Horizontal Curves Curve Types Geometric Definition Horizontal Curve Terms & Formulas

Horizontal Curves
Horizontal Curves
Curve Types
Curve Types
Geometric Definition
Horizontal Curve Terms & Formulas
Route Stationing
Curve Layout Methods
Horizontal Curves
Curve Types
Horizontal Curves
Degree of Curve
Horizontal Curves
Horizontal Curve Formulas
Horizontal Curves
Horizontal Curve Formulas
1. R =
5729.58' 1746.379m
=
Da
Da
2. L = 100'
I
I
= 30.480m
Da
Da
3. T = R tan( I / 2)
4. LC = 2 R sin( I / 2)
Horizontal Curves
Horizontal Curve Terms
Horizontal Curves
Horizontal Curve Formulas
5. E = T tan( I / 4)
6. M = E cos( I / 2)
7. PC STATION = PI − T
8. PT STATION = PC + L
Horizontal Curves
Example: Horizontal Circular Curve
Given: PI = 64+32.20
I = 24°20’ (Defl ∠) = 24.3333°
Da = 4°00’ (Selected)
(100’ arc for 4° ∠ Change)
Find: R, L, T, LC, E, M, PC, PT
Route Stationing
From example:
PTOLD = PI + T = 6432.20 + 308.82 = 67+41.02
PTNEW = 67+31.71
DIFF = 9.31’ (shortening of traverse-subtract from
station of next tangent point)
Horizontal Curves
Route Stationing
Preliminary - series of tangents ϖ deflections
@PI’s
Final - series of tangents and curves - total
traverse length shortened due to insertion
of
curves
Horizontal Curves
Curve Layout Methods
Radial - set up at center of curve (arc) &
swing radius through deflection angle
*not possible / practical on large radius
curves
Chord - deflection
Incremental chord (Transit, theodolite,
tape)
Sec24-7; Fig 24-5
Total chord (Total Station) Sec 24-10
Curve Layout Methods
Deflection ∠ to any point on curve
dp
sp
=
Da
I
=
100' L
⇒ dp =
s p Da
100'
=
s p Da
30.480 m
dp = angle subtended by arc from PC to point P
δp = deflection angle from PI to P, instr @ PC
sp = distance along curve in ft
Da = degree of curve
Horizontal Curves
Curve Layout Methods
Horizontal Curves
Curve Layout Methods
From geometry δp = dp /2 (*angle formed by
tangent &chord = ½ angle included by
chord)
s p Da
s p Da
90−δp
δp
∴δ p =
=
200 ' 60.960 m
δp
(c p / 2 ) c p
sin δ p =
=
R
2R
c p = 2 R sin δ p
Curve Layout Mehods
From example:
δ62
δ63
General relation for chords
s p Da
s p Da
δp =
=
c p = 2 R sin δ p
200 ' 60 .960 m
For full station where S = 100’
δ 100 ' =
D
2
c100 ' = 2 R sin(
D
)
2
s62 Da 76.62(4)
=
= 1°31'57"
200
200
c62 = 2 R sin δ 62 = 2(1432 .39 ) sin(1°31'57" ) = 76 .61'
δ 62 =