117 labex4 report data and computation

7/25/2019 117 LabEx4 Report Data and Computation

1/20

Design of Horizontal Curves 11

Data

In making the road alignment using a CADD software, most data can already be obtained. Some of them are the following:

No. Type Length Radius Direction Delta Angle

1 Line !!."m

S!#$ !% 11.#&'

2 Cur(e 1)1.*+

m

*-.---m -"+.+## d/

Cur(e 11.!""

m

1"+.")

m

-)!.#+11 d/

! Cur(e 1-1.!#!

m

1+1.+*

m

-+1.-# d/

" Cur(e ").--m *-.---m -.1- d/

#.1 S0iralLine )-.---m -1-.#+)- d/#.2 S0iralLine 1-#.""

m

S)$ !*%

+-."*&2$ Cur(e 1).)*m )--.---

m

--.!* d/

% Cur(e 1).*"*

m

--.---

m

-)".1*! d/

& Cur(e #.-!m --.---

m

-1."+! d/

'ase (oint )*tart of Align+ent, *TA ----/0 )1#-&$%".!2!, "!2$%#.&$/

DLA CR3, (. 4. A. GE 117 Construction and IndustrialSurveying


2/20


3hese are the only data I 0rocured from the 0rogram since I thought that they are already su4cient to sol(e for what is

asked5 that is the coordinates of s0ecial 0oints and each - meter full station. 6ther data I used for checking/ are the Start 7oints

and 'nd 7oints of each cur(e.

Co+putations

1./ Line 2"".2&2+ *"$5 "26 11.$27



3/20


3he 8rst element of the alignment is a line, stretching for a length of !!." meters. 3he com0utation of the coordinates of

- meter full stations in a line is similar to com0uting coordinates of a tra(erse line. 2e are to com0ute latitudes and de0artures of

lines of - meter lengths. Since this 0art of the alignment is a line, the a9imuth does not change at any 0oint. A line has no

deection angle and that bit of the com0utation is therefore not considered in this 0art of the alignment.

L8N 1

*TA Distan

ce

Azi+uth

)d/

Latitude Departure Northing asting

'( -;--- 1-"#*!.+

+

!+#*."#

-;-- - )-.1)--#

#*

1-.)*+1

#

1.")*!

*#

1-"##+.#

*#

!+*-)."-

"

-;-+- +- )-.1)--#

#*

1.#)#*)+

)).*#)#1)

#+

1-"#+.1

!

!+*-.*+

)#

-;-- - )-.1)--#

#*

)1."1-!"!

1

!-.*1-!#-

1

1-"#!).!

1)

!+*)#.#*

-

-;-*- *- )-.1)--#

#*

+.!+#+!

*

#.#+#+#

+*

1-"#+.*

##

!+*!+.#1

#+

-;1-- 1-- )-.1)--#

#*

!).1*+)-*

*+.*+*+

)!

1-"#).

+

!+*#1.!

+)

-;1- 1- )-.1)--#

#*

).*11*!-

)

1-1.11+

1

1-"#1.

-)

!+***.!"

11

-;1+- 1+- )-.1)--#

#*

#+.+!*-+"

11*.!!#""

*1

1-"#1-."

!+"-!.!

*



4/20


-;1- 1- )-.1)--#

#*

*!.-"+"1))

#

1)!.+"+*!

!

1-"#--.)

"

!+".+

+"

-;1*- 1*- )-.1)--#

#*

"!.#)1###!

+

1!.+)1#1

1*

1-"*".

"

!+")".+-

1#

-;-- -- )-.1)--#

#*

1-.)*+1

#

1".)*!

*#

1-"#".-

!!

!+"!.))

*

-;- - )-.1)--#

#*

11#.--!!-!

"

1*.)-!+

!

1-"*.+

1*

!+"#).#

!+

-;+- +- )-.1)--#

#*

1#.+)#-

1

-).+*

+

1-"!#.#

*

!+""-.1

)

(C1 -;!!."

!!." )-.1)--#

#*

1)!.##!)1

+

1.1"-

)

1-"+".

+"

!+)--).1

2./ Curve 11.%!#+ %-.---+ -&!.!2$$ )d/



5/20


3he ne


6/20


)# ) +*!1.#-#

**) *#

-;)+- *+.#-*)-.)))*-+

)

)).+)**

+

*-.*-!"1-

#1.!1*)+

!

)#.)!#1"1

""

1-"!##."

"#

!+)-+-.!1"

-;)-1-+.#-

*

)#.+"!##)

"

))".!*!

1#

"#.)"+!

"1.""!1-

)

))."-#1--

+"

1-"!!*.)

+"

!+)-)#.-"

1

-;)*-1+.#-

*

++.!##+)

1#

)+.#*#*

1

11.+!"+

!1

1-".+*+*#

)

!.#-)+)"

11

1-"!+-.1

#

!+)-*.*!

+

(RC

1

-;)*#.1)

*

1)1.*+

+#.1)*!

)+".)+)"

#*

11#.+)-!

))

11!.)"*-#!

*

1.#1)-#)

)1

1-"!)+.

!1

!+)-+.*#!

1

A9imuth of >orward 3angent: )-.1)--##* ; "+.+## ? )".!!###* ? #.""$$$$%%

./ Curve 121."&&+ 1&!.&2+ -".$!11 )d/



7/20


@ere we ha(e our 8rst 7oint of e(ersed Cur(ature, it is sol(ed

the same way as the 0re(ious cur(e, only that the a9imuths of

the deection angles here are subtracted instead of added to

obtain the a9imuths of the succeeding chords.

CR= 2

*TA

Arc

Lengt

h

De>ection

Angle )d/Azi+uth

Chord

DistanceLatitude Departure Northing asting

(RC

1

-;)*#.1)

*

).!!####

*

1-"!)+.

!1

!+)-+.*#

!1

-;+-- 1.* 1.*"-)##)+.#!+-

1

1.*!"-

11

1-.!#-!#

#.)1+##!"

1-"!).

#+

!+)-1#.!

-+

-;+- ).*+.*"+"#-

"

)1.#**-

#)

).*"*-

)

#."1#)""

1

1#.1)#*!

1-"!-.)

))

!+)--#.1

)*

-;++- !.*#.#*#!+

)*

*.#*"-1

)

!."""*1

-1

+.1*-")

1

!.)#"!--!

1-"+**.-

!

!+""".+"

!!



8/20


9/20




10/20


CR=

*TA

Arc

Lengt

h

De>ection

Angle )d/Azi+uth

Chord


(CC

1

-;!-*.#)

#

-.*1##*

1

1-"+-."

1

!+"*.!+

))-;!- 11.) .*+)!1!

1+)!*.!))

)

11.!""##

"#

11.!*)"

-.**+-11-# 1-"+-".

!

!+"*.*)

1#

-;!+- )1.) .)+-#))+

"*)!+.+#!"+

+)

)1.1""11"

1!

)1.-!+)

*

).--))+1+1 1-")*".*

#

!+"*".!+

-;!- !1.) 1-.)"#11!

+*)!-.+1"!

)

!-."*1"+#

"

!-.#-*"*

1

*.+*!-)1) 1-")#-.

!

!+""!.-

*)

-;!*- #1.) 1+.+!)+"#

+# )+.))1*-+

#-.!-")+"

+

*.!1"1

1.)#!+! 1-")!.)

""

!+)--).1

#1

-;-- "1.) 1*.!-"*#"

+!

)+.)-#"

*+

*".*)+**

1*

*!.++1)"+

#.!-#* 1-"))!.+

*

!+)-1).#"

""(RC

2

-;1-.)1

1-1.!#

!

-.-1)!)+-.1!)

#*

"".+---**

*+

").!))

)).+!!!*+ 1-")#.)

**

!+)--.1*

*"

A9imuth of >orward 3angent: -.*1##*1 +1.-# ? +-.)*-1* ?1&.#1&$$%

"./ Curve &.-2-+ %-.---+ -##.#21- )d/



11/20


In this cur(e, we could see the second 7oint of e(ersed

Cur(ature, therefore, we now re(ert back to adding the

deection angles to obtain the a9imuths of our chords.

CR= !

*TA

Arc

Length

De>ection

Angle )d/ Azi+uth

Chord

Distance Latitude Departure Northing asting(RC

2

-;1-.)1

)1".1)"##

*

1-")#.)*

*

!+)--.1*

*"-;- ".** ).+"##!

*

)).-*)!+

".*1"+

#+

#.#+-"!1-+

+

!.*1!-"-

-)

1-")1".+

#

!+)-.--

+!

-;+- ".** 1-.)1*+"

)

))-.+!

#

".!1*-*+

*#

!.)!!1

+

1+.+"+#"

#)

1-")-1.#

!+)-)+.*)

*+

-;- +".** 1#.#")")1 ))#.+-##-

"

+*.*")+1!

*)

+!.1+1*!-"

1*.#*)#*

"

1-"*.+

#

!+)-)*."#

#

-;*- ".** +."!!)-1

#

)++.!"#"

1

#.!-!##)

#"

!.-#)*!-

)

1#."1++

)*

1-".)1

!+)-)*.1!

-+

-;#-- *".** ).11#)-"+ )!1.#)1*# *!.-+#1 1.))!) 1-"+).- !+)-).+



12/20


+ + *+.1*-+))

*

-" *

C* -;#-).))

").- )).)1-! )!."++##

*

*#.**1!

!

*#.1""--""

*

1-.*))*1

*"

1-"+-.1*

"

!+)-)1.-1

)

A9imuth of >orward 3angent: )1".1)"##* ; .1- ? )*.)+"##* ? 2#.2!&$$%

#.1./ *piral?Line -.---+ -1-.$!- )d/

I sol(ed the s0iral in the same way I sol(ed the circular cur(es,

only the ratio of the deection angles of the s0iral is e=ual to

B) of that of its angle of intersection B)/ since this is an

e


13/20


*(8RAL

*TA

Arc

Leng

th

De>ection

Angle )d/@

Chord

DistanceAzi+uth Latitude Departure Northing asting

C* -;#-).)

)

#.1 .)+"##

*

1-"+-.1

*"

!+)-)1.-1

)-;#- 1.

*

.1-*+#!

1.+1

1)

-.)1!#"

+

1.!!1"

-)

*.++!*!

)

1+.!)+!!

"

#.")*+#

1-"!.!

)

!+)-).-#

+1

*T -;#)).)

)

)- #.1 ".*"+!)1

!

1.*#! "."!)#+

-1

)).)""##

*

!.--#"!

1.+*#)*1

+

1-"1!.1

*

!+)-1+.!

+"

A9imuth of >orward 3angent: .)+"##* ; 1-.#+) ?#.&$$&$$%

#.2./ *piral?Line 1-$.&2&+ *#5 "%6 !-.&%7B

@ere we ha(e the line connected to our s0iral5 sol(ed in

the same way as a tra(erse line.



14/20


L8N 2

*TA Distanc

e

Azi+uth

)d/

Latitude Departure Northing asting

*T -;#)).))

1-"1!.1* !+)-1+.!+

"

-;#+- .* )."##"##* !.)*+)!*+ +.-1-*!!++* 1-"-".*!! !+)-1-.!1+-;#- .* )."##"##* 1.)-+1#**# 1.-+1-1!# 1-"1").*#* !+""*.+*)

"-;#*- +.* )."##"##* )#.*1!1+1 *.-#11#-# 1-"1##." !+"*.+!)

#-;*-- .* )."##"##* !).!**+"++ +-.1-1)))" 1-"11.") !+"#+.+)

-;*- *.* )."##"##* ".)1*+#) !.1)1+"# 1-"1+!."+ !+".)")

+-;*+- 1-.* )."##"##* *!.1)!-- +.11!#-1 1-"1"."* !+"!-.))

(C2 -;*+1.1

1-#."" )."##"##* *.-*"1-1 +."-1!* 1-"1*."1 !+"+".-+#

$./ Curve 1.2%+ --.---+ --2."2%2 )d/

3his cur(e is com0ounded to our 0re(ious line, the a9imuth of

its back tangent is therefore e=ual to the a9imuth of the line. Itis sol(ed also similarly as the 0re(ious cur(es, with the

deection angles being added to obtain the a9imuths of the

chords.



15/20


CR= "

*TA

Arc

Lengt

h

De>ecti

on

Angle

)d/

Azi+uthChord


(C2 -;*+1.1

)."##"##* 1-"1*."1 !+"+".-+#

(CC2 -;*!+.+

""

1).)* 1.+1 )*.+-##* 1).)!!-

)+

1-.)"---!

*.1"))-*

#

1-"11*.!! !+"+1.+1

1!

A9imuth of >orward 3angent: )."##"##* ; .!*?&."-#1$$%2

%./ Curve 1#.%&%+ 2--.---+ -&.21%" )d/

Another cur(e, sol(ed similarly as the 0re(ious ones, with

deection angles being added to obtain a9imuths, and chord

distances ser(ing as tra(erselike line distances.



16/20


CR= #

*TA

Arc

Lengt

h

De>ection

Angle )d/Azi+uth

Chord


(CC2 -;*!+.+

""

)".!-1##*

1-"11*.!

!!+"+1.+11!

-;*- !.!-1 -.#*#"+!

+-."+1+-

#

!.!--*+

"1

+.1"!*-!

1

).!!#+!"+"

)

1-"11+.)

"!+")#.*!+

-;**- !.!-1 ).!#!"-

+

+).1!*")#+

!.+*)*-1

*1

1*.!*")*"!

"

1#.+)1!++

#

1-"-""."#

!+")."*

-;"-- +!.!-1 .!1#!!#!

+.-)#)+!

#

+!.+-)-+

#+

)1.!-**

*

).#)")"1-"-*#.-)

"!+"-*.#)*

-;"- !.!-1 ".)*)!)" +*.***!)1#

!.-**+)

+.*#!1)"

+".1)-+1!#

"

1-"-#!.**

!+*".*11

-;"+- *!.!-1 1.+#1!1-

!

!1.#!))**

#

*+.*!1)

1"

!.!#-+

"

.)*+#!)1-"-.-)

*!+*#+.##)

-;"- 1-!.!-

1

1!.111"+* !+.1*1-

1-+.*))

!)

-.)*1*"**

+

*!.-!)

#

1-"-!*.1*

)!+*!.)*"

-;"*- 1!.!-

1

1#."##+!)

!

!#.+*")1

1).+!)*

!)

.)1"+#

1

1-+.-"*"11

+

1-"-!.-

)!+*)#.)1

(RC -;""1.)

"#

1).*"

*

1".-"! !".11!+#*

1)+.+1+

1

*."-#!-"!

+

11!.-++!

#

1-"-+".!

#!+*.-!1

A9imuth of >orward 3angent: )".!-1##*; )".1*! ?$%.$2!#$$%!

&./ Curve $#.#-"+ 2--.---+ -21.&!"# )d/

And 8nally, our last cur(e, which starts at the third 7oint of

e(ersed Cur(ature, and is therefore sol(ed by subtracting the

deection angles from the 0re(ious a9imuths5 but other

factors are sol(ed in the same way as the other cur(es.



17/20


CR= $

*TA

Arc

Lengt

h

De>ection

Angle )d/Azi+uth

Chord


(RC -;""1.)

"#

#*.#+##

*+

1-"-+".!

#

!+*.-

!11;--- *.-) 1.)*+

#

##.+")"!

)#

*.-"1)

1

1.*""1#*

*.)"*1)!+#

!

1-"-+#.#"

+

!+*1#.*-

#

1;-- *.-) +.-"#-!)

-#

#+.#1

!)

*.!#*+#"+

+

#.!#!"-!#

#.!!-)1

)

1-"-+.-*

1

!+#"*.+

"1

1;-+- +*.-) ."1*)-1

+#

#1.#*+#

"

+*.+*))"

"

1!.1#*""

+.-+#*"1

+

1-"-)+.+*

+

!+#*-.1!

#

1;-- *.-) ".*-)"

*#

*.*"*-#)

*!

*.*1"

*

+.!##"#!*

).**")*

1-"-!.-#"

!+#.!1

( 1;-*.-

-

#.-! 1-."#* #.#!1*##

*+

#.1)#1*!

*

*.*")-*

#-.+*""+*

#

1-"--.*)!+#!!.#)

1

A9imuth of >orward 3angent: #*.#+##*+ F 1."+! ? "#.$$&-$$%!

Coordinates At - Geter >ull Stationing And At S0ecial 7oints

*TA Northing asting

'( -;--- 1-"#*!.++ !+#*."#

-;-- 1-"##+.#*# !+*-)."-"



18/20


-;-+- 1-"#+.1! !+*-.*+)#

-;-- 1-"#!).!1) !+*)#.#*-

-;-*- 1-"#+.*## !+*!+.#1#+

-;1-- 1-"#).+ !+*#1.!+)

-;1- 1-"#1.-) !+***.!"11 -;1+- 1-"#1-." !+"-!.!*

-;1- 1-"#--.)" !+".++"

-;1*- 1-"*"." !+")".+-1#

-;-- 1-"#".-!! !+"!.))*

-;- 1-"*.+1* !+"#).#!+

-;+- 1-"!#.#* !+""-.1)

(C1 -;!!.

"

1-"+".+" !+)--).1

-;- 1-"+#.-" !+)--#.-#) -;*- 1-")).!11 !+)-1.#+1!

-;)-- 1-"1.#*) !+)-).-"!

-;)- 1-"!"#.**# !+)-)".--1

-;)+- 1-"!##.""# !+)-+-.!1"

-;)- 1-"!!*.)+" !+)-)#.-"1

-;)*- 1-"!+-.1# !+)-*.*!+

(RC1 -;)*#.1

)*

1-"!)+.!1 !+)-+.*#!1

-;+-- 1-"!).#+ !+)-1#.!-+ -;+- 1-"!-.))) !+)--#.1)*

-;++- 1-"+**.-! !+""".+"!!

-;+- 1-"+".-1 !+"")."11



19/20


-;+*- 1-"++".!1 !+"*".-!

-;!-- 1-"+".! !+"*.*)

(CC1 -;!-*.#

)#

1-"+-."1 !+"*.!+))

-;!- 1-"+-".! !+"*.*)1#

-;!+- 1-")*".*# !+"*".!+

-;!- 1-")#-.! !+""!.-*)

-;!*- 1-")!.)"" !+)--).1#1

-;-- 1-"))!.+* !+)-1).#"""

(RC2 -;1-.)

1

1-")#.)** !+)--.1**"

-;- 1-")1".+# !+)-.--+!

-;+- 1-")-1.# !+)-)+.*)*+

-;- 1-"*.+# !+)-)*."##

-;*- 1-".)1 !+)-)*.1!-+

-;#-- 1-"+).-* !+)-).+

C* -;#-).)

)

1-"+-.1*" !+)-)1.-1)

-;#- 1-"!.!) !+)-).-#+1

*T -;#)).)

)

1-"1!.1* !+)-1+.!+"

-;#+- 1-"-".*!! !+)-1-.!1+

-;#- 1-"1").*#* !+""*.+*)"

-;#*- 1-"1##." !+"*.+!)#

-;*-- 1-"11.") !+"#+.+)

-;*- 1-"1+!."+ !+".)")+

-;*+- 1-"1"."* !+"!-.))



20/20


(C2 -;*+1.

1

1-"1*."1 !+"+".-+#

(CC2 -;*!+.+

""

1-"11*.!! !+"+1.+11!

-;*- 1-"11+.)" !+")#.*!+

-;**- 1-"-""."# !+")."* -;"-- 1-"-*#.-)" !+"-*.#)*

-;"- 1-"-#!.** !+*".*11

-;"+- 1-"-.-)* !+*#+.##)

-;"- 1-"-!*.1*) !+*!.)*"

-;"*- 1-"-!.-) !+*)#.)1

(RC -;""1.)

"#

1-"-+".!# !+*.-!1

1;--- 1-"-+#.#"+ !+*1#.*-#

1;-- 1-"-+.-*1 !+#"*.+"1

1;-+- 1-"-)+.+*+ !+#*-.1!#

1;-- 1-"-!.-#" !+#.!1

( 1;-*.-

-

1-"--.*) !+#!!.#)1


117 labex4 report data and computation

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