help · WIRE - wires and sag

WIRE - wires and sag

Sag, tension and support forces of one span - single conductor, N-FL or R-FL - with the drawing and every formula.

WIRE in the top bar opens the calculator, when your licence plan includes it (Licence plans). It calculates one span between two supports A and B, with the method of the SBB tool Dh_Hf v250526, and shows how each number is found.

The three systems

  • Single conductor: a wire with fixed ends - a feeder or return conductor. Its tension changes with the temperature and with ice.
  • N-FL: a catenary whose messenger is fixed at the ends and whose contact wire is tensioned by weights. The messenger's tension changes with the temperature; the table gives it from -20 to 80 °C.
  • R-FL: messenger and contact wire both tensioned by weights. The tensions stay constant; only ice and a worn contact wire change the sag.

Choose the system at the top. The conductors and catenaries come from the catalogue: the standard ones and those of your company (Catalogue).

The inputs

Every field says its unit and what it means. The span c is the horizontal distance from A to B; Δh is how much lower B is than A. Ice or snow (7 or 15 N/m) counts only at -5 °C, as SBB rule 0161.1013.0004 says.

  • Single conductor: the tension is known at one temperature - or, if it is not, from three points of the curve: A, B and a measured point below the chord.
  • N-FL: the installation tension of the unloaded messenger (before the contact wire is hung) at its temperature - or, with Known from, the loaded messenger tension at a table temperature, as the wire loads give it (Basis 10 kN at -20 °C): the page then finds the installation tension - and the contact wire tension. With the span model c_m the tension table is calculated for the ideal span of the tensioning section, the sag for this span.
  • R-FL: the messenger's and the contact wire's tension.

If a catenary has no typical tensions in the catalogue, reference values are filled in and the page says so - enter your own.

Every change recalculates at once. Calculate does the same without script. The page's address holds the whole calculation: keep it as a bookmark or send it, and it opens with the same values.

The page on one screen

The page is laid out like a CAD program and fits the window. At the top the bar names the calculation (system and wire or catenary) and holds the Standard toolbar: New calculation, Open the wire catalogue for its editors, and save - it saves the wire load, or a new wire into the catalogue. Beside it the three systems are tabs.

  • Left - the inputs, as a list of properties in groups: click a group's title to open or close it; a closed group shows its values in one line, and the page remembers which groups you keep open. A field's explanation appears while you type in it and when you point at it.
  • Middle - the window: its tabs Drawing, Charts, Tension table, Contact wire heights and Calculation, after them, in the same header, the toolbar with PDF and Print view; below, the view itself. The open tab is part of the address, so a bookmark opens it again.
  • Right - the results: the main values, the support forces, the sag at the points you entered; the second tab holds Wire load.

Each column scrolls in its own box, never the page; the status bar at the bottom names the units and the sag engine. On a small screen the columns stand one below the other.

Printing

PDF gives the calculation as a PDF file. Print view shows the same document as A4 pages, with Back to the calculation, PDF and Print at the top. The pages have the margins of the BEAM report, and page 1 says where the calculation opens again.

The results

  • the headline values: the tension, the messenger's and the contact wire's sag, the virtual span;
  • the drawing of the span: the supports, the messenger, the contact wire with the droppers, the chord (dotted) and the sag of the state shown, beside other states for comparison (10 °C, -20 °C, 80 °C, ice). Heights are drawn × k - sags are centimetres over tens of metres - and the drawing says by how much; choose k yourself under Vertical exaggeration;
  • the support forces at A and B: the vertical force F_V, which loads the mast, and the pull F_Z;
  • the sag at any points you enter - each drawn on the span, numbered like the table;
  • for a single conductor and N-FL the charts of tension and sag against the temperature, and the tension table.

Show the calculation

Show the calculation lists, for every step, the formula, the numbers put in and the result, with the section of the method. This is what a checking engineer reads. The main formulas:

  • the state-change equation - how the tension follows the temperature from the length of the wire: the elastic and thermal stretch equals the change of length from the sag;
  • the catenary's sag: the contact wire is level at 10 °C; after that it follows the change of the messenger's shape, so the messenger hangs like one wire with the tension messenger + contact wire under an effective load;
  • the sag of an inclined span from the virtual span a (the parabola's vertex);
  • the support forces from the catenary.

The method, with every formula: Method and formulas.

Reading values on the pictures

Point at the span drawing or a chart: a line follows the pointer, and a box shows every curve's value at that position with its unit - on the drawing the distance from A, each state's sag below the chord and the contact wire's own sag in mm; on a chart the temperature and each curve's tension or sag. With the keyboard, move to the picture (Tab) and use the arrow keys; Shift moves in larger steps, Home and End go to the ends.

Choices that don't apply

Where only certain values make sense, the field is a list. A choice that would make the calculation impossible is greyed out, and it becomes available as soon as it applies: ice or snow only at -5 °C, the covered part of the span only with ice case P1.2, P1.2 not together with P1.1 / P1.3. Fields that belong to another choice are hidden until that choice is made.

Defining wires for the mast calculation

The page also makes the wires the mast calculation uses. The railways save them: catalogue editors whose licence includes Own wires and wire loads save into their WIRE set (Catalogue). Everyone else calculates with a typed wire and sees the values, without saving.

  1. A new wire: choose New wire ... at the end of the conductor list and type its data sheet values - weight per metre, cross-section, modulus of elasticity, thermal expansion, diameter. Without a wind load the page takes 0.675 kN/m² × diameter, as the standard wires. The results use the new wire at once, with the catalogue's plausibility checks. Save the wire in the catalogue puts it into the catalogue and chooses it.
  2. Its tensions: under the known state, give the tension at its temperature - usually at -20 °C. The page shows the bare wire's tension at -20, -5 and +5 °C for this span, and the weight and wind per metre. Save as wire load saves them as a wire load with names in four languages - type condA for a conductor along the track, condT for a feeder across the track from a switching post -, which you can change before saving.
  3. A catenary gives two wire loads, saved together with Save both as wire loads: the messenger (condSN / condSR) and the contact wire (condCN / condCR), each with its own weight and wind. On N-FL the messenger's tensions come from the tension table, the contact wire's is Z_f; on R-FL both are tensioned by weights, so their values are the same at every temperature.

For a bundle of single conductors, set Conductors side by side (single conductors only - a catenary is always one): every value of the wire load is multiplied, and the name starts with 2x, 3x, ... - the sag stays that of one conductor. A fixed wire's tensions depend on the span, so the name says it, and every wire load keeps the address of its calculation: it opens again with the same values.

Design contact wire heights

For N-FL and R-FL the page also gives hf_min and hf_max after AB-EBV 2024 Art. 5.2.1 and 5.2.2. Enter the track under Contact wire heights (AB-EBV 2024): the structure gauge, the voltage, ballast, the speed, a level crossing, the allowances f and H, and for N-FL the conductor temperatures (the warmest for hf_min, the coldest for hf_max) - the contact wire's sag comes from the tension table. For R-FL the ice case decides the contact wire's sag with ice.

The ladder shows how each height is made: hf_min built up from the structure gauge, one block per allowance; hf_max built down from the absolute maximum. Between them lies the band a design height may use - green when it exists, red when hf_min lies above hf_max. Enter a design height under Planned design height and the page says whether it lies inside the band. The two tables list every allowance in mm.

The SBB tables for the contact wire heights hold only certain spans (60 to 26 m, and 24, 20, 16, 12, 8 m); for another span the page says so and shows the sag without the heights.

Where the calculator differs from the SBB tool

It reproduces the SBB tool - checked against twelve of its calculations. In two places the tool is inconsistent, and the calculator is not: with ice on an R-FL, the tool leaves the ice out of the vertical support force (the page shows the tool's value in a note); and the tool's single conductor table uses the height difference of the previous calculation.

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