12-12-22-Compound curves.pdf

Survey

1. COMPOUNDCURVE:-
P.C.C.
P.C.
P.T.
P.I.

2. •Inthefigureitis shownthat acompound
curve whichis tangential in three straights
AB, BC and KMat T1,T2 and N respectively.
•The two circular arcs T1N and NT2 having
centres at thepointN,OSandOLbeingin
straightline.Thearchavinga smallerradius
may befirstorsecond.
Let, the tangentsABandBCintersectatthe
pointB,KM andBCatM.

3. Notation:-
Let,Rs= thesmallerradiusOsT1.
RL=thelargerradiusOLT2.
ø=thedeflectionanglebetweenthereartangent
(AB)and forward tangent(BC)
α=thedeflectionanglebetweenthereartangent
(AB)and common tangent(KM) =<BKM.
β=thedeflectionanglebetweentheforward
tangent(BC) andcommontangent
(KM)=<BMK.
Ts= the smaller tangentlength(BT1)
TL= the largertangent length(BT2)
ts= thelengthofthe tangenttothearc(NT1)having
a smallerradius
tL=the lengthof thetangenttothe arc(NT2) having
a largerradius.

4. Elementsof thecompoundcurve:-
Ø=α+β
KN= KT1 =ts=Rstan(α/
2
)
MN = MT2=t
L
=R
L
tan(β/
2
)
Lengthofcommon tangent(KM)=
KM= KN+MN= Rstan(α/
2
)+RLtan(β/
2)
Inthe∆BKM,
Now
………….(A)
…………..(B)

5. Substitutingthe valuesof tsandt
L
in
theequationAandBweget,
Ofthe sevenquantitiesRs,R
L
,Ts,T
L
,Ø,α
andβ,four must be known.Then remaining
threemaybe calculatedfromtheabove
equations,
The followingequationgivestherelationship
betweentheseven elementsinvolvedin
compact form
Ø=α+β

6. Setting out Procedure:-
Thecurvemay besetoutbythemethod ofdeflectionanglesfrom
the two points T1 and N, the first branch from T1 and second from
N.
1.Thefour quantitiesofthecurve beingknown,calculatethe
otherthree.
2.LocateB,T1andT2asalreadyexplained,obtain
thechainageofT1fromtheknownchainageof B.
3.Calculatethelengthofthefirstarcandaddittothechainage
of T1to obtain the chainage of N. Similarly, compute the
lengthof thesecondarcwhichaddedto thechainageof
chainageofN givesthechainageofT2.

7. Procedure:-
4.Calculatethedeflectionanglesforboth thearcs.
5.With thetheodolitesetupoverT1setoutthe
firstbranchalreadyexplaininRankine’s
method.
6.Shift the instrument and set up at N, with the
vernier set to (α/2)behindzeroi.e.(360–α/2),
take a backsightonT1and plungethe telescope
whichisthus directedalongT1Nproduced. ( if
the telescope is now swing through an angle α / 2
the line of sight will be directed along the
common tangent NM andthe vernierwillread
360)

8. 7.Settheverniertothefirstdeflectionangle∆1ascalculated
forthesecondarc.
8.Repeattheprocessuntiltheendofthesecondarcisreached
i.e.T2.Check:-

9. Problem

10. Long chord of First curve

11. Ts = T1B = t1+D1B
?5?
qgl
Δ
6
= ?5?6
qgl5<4?
Δ
ts+tL
Ts =