As a civil engineer or construction professional, having a solid grasp of types of curves | horizontal and vertical curves in surveying | road survey can make a significant difference in your project outcomes. This detailed article covers all the key aspects that every site engineer and civil engineering student should be familiar with.
During the survey of the alignment of a project involving roads or railways, the direction of the line may change due to some unavoidable circumstances. The angle of the change in direction is known as the deflection angle. For it to be possible for a vehicle to run easily along the road or railway track, the two straight lines (the original line and the deflected line) are connected by an arc (Fig. below) which is known as the curve of the road or track.
Curve of Road
When the curve is provided in the horizontal plane, it is known as a horizontal curve.
DEFINITIONS AND EXPLANATIONS OF DIFFERENT TERMS
Degree of a Curve
1. Degree of Curve
The angle a unit chord of 30 m length subtends at the centre of the circle formed by the curve is known as the degree of the curve. It is designated as D (Fig. above).
A curve may be designated according to either the radius or the degree of the curve.
When the unit chord subtends an angle of 1°, it is called a one-degree curve, when the angle is 2°, a two-degree curve, and so on.
It may be calculated that the radius of a one-degree curve is 1,719 m.
2. Relation between Radius and Degree of Curve
Radius and Degree of a Curve
Let AB be the unit chord of 30 m, O the centre, R the radius and D the degree of the curve (Fig. above).
3. Superelevations
When a particle moves in a circular path, a force (known as centrifugal force) acts upon it and tends to push it away from the centre.
Similarly, when a vehicle suddenly moves from a straight to a curved path, the centrifugal force tends to push the vehicle away
from the road or track. This is because there is no component force to counterbalance this centrifugal force.
To counterbalance the centrifugal force, the outer edge of the road or rail is raised to some height (with respect to the inner edge), so that the sine component of the weight of the vehicle (W sin θ) may counterbalance the overturning force, The height through which the outer edge of the road or rail is raised is known as superelevation or cant.
Superelevation
In Fig. below, P is the centrifugal force, W sin θ is the component of the weight of the vehicle, and h is the superelevation given to the road or rail. For equilibrium,
Where, b = width of the road in metres
G = distance between centres of rails (gauge) in metres
R = radius of the curve in metres
g = acceleration due to gravity = 9.8 m/s2
V = speed of the vehicle in metres per second
h = superelevation in metres.
4. Centrifugal Ratio
The ratio between the centrifugal force and the weight of the vehicle is known as the centrifugal ratio.
TYPES OF HORIZONTAL CURVES
1. Simple Circular Curve
When a curve consists of a single arc with a constant radius connecting the two tangents, it is said to be a circular curve (Fig. below).
Circular Curve
2. Compound Curve
When a curve consists of two or more arcs with different radii, it is called a compound curve. Such a curve lies on the same side of a common tangent and the centres of the different arcs lie on the same side of their respective tangents (Fig. below).
Compound Curve
3. Reverse Curve
A reverse curve consists of two arcs bending in opposite directions. Their centres lie on opposite sides of the curve. Their radii may be either equal or different, and they have one common tangent (Fig. below).
Reverse Curve
4. Transition Curve
A curve of the variable radius is known as a transition curve. It is also called a spiral curve or easement curve. In railways, such a curve is provided on both sides of a circular curve to minimise superelevation. Excessive superelevation may cause wear and tear of the rail section and discomfort to passengers (Fig. below).
Transition Curve
5. Lemniscate Curve
A lemniscate curve is similar to a transition curve and is generally adopted in city roads where the deflection angle is large. In Fig. 10.9, OPD shows the shape of such a curve. The curve is designed by taking a major axis OD, minor axis PP′, with origin O, and axes OA and OB. OP(ρ) is known as the polar ray and α as the polar angle.
Lemniscate Curve
TYPES OF VERTICAL CURVES
When two different gradients meet at a point along a road surface, they form a sharp point at the apex. Unless this apex point is rounded off to form a smooth curve, no vehicle can move along that portion of the road. So, for the smooth and safe running of vehicles, the meeting point of the gradients is rounded off to form a smooth curve in a vertical plane. This curve is known as a vertical curve.
Generally, the parabolic curves are preferred as it is easy to work out the minimum sight distance in their case. The minimum sight distance is an important factor to be considered while calculating the length of the vertical curve.
The gradient is expressed in two ways:
a) As a percentage, e.g. 1%, 1.5%, etc.
b) As 1 in n, where n is the horizontal distance and 1 represents vertical distance, e.g. 1 in 100, 1 in 200, etc.
Again, the gradient may be ‘rise’ or ‘fall’. An up gradient is known as ‘rise’ and is denoted by a positive sign. A down gradient is known as ‘fall’ and is indicated by a negative sign.
Rate of Change of Grade
The characteristic of a parabolic curve is that the gradient changes from point to point but the rate of change in grade remains constant. Hence, for finding the length of the vertical curve, the rate of change of grade should be an essential consideration as this factor remains constant throughout the length of the vertical curve.
Generally, the recommended rate of change of grade is 0.1% per 30 m at summits and 0.05% per 30 m at sags.
Length of Vertical Curve
Example: Let us find the length of the vertical curve connecting two grades +0.5% and –0.4% where the rate of change of grade is 0.1%.
Length of vertical curve = (0.5-(-0.4)x30)/0.1 = ((0.5+0.4)x30x10)/1 = 0.9 x 30 x 10 = 270 m
Types of Vertical Curves
Summit Curves
· The tangent correction method
· The chord gradient method
Why Curve is Provided?
Having a straight highway or railroad in a country is practically feasible or impossible. Some changes in the direction of their alignment are required for terrain, culture, feature or other unavoidable reasons.
Such direction change can not be sharp but should be gradual, it is necessary to introduce curves between straight lines.
What are the two types of curves used in road surveys?
There are two types of curves provided mainly
a) Horizontal Curve
b) Vertical Curve
What are the Types of Horizontal Curve?
Simple Curve
Compound Curve
Reverse Curve
Transition or Spiral Curve
Conclusion
Understanding types of curves | horizontal and vertical curves in surveying | road survey is a fundamental part of becoming a competent civil engineer. We have tried to cover every important aspect in this article so you can confidently apply this knowledge in real-world construction scenarios. Stay tuned to CivilNotess for more valuable content tailored for civil engineering professionals.
❓ Frequently Asked Questions (FAQ)
Why is surveying important in construction?
Surveying is critical in construction because it helps establish accurate measurements, positions, and levels on the ground. Without proper surveying, structures could be misaligned, leading to costly errors and structural issues.
What are the most common surveying instruments?
The most commonly used surveying instruments include the auto level, theodolite, total station, GPS equipment, chain, tape measure, and ranging rods. The choice of instrument depends on the type and precision of the survey required.