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Mapua Institute of Technology

School of Civil Engineering and Environmental and Sanitary EngineeringElementary Surveying

ADVANCE FIELD MANUAL

FIELDWORK NO. 2LAYING A SIMPLE CURVE BY USING TAPE ALONE

(THE INCREMENTAL CHORDS AND TANGENT OFFSET METHOD)

CE121F / B2

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GRADE

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Straight (tangent) sections of most types of transportation routes, suchas highways, railroads, and pipelines, are connected by curves in both the

horiontal and vertical planes! An e"ception is a transmission line, in which aseries of straight lines is used with abrupt angular changes at tower locations needed!

#his $eldwor% also tac%les about simple curves but this time it is not thesame as the previous $eldwor%! &ere it is e"pected to use a tape alone in asimple curve! 't will be discuss here the two methods that we used namely theincremental method and the tangent oset method!

'n this $eldwor%, students are e"pected to practice on to verify the

%nown formula in getting a chord by getting the actual length of the chordusing the deection angle of the given data!

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Ob5#"!6#+

*! #o be able to lay a simple curve by using the tape alone!

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R&'# P*3#+

Surveying instrument consisting of a

straight rod painted in bands of

alternate red and white each one foot

wide! +sed for sighting by surveyors

C8&3

is a soft, white, porous sedimentary carbonat

roc%, a form of limestone composed of th

mineral calcit

, #"# "&0#

used in surveyingfor measuring

&oriontal, vertical or slope distances! #ape

are issued in various lengths and widths and

graduated in variety of ways!

https://en.wikipedia.org/wiki/Surveyinghttps://en.wikipedia.org/wiki/Surveying

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PROCEDURES

1. #he professor gives the following data' - .......R - .......Station /0 (preferably not on full station).........Adopt 1ull chord length of ...... m

2. #he professor assigns the location of /0 in the $eld, together with the direction of the

bac%ward tangent! (2ote 3e very careful in assigning the location of station /0 and

direction of the bac%ward tangent so that the curve will not be obstructed by any large

permanent structure!)

-. #he students&. 0ompute the central incremental angle of the simple curve assigned, 4c and Sta /#b. 0ompute the incremental tangent oset distances " and y of each intermediate

stations before going to the $eld!. 0ompute the $rst oset distances " and y using the formula#he tangent oset distance "*must be solved using :1;1< *+($1/2)#he tangent oset distance y*must be solved using %1;2< +!'($1/2)$. 0ompute the second oset distances " and y using the formula#he tangent oset distance "5must be solved using :2 ;

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. Station 3 is now laid on the ground using the procedure below!&. #he front tape man holds the 7 mar% of the tape at station A!b. #he tangent oset tape man (man at station 839) holds and locates the length "5

mar%, loop the tape and hold also the ne"t full meter length!. #he point 3 tape man locates and holds the length of the tape from the tangent

oset tape man: he also loops the tape and holds the ne"t full meter length of thetape! #he front tape man while holding the ero mar% of the tape also holds the c

tape length distance from point 3 tape man!$.#he front tape man and tangent oset tapeman align themselves in the direction

along the prolongation of line /0 to A!?. Station 0 and other full stations are now laid on the ground using the same procedures a

to d!

Station /# is laid in the same manner as above but this time with a chord length of

only c5!

Determine the percentage of error by using the formula

ERROR=|Computed Long Chord LengthMeasured Long Chord LengthComputed LongChord Length |100

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COMPUTATIONS

#he tangent oset distance "*:1;1< *+($1/2)

#he tangent oset distance y*%1;2< +!'($1/2)

#he tangent oset distance "5:2 ;

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P#3!!'&% $&"& +8##"

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D&"& Su003!#$I- ;

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- (;< F*=7)(=7) - >7!;

C1- >7 @ >5= - *5 m

C2- *=!; m

$1-5 sin@*(*5F(5=7)) -*-?.

D*- 5 sin@*(57F(5=7)) - 1>*21>>.>

$2-5 sin@*(*=!;F(5=7)) -1-*2-.1>

O+#" D!+"&'#+@

: PCA- *5cos( ) - **!> m

: AB- *5cos( ) - *>!;7 m

: BC- *5cos(1>*21>>.>) - *>!6= m

: CD- *5cos(1>*21>>.>) - *>!6= m

: DPT- *5cos( ) - *=!5* m

% PCA- *5sin( ) - 7!>7 m

% AB- *5sin( ) - 6!>= m

% BC- *5sin (1>*21>>.>) - !>; m

% CD- *5sin(1>*21>>.>) - !>; m

% DPT- *5sin( ) - !

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F!'&3 $&"& +8##"

D&"#@ O"*b# 1- 2,1 G*u0 N*. @ 1T!#@ 12@,, L*&"!*'@ Lu'#"& P&9 W#&"8#@ Su''% P*4#++*@ E'. I& B&3*!+

D&"& Su003!#$

I- ;

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C1- >7 @ >5= - *5 m

C2- *=!; m

$1-5 sin@*(*5F(5=7)) -*-?.

D*- 5 sin@*(57F(5=7)) - 1>*21>>.>

$2-5 sin@*(*=!;F(5=7)) -1-*2-.1>

O+#" D!+"&'#+@

: PCA- *5cos( ) - **!> m

: AB- *5cos( ) - *>!;7 m : BC- *5cos(1>*21>>.>) - *>!6= m

: CD- *5cos(1>*21>>.>) - *>!6= m

: DPT- *5cos( ) - *=!5* m

% PCA- *5sin( ) - 7!>7 m

% AB- *5sin( ) - 6!>= m

% BC- *5sin (1>*21>>.>) - !>; m

% CD- *5sin(1>*21>>.>) - !>; m

% DPT- *5sin( ) - !

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S9#"8

4aying out the oset distance fo

" and y!

#o ma%e sure that the angle between side " and

side y is an right angle

#his what it loo%s li%e to complete

a single loop! 1rom /0 to A prime to

A bac% to /0!

Ieasuring the actual length of the chord

using the brea%ing the tape method!

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R#+#&8 &'$ $!+u++!*'

0urves are regular bends provided in the lines of communication li%e roads, railways and

canals etc! to bring about gradual change of direction! #hey enable the vehicle to pass from one pa

on to another when the two paths meet at an angle! #hey are also used in the vertical plane at all

changes of grade to avoid the abrupt change of grade at the ape"!

#here are two types of curves, vertical and horiontal curves! 0urves provided in the horion

plane to have the gradual change in direction are %nown as horiontal curves! 0urves provided in th

vertical plane to obtain the gradual change in grade are called as vertical curves! Jertical curves m

be circular or parabolic and are generally arcs of parabolas! #hey are laid out on the ground along t

center line of the wor%!

&oriontal 0urves used in horiontal planes to connect

two straight tangent sections!

Simple 0urve A circular arc connecting two tangents

0ompound 0urve #wo or more circular arcs of dierent

radii tangent to each other!

3ro%en@bac% 0urve 0ombination of a short length of

tangent connecting two circular arcs that have centers o

the same side! Reverse 0urve #wo circular arcs tangent t

each other, with their centers

#A2GE2# 11SE#

ccasions arise on location where the use of osets from

the semi@tangents to intermediate points on a circular cur

are mandatory! #he accuracy of points set by osets is de

pendent upon the method used in setting them, and

the practice of placing curve points by lining in sta%es by e

and turning of right@angles by hand methods is

unsatisfactory! Even though tangent osets are used, the

$eld notes for the curve should be completed showing the

de$ections in the normal manner shown!

#he method of tangent osets reKuires that distances (t

be established along the semi@tangent, measured from the /!0! (or /!#!) and osets (ty) perpendiculto that tangent be measured out to the points reKuired on the curve!

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#his $eldwor% taught me on how to get the tangent oset that we used

to create the large chord! Also in this $eldwor%, it helped us to improve our

s%ills in using the tape measure and gain techniKues to reduce the errors of

the measurements! Also it is also a great way to improve our %nowledge on

how to use the range poles to ma%e sure that we are on the right path!

#his $eldwor% is very challenging for us especially we encounter many

problems! At $rst we didn9t fully understand the $eldwor% so we came up wit

the wrong measurement! Second since it is hard to use the brea%ing the tape

method in this $eldwor%, we had errors especially the sagging of the tape

measure! 4astly, since we don9t have a theodolite, we had a hard time on

$nding the location for our ne"t station since to ma%e data accurate, thepoints must be located on the proper place and aligned to the previous point

Also the oset for the y must be perpendicular to the side ",which is hard to

assume a perpendicular angle!

Some recommendation for this $eldwor% is by laying out the given

measurement, ma%e sure that reduce the sagging of the tape! 't is also

important that the front tape man should properly hold the tape to avoid the

dislocation for the point! 't is still advised to have a theodolite for chec%ing if

the two points lie on the same line!

Application of these simple curves is 'n the geometric design of

motorways, railways, pipelines, etc!, the design and setting out of curves is a

important aspect of the engineers wor%! #he initial design is usually based on

a series of straight sections whose positions are de$ned largely by the

topography of the area! #he intersections of pairs of straights are then

connected by horiontal curves!