GEFS (FOUNDAMENTALS OF SURVEYING)
CBLAMSIS UNIVERSITY OF THE CORDILLERAS SIMPLE CURVES
HORIZONTAL CURVES
TOPICS:
1. Steps in determining the best route connecting two termini
2. Horizontal Alignment (simple Curve)
Steps in determining the best route connecting two termini
Reading assignment
Reference: Railroad Curves and Earthworks by Frank Allen (Chapters 1 to 3)
Simple Curves
Simple curve is an arc of a circle use to connect two intersecting tangents in the
horizontal alignment of highways.
Elements of a Simple Curve:
T = Tangential Distance
E = External Distance
M = Middle Ordinate
L = Length of Curve
LC = Length of Long Chord
I = Angle of Intersection (Central Angle)
R = Radius of Curvature
PC = Point of Curvature
PT = Point of Tangency
PI = Point of Intersection (V = Vertex)
D = Degree of Curve
In metric system, the degree of curve, D, is the angle subtended by a 20-
meter arc (arc definition) or a 20 meter chord (chord definition).
Formulas:
𝐼
𝑇 = 𝑅 tan
2
𝐼
𝐸 = 𝑅 (𝑠𝑒𝑐 − 1)
2
𝐼
𝑀 = 𝑅 (1 − 𝑐𝑜𝑠 )
2
𝐼
𝐿𝐶 = 2𝑅 sin
2
1 | 16
,GEFS (FOUNDAMENTALS OF SURVEYING)
CBLAMSIS UNIVERSITY OF THE CORDILLERAS SIMPLE CURVES
20𝐼
𝐿=
𝐷
1145.916
𝐷= (arc definition)
𝑅
10 𝐷
𝑅= 𝐷 = 10 csc (chord definition)
𝑠𝑖𝑛 2
2
Metric Stationing
In metric stationing, the length of a full station is equal to 20 meters. i.e. origin station is
00 + 000 and the next full station is 00 + 020, then 00 + 040 etc. Generally, stations that
are divisible by twenty are full stations and those are not are called sub-stations. The
number before the plus sign in a stationing represent distance in kilometers and the
number after the plus sign is distance in meters. i.e. Sta. 45 + 250, the station is 45 Km
and 250 m away from Sta. 00 + 000.
HOW TO READ A KILOMETER POST
The kilometer post information
KM means that the point (station) is 225
225 kilometers from station 00 + 000
B (Manila) and 10 kilometers away to
the nearest locality, B, (town or city)
10
that is to be reach.
KM. POST
2 | 16
, GEFS (FOUNDAMENTALS OF SURVEYING)
CBLAMSIS UNIVERSITY OF THE CORDILLERAS SIMPLE CURVES
Derivation of the formulas
3 | 16
CBLAMSIS UNIVERSITY OF THE CORDILLERAS SIMPLE CURVES
HORIZONTAL CURVES
TOPICS:
1. Steps in determining the best route connecting two termini
2. Horizontal Alignment (simple Curve)
Steps in determining the best route connecting two termini
Reading assignment
Reference: Railroad Curves and Earthworks by Frank Allen (Chapters 1 to 3)
Simple Curves
Simple curve is an arc of a circle use to connect two intersecting tangents in the
horizontal alignment of highways.
Elements of a Simple Curve:
T = Tangential Distance
E = External Distance
M = Middle Ordinate
L = Length of Curve
LC = Length of Long Chord
I = Angle of Intersection (Central Angle)
R = Radius of Curvature
PC = Point of Curvature
PT = Point of Tangency
PI = Point of Intersection (V = Vertex)
D = Degree of Curve
In metric system, the degree of curve, D, is the angle subtended by a 20-
meter arc (arc definition) or a 20 meter chord (chord definition).
Formulas:
𝐼
𝑇 = 𝑅 tan
2
𝐼
𝐸 = 𝑅 (𝑠𝑒𝑐 − 1)
2
𝐼
𝑀 = 𝑅 (1 − 𝑐𝑜𝑠 )
2
𝐼
𝐿𝐶 = 2𝑅 sin
2
1 | 16
,GEFS (FOUNDAMENTALS OF SURVEYING)
CBLAMSIS UNIVERSITY OF THE CORDILLERAS SIMPLE CURVES
20𝐼
𝐿=
𝐷
1145.916
𝐷= (arc definition)
𝑅
10 𝐷
𝑅= 𝐷 = 10 csc (chord definition)
𝑠𝑖𝑛 2
2
Metric Stationing
In metric stationing, the length of a full station is equal to 20 meters. i.e. origin station is
00 + 000 and the next full station is 00 + 020, then 00 + 040 etc. Generally, stations that
are divisible by twenty are full stations and those are not are called sub-stations. The
number before the plus sign in a stationing represent distance in kilometers and the
number after the plus sign is distance in meters. i.e. Sta. 45 + 250, the station is 45 Km
and 250 m away from Sta. 00 + 000.
HOW TO READ A KILOMETER POST
The kilometer post information
KM means that the point (station) is 225
225 kilometers from station 00 + 000
B (Manila) and 10 kilometers away to
the nearest locality, B, (town or city)
10
that is to be reach.
KM. POST
2 | 16
, GEFS (FOUNDAMENTALS OF SURVEYING)
CBLAMSIS UNIVERSITY OF THE CORDILLERAS SIMPLE CURVES
Derivation of the formulas
3 | 16
