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

Cant Calculation

Computes equilibrium cant, cant deficiency, and maximum allowable speed for curved railway track sections using the ARTC ETS-05-00 / AREMA formula E_eq = C * V^2 / R. Supports both standard and narrow gauge constants, and is used in track geometry design to balance passenger comfort against derailment risk on curves.

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

Standards

AREMA MRE Chapter 5ARTC ETS-05-00FRA 49 CFR Part 213

Tags

cantcivilcurvesdeterministicrailsuperelevationtrack-geometry

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

5 inputs

Always given

Included directly in every task prompt.

2

  • Design speed

    design_speed_km_h

    Design operating speed V

    20 – 250 km/h

  • Curve radius

    curve_radius_m

    Horizontal curve radius R

    150 – 5000 m

Derived from scenario

Sampled from the scenario and inferable from its description.

2

  • Actual cant

    actual_cant_mm

    Applied (actual) cant E_a

    Derived from the archetype scenario. Hidden at hard difficulty.

    0 – 150 mm

  • Max cant deficiency

    max_cant_deficiency_mm

    Maximum allowable cant deficiency C_d_max

    Derived from the archetype scenario. Hidden at hard difficulty.

    50 – 110 mm

Optional

Used only when the sampled task needs this part of the contract.

1

  • Gauge type

    gauge_type

    Track gauge classification

    Optional input.

    standardnarrow

Scored outputs

3 outputs

Equilibrium cant

equilibrium_cant_mm

Equilibrium cant E_eq (mm)

Scores if within ±3% of the reference value.

Cant deficiency

cant_deficiency_mm

Cant deficiency C_d = E_eq - E_a (mm)

Scores if within ±3% of the reference value.

Maximum speed km h

maximum_speed_km_h

Maximum allowable speed V_max (km/h)

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

All parameters given, gentle curves on mainline or branch

Gauge type restricted to: standard

medium

All inputs given

All parameters given, any corridor type including tight metro curves and high speed

hard

Some inputs hidden

Actual cant and max deficiency hidden — agent must infer from corridor type and operating context

Hidden inputs

  • Actual cantactual_cant_mm
  • Max cant deficiencymax_cant_deficiency_mm

Prompt replacement text

The track is a {{ archetype.description }} ({{ archetype.site_context }})

Task bundle

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

/workspace

  • instruction.md
  • cant-calculation_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 civil engineer specializing in railway track geometry and alignment design.2 3## Problem4 5Determine the equilibrium cant (superelevation), cant deficiency, and maximum allowable speed for a curved track section.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Design speed (V) | {{ design_speed_km_h }} | km/h |12| Curve radius (R) | {{ curve_radius_m }} | m |13{% if actual_cant_mm is defined %}14| Actual cant (E_a) | {{ actual_cant_mm }} | mm |15{% endif %}16{% if max_cant_deficiency_mm is defined %}17| Max cant deficiency (C_d_max) | {{ max_cant_deficiency_mm }} | mm |18{% endif %}19{% if gauge_type is defined %}20| Gauge type | {{ gauge_type }} | - |21{% endif %}22{% if archetype_description is defined %}23 24### Site Conditions25 26{{ archetype_description }}27{% endif %}28 29{% if tool_available %}30## Available Tool31 32A cant calculation tool is available at `/workspace/{{ meta.name }}_calc.py`. Run it with:33 34```bash35python3 /workspace/{{ meta.name }}_calc.py --help36```37 38You may use this tool to verify your calculations or compute values directly.39{% endif %}40 41## Required42 43Calculate the following:44 451. Equilibrium cant E_eq (mm)462. Cant deficiency C_d (mm)473. Maximum allowable speed V_max (km/h)48 49## Applicable Standards50 51- ARTC Engineering Track Standard ETS-05-00 (Track Geometry)52- AREMA Manual for Railway Engineering, Chapter 5 (Track)53- FRA 49 CFR Part 213 (Track Safety Standards)54 55## Constraints56 57- No internet access is available. Work from engineering knowledge and the provided tool.58- Use the ARTC/AREMA equilibrium cant formula:59 - E_eq = C * V^2 / R60 - where C = 11.82 for standard gauge (1435 mm), C = 8.90 for narrow gauge (1067 mm)61 - V is design speed in km/h, R is curve radius in metres, E_eq is in mm62- Calculate cant deficiency:63 - C_d = E_eq - E_a64 - where E_a is the actual (applied) cant in mm65- Calculate maximum allowable speed from actual cant and maximum deficiency:66 - V_max = sqrt(R * (E_a + C_d_max) / C)67 - where C_d_max is the maximum allowable cant deficiency in mm68{% if gauge_type is not defined %}69- Use standard gauge (C = 11.82) unless otherwise specified70{% endif %}71 72## Output Format73 74Show your step-by-step working in Markdown. At the end of your solution, include a JSON block with your final answers in exactly this format:75 76```json77{78 "equilibrium_cant_mm": <numeric_value>,79 "cant_deficiency_mm": <numeric_value>,80 "maximum_speed_km_h": <numeric_value>81}82```83 84Write your complete solution to `/workspace/output.md`.85

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.

Urban metro

urban_metro

Urban metro or light rail line with tight curves and frequent stops

sydney-metro-northwestmelbourne-metro-tunnelbrisbane-cross-river-rail
Parameter ranges
curve_radius_m
150 – 400
design_speed_km_h
40 – 80
actual_cant_mm
40 – 100
max_cant_deficiency_mm
50 – 75

Mainline freight

mainline_freight

Mainline freight corridor with gentle curves and heavy axle loads

artc-hunter-valley-coalartc-north-south-corridorpilbara-iron-ore-wa
Parameter ranges
curve_radius_m
800 – 3000
design_speed_km_h
60 – 115
actual_cant_mm
30 – 80
max_cant_deficiency_mm
50 – 75

High speed passenger

high_speed_passenger

High-speed passenger rail corridor with sweeping curves

sydney-melbourne-hsrbrisbane-gold-coast-fast-railperth-bunbury-fast-rail
Parameter ranges
curve_radius_m
1500 – 5000
design_speed_km_h
130 – 250
actual_cant_mm
80 – 150
max_cant_deficiency_mm
75 – 110

Branch line

branch_line

Regional branch line with moderate curves and mixed traffic

nsw-north-coast-linevic-geelong-warrnamboolqld-western-line
Parameter ranges
curve_radius_m
200 – 800
design_speed_km_h
20 – 80
actual_cant_mm
20 – 80
max_cant_deficiency_mm
50 – 75

Example task

sydney-metro-northwest-urban-metro-preview — hard difficulty, some inputs hidden.

Urban metro or light rail line with tight curves and frequent stops. sydney-metro-northwest. Required outputs: equilibrium_cant_mm, cant_deficiency_mm, maximum_speed_km_h

The model sees

Scenario context and visible inputs.

design_speed_km_h
40 to 80 km/h
curve_radius_m
150 to 400 m
gauge_type
standard

Executable tool: cant-calculation_calc.py

The model must infer

Inputs withheld at this difficulty.

  • Max cant deficiency

    max_cant_deficiency_mm

  • Actual cant

    actual_cant_mm

Stand-in text in the prompt

The track is a {{ archetype.description }} ({{ archetype.site_context }})

The model must produce

The scored JSON answer schema.

{
  "equilibrium_cant_mm": <number>,
  "cant_deficiency_mm": <number>,
  "maximum_speed_km_h": <number>
}
  • equilibrium_cant_mm · scored within ±3%
  • cant_deficiency_mm · scored within ±3%
  • maximum_speed_km_h · scored within ±3%