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

Curve Elements

Computes the geometric elements of a simple horizontal circular curve given the radius, deflection angle, and intersection-point chainage, per AGRD Part 3. Derives tangent length (T = R tan(delta/2)), arc length, external distance, mid-ordinate, and PC/PT chainages. Used in road and rail alignment design to set out curve geometry in the field.

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

Standards

AGRD Part 3

Tags

chainagecivilcurvesdeterministichorizontal-geometryroads

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

3 inputs

Always given

Included directly in every task prompt.

2

  • Curve radius

    curve_radius_m

    Horizontal curve radius R

    25 – 2000 m

  • Deflection angle deg

    deflection_angle_deg

    Deflection (intersection) angle Δ between tangents

    5 – 120 degrees

Hidden at higher difficulty

Visible in easier tasks and withheld in one or more harder tiers.

1

  • Ip chainage

    ip_chainage_m

    Chainage of the intersection point (IP)

    Hidden at hard difficulty.

    100 – 50000 m

Scored outputs

6 outputs

Tangent length

tangent_length_m

Tangent length T (m)

Scores if within ±3% of the reference value.

Arc length

arc_length_m

Arc length L (m)

Scores if within ±3% of the reference value.

External distance

external_distance_m

External distance E (m)

Scores if within ±3% of the reference value.

Mid ordinate

mid_ordinate_m

Mid-ordinate M (m)

Scores if within ±3% of the reference value.

Pc chainage

pc_chainage_m

Chainage of the point of curvature PC (m)

Scores if within ±3% of the reference value.

Pt chainage

pt_chainage_m

Chainage of the point of tangency PT (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

All parameters given, gentle curve on a rural highway

medium

All inputs given

All parameters given, any road type and curve geometry

hard

Some inputs hidden

IP chainage hidden — agent must back-calculate from PC chainage and tangent length

Hidden inputs

  • Ip chainageip_chainage_m

Prompt replacement text

The PC (point of curvature) is at chainage {{ pc_chainage_m }} m

Task bundle

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

/workspace

  • instruction.md
  • curve-elements_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 road geometry and horizontal alignment design.2 3## Problem4 5Calculate the full set of horizontal curve elements for a simple circular curve.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Curve radius (R) | {{ curve_radius_m }} | m |12| Deflection angle (Δ) | {{ deflection_angle_deg }} | degrees |13{% if ip_chainage_m is defined %}14| IP chainage | {{ ip_chainage_m }} | m |15{% endif %}16{% if pc_chainage_m is defined and ip_chainage_m is not defined %}17 18### Additional Information19 20{{ replacement_text }}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 curve elements 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. Tangent length T (m)462. Arc length L (m)473. External distance E (m)484. Mid-ordinate M (m)495. PC chainage (m) — chainage of the point of curvature506. PT chainage (m) — chainage of the point of tangency51 52## Applicable Standards53 54- Austroads Guide to Road Design Part 3 (AGRD Part 3)55 56## Constraints57 58- No internet access is available. Work from engineering knowledge and the provided tool.59- Use the following standard horizontal curve formulas:60 - Tangent length: T = R × tan(Δ/2)61 - Arc length: L = R × Δ (where Δ is in radians)62 - External distance: E = R × (1/cos(Δ/2) − 1)63 - Mid-ordinate: M = R × (1 − cos(Δ/2))64 - PC chainage = IP chainage − T65 - PT chainage = PC chainage + L66{% if ip_chainage_m is not defined %}67 - IP chainage = PC chainage + T (back-calculate from the given PC chainage)68{% endif %}69- Convert the deflection angle from degrees to radians before applying trigonometric functions.70 71## Output Format72 73Show 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:74 75```json76{77 "tangent_length_m": <numeric_value>,78 "arc_length_m": <numeric_value>,79 "external_distance_m": <numeric_value>,80 "mid_ordinate_m": <numeric_value>,81 "pc_chainage_m": <numeric_value>,82 "pt_chainage_m": <numeric_value>83}84```85 86Write your complete solution to `/workspace/output.md`.87

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 intersection

urban_intersection

Urban intersection approach with tight curve radius and large deflection angle

sydney-cbd-intersectionmelbourne-city-roundaboutbrisbane-inner-junction
Parameter ranges
curve_radius_m
25 – 100
deflection_angle_deg
60 – 120

Rural highway

rural_highway

Rural two-lane highway with large-radius sweeping curves

bruce-highway-qldpacific-highway-nswhume-highway-vic
Parameter ranges
curve_radius_m
300 – 1200
deflection_angle_deg
15 – 60

Motorway ramp

motorway_ramp

Motorway on/off ramp with moderate radius and variable deflection

m1-pacific-motorway-rampm2-hills-motorway-rampcitylink-melbourne-ramp
Parameter ranges
curve_radius_m
80 – 250
deflection_angle_deg
30 – 90

Residential street

residential_street

Low-speed residential street with tight geometry

suburban-cul-de-sacestate-road-curvelocal-collector-bend
Parameter ranges
curve_radius_m
25 – 80
deflection_angle_deg
20 – 90

Example task

sydney-cbd-intersection-urban-intersection-preview — hard difficulty, some inputs hidden.

Urban intersection approach with tight curve radius and large deflection angle. sydney-cbd-intersection. Required outputs: tangent_length_m, arc_length_m, external_distance_m, mid_ordinate_m, pc_chainage_m, pt_chainage_m

The model sees

Scenario context and visible inputs.

curve_radius_m
25 to 100 m
deflection_angle_deg
60 to 120 degrees

Executable tool: curve-elements_calc.py

The model must infer

Inputs withheld at this difficulty.

  • Ip chainage

    ip_chainage_m

Stand-in text in the prompt

The PC (point of curvature) is at chainage {{ pc_chainage_m }} m

The model must produce

The scored JSON answer schema.

{
  "tangent_length_m": <number>,
  "arc_length_m": <number>,
  "external_distance_m": <number>,
  "mid_ordinate_m": <number>,
  "pc_chainage_m": <number>,
  "pt_chainage_m": <number>
}
  • tangent_length_m · scored within ±3%
  • arc_length_m · scored within ±3%
  • external_distance_m · scored within ±3%
  • mid_ordinate_m · scored within ±3%
  • pc_chainage_m · scored within ±3%
  • pt_chainage_m · scored within ±3%