Axis (traffic route)
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In the case of traffic routes, the axis has the character of a mathematically defined guideline for the course of the route. This solid line is the main axis. If edges or accompanying structures are also defined by axes, these lines are called edge or minor axes.
The main axis of traffic routes is usually in the middle of the structure. For single -lane roads and single-track railways , this is the middle of the carriageway or track . In the case of multi-lane roads and multi-track railway lines, the axis is in the middle of the overall cross-section. The term "axis" is used for the floor plan in the site plan and serves to define the horizontal course of the route. In the case of the elevation view, the elevation plan , on the other hand, the term " gradient " is common to define the height profile in the course of the route.
features
The axis (site plan) is composed of the elements straight line , circular arc and clothoid as transition arcs . The gradient is formed as a polygon from straight lines, the nodes of which are called tangent cuts (TS). The fillets in the tangent sections, peaks and troughs , are square parabolas , whose characteristic "radius" is the radius of curvature at the tangent intersection.
The axis and gradient have an identical zero point. A specific point on the axis or the gradient is clearly defined three-dimensionally in a Cartesian coordinate system (X / Y / Z) by specifying the length relative to the zero point . The X and Y coordinates are determined by the axis calculation, the Z coordinates by the gradient calculation. The distance from the zero point is the horizontally measured development length of the route and is referred to as stationing, kilometering or hectometering. For example, a point at a distance of 1534 m from the zero point has the following station designation:
| with kilometrage | |
| with hectometry |
Points that are to the side of the axis are mapped perpendicularly to the axis and determined by the station of the plumb line and the transverse distance D to the axis. With a negative transverse distance, the point is to the left of the axis in the stationing direction, whereas with a positive distance, it is on the right. The height is often determined as the height difference relative to the height of the plumb line. To display the structure in its entire width, for example in the slope band (lane edges in road construction) or cant band (rail height in railway construction), the distance to the zero point - the stationing - thus forms the horizontal display axis X, in the vertical direction Y the relative height differences are at the height of the axis point.
The axis as a reference line
When planning a traffic structure, specialist engineers from several disciplines work closely together , for example civil engineers , surveyors , landscape and structural engineers , which requires constant coordination in all planning and construction phases. A simple and unambiguous assignment of each component to an overall measure is effectively supported by this type of spatial definition of the building, which has proven itself in practice, because it is possible to bring the individual specialist plans into mutual reference.
For engineering structures on the side of the axis such as B. Retaining walls, however , in the execution planning, the exclusive reference to the main axis is not necessarily recommended if the structure is curved. The curvature of the axis results in length distortions on the side of the axis, which can lead to errors when using prefabricated parts or when constructing formwork if they are not taken into account. Here, a separate building axis is used, which is placed in such a way that the true length corresponds to the development length on this axis within the building tolerance. By specifying and displaying some essential points twice on both axes, however, it is possible to restore the connection to the main axis at any point at any time. This also makes it easier to produce handy, clear detailed plans with a high level of information. This relieves the load on the basic plan and makes it clearer because the engineering structures only have to be displayed there as graphical information without details, which is completely sufficient for a sufficient combination of both plans. The planning representation of the building with a basic plan, which is flanked with many detailed plans, is standard today. The main axis does not lose any of its importance because its function for dimensioning the structure and as a basic line for the clear localization of individual components in the planning section remains unaffected. In contrast, short-term optimization and adaptation of the components with relatively little effort is made easier. A prerequisite for this, however, is good central coordination and monitoring that all documents are up-to-date when drawing up drawings for construction.
Attachment number, scope, content and representation by means of location and height plans, standard cross-sections, detailed plans, etc. are regulated in the guidelines for the creation of uniform design documents in road construction - RE of the Federal Ministry of Transport and explained by sample plans . This makes working with the plans easier and provides information on which data should be entered and which character patterns should be used for general legibility of the plans. This largely rules out misunderstandings when interpreting the documents.
Definition of the main axis points
The axis of a traffic route is a line object that is composed of several individual elements, usually straight lines, arcs and clothoids. In this case, the definition of a contiguous line object also applies to an axis:
- The line has a start and end point. If the line describes the circumference of an area, the start and end points are identical.
- Theoretically, the number of line elements is arbitrarily large, but for practical reasons it is limited to a maximum number that is within the scope of manageable processing. For example, a limit value of 1024 elements is common.
- The junction points of the line elements are the nodes of the line and must be present in coordinates (X / Y / optionally Z).
- In addition to these nodes, the elements must be described by additional information so that any intermediate point on the element can be calculated. This only applies to a straight line. A circular arc requires the specification of the radius, the course of the curvature is defined with –R for left arcs and + R for right arcs. A clothoid section requires the specification of parameter A, the course of the curvature is also determined here by the sign . In addition, the start and end radius must be specified so that a clear description of the section is available.
The line definition for axes is extended by the station, the added length of all elements up to the respective node, which is also saved at this node. - If you include this extension in the general line data set, you can work on all line objects with axis calculation programs, which offer considerably more comfort and flexibility in the calculation.
For the main axis of a traffic route, the condition exists that the element joint points do not have angular jumps but a common tangent. If the entire main axis is routed dynamically and the transition from straight lines to circular arcs or between two circular arcs with clothoids as transition elements is calculated, there are also no radial jumps in the element joints. In principle, angular and radius jumps are of course also permissible for axis calculations, just not with a dynamic driving approach for traffic routes. A curb line with bulges for parking spaces is not subject to this requirement and can still be defined as an axis.
These basic data of an axis, stored in the nodes, which define the element changes of the line object in the sequence with ascending station, are called axis main points. The same procedure is used for the gradient and the lists with the changes in width and bank slope in the course of the route. Intermediate points within the axle elements are calculated with the help of this basic data and called small axle points as dependent points.
Influences of EDP on planning and construction from 1970
Characteristic for the era before 1980 was a largely graphic construction of the axis in the preliminary draft and draft phase on the drawing board without detailed calculations. Especially for this there were curve and clothoid rulers and special tables in clothoid tables to insert between other axis elements. Only the surveyor commissioned with the implementation converted this data into the global reference system during the implementation planning and created the layout plans for the construction site. Due to the complex and time-consuming calculation work that the surveyor had to do, however, the use of computers with special programs in this area established itself as early as around 1970, i.e. before the start of the modern, decentralized PC era. Medium-sized data technology systems were used in data centers or, in large offices, their own central computer, controlled by punched cards or punched strips , which at this time were replaced relatively quickly by screen terminals that communicated directly with the computer. The printed data lists formed the basis for mapping the axis points and drawing up the planning on transparent paper or drawing film with black, well-covering ink . These plans were duplicated using blueprints and - if necessary - colored by hand.
Many specialist planners used to define their planning contributions using information at right angles and parallel to the specified axis. The computing effort was reduced to the necessary minimum, for many of these calculations the slide rule was sufficient. Nowadays, with automatic calculation by CAD programs, approximation methods with little calculation effort are of course no longer important; however, they are occasionally still helpful as a "stopgap" for small, unpredictable changes and adjustments directly on the construction site.
Surveyors who were entrusted with the stakeout work also switched to auxiliary lines that required less computational effort with trigonometric functions . For one axis z. B. calculated the tangents of the axis elements with their intersection and staked and marketed on site as a polygon. Based on this polygon, the compression of the axis points for the construction could be calculated with simple means orthogonally to the tangents, for which often slide rules and parabolas were sufficient. In a second step, surveyors and one or two assistants transferred the axis points from these tangents to the terrain using alignment poles , angled prism and measuring tape . Finally, the heights of the axle blocks were determined by leveling and the differences to the planned target height were calculated. Setting out according to this method with simple devices was time-consuming and had to be planned well in advance in the construction process. With the handover of the axis staking out to the construction company, the subsequent securing of the staking out and measuring of the edges became the responsibility of the company. From the standard cross-sections and cross- section drawings of the planning documents, site managers and foremen were able to take the relative distances and height differences of other building lines to the axis and transfer them to the terrain from the axis peg.
Until the early 1980s, junctions and independently routed road edges were often only designed with drawings. On the construction site, the dimensions were taken from the plan, roughly staked out with simple surveying equipment and then brought into a pleasing form by means of "alignments" and small, freehand corrections. If a site manager had a sure feeling for constructive relationships and had some experience with this method, the results were even surprisingly good. However, it took a lot of time and required at least two assistants.
Since around 1980, however, measurements have been made almost exclusively with electronic tachymeter instruments and staked out via direction and route ( polar coordinates ). Electronic computers with high storage capacity and special programs are integrated in these instruments. For this purpose, the basic data is transferred to the device in the office, or the device is automatically controlled from a mobile computer when it is used. For this, the basic data of the main and secondary axes of an axis are sufficient to immediately convert any point, including any necessary constant parallel shifts, for staking out. This eliminates the need to prepare stakeout plans and data lists on paper. This method is very flexible, because the density of the point sequence can be adapted to the respective requirements directly on site. The high cost of surveying equipment is quickly amortized because the time and personnel expenditure is much lower than with simple methods.
Bulldozers , graders , pavers and tunneling machines can already be controlled directly via GPS receivers or fully automatic electronic total station instruments with independent tracking and additional sensors on the blade, the screed or the milling head, if they are designed for this and have a control computer that supports them It summarizes basic information on the actual position, determines the associated target position from the stored basic data of the axis, and makes the corrections in real time using a target / actual comparison. It is only a matter of time and further falling hardware and software costs before such control systems become part of the basic equipment.
Due to the rapid development of computer and device performance as integrated systems, today's plans rely on the main axis as a reference and order system on a large number of other secondary axes that provide specific data for islands , edge lines within junctions and road widenings. They can be mathematically related to the main axis in any density and then provide the values for the lane width and cross slope in the system of the main axis. These calculations are carried out automatically by appropriate programs after a few control data have been specified. Lengthy, cumbersome manual calculations are no longer necessary. If the main axis and minor axes are calculated in a uniform global coordinate system, the relationship between them can be established at any time. Therefore, as the first step in the planning process, the global reference system is defined as binding for all parties involved.
The axis as the basis of assessment for a traffic route
There are basically three different starting situations:
| Minimum radii and minimum lengths of the circular arcs | ||
| V E [km / h] | min R [m] | min L [m] |
| 60 | 120 | 35 |
| 80 | 250 | 45 |
| 100 | 450 | 55 |
- Renewal of an existing road or railway line as a maintenance measure. Here the old axle is retained and only the discontinuities and defects caused by wear and tear and settlement are eliminated. No planning process is necessary here, as the route that has already been approved is not being changed, only being renovated, whereby minor changes are also permitted and customary.
- New construction of a route in the area of the route variant selected by the preliminary investigations. Here the planners must define an axis that fits into the specified corridor and lies within the specifications of the technical guidelines, which, depending on the importance of the route, are specified by the building contractor as a basis for assessment. In the course of the planning, the measure goes through the prescribed examination, hearing, approval and coordination procedures with landscape planners, nature conservation, authorities that are subject to a hearing, interest groups, etc. (see accompanying landscape conservation plan ).
| Minimum clothoid parameters | |
| V E [km / h] | min A [m] |
| 60 | 40 |
| 80 | 80 |
| 100 | 150 |
- Expansion of an existing route with improvement of the alignment in position and height. The aim of this measure is to improve the performance of the route within the framework of the existing route and its peripheral areas. This leads to sections with full expansion and deviations from the existing stock and to sections with partial expansion of the existing route on a new axis to be determined. In this case, too, because of the full expansion sections, the planning is subject to the multi-stage testing, hearing and approval program as with the new building.
| Maximum longitudinal gradients ( road category A ) | |
| V E [km / h] | Max. s [%] |
| 60 | 8.0 |
| 80 | 6.0 |
| 100 | 4.5 |
The rated values for a road are taken into account when calculating the axles according to the specified design speed V E. This is a speed that enables safe driving of the route on a wet but clean road with a surface of average roughness even in the case of the minimum values listed below. The design speed depends on the importance of a traffic connection in the network as well as economic efficiency and is higher for long-distance connections than for roads that only serve regional traffic. This is also taken into account in the cross-sectional dimensioning, although the daily traffic volume also has a very decisive influence.
| Summit minimum radius (with sufficient stopping distance ) | |
| V E [km / h] | min. H K [m] |
| 60 | 2400 |
| 80 | 4400 |
| 100 | 8300 |
From a strictly mathematical point of view, the axis of traffic routes is only an auxiliary line for dimensioning and implementation during construction. However, their respective definition is expressed very clearly in the character of the route and has a lasting impact on the spatial lines. Some important rated values for the design speeds V E = 60 km / h to V E = 100 km / h are listed on the right. These values apply to the main axis of the road, which for this reason lies in the middle of the structure and thus represents the mean value.
The transverse slope for drainage of the roadway is usually 2.5% and increases to a maximum of 7.5% for sufficient introduction of the transverse forces when cornering into the roadway. The minimum radii and minimum parameters of clothoids when dimensioning according to the design speed V E are matched to this value.
Design methodology and routing parameters are presented and specified in the guidelines for the construction of roads - Part: Routing (RAS-L) of the Federal Ministry of Transport.
| Minimum tub diameter | |
| V E [km / h] | min. H W [m] |
| 60 | 750 |
| 80 | 1300 |
| 100 | 3800 |
Effects of the dimensioning on the axis definition
A comparison of the table values shows that this has a decisive influence on the variability when adapting to the existing terrain of the route. A high design speed on difficult terrain requires far greater and broader interventions in the landscape than at low design speeds. The planning process is also influenced by this, because high landscape consumption leads to longer planning and approval processes, as there are more affected people, which makes difficult land acquisition procedures necessary and the compensatory measures for this intervention sometimes have to be arranged and planned over a large area (see accompanying landscape conservation plan ). The same applies to the construction costs of the measure, which increase disproportionately with increasing design speed and cross-sectional width.
This also applies to the construction of railway lines. Here, however, there is a possibility of comparison over a good 150 years as to how the planning and thus the routing and axis definition changed over time with the structural possibilities of the respective time. It is striking, for example, how mountain railways of the 19th century were based on the difficult topography with relatively small corrections and used every opportunity to gain height by extending the route through large loops in side valleys in order to achieve the maximum gradient of around 2.5% to keep. Driving time and average speed only played a secondary role, overcoming the mountain range was clearly in the foreground. Almost twice the length of the route as the crow flies at a speed of only 25 to 30 km / h on the curvy route was a huge step forward compared to horse-drawn carriage traffic , which nevertheless brought enormous time savings and increased transport capacity with high reliability.
Large bridges and tunnels were very difficult and costly to carry out under the given conditions without mechanical support. Because most of the material used had to be obtained on site, it had to be adapted to the local environment. The performance of the steam locomotives of the time also restricted the freedom of design. This is how engineering structures came into being, which, given these limited possibilities, still deserve the highest recognition as pioneering achievements. (Examples: Semmering Railway , Brennerbahn , Gotthard Railway )
Such adjustments are no longer necessary today, as the construction of the Gotthard Base Tunnel shows. That does not mean, however, that there are no imperatives to adapt; however, these have fundamentally shifted. The high density of settlements as well as landscape and environmental protection require solutions that, with a sense of proportion with the specifications and good coordination with all those concerned in the run-up to the detailed planning, lead to a high level of acceptance. As a working basis, the axis of a traffic route can be flexibly adapted to the respective requirements, both in the 19th century, who believed in progress and was enthusiastic about technology, when only the costs and structural feasibility counted, as well as in today's times, where it is important, the technical To reconcile opportunities with the needs of residents and road users as well as landscape and environmental protection. The need to realize a building project at reasonable costs is still there, but the consideration and weighting of other influencing factors is much more important today than the mere feasibility.
As a mathematical model of a line composed of individual elements, the axis can be used as universally and value-free as the coordinate system on which it is based.
See also
Norms and standards
- Research Society for Roads and Transport: Guidelines for the construction of roads - Part: Lines , Edition 1995. FGSV-Verlag, Cologne
- Research company for roads and traffic: Guidelines for the construction of roads - Part: Cross section , edition 1996. FGSV-Verlag, Cologne
literature
- Günter Wolf: Road planning . Werner Verlag, 2005, ISBN 3-8041-5003-9 , p. 105 ff.
- Ferdinand Wöckel: Guide for railway construction . Publishing company Rudolf Müller, Cologne-Braunsfeld 1963
- Henning Natzschka: Road construction - design and construction technology . BG Teubner Verlag, 2003, ISBN 3-519-15256-8 , pp. 119 ff.
- Volker Matthews: Railway construction . BG Teubner Verlag, 2007, ISBN 3-8351-0013-0 , p. 66 ff.