In the study of software project scheduling, the Putnam–Norden–Rayleigh curve, also known as the PNR curve, is an equation specifying the relationship between applied effort and delivery tim…Full description
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Spiral Curve Spirals are used to overcome the abrupt change in curvature and superelevation that occurs between tangent and circular curve. The spiral curve is used to gradually change the curvature and superelevation of the road, thus called transition curve.
Elements of Spiral Curve
= Tangent to spiral TS = = Spiral to curve SC = = Curve to spiral CS = = Spiral to tangent ST = = Long tangent LT = = Short tangent ST = R = Radius of simple curve T s = Spiral tangent distance T c = Circular curve tangent to any point along L = Length of spiral from TS to the spiral Ls = Length of spiral = Point of intersection PI = = Angle of intersection I = I c = Angle of intersection of the simple curve
p = Length of throw or the distance from tangent that the circular curve has been offset = Offset distance (right angle distance) from X = tangent to any point on the spiral X c = Offset distance (right angle distance) from tangent to SC = Distance along tangent to any point on the Y = spiral to point at Y c = Distance along tangent from TS to right angle to SC E s = External distance of the simple curve θ = Spiral angle from tangent to any point on the spiral θs = Spiral angle from tangent to SC = Deflection angle from TS to to any point on the i = spiral, it is proportional to the square of its distance to SC i s = Deflection angle from TS to D = Degree of spiral curve at any point Dc = Degree of simple curve
Formulas for Spiral Curves
A spiral curve having a length of 100m is to be laid out in a certain portion of road. The degr ee of the central curve is 6 degrees. 1.
Find the offset distance at the first quarter point of spiral.
=
= 2.
3600 (°)
6
=
=
3600 (6°)
= 190.99
25
= 0.14 6(190.99)(100)
Determine the spiral angle at the third quarter
3.
easement curve if the spiral angle at SC is 12 degrees and the offset distance at SC is 8.4m? Distance along the tangent is 79.62m. 79 .62m. 2. The length of throw of a spiral is 1.42m. What is the corresponding offset distance at SC? 3. An 80m spiral curve connects the central curve of
Compute the maximum speed of the car that could pass through the spiral without skidding.
=
1. What is the length of the long tangent of a spiral
radius 200m. Determine the spiral angle at SC.
point of spiral.
Ɵ=
EXERCISES
0.036
; 100 100 =
= 80.95 ℎ
0.036
4. The radius of the interior curve of a spiral easement curve is 190m. If the length of the spiral is 80 m and the length of the throw is 2.3m, determine the external distance if the angle of intersection of the tangents is 42 degrees.
Stationing of the summit. Sta. HP = Sta. V – L1+X Sta. HP = 4+456.36
An unsymmetrical parabolic curve connects a +4.2% grade and a -3.4% grade. The length of curve on the left side of the vertex is 80m and 110m on the other side. if the stationing of the point of intersection is 4+460 and its elev is 145.2 m.
3. elevation of the summit. Elev summit = Elev V – L(g) +Area of triangle Elev Summit = 145.2 – 80(.042)+.5*76.36*.042 Elev summit = 143.44m
Exercise A vertical highway curve has an approach grade of +7% meeting -4% grade at the vertex. it is required to connect the two tangents with unsymmetrical vertical parabolic curve. the c urve has an offset of 1.32m directly below t he intersection of the tangents. locate the position of the summit from the PC. the vertical curve has a length of 60m on the side of the PC and 40m from the side of the PT.