ADVANCED SURVERING FIELD MANUAL

FIELD WORK NO. 1

COURSE AND SECTION: CE121F / B2

SUBMITTED BY: NAME: RAMIREZ, CHARLES JON N. STUDENT NO.: 2013150342

GROUP NO.: _3_ CHIEF OF PARTY: Ander

DATE OF FIELD WORK: 10/8/15 DATE OF SUBMISSION: 10/16/15

SUBMITTED TO:

INSTRUCTOR: ENGR. BALMORIS

LAYING OF A SIMPLE CURVE BY TRANSIT AND TAPE

(THE INCREMENTAL CHORD AND DEFLECTION ANGLE METHOD)

GRADE

Table of Contents

Introduction 2

Objectives and Instruments 3

Procedures 5

Computations 8

Preliminary Data Sheet 9

Final Data Sheet 12

Research and Discussion 15

Conclusion 18

INTRODUCTION

Circular curves are used to join intersecting straight lines (or

tangents). Circular curves are assumed to be concave. Horizontal

circular curves are used to transition the change in alignment at

angle points in the tangent (straight) portions of alignments. The four

types of circular curves are simple, compound, broken back and

reverse curves.

A simple curve is a circular arc,

extending from one tangent to the next. A

curve is said to be simple when it has the

same radius throughout and consists of

single arc of circle with two tangents

meeting at actual point of intersection of

roads.

The point where the curve leaves

the first tangent is called the “point of

curvature” (P.C.) and the point where

the curve joins the second tangent is

called the “point of tangency” (P.T.). The

P.C. and P.T. are often called the

tangent points. If the tangent is to be

produced, they will meet in a point of intersection called the

“vertex”. The distance from the vertex to P.C. or P.T. is called the

“tangent distance”. The distance from the vertex to the curve is

called the “external distance”. While the line joining the middle of

the curve and the middle of the chord joining the P.C. and P.T. is

called the middle ordinate.

OBJECTIVES

1. To be able to lay a simple curve by deflection angle.

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

transit effectively.

INSTRUMENTS

1. Range Poles

- Is a surveying instrument consisting of a

straight rod painted in bands of

alternate red and white each one foot

wide. It is used for sighting by

surveyors.

2. Chalk

- is a soft, white, porous

sedimentary carbonate

rock, a form of limestone

composed of the mineral

calcite.

3. 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.

4. Marking Pins

- These 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.

5. Theodolite

- An 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.

PROCEDURES

Procedure:

1. The professor gives the following data:

a. R = ___________m

b. 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.

COMPUTATIONS

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

FINAL DATA SHEET

Date: October 08, 2015 Group No. : 1

Time: 12:00 Location: Luneta Park

Weather: Sunny Professor: Engr. Ira Balmoris

Data Supplied:

R1 = 80m

Backward Tangent Direction: 48030’

Forward Tangent Direction: 113o30’

Station of the Vertex: 30 + 001

Adopt Full Chord Length: 20m

Station Incremental

Chord

Central

Incremental

Chord

Deflection

Angle From

Back Tangent Occupied Observed

PC A 10 7o9’43.1’’ 3O34’59.96’’

PC B 20 14o19’26.2’’ 10o44’43.06’’

PC C 20 14o19’26.2’’ 17o54’26.16’’

PC D 20 14o19’26.2’’ 25o4’9.26’’

PC PT 20 14o19’26.2’’ 32o30’

Computed Length of the Chord: 85.97 m

Actual Length of the Chord: 81.10 m

Computations I = Front Azimuth - Back Azimuth T = R tan (I/2)

= 113o30 – 48o30 = 80 tan (65o/2)

= 65o = 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) = 7o9’43.1’’

CIAPC-A =(20/80)(180/pi) = 14o19’26.2’’

CIAPC-B =(20/80)(180/pi) = 14o19’26.2’’

CIAPC-C =(20/80)(180/pi) = 14o19’26.2’’

CIAPC-PT =(20/80)(180/pi) = 14o19’26.2’’

d1 =2 sin (1o/2*80) = 7o9’59.92’’’

Deflection Pc-A = d0/2 = 3O34’59.96’’

Deflection Pc-B = (d1o + Do)/2 = 10o44’43.06’’

Deflection Pc-c = (d1o + 2Do)/2 = 17o54’26.16’’

Deflection Pc-D = (d1o + 3Do)/2 = 25o4’9.26’’

Deflection Pc-Pt = I/2 = 32o30’

SKETCH

Some computations were

done before the fieldwork

started.

Setting up the theodolite over

the vertex V and sighting PC and PT

using the computed length of the

tangent segments. Then locating

and marking PC and PT using a

chalk.

Comparing the actual length

of the chord to the computed total

length of the chord of the simple

curve.

RESEARCH AND DISCUSSION

In this first field work of CE121F entitled “Laying of a Simple

Curve by Transit and Tape”, the main objective is to be able to lay a

simple curve by deflection angle. In this fieldwork we lay a simple

curve using theodolite and tape by incremental chord and

deflection angle method. We were given a radius and an azimuth

where the point of curvature is to locate. And then data needed in

the fieldwork is calculated first before proceeding. The fieldwork was

conducted at Luneta Park, Manila.

Laying a simple curve can be done in several methods – by

deflection angle method, tangent offset method and double-

deflection angle method. Deflection angle method uses a transit

and tape, tangent offset method uses a measuring tape only while

double-deflection method uses a theodolite or transit only.

In the deflection angle 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.

The tangent-offset method is a surveying method for laying out

a land profile in hilly terrain. A vertical curve is used to connect two

grade lines marking the beginning and end of an upward or

downward curve. The vertical curve is tangent to the grade lines.

The layout is made by offsets from the tangent. The offset distance

from the tangent varies as the square of the distance along the

tangent.

In double-deflection angle method, angular measurements are

done by two theodolites. The instruments are set-up at the point of

tangency and point of curvature obtaining two lines of sight. The

intersections of the line of sight are plotted to determine the points

on the curve.

A simple curve is a circular arc, extending from one tangent to

the next. A curve is said to be simple when it has the same radius

throughout and consists of single arc of circle with two tangents

meeting at actual point of intersection of roads. As the degree of

curve increases, the radius decreases. It should be noted that for a

given intersecting angle or central angle, when using the arc

definition, all the elements of the curve are inversely proportioned to

the degree of curve. This definition is primarily used by civilian

engineers in highway construction.

The radius and the degree of curve are not inversely

proportional even though, as in the arc definition, the larger the

degree of curve the “sharper” the curve and the shorter the radius.

The chord definition is used primarily on railroads in civilian practice

and for both roads and railroads by the military.

On curves with long radii, it is

impractical to stake the curve by locating

the center of the circle and swinging the

arc with a tape. The surveyor lays these

curves out by staking the ends of a series of

chords (figure 3-4). Since the ends of the

chords lie on the circumference of the curve, the surveyor defines

the arc in the field. The length of the chords varies with the degree of

curve.

CONCLUSION

With this fieldwork we were able to lay a simple curve by

deflection angle and master the skill in leveling, orienting and using

the transit effectively. In performing this fieldwork, I have learned to

determine the points on a simple curve by setting the deflection

angles using the theodolite. From that, I was able to get the

intersection of the lines of sight from the two instruments, locating the

points along the curve in order to lay out the simple curve. I have

also found out that this process of laying out curves can be

accurately done on an uneven ground. Since this fieldwork requires

the use of the theodolite, I was able to master the skills in setting up,

leveling and orienting the instrument.

It can be observed from the data gathered that the measured

values are quite close to the actual length of the chord, thus, the

data acquired is accurate and reasonable. There are several

reasons that caused a discrepancy between the actual and

experimental values for the long chord. First is, the theodolite might

not be leveled properly and the line of sight might not be normal to

the horizontal axis of the instrument. Another is, the theodolite can

only accurately measure up to minutes but the computed deflection

angle contains second measurements. Approximating these values

can cause errors in this work, therefore affecting the measured

values in the data. Also, in measuring the experimental length of the

chord there are some taping factors that could affect the true

measurements, like the correction due to sag, correction due to

temperature, and correction due to pull. Lastly, getting the

intersection of the two lines of sight might not be accurately done

particularly when the tapes are not straightly aligned to the line of

sight.

In order to minimize the error, it is recommended that in

measuring the chord make sure that the tape should not be long so

that the correction in taping will be minimize. Also, make sure that

you are always in line of sight with the theodolite. Lastly, it is

recommended that you should follow all of the instructions written in

the manual to commit less human errors and to save some time that

will hinder the group to finish the experiment early.

In highways or railroad construction, the curves most generally

used presently are circular curves although parabolic and other

curves are sometimes used. By knowing the knowledge of simple

curves, the surveyor learns to locate points using angles and

distances. In construction surveying, the surveyor must often establish

the line of a curve for road layout or some other construction. The

surveyor can establish curves of short radius, usually less than one

tape length, by holding one end of the tape at the center of the

circle and swinging the tape in an arc, marking as many points as

desired.

Furthermore, in the design of roads or railways, straight sections

of road or track are connected by curves of constant or varying

radius as shown below. The purpose of these curves is to deflect a

vehicle travelling along one of the straights safely and comfortably

through a deflection angle θ to enable it to continue its journey

along the other straight.

In the end our group worked as a unit and finished the first of

fieldwork of CE121 successfully.