LIVEdataset aec-bench@releasetasks 552models 18last submission … · built …
electricalwith-tool

Single Span Sag Tension

Computes mid-span sag, wire length, and catenary constant for a single level span of overhead contact wire used in rail electrification. Applies both the parabolic approximation (S = wL^2/8T) and exact catenary equations per EN 50119, enabling comparison of the two methods across light rail, mainline, and high-speed catenary scenarios.

with-tool: The model is given an executable Python calculator script.

Standards

EN 50119EN 50367

Tags

catenarydeterministicelectricaloverhead-wiresag-tension

How this task is generated

One template produces many comparable benchmark tasks while keeping the scoring contract fixed.

  1. 01

    Template

    The reusable contract shown on this page.

  2. 02

    Scenario

    An archetype and site context are sampled.

  3. 03

    Difficulty tier

    Inputs may be hidden at harder tiers.

  4. 04

    Task prompt

    The model responds with the declared outputs.

Parameters

Inputs the model receives, and the outputs it is scored on.

Inputs

4 inputs

Always given

Included directly in every task prompt.

3

  • Span length

    span_length_m

    Horizontal span length between supports

    20 – 120 m

  • Horizontal tension

    horizontal_tension_n

    Horizontal component of wire tension at mid-span

    5000 – 30000 N

  • Wire diameter

    wire_diameter_mm

    Outer diameter of the contact wire

    8 – 16 mm

Derived from scenario

Sampled from the scenario and inferable from its description.

1

  • Wire weight per m n

    wire_weight_per_m_n

    Wire weight per unit length (gravitational force per metre)

    Derived from the archetype scenario. Hidden at hard difficulty.

    3 – 30 N/m

Scored outputs

4 outputs

Sag

sag_m

Mid-span sag using parabolic approximation (m)

Scores if within ±3% of the reference value.

Sag catenary

sag_catenary_m

Mid-span sag using exact catenary equation (m)

Scores if within ±3% of the reference value.

Wire length

wire_length_m

Total wire length in the span using catenary equation (m)

Scores if within ±3% of the reference value.

Catenary constant

catenary_constant_m

Catenary constant C = T / w (m)

Scores if within ±3% of the reference value.

Difficulty

Each template is sampled at three tiers. Harder tiers may hide inputs, forcing the model to infer them from the scenario description.

easy

All inputs given

Short spans, all params given, light rail scenarios

Span length restricted to: {'min': 25.0, 'max': 40.0}

medium

All inputs given

Any span length and wire type, all params given

hard

Some inputs hidden

Wire weight hidden, agent must infer from wire diameter and material context

Hidden inputs

  • Wire weight per m nwire_weight_per_m_n

Prompt replacement text

The installation uses {{ archetype.description }} practices along the {{ archetype.site_context }} corridor

Task bundle

The exact instruction and parameter contract used to generate this task, pinned to the published library source.

/workspace

  • instruction.md
  • single-span-sag-tension_calc.py

Teal lines show Jinja input conditions, not task visibility policy. A line renders only when that input or tool is visible.

1You are a senior electrical engineer specializing in overhead contact line design for rail electrification.2 3## Problem4 5Calculate the mid-span sag (parabolic and exact catenary), wire length, and catenary constant for a single level span of overhead contact wire per EN 50119.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Span length (L) | {{ span_length_m }} | m |12{% if wire_weight_per_m_n is defined %}13| Wire weight per unit length (w) | {{ wire_weight_per_m_n }} | N/m |14{% endif %}15| Horizontal tension (T) | {{ horizontal_tension_n }} | N |16| Wire diameter | {{ wire_diameter_mm }} | mm |17{% if archetype_description is defined %}18 19### Installation Context20 21{{ archetype_description }}22{% endif %}23 24{% if tool_available %}25## Available Tool26 27A sag-tension calculation tool is available at `/workspace/single-span-sag-tension_calc.py`. Run it with:28 29```bash30python3 /workspace/single-span-sag-tension_calc.py --help31```32 33You may use this tool to verify your calculations or compute values directly.34{% endif %}35 36## Required37 38Calculate the following:39 401. Mid-span sag using the parabolic approximation (m)412. Mid-span sag using the exact catenary equation (m)423. Total wire length in the span using the catenary equation (m)434. Catenary constant C (m)44 45## Applicable Standards46 47- EN 50119 — Railway applications — Fixed installations — Electric traction overhead contact lines48- EN 50367 — Railway applications — Current collection systems — Technical criteria for the interaction between pantograph and overhead contact line49 50## Constraints51 52- No internet access is available. Work from engineering knowledge and the provided tool.53- Use the following equations:54 - Catenary constant: C = T / w, where T is horizontal tension (N) and w is weight per unit length (N/m)55 - Parabolic sag: S = w * L^2 / (8 * T), where L is span length (m)56 - Exact catenary sag: S_cat = C * (cosh(L / (2 * C)) - 1)57 - Wire length (catenary): l = 2 * C * sinh(L / (2 * C))58- The parabolic approximation is valid when sag is less than about 5% of span length. The exact catenary gives the precise result regardless of sag-to-span ratio.59- cosh and sinh are hyperbolic cosine and sine functions respectively.60 61## Output Format62 63Show your step-by-step working in Markdown, including the catenary constant calculation, both sag methods, and the wire length computation. At the end of your solution, include a JSON block with your final answers in exactly this format:64 65```json66{67 "sag_m": <numeric_value>,68 "sag_catenary_m": <numeric_value>,69 "wire_length_m": <numeric_value>,70 "catenary_constant_m": <numeric_value>71}72```73 74Write your complete solution to `/workspace/output.md`.75

Scenario archetypes

Each generated task is drawn from one of these realistic scenario bands.

Site contexts ground each scenario in a real locale the model can use to infer hidden values.

Light rail copper

light_rail_copper

Light rail copper contact wire (Cu AC-100)

sydney-light-railmelbourne-tram-network
Parameter ranges
span_length_m
25 – 50
wire_weight_per_m_n
8 – 10
horizontal_tension_n
8000 – 12000
wire_diameter_mm
10 – 12

Mainline catenary

mainline_catenary

Mainline rail catenary with CuAg AC-120 contact wire (nominal 10.8-12.5 N/m)

brisbane-cross-river-railsydney-metro-northwest
Parameter ranges
span_length_m
45 – 75
wire_weight_per_m_n
10.8 – 12.5
horizontal_tension_n
10000 – 20000
wire_diameter_mm
12 – 14

High speed catenary

high_speed_catenary

High-speed rail catenary with CuAg AC-150 contact wire (nominal 14.5-16.0 N/m)

melbourne-geelong-fast-railsydney-newcastle-corridor
Parameter ranges
span_length_m
55 – 120
wire_weight_per_m_n
14.5 – 16
horizontal_tension_n
15000 – 30000
wire_diameter_mm
13 – 16

Example task

brisbane-cross-river-rail-mainline-catenary-preview — hard difficulty, some inputs hidden.

Mainline rail catenary with CuAg AC-120 contact wire (nominal 10.8-12.5 N/m). brisbane-cross-river-rail. Required outputs: sag_m, sag_catenary_m, wire_length_m, catenary_constant_m

The model sees

Scenario context and visible inputs.

span_length_m
45 to 75 m
horizontal_tension_n
10000 to 20000 N
wire_diameter_mm
12 to 14 mm

Executable tool: single-span-sag-tension_calc.py

The model must infer

Inputs withheld at this difficulty.

  • Wire weight per m n

    wire_weight_per_m_n

Stand-in text in the prompt

The installation uses {{ archetype.description }} practices along the {{ archetype.site_context }} corridor

The model must produce

The scored JSON answer schema.

{
  "sag_m": <number>,
  "sag_catenary_m": <number>,
  "wire_length_m": <number>,
  "catenary_constant_m": <number>
}
  • sag_m · scored within ±3%
  • sag_catenary_m · scored within ±3%
  • wire_length_m · scored within ±3%
  • catenary_constant_m · scored within ±3%