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Composite Horizontal Curve

The document discusses the design and implementation of composite horizontal curves, focusing on the use of transition curves to manage radial forces as vehicles enter or exit circular curves. It highlights the Euler spiral as a common design choice for transition curves and provides mathematical formulas for calculating various parameters related to the curves. Additionally, it addresses the importance of superelevation runoff and limiting rates in the design process.

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ahmedmoreano
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5 views17 pages

Composite Horizontal Curve

The document discusses the design and implementation of composite horizontal curves, focusing on the use of transition curves to manage radial forces as vehicles enter or exit circular curves. It highlights the Euler spiral as a common design choice for transition curves and provides mathematical formulas for calculating various parameters related to the curves. Additionally, it addresses the importance of superelevation runoff and limiting rates in the design process.

Uploaded by

ahmedmoreano
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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composite horizontal curve

composite horizontal curve


Transition curve
• Transition curves are placed
between tangents and
circular curves or between
two adjacent circular curves
having substantially different
radii. The use of transition
curves provides a vehicle
path that gradually increases
or decreases the radial force
as the vehicle enters or
leaves a circular curve.
Transition curve
Generally, the Euler spiral, which is
also known as the clothoid, is used
in the design
of spiral transition curves.
Composite curve
𝐿𝑠
𝜃𝑠 = ( 𝑖𝑛 𝑟𝑎𝑑𝑖𝑎𝑛 )
2𝑅𝑐
𝐿𝑠 180
∆𝑠 = 𝑥 ( 𝑖𝑛 𝑑𝑒𝑔𝑟𝑒𝑒 )
2𝑅𝑐 𝜋

∆𝑐 = ∆ − 2∆𝑠 ( 𝑖𝑛 𝑑𝑒𝑔𝑟𝑒𝑒 )

𝑝 = 𝑌𝑠 − 𝑅𝑐 (1 − cos 𝜃𝑠 ) (𝑖𝑛 𝑟𝑎𝑑𝑖𝑎𝑛) )


∆
𝑇 ′ = (𝑅𝑐 + 𝑝) tan( 2) (𝑖𝑛 𝑑𝑒𝑔𝑟𝑒𝑒 )
𝑘 = 𝑋𝑠 − 𝑅𝑐 (sin 𝜃𝑠 ) (𝑖𝑛 𝑟𝑎𝑑𝑖𝑎𝑛)

𝐿𝑐 = 𝑅𝑐 ∆𝑟𝑎𝑑 − 𝐿𝑠 ( 𝑖𝑛 𝑟𝑎𝑑𝑖𝑎𝑛 )
• Minimum length of spiral
• Maximum length of spiral
Length of superelevation runoff
• Length of superelevation runoff
• In transition design with a spiral curve, it is
recommended that the superelevation runoff
be accomplished over the length of spiral.
• The length of spiral should meet the length of
runoff limitation.
•
• Limiting superelevation rates
• relative gradient of the pavement edge may
increase by 50% of the original relative gradient
represented in (Table 3-15)
• Length of tangent runout
Stations for the composite curve
TS ( beginning of the composite curve,
beginning of the first transition curve )
TS = PI – ( T’ + K)

SC (beginning of the circular curve )


SC = TS +Ls

CS (end of the circular curve, beginning of


the second transition curve )
CS = SC+ Lc

ST (end of the second transition curve,


end of the composite curve)
ST= Cs+Ls

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