Wednesday, March 30, 2011

Highway line ( curve, vertical curve , circular curve , ramp ) coordinates the formula _ ★ ★

 Coordinates of some line
highway, elevation formula (curve, vertical curve, circular curve, ramp)

one point on Curve Coordinate Calculation

known: ① ZH Curve points from any point on the length: l

② circular curve radius: R

③ transition curve length: l0

④ steering angle coefficient: K (1 or -1)

⑤ azimuth tangent points over ZH: α
ZH
⑥ point coordinates: xZ, yZ

calculation:



Description: When the curve for the left steering, K = 1, for the right steering, K =- 1,

formula n values ​​are as follows:



when calculating the second coordinates of points on the transition curve, then:

l is the length of the point HZ
HZ
α is the tangent through the point plus 180 ° azimuth

K value and the reverse calculation of the first transition curve

xZ, yZ coordinates for the point of HZ


tangent angle formula:


Second, the circular curve point coordinates calculated

known: ① ZH circular curve points from any point on the length: l

② circular curve radius: R

③ transition curve length: l0

④ steering angle coefficient: K (1 or -1)

⑤ azimuth tangent points over ZH: α
ZH
⑥ point coordinates: xZ, yZ

calculation:



Description: When the curve for the left steering, K = 1, for the right steering, K =- 1,

formula n values ​​are as follows:


HZ
When only know the coordinates of points, then:

l is the length of the point HZ
HZ
α is the tangent through the point plus 180 ° azimuth

K value and know when the opposite point coordinates ZH

xZ, yZ coordinates for the point of HZ



three factor formula curve


Description of the symbols
formula:

l - any point to the starting point of the curve length (or slow song slow song at any point to the starting point of the length)

l1 - the length of the first transition curve

l2 - length of the second transition curve

l0 - corresponding to the length of transition curve

R - radius of circular curve

R1 - starting at the radius of the curve

R2 - at the end of the radius curves

P1 - the starting point of the curvature curve

P2 - at the end of the curvature of curve

α - angle value curve


IV calculated vertical elevation of the curve

known: ① the first grade: i1 (uphill for the

② The second slope: i2 (uphill for the

③ Change Point Stake: SZ

④ Change Point Elevation: HZ

⑤ tangent vertical curve length: T
Stake the unknown point
⑥: S



calculation:



five, high ease the transition section of the cross slope calculations



known: figure,

first cross slope: i1

second cross slope: i2

transition length: L

be seek the cross slope from the second point (end of transition section) of the distance: x

requirements: be at the cross slope requirements: i

Solution: d = x / L

i = (i2-i1) (1-3d2 +2 d3) + i1


six coordinate calculation ramp

known: ① the unknown point Stake: K

② curve starting Stake: K0

③ curve end Stake: K1

④ curve point coordinates: x0, y0

⑤ curve tangent point azimuth: α0

⑥ curve of the starting point of curvature: P0 (left as

⑦ curve at the end of the curvature: P1 (turn left as

requirements: ① line coordinates of points on the ramp: x, y

② the tangent point of the unknown azimuth: αT

calculation:



Note: sgn (x) function is to take the sign function, when x <0 时 sgn (x) =- 1, when x> 0 时 sgn (x) = 1, when x = 0, sgn (x) = 0. In the calculator, if this function can be compiled program instead of a kid.

Reprinted from: Highway line (curve, vertical curve, circular curve, ramp) coordinates the formula .

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