ROUTE SURVEYING
SIMPLE CURVE COMPOUND CURVE
Radius: R1=radius of first curve PC(E)
1145.916 R1=radius of second curve PT(E)
𝑅=
𝐷
CT=common tangent
Length of Curve:
I=angle of intersection/central angle of PCE and
𝜋𝑅𝐼 PTE
𝐿=
180
𝐶𝑇 = 𝑇1 + 𝑇2
Tangent distance:
𝐼 = 𝐼1 + 𝐼2
𝐼
𝑇 = 𝑅 tan
2 Length of the chord:
External Distance:
I1 /2 C I2/2
𝐼
𝐸 = 𝑅 [sec − 1] C1 C2
2
Middle distance: PC L PT
𝐼 Use cosine law to solve L
𝑀 = 𝑅 [1 − cos ]
2 𝐿2 = 𝐶12 + 𝐶22 − 𝐶1 𝐶2 𝐶𝑜𝑠 (𝐶°)
Chord distance:
𝐼
𝐶 = 2𝑅𝑠𝑖𝑛 Angle of the first tangent:
2
𝐶2 𝐿
Stationing distance: =
sin 𝜃1 sin 𝐶°
𝑆 = 𝑅𝜃𝑝𝑜𝑖𝑛𝑡 (length of curve)
Angle of the second tangent:
Station of point = 𝑃𝐶 + 𝑆
𝜃2 = 180° − 𝐶° − 𝜃1
𝐶1 𝐿
=
sin 𝜃2 sin 𝐶°
Offset Distance (y):
𝑦 𝑦
𝑡𝑎𝑛 𝜃 = 𝑜𝑟 tan 𝜃 =
𝐵𝑇 𝐹𝑇
𝑅−𝑦
cos 2𝜃 =
𝑅
ROUTE SURVEYING
REVERSE CURVE SPIRAL CURVE
Equal Radii: Considering at any point:
𝑞𝑢𝑎𝑟𝑡𝑒𝑟𝑠
𝐿= (𝐿𝑐 )
4
Spiral angle:
𝐿2 180
𝑠= [ ]
2𝑅𝑐 𝐿𝑐 𝜋
Offset Distance from the tangent at SC:
𝐿3
𝑥=
Let y =parallel tangent 6𝑅𝑐 𝐿𝑐
C=chord length PC to PT Distance along tangent at any point:
Solve I: 𝐿5
𝑦=𝐿−
40𝑅𝑐2 𝐿2𝑐
𝐼 𝑦
sin = Deflection angle:
2 𝐶
𝑠
𝑖=
Radius of reverse curve: 3
𝐶 𝐼
= 2𝑅𝑠𝑖𝑛
2 2
Considering without any point:
Length of tangent in common direction at
Spiral angle:
station PC:
𝐿𝑐 180
𝐼 𝑠𝑐 = [ ]
𝑇 = 2𝑅𝑠𝑖𝑛 2𝑅𝑐 𝜋
2 𝐷𝐶 𝐿𝑐
𝑠𝑐 =
40
Length of tangent in station PRC: Offset Distance from the tangent at SC:
𝐼
𝑇 = 𝑅𝑠𝑖𝑛 𝐿2𝑐
2 𝑥𝑐 =
6𝑅𝑐
Distance along tangent at any point:
𝐿3𝑐
𝑦𝑐 = 𝐿𝑐 −
40𝑅𝑐2
Deflection angle:
𝑠𝑐
𝑖=
3
Length of thrown:
𝑥𝑐
𝑃=
4
ROUTE SURVEYING
Tangent distance for spiral: 𝐿(𝑔1 )
𝑆1 =
𝑔1 − 𝑔2
𝐿𝑐 𝐼
𝑇𝑠 = + [𝑅𝑐 + 𝑃] tan
2 2 𝑦 𝐻
2 =
External Distance for spiral: 𝑆1 𝐿 2
(2)
𝐼
𝐸𝑠 = [𝑅𝑐 + 𝑃] sec − 𝑅𝐶
2
Super elevation when K=velocity in kph: UNSYMMETRICAL PARABOLIC CURVE
𝐿2 (𝑔1 − 𝑔2 )
0.0079(𝐾)2 𝐻=
𝑒= 2(𝐿)
𝑅𝑐
𝐾2 𝐿21 (𝑔1 ) 𝐿1 𝑔1
𝑅= 𝑆1 = , 𝑤ℎ𝑒𝑛 <𝐻
127(𝑒 + 𝑓) 2𝐻 2
Length of spiral: 2𝐻𝐿2
𝐿1 =
𝐿2 (𝑔1 − 𝑔2 ) − 2𝐻
0.036𝐾 3
𝐿𝑐 = 𝑦1 𝐻
𝑅
2 =
𝑆1 𝐿 2
Square of the length T.S ( 21 )
𝑖 𝐿2 𝑦1 𝐻
= 2 2 =
𝑖𝑐 𝐿𝑐 𝑆2 𝐿 2
( 22 )
𝐷 𝐿
=
𝐷𝑐 𝐿𝑐
PARABOLIC CURVE
Change of grade:
g1= when negative
g2= when positive
𝑔2 − 𝑔1
𝑟=
𝑛
Length of curve:
𝐿 = 𝑛(20)
𝐿 = 𝐾(𝑔2 − 𝑔1 )
K=length of curve per 1 degree
Length of the highest point:
𝐿
𝐻 = [𝑔2 − 𝑔1 ]
8
