A method for obtaining parameters of known points in railway engineering

Abstract

This invention relates to the field of railway engineering technology and discloses a method for obtaining parameters of known points in railway engineering. First, the coordinates of point P in an independent coordinate system are calculated. Then, the length from point P1 to the starting point of the transition curve is calculated. Next, based on the coordinates of points P and P1, the length from point P2 to the starting point of the transition curve is calculated. Finally, the station number and offset of the known point are calculated. The method for obtaining parameters of known points in railway engineering provided by this invention has clear logic, is easy to implement on a calculator, and can efficiently and accurately calculate the station number and offset of known points. It can provide important technical support for railway engineering surveying (side stake setting, centerline restoration, etc.).

Description

Technical Field

[0001] This invention relates to the field of railway engineering technology, and in particular to a method for obtaining parameters of known points in railway engineering. Background Technology

[0002] During the surveying process of railway lines, it is necessary to obtain parameters of known points (such as line mileage and offset from the centerline). This leads to numerous problems involving calculating coordinates from mileage and recalculating mileage from coordinates, such as centerline layout, side stake layout, and centerline resurvey. Methods for calculating mileage from coordinates have been extensively discussed, with corresponding methods for straight sections, circular curves, and transition curves. The main methods are the direct method and the iterative method. The direct method corresponds to the intersection method, while the iterative method corresponds to the line element method. The tangent iteration method is more versatile and can calculate all types of alignments.

[0003] However, existing calculation methods still have the following drawbacks: the direct method of calculating mileage from coordinates is simple and efficient for straight and circular curve segments, and more complex for transition curve segments, but it does not require iteration and is easy to program with a calculator. The biggest drawback of the direct method is that its accuracy cannot be guaranteed. Among iterative methods, the tangent iteration method has strong versatility and can calculate all types of lines, but because it requires iteration and depends on the mileage forward coordinate calculation algorithm, the calculation speed is slow and the efficiency is low.

[0004] Therefore, there is an urgent need to propose a fast and high-precision method for obtaining parameters of known points in line engineering to solve the problems existing in the current technology. Summary of the Invention

[0005] The purpose of this invention is to provide a method for obtaining parameters of known points in railway engineering, the specific technical solution of which is as follows:

[0006] A method for obtaining parameters of known points in railway line engineering includes the following steps:

[0007] Step 1: Obtain point P(X) P ,Y P The line's planar coordinates and the line design coordinates (X, H) of the transition curve's starting point ZH point. ZH ,Y ZH ) and the coordinates and azimuth α of point ZH; based on the known point P(X P ,Y P The line's planar coordinates and the line design coordinates (X, H) of the transition curve's starting point ZH point. ZH ,Y ZH ) and the coordinates of point P in the independent coordinate system by calculating the azimuth angle α of point ZH. P ,y P );

[0008] Step 2: Based on the x-coordinate of point P in the independent coordinate systemP Calculate the length l1 of the line from point P1 to point ZH. Point P1 is the intersection of the perpendicular line drawn from point P to the x-axis of the independent coordinate system and the transition curve.

[0009] Step 3: Calculate the coordinates (x1, y1) of point P1 in the independent coordinate system and the angle β1 that point P1 rotates relative to point ZH based on the line length l1;

[0010] Step 4: Calculate the line length l2 from point P2 to point ZH and the angle β2 that P2 turns relative to point ZH. Point P2 is the projection point of point P on the transition curve.

[0011] Step 5: Calculate the mileage K of the route to point P. P And the offset d from the midline.

[0012] Preferably, before step one, it is further included to determine whether the transition curve is an incomplete transition curve; if it is an incomplete transition curve, it is supplemented into a complete transition curve.

[0013] Preferably, the coordinates (x, y) of point P in step one in the independent coordinate system are... P ,y P Calculated using the following formula:

[0014]

[0015] v ZH-P =(X P -X ZH Y P -Y ZH );

[0016] n HZ = (cosα, sinα);

[0017] Among them, v ZH-P Let n be the vector from point ZH to point P. HZ Let ZH be the tangent vector at point ZH.

[0018] Preferably, the line length l1 from point P1 to point ZH in step two is calculated using the following formula:

[0019]

[0020] Where C is the parameter of the transition curve.

[0021] Preferably, the coordinates (x1, y1) of point P1 in step three in the independent coordinate system are calculated using the following formula:

[0022]

[0023] Preferably, the angle β1 through which point P1 rotates relative to point ZH in step three is calculated by the following formula:

[0024]

[0025] Preferably, the line length l2 from point P2 to point ZH in step four is calculated using the following formula:

[0026] l2 = l1 + dl;

[0027] dl = dysinβ1 + dycosβ1dβ;

[0028] dy = y P -y1;

[0029]

[0030] Where dl is the length of the line from point P2 to point P1; dβ is the angle through which point P2 rotates relative to point P1.

[0031] Preferably, the angle β2 that point P2 rotates relative to point ZH in step four is calculated using the following formula:

[0032]

[0033] Preferably, the route mileage K of point P in step five is... P The offset d from the centerline is calculated using the following formula:

[0034] K P =K ZH +l2;

[0035]

[0036] Among them, K ZH y1 is the mileage of point ZH in the line; y2 is the ordinate of phase P2 in the independent coordinate system; when d is positive, point P is on the left side of the line's direction of travel; when d is negative, point P is on the right side of the line's direction of travel.

[0037] Preferably, the ordinate y2 of phase P2 in the independent coordinate system is calculated by the following formula:

[0038]

[0039] The application of the technical solution of the present invention has the following beneficial effects:

[0040] A method for obtaining parameters of known points in railway line engineering is disclosed. First, the coordinates of point P in an independent coordinate system are determined. Then, the length from point P1 to the starting point of the transition curve is calculated. Next, based on the coordinates of points P and P1, the length from point P2 to the starting point of the transition curve is calculated. Finally, the station number and offset of the known point are calculated. This method for obtaining parameters of known points in railway line engineering is logically clear, easy to implement on a calculator, and can efficiently and accurately calculate the station number and offset of known points. It can provide important technical support for railway line engineering surveying (stake setting, centerline restoration, etc.).

[0041] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the figures. Attached Figure Description

[0042] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0043] Figure 1 This is a schematic diagram illustrating the calculation principle of the parameter acquisition method for known points in the line engineering of this embodiment;

[0044] Figure 2 This is a schematic diagram illustrating the calculation principle of dl in the parameter acquisition method for known points in the line engineering of this embodiment. Detailed Implementation

[0045] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0046] Example:

[0047] This invention provides route design information for a highway tunnel section, as shown in Table 1 below. The known plane coordinates (X, Y, F) of point P are given. P ,Y P The coordinates of the line design (X) are (3215307.9211, 489564.6163), the starting point ZH of the transition curve. ZH ,Y ZH And the coordinate azimuth α of point ZH; in meters, now calculate its station number K according to the method of the present invention. P and offset d (actual value is K) P =11300m, d=-30m).

[0048] Table 1. Partial Route Design Information for a Certain Expressway

[0049]

[0050] like Figure 1As shown, a method for obtaining parameters of known points in a railway line project includes the following steps:

[0051] First, determine whether the transition curve is an incomplete transition curve; if it is an incomplete transition curve, then complete it into a complete transition curve.

[0052] Step 1: Based on the known point P(X) P ,Y P The line's planar coordinates and the line design coordinates (X, H) of the transition curve's starting point ZH point. ZH ,Y ZH ) and the coordinates of point P in the independent coordinate system by calculating the azimuth angle α of point ZH. P ,y P );

[0053] The coordinates (x, y) of point P in step one in the independent coordinate system P ,y P Calculated using the following formula:

[0054]

[0055] v ZH-P =(X P -X ZH Y P -Y ZH );

[0056] n HZ = (cosα, sinα);

[0057] Among them, v ZH-P Let n be the vector from point ZH to point P. HZ Let ZH be the tangent vector at point ZH.

[0058] Finally, we get (x) P ,y P The value is (90.38042, 30.32531).

[0059] Step 2: Based on the x-coordinate of point P in the independent coordinate system P Calculate the length l1 of the line from point P1 to point ZH. Point P1 is the intersection of the perpendicular line drawn from point P to the x-axis of the independent coordinate system and the transition curve.

[0060] The length l1 of the line from point P1 to point ZH in step two is calculated by the following formula:

[0061]

[0062] Where C is the parameter of the transition curve.

[0063] We get l1 = 90.38147.

[0064] Step 3: Calculate the coordinates (x1, y1) of point P1 in the independent coordinate system based on the line length l1, and the angle β1 through which point P1 rotates relative to point ZH;

[0065] The coordinates (x1, y1) of point P1 in the independent coordinate system in step three are calculated using the following formula:

[0066]

[0067] The angle β1 that point P1 rotates relative to point ZH in step three is calculated using the following formula:

[0068]

[0069] The final result is (x1, y1) as (90.38042, 0.32356), β1 = 0.01074007.

[0070] Step 4: Calculate the line length l2 from point P2 to point ZH, and the angle β2 that P2 turns relative to point ZH. Point P2 is the projection point of point P on the transition curve.

[0071] The length l2 of the line from point P2 to point ZH in step four is calculated by the following formula:

[0072] l2 = l1 + dl;

[0073] dl = dysinβ1 + dycosβ1dβ;

[0074] dy = y P -y1;

[0075]

[0076] Where dl is the length of the line from point P2 to point P1; dβ is the angle through which point P2 rotates relative to point P1.

[0077] The angle β2 that point P2 rotates relative to point ZH in step four is calculated using the following formula:

[0078]

[0079] The final values ​​obtained are l2 = 90.705996 and β2 = 0.010817341.

[0080] Step 5: Calculate the mileage K of the route to point P. P And the offset d from the midline;

[0081] The route mileage K of point P in step five P The offset d from the centerline is calculated using the following formula:

[0082] K P =K ZH +l2;

[0083]

[0084] Among them, K ZH y1 is the mileage of point ZH in the line; y2 is the ordinate of phase P2 in the independent coordinate system; when d is positive, point P is on the left side of the line's direction of travel; when d is negative, point P is on the right side of the line's direction of travel.

[0085] The ordinate y2 of phase P2 in the independent coordinate system is calculated by the following formula:

[0086]

[0087] Finally, we get K. P =11300.00000m, d=-30.00000m, which are the station number and offset of point P.

[0088] It can be seen that the technical method provided by the present invention has a back-calculation accuracy better than 0.1 mm, which meets the actual needs of line engineering.

[0089] The method for obtaining parameters of known points in this railway line project first determines the coordinates of point P in an independent coordinate system; then, it calculates the length from point P1 to the starting point of the transition curve; next, it calculates the length from point P2 to the starting point of the transition curve based on the coordinates of points P and P1; finally, it calculates the station number and offset of the known points. This invention provides a logically clear method for obtaining parameters of known points in railway line projects, which is easy to implement on a calculator and can efficiently and accurately calculate the station number and offset of known points. It can provide important technical support for railway line engineering surveying (side stake setting, centerline restoration, etc.).

[0090] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for obtaining parameters of known points in a railway line project, characterized in that, Includes the following steps: Step 1: Obtain point P(X) P ,Y P The line's planar coordinates and the line design coordinates (X, H) of the transition curve's starting point ZH point. ZH ,Y ZH And the coordinates and azimuth α of point ZH; based on the known point P(X P ,Y P The line's planar coordinates and the line design coordinates (X, H) of the transition curve's starting point ZH point. ZH ,Y ZH ) and the coordinates of point P in the independent coordinate system by calculating the azimuth angle α of point ZH. P ,y P ); Step 2: Based on the x-coordinate of point P in the independent coordinate system P Calculate the length l1 of the line from point P1 to point ZH. Point P1 is the intersection of the perpendicular line drawn from point P to the x-axis of the independent coordinate system and the transition curve. Step 3: Calculate the coordinates (x1, y1) of point P1 in the independent coordinate system and the angle β1 that point P1 rotates relative to point ZH based on the line length l1; Step 4: Calculate the line length l2 from point P2 to point ZH and the angle β2 that P2 turns relative to point ZH. Point P2 is the projection point of point P on the transition curve. Step 5: Calculate the mileage K of the route to point P. P And the offset d from the midline.

2. The method for obtaining parameters of known points in a railway line project according to claim 1, characterized in that, It also includes determining, before step one, whether the transition curve is an incomplete transition curve; if it is an incomplete transition curve, it is then completed into a complete transition curve.

3. The method for obtaining parameters of known points in a railway line project according to claim 2, characterized in that, The coordinates (x, y) of point P in step one in the independent coordinate system P ,y P Calculated using the following formula: v ZH-P =(X P -X ZH ,AND P -AND ZH ); n HZ =(cosα,sinα); Among them, v ZH-P Let n be the vector from point ZH to point P. HZ Let be the tangent vector at point ZH.

4. The method for obtaining parameters of known points in a railway line project according to claim 3, characterized in that, The length l1 of the line from point P1 to point ZH in step two is calculated by the following formula: Where C is the parameter of the transition curve.

5. The method for obtaining parameters of known points in a railway line project according to claim 4, characterized in that, The coordinates (x1, y1) of point P1 in the independent coordinate system in step three are calculated using the following formula:

6. The method for obtaining parameters of known points in a railway line project according to claim 5, characterized in that, The angle β1 that point P1 rotates relative to point ZH in step three is calculated using the following formula:

7. The method for obtaining parameters of known points in a railway line project according to claim 6, characterized in that, The length l2 of the line from point P2 to point ZH in step four is calculated by the following formula: l2＝l1+dl； dl = dysinβ1 + dycosβ1dβ; dy=y P -y1: Where dl is the length of the line from point P2 to point P1; dβ is the angle through which point P2 rotates relative to point P1.

8. The method for obtaining parameters of known points in a railway line project according to claim 7, characterized in that, The angle β2 that point P2 rotates relative to point ZH in step four is calculated using the following formula:

9. The method for obtaining parameters of known points in a railway line project according to claim 8, characterized in that, The route mileage K of point P in step five P The offset d from the centerline is calculated using the following formula: K P =K ZH +l2; Among them, K ZH y1 is the mileage of point ZH in the line; y2 is the ordinate of phase P2 in the independent coordinate system; when d is positive, point P is on the left side of the line's direction of travel; when d is negative, point P is on the right side of the line's direction of travel.

10. The method for obtaining parameters of known points in a railway line project according to claim 9, characterized in that, The ordinate y2 of phase P2 in the independent coordinate system is calculated by the following formula:

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