Road curve with transition curve and its forming method
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A road, mitigation technology, applied in the direction of roads, roads, buildings, etc.
Inactive Publication Date: 2016-06-08
徐寅喆 +1
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[0015] The purpose of the present invention is to provide a method of forming a road curve transition curve, to overcome the problems associated with the existing clothoid curve, which can be more conveniently used in engineering practice
Method used
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Embodiment 1
[0112] Embodiment one: see attached Figure 5 Middle curve I, which is a transitional curve entering the arc in the first quadrant.
[0113] L=1.005592750000000e+004,
[0114] H=1.664578400000000e+003,
[0115] R=10000,
[0116] α=30°,
[0117] β=109°,
[0118] K=-2.90421087767583,
[0119] a 0 =-1.610277999970065e+006,
[0120] a 1 =9.424571760265145e+002,
[0121] a 2 =-0.21897898908567,
[0122] a 3 = 2.537499259922972e-005,
[0123] a 4 =-1.466505605396334e-009,
[0124] a 5 = 3.375495517833180e-014,
[0125] L 0 =3.621618551054907e+003.
Embodiment 2
[0126] Embodiment two: see attached Figure 5 The middle curve II, which is a transition curve away from the arc in the first quadrant, has no arc segment between curves I and II, and the two transition curves are directly connected.
[0127] L=6.469530700000000e+003,
[0128] H=7.876399500000000e+003,
[0129] R=10000,
[0130] α=30°,
[0131] β=131°,
[0132] K=-1.15036840722101,
[0133] a 0 =9.789219497546875e+004,
[0134] a 1 =-58.80742441593074,
[0135] a 2 =0.01615679296782,
[0136] a 3 = -2.276264187378184e-006,
[0137] a 4 = 1.616646158872672e-010,
[0138] a 5 = -4.644481424436472e-015,
[0139] L 0 =3.621561462599412e+003.
Embodiment 3
[0140] Embodiment three: see attached Figure 5 Middle curve III, which is a transition curve away from the arc in the first quadrant.
[0141] L=1.664578400000000e+003,
[0142] H=1.005592750000000e+004,
[0143] R=10000,
[0144] α=60°,
[0145] β=161°,
[0146] K=-0.34432761328967,
[0147] a 0 =1.065537723646134e+004,
[0148] a 1 =-0.39126166549048,
[0149] a 2 = 2.774773800972551e-005,
[0150] a 3 =-5.375663085527373e-009,
[0151] a 4 =-1.273466679849551e-015,
[0152] a 5 =-1.912144609343186e-017,
[0153] L 0 =3.621695559129405e+003.
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Abstract
A method for forming an easement curve for road curve. The easement curve is used for connecting a transition curve segment DE between a circular curve segment CD with a curvature of 1/R and a straight line segment EF with a curvature of 0. The method comprises: establishing a rectangular coordinate system with an origin of coordinates being at a center of the circular curve CD; in the rectangular coordinate system, enabling the curve segment DE to satisfy (I), n being an integer with a minimum value of 5, ai=fi(H, L, a, R, K), f(x) satisfying that C and D at least have continuous second derivative. The road curve formed by using this method can implement continuous transition of a curvature between the straight line and the circular curve and a curvature change rate.
Description
technical field [0001] The invention relates to a method for forming a road curve relaxation curve, in particular to a method for forming a relaxation curve suitable for highways, railways, urban elevated roads, rail transit, especially expressways, high-speed railways, overpasses, and up and down ramps . Background technique [0002] In the construction of highways, railways, urban elevated roads, rail transit, especially highways, high-speed railways, and overpasses, it is impossible to design all straight roads due to terrain constraints. [0003] In the current design of road curves, the transition curve (transition curve) widely used is the clothoid spiral (or Cornu'sspiral or Eulerspiral), which was discovered by Swiss mathematician Leonhard Paul Euler in the 18th century. The curvature radius of the line changes from ∞ continuously to a fixed radius R, that is, the curvature changes from 0 to 1 / R continuously. One of the basic linetypes of design. It is currently u...
Claims
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