EEEEEEEEEEEEEE

THRZSURVEYING PAC

The program material contained herein is supplied without

representation or warranty of any kind. Hewlett-Packard

Company therefore assumes no responsibility and shall have

no liability, consequential or otherwise, of any kind arising

from the use of this program material or any part thereof.

INTRODUCTION

The programs contained in this booklet are a brief

representation of the many problems which may

be solved on the HP-35 Pocket Calculator. The

intention is to provide routines for the more

widely encountered areas of surveying--traverses,

intersects, curves, areas, and triangles.

We hope that you find this booklet useful in your

day-to-day calculations.

Civil Engineering Products

Note: is used to denote the key

throughout the tables in this text.

TABLE OF CONTENTS

DEGREE CONVERSIONS

Degrees, Minutes, Seconds to DecimalEquivalent (Includes note on bearing toazimuth conversion) ............... 4

Decimal Degrees to Degrees, Minutes,Seconds ................... ... 5

TRAVERSES

Field Angle Traverse ............... 6

Bearing Traverse . .. ............... 12

Inverse - Distance and Bearing FromCoordinates . . ................... 14

Area of a Traverse From Coordinates . ... 16

Slope Distance Reduction ........... 19

INTERSECTS

Distance - Distance Intersect . .. ....... 23

Angle - Angle Intersect . ............ 27

TRIANGLES

Triangle Solution - Given Three Sides . ... 30

Triangle Solution - Given Two Anglesand Included Side . . .. ............. 32

Triangle Solution - Given Two Sides andAngle Opposite One of Them ......... 34

Area of a Triangle - Given Three Sides ... 36

2

CURVES

Curve Solution - Given Central Angleand Tangent Distance .............. 38

Curve Solution - Given Central AngleandRadius ..................... 40

Curve Area - Given Central AngleandRadius ..................... 42

Curve Layout - Deflection AnglesFromTangent ................... 44

Elevations Along a Vertical Curve . ... .. 46

DEGREES,MINUTES,SECONDSTODECIMALEQUIVALENT

LINE

DATA

OPERATIONS

DISPLAY

REMARKS

1.Lello][stof

[|

2.De

gree

se[

JCJC]

3.

|

Minutes

vt

JLJL

_JL

]a.

|

Seco

nds

Reu[

=J[

+]

J[|

5.IRCL]

l+

][

+I

I]

I]

Deci

mal

Degr

ees

Record

-SeeNote

1

Note

1:To

convertbearingto

azimuth:

Ifbearing

isSE

orNW,

pressE

.Then

ifbearing

isSE

orSW,pressm

s180,'.

Then

ifbearing

isNW,pressm,

360,H

DECIMALDEGREESTODEGREES,MINUTES,SECONDS

LINE

DATA

OPERATIONS

DISPLAY

REMARKS

1.DecimalDegrees

|ENT|

|I

|I[_]u

2.IntegerDegreesB

[:],:l[:

I:]

Degrees

Record

3.[(JCeoI]

4,IntegerMinutes

||

Il

||

I|

|I

Minutes

Record

5.I—][G”O”XH

lSe

cond

sRe

cord

FIELDANGLETRAVERSE

Azimuthof

Trav

erse

Leg=Refe

renc

eBearing+

Fiel

dAngle

Hori

zont

alDistance

=Slopedistance

sin(Z

enit

h)

N_=N,

+Ho

rizo

ntal

Distance

cos(Azimuthof

Trav

erse

Leg)

no}

E,,=E,

+Ho

rizo

ntal

Distance

sin(A

zimu

thof

Trav

erse

Leg)

Example:

6

1Fiel

dData

Refe

renc

eBearing

1>6:

N17°2345”W

Starting

Coordinates:

N,

=10,000.000,E,

=10,000.000

Point

—_— NN <t n \O —

FieldAn

gle

87°2217

38°06

’54”

92°

13’06

”

133°

12’46”

137°

46

30”

53°1647

7

ComputedData

Point

— N on <

N

10,000

.000

10,2

55.2

51

10,0

96.8

59

10,8

97.362

Right

Deflection

Right

Righ

tDeflectionLeft

Left

Right

E

10,0

00.0

00

10,700.367

11,185.240

11,4

81.4

96

Zeni

thAngle

88°07’18”

89°54’07

”

91°1331”

Horizontal

90°48’57”

89°41’55”

Point

N

SlopeDi

stan

ce

745.832

510.089

853.760

1053916

789.671

784.406

E

5 6 1

10,487.192

10,748.438

9,999.933

10,510.672

9,765.552

10,000.107

FIELDANGLETRAVERSE

(Continued)

ComputedAzimuth6>1:

162°36’03”

..AngularClosure=12”

Posi

tion

Clos

ure(BeforeAdjustmentof

Angl

es):

LengthofTr

aver

se=4738

Corry=+0.067

, Corrg=

—0.107

Prec

isio

nRa

tio=

1/37,600

(Cor

ry)?

+(C

orrg

)2=0.126

LINE

DATA

OPERATIONS

DISPLAY

REMARKS

g:;(

:ir:

v;gegreesm

[:][:lI:[:

Minutes

I—EN—Tl'_|

[_—]l——]m

seors

(e8] (

8][0] (=[

] Ce

LoLI

L1|

Seama™

|

seeNote

[sTo

]I

I|

Retm

amno

Fiel

dAngle

Degr

ees

vt

IJL

JL_|

Minutes

vt

JLJC

J[|

Seconds

IENT”5|[0H+”+]

LeJloJl=][+][

|Decimal

Field

Angle

SeeNote2

[re[+

JC

JCI

SeeNote3

stolt

J[_

J[_J

{]

DecimalAzimuth

ofTraverse

Leg

SeeNote4

Zenith

(Ver

t)AngleDegrees

[0O

|I|

13.

Minutes

vt1JCJC]

14.

Seconds BT

[eoI=]]

15. CeI1]

DecimalZenith

(Vert.)Angle

SeeNote

5

16.

(sJC

JC]

SlopeDistanceCIJCI

Horizontal

Distance

18. [RcL][enT][cos][xZY][sIN]

19.o]

Latitude

20.

PreviousNorthing L0

JCJCJC

]Current

Nort

hing

|Record

21.

O]JCIC]

Departure

22.

Previous

Easting L

JCJC

JL

]Record

CurrentEasting

SeeNotes6&

7

10

Note

1:

Note

2:

Note

3:

Note

4:

Note

5:

Note

6:

Note

7:

Note

8:

FIELDANGLETRAVERSE

(Continued)

Ifthe

first

fiel

dan

gle

isanan

gle

rightoran

gle

left,the

ref.

bearingdi

rect

ion

isAWAY

fromthe

firs

tpo

int.

If

the

first

fieldangle

isade

flec

tion

rightor

left

,the

ref.

bearingdi

rect

ion

isTOWARDS

thefirstpo

int.

ForSE

orNW

ref.

bear

ing,

depr

ess

[c#s]

.Then

forSE

orSW

ref.

bear

ing,

depress[enter

+],18

0,(+

]orfo

rNW

ref.

bear

-ing,

depress [enter

1],36

0,(+).

SeeNote

8.

Depress

[cns

]fo

ran

gle

left

orde

flec

tion

left.

Idi

spla

yis

greaterthan

360,

depress36

0,[=

].If

display is

less

than

zero,depress36

0,+]

.SeeNo

te8.

Ifa

slope

dist

ance

istobe

entered,

continueon

line

12,

Ifahorizontal

distance

isto

be

entered,enterthe

horizontaldi

stan

ce,skip

to

line

18andcontinue.

Ifve

rtic

alan

gles

areobserved

inst

eadof

zeni

thangles,depress

[cos|

insteadof

[sin

]in

line

16.

Ifthene

xtfi

eldan

gle

isan

angle

rightor

angl

ele

ft,depress[,

then

ifdisplaybecomes1)

grea

terthan

180,

depress

180,E]

;or

2)less

than

180,depress180H

Then

returnto

line

5andcontinue;or

ifthenext

field

angle

isade

flec

tion

rightor

left,returnto

line

6and

continue.

Afterthe

last

coordinatesar

ecomputed,

acheckon

theangularclosurecanbemade

asfollows:

Depressfl

and

convertthedisplayeddecimal

angl

etode

gree

s,minutesandseconds.

Thiscomputed

clos

ingazimuthcan

thenbechecked

againsttheac

tual

clos

ingazimuth.

Ifasurveyor

does

not

feel

uncomfortable

with

azimuths

greaterthan360°

orwith

nega

tive

azimuths,

the

statements

about

adding

(or

subt

ract

ing)

360

innotes

(1)and

(3)

can

be

igno

red.

These

operationwere

empc!oyed

sole

lytokeep

theazimuth

valu

esin

the

rangemost

usedby

the

surveyor,

i.e.,

inthe

range

0"to

360

.These

““corrections’’ar

enot

really

necessarywhen

usin

gtheModel

35.

SALON

11

12

BEARINGTRAVERSE

N,+1=N,

+Di

stance

cos(Bearing)

E,+q

=E,+Di

stan

cesin(B

eari

ng)

10710.491

10721.159

Example:

10333.208

11620.338

10,000.000

E_,=10,000.000

I

2

/9,500.001

10,0

00.0

00

9136.365

11278.203

LINE

DATA

OPERATIONS

DISPLAY

REMARKS

Beginning

North

(Ng)

[stol

[J[

JC_J[C_]

Beginning

East

(E,)

vtJC

JCI

BearingDegreesvyJC

JC]

Minutes

[EnT|[

6J{

oJ[

+|[

+|

Seconds

[ent](3

](6][

0][

0

LJ0

JCJ0

]Decimal

Bearing

SeeNote

1

[eEnT][sIN][x

2Y][

cos]

[]

Distance ]

[Fe]

(-17o)[

New

Northing

Record

Distance Lx

L+

J0CJC

JC|

New

Easting

Record LL

JCJC

JC]

GoTo

Line

3ForNext

Leg

Note

1:If

bearing

isSE

orNW,

pres

s[c

s].Then

ifbe

arin

gisSE

orSW

,press

[ent

er+]

180

,(+]

).Thenproceed

tone

xtline.

INVERSE

-DISTANCEANDBEARINGFROMCOORDINATES

E,-E

Bearing

=tan~

—2—

arin

gta

n<-

1)

Distance

=\/(E2-E;)?+(N,-N;)?

P =Example:

N,=10,000

E,;=10,000

N,

9,000

E,=10,500

Distance=1118.034

Bearing=S

26°

33’54”E

(N,.E,)

15

LINE

DATA

OPERATIONS

DISPLAY

REMARKS

Easting, et

JCJL

1L|

East

ing, [=

|[enT]

[enT

][x][sTO]

Northing, vt

JCJL

JL|

Northing, L=

|[en

T][ent][

x|[RcL]

L+v

1LL]

Distance

Record

LR|+

||aRc](tan][

|Decimal

Bearing

SeeNote

1

et

JCJC

1L]

IntegerDegrees L

JCJC10

BearingDegrees

Record

L=J0lse][

o]lsto][x|

Inte

gerMinutes LI

JCJC

10]

BearingMinutes

Record

1. (=]e

[xJC_1]

BearingSeconds

Record 12

.

LJCJCJC

JC]

R

eturntoLine

1

bear

ing

isnegative,pr

essE

befo

repr

ocee

ding

tone

xtline.

Note

1:If

decimal

bearing

ispositive,

bearing

isNE

orSW.

Ifdecimal

bearing

isne

gati

ve,bearing

isSE

orNW.

If

16

AREAOFATRAVERSEFROMCOORDINATES

1A==

|E1(N

2-N,

)H{

Ep(N

3-Np

)+Eg(N

g=Ny

)+

..+By(N,=N

y)|+

Eo(N

y=N

,)

Example:

EN

100.

29491.72

447.68

823.14

774.43

648.

49

753.

4831

8.75

61091

72.23

229.34

223.

35

100.

29491.72

— AN N <t n O — Area=328.277.19

17

LINE

DATA

OPERATIONS

DISPLAY

REMARKS

[eer]C

JCJCI

Star

ting

Easting

[ENTJ

L]

[]

[]

[]

Star

ting

Northing

[ENTJ

[]

[]

[][

j

Next

Easting

[enT

][R!

|[

x|[RcL][x2ZY] L=Jisro]_JL_JL_J

Next

Nort

hing

[ENT|[

R}| [

X|[

ReL]

[+

]

7. [s

To][

RiJ(

x2v]

[][

]SeeNote

1

8. (R

EL|[

ENT|

[2

|[=

|[][

Area

SeeNote2/Record Note

1:Return

toli

ne4

until

starting

coordinateshavebeen

re-e

nter

ed,thenproceedthrough

toline

8to

obtain

area

.

Note

2:Negativeva

lues

may

resu

lt.

Absolutevalue

isrecorded.

18

SLOPEDISTANCEREDUCTION

S=I

§Ht.

ofD.

M.)—(Ht.

ofTh

eo.)

-(Ht.

ofD.

M.target)+(Ht.

ofTheo.

targ

et)]

k=S

-sin(Z

enit

h)p=S

-cos(Z

enit

h)

Horizontal

Distance

=(

(Slope

dist

ance

)?-k2+p)

(sin

(Zen

ith)

)

19

Example:

Ht.ofDM.=5.87

Zeni

thAngle=93°

13’00”

Ht.of

Theo.=5.12

Slop

eDi

stan

ce=487.132

Ht.ofDM.

Tgt.=491

Horizontal

Dist

ance

=486.307

Ht.of

Theo.Tgt.

=5.17

HORIZONTALDISTANCE—————————

ZENITH

ANG.I:E

l‘fi

HTOFDM

T

HTOFTHEO

HTOFTHEOTGT

] HTOFDMTGT

{

20

SLOPEDISTANCEREDUCTION

(Continued)

LINE

DATA

OPERATIONS

DISPLAY

REMARKS

LeLo

]lsTo][

||

ZenithDegrees Nt[

J[]

J

Minutes vt

J[JLJ{

]

Seconds [Rec

][=J[

+J(ReL][

=|

L+J[

enT]

[enT

][]|

]

Ht.D.M. vt

JLJL

]I]

Ht.Theo. =]

_JC_JL

i|

Ht.D.M.

Tqgt.

Ht.Theo.

Tgt.

L+|lsTo][Ri][

]|

lcos

|[r

eL]

[x

|[]|

] JSeeNote1/Record

11.

m@]m

[ED

kSeeNote1/Record

12.

13.

SlopeDistance

LEN_T]u__l

L___lL:_’L_]

14.

ke]v

] 15

.

P[

+J[RCL][X

][

”]

Hori

zont

alDi

st.

Reco

rd

Note

1:Valuesof

pand

kmay

be

nega

tive

.Be

sure

tore

tain

sign

when

reen

teri

ngat

line

s14and

15.

21

Submitted

by:

RobertT.

Elli

otOhio

Dept.of

Highways

P.O.

Box272

Lebanon,Ohio45036

SHLON

22

23

Example:

N,=1000

E,=1000

N,=1250

E,

2000

N,

1614.409

E;

1657.649

N,

767.353

E,=

1869

.411

DISTANCE

-DISTANCEINTERSECT

B=500

A=900

$=29.017°

Azimuth,

5,=75°

57"50”

Distance,5,=1030.776

_;(Distance,

;)2

+A2

-B2?

2(A)(Distance,)

N=N,+Acos(Az*¢)

E=E,+Asin(Az*¢)

¢=cos

24

DISTANCE

-DISTANCEINTERSECT

(Continued)

LINE

DATA

OPERATIONS

DISPLAY

REMARKS

Entj

(JC_JLL]

e1]

vt

[JL

J(]

L=Jl

ent]

[x

J[+

][sT0]

:2

(Distance,)

e1

JCI

DistanceB

vt=1JC]

DistanceA

[ENT

][EN

T][R

IJ[

XJ[

+]

[xz](=

][ar

c)[co

s][s7

o] 10

. A

zimuth1>2

Degrees

vlJLL

25

1. ExCJC

(]

12.

Seconds

[ENT|[

6|[

o|[

=||

+|

13. I__s_]LO_JLH_"‘

HRCLI

@SeeNote

1

14. L+

J[E

nT][

sin]

[x2v

][co

s]

DistanceA

[STOJ

[X

J[

][

][

]

NL]~

[Reu][x2v](R[x][

]

E,L+

JLI

JL1]&

Reco

rd Note

1:If

solu

tion

desi

red

isto

left

ofline1>

2,pressE

beforeproceedingto

line

14.

SALON

26

27

ANGLE

-ANGLEINTERSECT

Example:

A=

76°30°

00"

Ng=3200.000

¢B=

38°2

0°00

”Eg

4200

.000

N,=5

200.

000

6143.552

E,=61

00.0

0044

67.7

74

oO oZ /|

—E5

-Eg+Ng

cotA

+N,

cotB

cotA+cotB NB-NA

+E,3COtA+EA

cotB

cotA+cotB

28

ANGLE

-ANGLEINTERSECT(Continued)

LINE

DATA

OPERATIONS

DISPLAY

REMARKS

Le

Lo

Jsto][

]|

AngleB

Degrees

Minutes En

tjJL

1[I

Seconds

Jvl

JC10

JC| | |

Recf

[+J{

+][

]I

[Reu][

J[+J[van][1/x]

AngleA

Degrees et

JCJL

JC]

Minutes (Rev)(

=J[+

][][]

Seconds [re

d](=

)[re

d)L2=]

[tan][1/x][sTO][RY|[

|

10.

[EnT](ent]

{J[

[|

29

Lt

JCJC

10]

L-Jlred)lJLJL]

LIII]

[+][

x2v]

[enT

][EnT][R

eL]

[+

]bey][]]

Record

[r](]

[ene]

[enr)[

evil

J[_J

CJ[

]

18. Lx

Ji-JLJL]

19.

(I0]

20. 21

.

Fed1]

R

ecord

30

Example:

A:

B=

TRIANGLESOLUTION

-GIVENTHREE

SIDES

2489.621

a=

48°0

0°00

”

2543

.150

b=

49°2313”

3322

.312

c=

82°36°47”

R2TAN(5

(S

-A)(S

-B)

(S8-

C)

S

%(A+B+C)

31

LINE

DATA

OPERATIONS

DISPLAY

REMARKS

Side

A Entj

{ent

]{ JL

JL|

SideB [en

t)(RI

I

SideC (stof[

+J[

2J[

=|[r

e]

N |m |«

[x2v][sTo][x2v][

-|[eNT]

o

LRJ[

RYJ[

ReL|

[x2Y

][—

|

(x2v

][red]kv(=

](] Lx

[x

J[ret][

+J[

vx] x2v|[=

|[ar

c][T

aN][

2|

L

JCJL

JL_J

C|

DecimalAngle¢

See

Note

1

Inte

ger

Degrees

Degrees

Record

11. L-JLe

J[o]

J[x]

|

12.

IntegerMinutes LI

JCJC

JCJ | |

LJL

JLJL

iMinutes

Record

13.

L-JLe]Jlo]J{x][

]| Seconds

Record Note

1:Anglebmay

beobtainedby

reve

rsin

gthedataen

trie

sat

line

s2and

3.

32

TRIANGLESOLUTION

-GIVENTWOANGLESANDINCLUDEDSIDE

Example:

A=

2489.621

a=

48°0

0’00”

B=

2543

.150

b=49°23

13"

C=

3322

.312

c=

82°3647

"

Bsina

sinb

Bsin

¢

sinb

(LAWOFSINES)

A=

C=

33

LINE

DATA

OPERATIONS

DISPLAY

REMARKS

lcer

][6

|[o

J[sT

o][

|

Angle

aDegreesv

JCJC]

Minutesv

JCJC]

Seconds [Red)[

=J[

+][

][]

[red(=)[+JC_JC]

Angle

cDegrees]

JC]

Minutes

Fed(LI

Seconds [Re

d][

[re)(=

][+

[Ent)

(aL][+(5][

10.

Side

Bv

[+

x2v]

[siv

](x2

¥]

11.

EnT)(R[]JC]

SideA

(Reds][xJ

CI]

SideC

34

Example:

A=

6.00

a=

B=

10.7

0b=

C=1182

c=

AcuteAngl

eb

TRIANGLESOLUTION

GIVENTWOSIDES&ANGLEOPPOSITEONEOFTHEM

30°23°17”

64°26

’117

85°

10’32” b=sin~!

<

C C=

A=

6.00

a=

30°23°17”

B=

10.7

0b=

115°3349”

C=

6.64

c=

34°02’54”

Bsin

a

A

ObtuseAngleb

180-

(a+b)

Asin

¢ sin

a

(LAW

OFSI

NES)

35

LINE

DATA

OPERATIONS

DISPLAY

REMARKS

[eer)e

Lovl]

Angle

aDegrees vt

JLJL(|

Minutes Red{

+JL

+JL

JL]

Seconds [Rec]

[+

J{re

r][

=J[

+|

[sTo][siv]]

][]

Side

B [E

NT][R[

xJ[x2Y][

+|

SideA (=

[en1

)(AR(v[

AnglebDecimal

SeeNote1/Record

e[+1L

JC_J

C]

Angleb+

aDecimal

SeeNote

2

L1L8

J[ofxav[

-]Angle

¢Decimal

Record

10.

(5]Y]1

] Si

deC

Record Note

1:

Note

2:

To

solv

eth

eproblemwhere

angleb

isobtuse,

press:

180,n

,[3

beforeproceedingto

line

8.

Sinceth

esum

ofangles

ofatr

iang

lemustbe

1800,thesum

ofan

gles

band

acannotbegr

eate

rthan

180.

Ifthe

displayexceeds180°

there

isonlyone

solu

tion

,withan

glebac

ute.

36

AREAOFATRIANGLE

-GIVENTHREESIDES

Example:

Area

=VS(S-A)(S

-B)(S

-C)

WhereS=%(A+B+0)

A,

B,C=LengthsofIn

divi

dual

Side

s

A=2489.621

B=2543.150

C=3322.312

Area=3139465.857

37

LINE

DATA

OPERATIONS

DISPLAY

REMARKS

SideA En

tjJL

JCJ[_]

SideB vty

JL_JL(]

Side

C [sTo

][x2V|

[enT

]|RV

][+

|

[x2v

][en

t][R

e][

+J[

2|

[+

[rer][x2v][

sTo]

[x2¥

]

=]

[rer

][x

][re

r][x

2¥]

(]2v

](=]b2

[Ret

]

xeY)[][

VX

Area

Record

38

CURVESOLUTION

-GIVENCENTRALANGLEANDTANGENTDISTANCE

Example:

R=Tangent/tan

(A/2)

Chord=2R

sin(A/2)

PC

ArcLength=RA

n/180

ARCLFNGTH

CHORD

“72'636)

PT

(22.

7532

°)|

1/zA""]

CENTRALANGLE

A(4

5°30

’23")

RADIUS

(223.181)

39

LINE

DATA

OPERATIONS

DISPLAY

REMARKS

(e

J[o)

sTolJ]

ADegrees

eyJCJC

0]

Minutesv

JCJC0]

Seconds [Rev

][=

J[+

J[Ret][

=]

Iz

=]sm

l]

Decimal

%2A

Tangent

Distance [En

t)[re

e][ra

n][)]

Radius

Record

[enT][

EnT]

[Re]

[sin

]X

]I

00]

Chord

Record

(R

(red(xI

O]

J[e][

]Record

40

CURVESOLUTION

-GIVENCENTRALANGLE&RADIUS

Example:

Chord=2R

sin(A/2)

Tang

ent=R

tan(A

/2)

PC

ArcLength=RA/180

ARCLFNGTH

CHORD

{172.636)

(22.7532°)

l%A“.‘

CENTRALANGLE

(45°

30

23")

RADIUS

(223.181)

41

LINE

DATA

OPERATIONS

DISPLAY

REMARKS

ADegrees v

JCI

Minutes entf

[JL

JL][

]

Seconds

lENT][

6|[

oJ[sTo][

|

L+][

+J{

red)

[=

J[+

|

L2(=]

JCJL

]Decimal%A

[enT](e

nt](T

an][

][]

Radius st

oliJ[_J[_J[

|TangentDistance

Record

[RI]

[siN

][re

L]|

x|[

2]

LJ

JCJE

JC|

Chord

Record

LR

[Rec

][x[

=][x|

LoJo

=11]

ArcLength

Record

42

Example:

V.

CURVEAREA

-GIVENCENTRALANGLE&RADIUS

360°

2AREA

o~

(396

7.42

0)

/s—sanh

SegmentArea

=1R2<A

>1

R2

sin(A°)

SECTORAREA

38943.236

CENTRALANGLE

A

(45°

30’30”)

RADIUS

I(313.146)

Se

ctor

Area=R2

A_

360

43

LINE

DATA

OPERATIONS

DISPLAY

REMARKS

Le(o

]fstof{f

J[]

ADegreesvJCL]

Minutes

vyJC0]

Seconds [Red][+

J[+

J[ReL][

=|

()(vlv

(]]

L3](se

J{oJl=][

|

Radius [EnT][

x][

enT]

[RI

][x

]

SectorArea

(xav][

sin]

przv](eX

IR[]

SegmentArea

44

CURVELAYOUT

-DEFLECTIONANGLESFROMTANGENT

Deflection/ft=180/(2mR)

Deflection

Angle=ArcX

Deflection/ft.

/o

.ST

ATIO

NLongChord

=2Radius

Sin

(Def

lect

ionAn

gle)

Example:

Radi

us=90

0.00

Ft.

Arc

Long

Station

Length

Deflection

Chord

12+

57.0

0(P

oint

ofCu

rvat

ure,

P.C.

)

12+

75.0

018.00

00°3

4'23

" 1

8.00

12+88.50

31.5

001°00'10"

31.

5013+

00.0

043

.00

01°22'07"

43.00

13+2

5.00

68.0

002°09'52"

67.98

13+

50.0

093.00

02°5

7'37

"9296

ArcLength=

Differ

ence

inSt

atio

ns

QHOHI ONO1

45

LINE

DATA

OPERATIONS

DISPLAY

REMARKS

1.

Radius

[enT|[

2][

x|[enT][ENT]

2

L1][

8[

o][e

nt]{

7|

3.=]2y=]

[so](]

4.ledf

JLJL

I]

hDeci

5Fr

omPo

.CxICJC1]

defiec

tion

6.[E

nT]l

ent|

[J[J[

|

Deflection

7.|

Dogres

sCICJCJC

]oo

Record

8.

L=JLeJ[o][x]

Deflection

Minu

tes

Record

0.Meger,

CI

JC10l

Deflection

Seconds

10.L-Jle]lo][x]]

Record

mm el

1.(reLTI

12,

(sin]|

x|[

||

1||

LongChord

SeeNote

1

13.

|CLX|

I|

|I

II

|I

ReturntoLine4

Note

1:Computation

ofthe

longchordcan

beomitted

ifregular

intervalsar

eusedfo

rwhichthesh

ortchord

remains

cons

tant

.Calculationthenonlyneededfo

rodd

inte

rval

s.

46

ELEVATIONSALONGAVERTICALCURVE

50(G

,-G,

)L

Example:

STATION

Begi

nnin

gGrade(G,)=

-1.065%

17+00.00

Endi

ngGr

ade(G

,)=+1.600%

18+00

.00

Elev

atio

nat

Begi

nnin

g(E

;)=

614.00

Ft.

19+00.00

Length

ofCurve(L)=

340

Ft.

28t00-08

Stat

ioni

ngIntervals=

100

Ft.

20+40.0

E,=E,

+G,

(Dis

tanc

ein

Stations)+

(Dis

tanc

ein

Stat

ions

)?2

ELEVATION

(Eg)

614.000

613.327

613.438

614.332

614910

Es

—X

(INSTATIONS)

1

REFERENCELEVEL

47

LINE

DATA

OPERATIONS

DISPLAY

REMARKS

G, e~

JLJL_JL

]Grades

in%

G, (=

J(s

J{o

][x]

[|

Length

ofCurve

(L)

LeJisollJLJL|

Beginning

Elevation(EO)v

JCI]

Distance

inSt

atio

ns(£

(o)(

)(]

(X

eLI

G,LI]

Elevation

(ES)

Record

]JCICI]

R

eturn

tostep

5

SHLON

48

5952-2401

-

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