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Laying of a simple curve by using the tape alone(Incremental chord and tangent o set method)

Table of contents

Introduction --------------------------------------------------------------2Objectives and instruments ---------------------------------------------- 3

Procedure and Computation --------------------------------------------4

Preliminary data sheet ----------------------------------------------------5 Final data sheet -------------------------------------------------------------7

Pictures ----------------------------------------------------------------------

!esearch and discussions ------------------------------------------------"#

Conclusion -------------------------------------------------------------------"2

Introduction

"

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Occasions arise on location $here the use o% o&sets %rom the semi-tan'entsto intermediate points on a circular curve are mandatory( )he accuracy o%points set by o&sets is dependent upon the method used in settin' them*and the practice o% placin' curve points by linin' in sta+es by eye andturnin' o% ri'ht-an'les by hand methods is unsatis%actory( ,ven thou'h

tan'ent o&sets are used* the eld notes %or the curve should be completedsho$in' the de.ections in the normal manner(

)he tan'ent o&set method is used to establish the points by directlymeasurin' %rom the bac+ or %or$ard tan'ent( I% desired* this can be doneaccurately $ith only a chain* thus eliminatin' the need to measure thean'les(

Instead o% measurin' an'les and distances alon' the arc o% the curve li+e $ehave done on our eld $or+ "* the tan'ent o&set method establishes the

desired stations $ith a direct measurement at a ri'ht an'le %rom the curve/stan'ents(

2

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Objectives:

"( )o be able to lay a simple curve by usin' the tape alone(

Instruments:

Tape

0sed to measure hori1ontal

distances as $ell as slopes( 0suallyin 3#m* 5#m or "##m in len'th(

Chalk so%t* $hite* porous sedimentarycarbonate roc+* a %orm o%limestone composed o% the mineralcalcite(

2 range poles

trai'ht round stal+s* 3 to 4 cm thic+and about 2 m lon'( )hey are madeo% $ood or metal( )hey are used tomar+ areas and to set out strai'ht lineson the eld( )hey are also used to mar+points $hich must be seen %rom adistance* in $hich case a .a' may beattached to improve the visibility (

Procedures:

3

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"( )he pro%essor 'ives the %ollo$in' dataI 6 ! 6tation PC pre%erably not on %ull station8dopt Full Chord len'th o%

2( )he pro%essor assi'ns the location o% PC in the eld* to'ether $ith thedirection o% the bac+$ard tan'ent( 9ote :e very care%ul in assi'nin'the location o% station PC and direction o% the bac+$ard tan'ent so thatthe curve $ill not be obstructed by any lar'e permanent structure(8

3( )he students3("( Compute the cental incremental an'le o% the simple curve

assi'ned* ; c and ta P)(3(2( Compute the incremental tan'ent o&set distances < and y

o% each intermediate stations be%ore 'oin' to the eld(3(3( Compute the rst o&set distances < and y usin' the

%ormula

)he tan'ent o&set distance < " must be solved usin' x 1 = c 1 cos ( d1

2)

)he tan'ent o&set distance y " must be solved usin' y1 = c 1 sin (d 12

)

3(4( Compute the second o&set distances < and y usin' the%ormula

)he tan'ent o&set distance < 2 must be solved usin' x2 = c cos (d 1 + D

2)

)he tan'ent o&set distance y 2 must be solved usin' y2 = c sin (d 1 + D

2)

3(5( Compute the succeedin' o&set distances < and y usin' the%ormula

)he tan'ent o&set distance < 3 must be solved usin' x3 = c cos ( D + D

2)

or x 3 = c cos ( D )

)he tan'ent o&set distance y 3 must be solved usin' y3 = c sin ( D + D

2)

or x 3 = c sin ( D )3(=( Compute the last o&set distances < and y usin' the %ormula

)he tan'ent o&set distance < n must be solved usin' xn= c cos (

d2 + D2

)

)he tan'ent o&set distance y n must be solved usin' yn= c sin (d 2 + D

2)

"(7( ;ay the curve in the eld startin' in the position o% the PC( )he process e

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4("( )he %ront tapeman should hold the # mar+ o% the tape atstation PC(

4(2( )he tan'ent o&set tapeman man at station /8 should holdand locate the len'th < " mar+* and loop the tape and holdalso the neetermine the percenta'e o% error bu usin' the %ormula

error =|computed long chord length measured longchord lengthcomputed long chord length |

5

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=

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inal !ata "heetield #or$ % Laying of "imple &urve by 'sing the Tape

lone (Incremental &hord and TangentO set ethod)>ate Oct "3* 2#"5 ?roup 9o( 4

)ime "2 ##pm ;ocation ;uneta Par+@eather Cloudy Pro%essor ,n'r( Ira :almoris

( >ata uppliedI =5A ! B#mtation o% the PC 2 2Bdopt Full Chord ;en'th o% 2# m

) )IO9 CDO!> C,9)! ;9?;,OFF ,) >I ) 9C,

OCC0PI,> O: ,!E,> G

PC "2 #A 4B/4"(B H

"2 #("7

: 2# "4A 25/=(22H " (37 4( B

: C 2#

"4A 2"/

2#(B3H " (3B 4( =C > 2# "5A 52/

"4(3H" (24 5(47

> , 2# "5A 52/"4(3H

" (24 5(47

, P) "B(7= "5A 52/2=(="H "B(#4 5("3

Computed ;en'th o% the Chord B5( 7 mctual ;en'th o% the Chord not applicable

:( Computation

ComputedC 1 = (29 +940 ) (29 +928 )= 12 m

C 2 : Lc= (65 ) (80 )( 180 )= 90.737 PT = (29 +940 )+(0 +090.757 )= 30 +018.76C 2 = 18.76

7

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easured

C 1 = 12.93 mC = 24.53 24.34 = 20.57 mC = 24.53 24.34 = 20.19 mC

=46.36

24.71

=21.65 m

C = 42.82 24.71 = 21.11 mC 2 = 41.36 23.17 = 18.19 m

x 1 = 12cos 14.47

17.4= 12 m y1 = 12 sin

14.47

17.4= 0.17 m

x 2 = 20 cos14.47 +14.36

2

= 19.36 m y2 = 20sin 14.47 +14.36

2

= 4.98 m

x 3 = 20 cos 14.36 +14.36

2= 19.38 m y3 = 20sin

14.36 +14.362

= 4.96 m

x 4 = 20 cos 17.4 +14.36

2= 19.24 m y 4 = 20 sin

17.4 +14.362

= 5.47 m

x 5 = 20 cos 17.4 +14.36

2= 19.24 m y5 = 20sin

17.4 +14.362

= 5.47 m

x 6 = 18.76 cos 17.4 +14.36

2= 18.04 m y6 = 18.76 sin

17.4 +14.362

= 5.13 m

PC PT = 114.66 m

B

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110.76 114.66 110.76

100 = 3.52

error =

Pictures:

easurin' the o&set o%Point to bac+ tan'ent(

;ay outin' station : bymaintainin' a ri'htan'le %rom station havin' :/ as the ri'htan'le(

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;ay outin' station Cusin' station : as 'uide(

*esearch and!iscussions

&onclusion:

fw2_ce121.docx

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