: Point of curvature (the beginning of the curve) PT: Point of tangency (the end of the curve)TC: Tangent to curveCT: Curve to tangent

R: Curve radiusT: Tangent distance (PC-PI or PI-PT)LC: Long chord (PC-PT)L: Length of the curve (along the curve)E: Length from the PI to the curve midpoint on a radial line.M: Middle ordinate. The radial distance from the midpoint of the long chord to the curves midpoint.POC: Any point on curve.POT: Any point on tangent.Da: Degree of any curve (arc definition)Dc: Degree of any curve (chord definition)I: Intersection angle (central angle)Laying out a curve by Deflection angle ( Rankine's Method)

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 sub-chords 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.

Except for unusual case the radii of curves on route surveys are too large to permit swinging an arc from the curve center. Circular curves are therefore laid out by more practical methods, including Deflection Angle, coordinates, tangent offsets, (4) chord offsets, (5) middle ordinates, and (6) ordinates from the 1ong chord. Layout by deflection angles been the standard approach,although with the advent of total station instruments, the coordinate method is used typically. Layout or a curve by deflection angles can be done by either the incremental chord method c the total chord method. ¡n year past, the incremental chord method was a1most used as it could be readily accomplished with a theodolite and tape.

ConclusionThis fieldwork taught me on how to get deflection angles

that we used to create the curve path. Also in this fieldwork we apply our knowledge on our pace factor, this helped me to know the use our own pace factor on farther distances. I also improved my knowledge on using the breaking the tape method which made our fieldwork easier.

This fieldwork is very challenging for us especially we encounter many problems. First, since we had a hard time in finding a position for the vertex since we need a large area that has fewer obstacles, this consumes us time since we need to pace the distance to make sure that it will be enough for the fieldwork. Next is the error that cannot be control which are the error due to sag, temperature and pull that will have a very small discrepancy in the data. And lastly is the computation, we had a mistake in solving for the incremental chord of the station PC - PT that had an effect on the measurement of the actual length of the chord when we measured.

Some recommendation to make sure that the data will be accurate. First is to pace the needed distance to make sure there will be no obstacle in doing your fieldwork. Second, make sure that the theodolite is set-up properly and balance to the ground. This will help to get an accurate data. Third, it is also better to use the breaking the tape method in measuring large distances especially to avoid the error due to sag and pull that will affect the data gathered. Fourth, to make sure that you are still on the correct path, you can use the range poles to verify if you are on the straight line or you can use the theodolite to sight if your position is correct on the deflection angle needed. Fifth, before starting the fieldwork make sure that you understand and know what to do in the field already and make sure you are on the right

track. It is also advisable to solve the unknowns beforehand since the needed data are already given before the fieldwork.

Application of these compund curves is In the geometric design of motorways, railways, pipelines, etc., the design and setting out of curves is an important aspect of the engineers work. The initial design is usually based on a series of straight sections whose positions are defined largely by the topography of the area. The intersections of pairs of straights are then connected by horizontal curves.