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2.3 Stadia

Measurements for

Inclined Sights

CE 371

Dr. SaMeH S. Ahmed

College of Engineering – MU 18-19/3

CE 371

Chapter 6: Surveying II

CE 371 CHAPTER 6

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Chapter 6 Other Curves

6.1 Compound Circular Curves

A compound curve consists of two (or more) circular curves between two main tangents

joined at point of compound curve (PCC). Curve at PC is designated as 1 (R1, L1, T1, etc)

and curve at PT is designated as 2 (R2, L2, T2, etc).

Fig. 6.1: Compound Circular Curve

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Elements of compound curve

PC = point of curvature

PT = point of tangency

PI = point of intersection

PCC = point of compound curve

T1 = length of tangent of the first curve

T2 = length of tangent of the second curve

V1 = vertex of the first curve

V2 = vertex of the second curve

I1 = central angle of the first curve

I2 = central angle of the second curve

I = angle of intersection = I1 + I2

Lc1 = length of first curve

Lc2 = length of second curve

L1 = length of first chord

L2 = length of second chord

L = length of long chord from PC to PT

T1 + T2 = length of common tangent measured from V1 to V2

θ = 180° - I

x and y can be found from triangle V1-V2-PI.

L can be found from triangle PC-PCC-PT

Finding the stationing of PT

Given the stationing of PC Sta PT = Sta PC + Lc1 + Lc2

Given the stationing of PI Sta PT = Sta PI – x − T1 + Lc1 + Lc2

Uses of compound curve:

Compound curves are used for applications where design constraints (topographic or cost of land) preclude the use of simple curves, they are usually found chiefly in the design of interchange loops and ramps.

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Problem

A compound curve has the following characteristics:

I1 = 24° D1 = 6°

I2 = 36° D2 = 4°

Stationing of P.C. = 85 + 42.5 S = 100 m

Compute the stationing of P.C.C.

Solution:

Length of curve 𝐿 = 𝑆(𝐼𝑜

𝐷𝑜)

𝐿𝑐1

24𝑜= (

100

6𝑜)

Lc1 = (24 * 100) / 6 = 400

Sta. P.C.C=Sta. P.C. + Lc1 = ( 85+ 42.5) + 400 = km 89 +42.5

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6.2 Reversed Curves

Reversed curve, Figure 6.2, though pleasing to the eye, would bring discomfort to motorist running at design speed. The instant change in direction at the PRC brought some safety problems. Despite this fact, reversed curves are being used with great success on park roads, formal paths, waterway channels, and the like.

Fig. 6.2: Reversed Curve

Elements of Reversed Curve

PC = point of curvature

PT = point of tangency

PRC = point of reversed curvature

T1 = length of tangent of the first curve

T2 = length of tangent of the second curve

V1 = vertex of the first curve

V2 = vertex of the second curve

I1 = central angle of the first curve

I2 = central angle of the second curve

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Lc1 = length of first curve

Lc2 = length of second curve

L1 = length of first chord

L2 = length of second chord

T1 + T2 = length of common tangent measured from V1 to V2

Finding the stationing of PT

Given the stationing of PC

Sta PT = Sta PC + Lc1 + Lc2

Given the stationing of V1

Sta PT = Sta V1 − T1 + Lc1 + Lc2

Reversed Curve for Nonparallel Tangents

Figure 6.3 is an example reversed curves of unequal radii connecting non-parallel tangents.

Fig. 6.3: Reversed Curve for Nonparallel Tangents

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Reversed Curve for Parallel Tangents

Figure 6.4 is an example of reversed curves of unequal radii connecting two parallel roads.

Fig. 6.4: Reversed Curve for Parallel Tangents

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6.3 Vertical Curves

Vertical curves are used in highway and street vertical alignment to provide a gradual change between two adjacent grade lines. They are parabolic and not circular like horizontal curves. Identifying the proper grade and the safe passing sight distance is the main design criterion of the vertical curve, In crest vertical curve the length should be enough to provide safe stopping sight distance and in sag vertical curve the length is important as it influences the factors such as headlight sight distance, rider comfort and drainage requirements.

Types of Vertical Curve:

6.3.1 Sag Curve

Sag Curves are those which change the alignment of the road from uphill to downhill,

6.3.2 Crest Curve/Summit Curve

Crest Curves are those which change the alignment of the road from downhill to

uphill. In designing crest vertical curves it is important that the grades be not] too high which makes it difficult for the motorists to travel upon it.