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

Min Curve Radius

Calculates the absolute minimum and desirable minimum horizontal curve radius for road design using R_min = V^2 / (127 * (e_max + f)) per Austroads Guide to Road Design Part 3 Section 7. The desirable radius uses a reduced friction factor (0.7f) for an additional safety margin. Used in road geometric design to ensure vehicle stability and driver comfort on horizontal curves.

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

Standards

AGRD Part 3 §7

Tags

civilcurvesdeterministichorizontal-geometryradiusroads

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

  • Design speed

    design_speed_km_h

    Design speed V

    40 – 130 km/h

  • Max superelevation pct

    max_superelevation_pct

    Maximum superelevation rate e_max

    3 – 8 %

Derived from scenario

Sampled from the scenario and inferable from its description.

1

  • Side friction factor

    side_friction_factor

    Side friction factor f (speed-dependent, from AGRD Table 7.5)

    Derived from the archetype scenario. Hidden at hard difficulty.

    0.09 – 0.35

Scored outputs

2 outputs

Min radius

min_radius_m

Absolute minimum horizontal curve radius R_min (m)

Scores if within ±3% of the reference value.

Desirable min radius

desirable_min_radius_m

Desirable minimum horizontal curve radius R_desirable (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, low-speed urban or suburban road

medium

All inputs given

All parameters given, any road type and speed environment

hard

Some inputs hidden

Side friction factor hidden — agent must infer f from design speed using AGRD Table 7.5

Hidden inputs

  • Side friction factorside_friction_factor

Prompt replacement text

The road is a {{ archetype.description }} ({{ archetype.site_context }}). Determine the appropriate side friction factor from AGRD Table 7.5 for the given design speed.

Task bundle

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

/workspace

  • instruction.md
  • min-curve-radius_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 5Determine the minimum horizontal curve radius and the desirable minimum horizontal curve radius for a road alignment.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Design speed (V) | {{ design_speed_km_h }} | km/h |12| Maximum superelevation rate (e_max) | {{ max_superelevation_pct }} | % |13{% if side_friction_factor is defined %}14| Side friction factor (f) | {{ side_friction_factor }} | - |15{% endif %}16{% if archetype_description is defined %}17 18### Site Conditions19 20{{ archetype_description }}21{% endif %}22 23{% if tool_available %}24## Available Tool25 26A minimum curve radius calculation tool is available at `/workspace/{{ meta.name }}_calc.py`. Run it with:27 28```bash29python3 /workspace/{{ meta.name }}_calc.py --help30```31 32You may use this tool to verify your calculations or compute values directly.33{% endif %}34 35## Required36 37Calculate the following:38 391. Absolute minimum horizontal curve radius R_min (m)402. Desirable minimum horizontal curve radius R_desirable (m)41 42## Applicable Standards43 44- Austroads Guide to Road Design Part 3 (AGRD Part 3 §7)45 46## Constraints47 48- No internet access is available. Work from engineering knowledge and the provided tool.49- Use the point-mass equilibrium equation for minimum curve radius:50 - R_min = V² / (127 × (e_max + f))51 - where V is design speed in km/h, e_max is the maximum superelevation rate as a decimal (e.g. 0.06 for 6%), and f is the side friction factor52- For the desirable minimum radius, use a reduced friction factor of 0.7 × f:53 - R_desirable = V² / (127 × (e_max + 0.7 × f))54{% if side_friction_factor is not defined %}55- Side friction factors from AGRD Table 7.5 (speed → f):56 40 km/h → 0.35, 50 → 0.33, 60 → 0.30, 70 → 0.26, 80 → 0.22, 90 → 0.19, 100 → 0.16, 110 → 0.13, 120 → 0.11, 130 → 0.0957{% endif %}58 59## Output Format60 61Show 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:62 63```json64{65 "min_radius_m": <numeric_value>,66 "desirable_min_radius_m": <numeric_value>67}68```69 70Write your complete solution to `/workspace/output.md`.71

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 local

urban_local

Low-speed urban local road with frequent intersections and pedestrian activity

sydney-local-streetmelbourne-inner-suburbbrisbane-residential-road
Parameter ranges
design_speed_km_h
40 – 60
max_superelevation_pct
3 – 4
side_friction_factor
0.3 – 0.35

Suburban arterial

suburban_arterial

Suburban arterial road with moderate traffic and signalised intersections

sydney-parramatta-roadmelbourne-springvale-roadbrisbane-waterworks-road
Parameter ranges
design_speed_km_h
60 – 80
max_superelevation_pct
5 – 6
side_friction_factor
0.22 – 0.3

Rural highway

rural_highway

Rural two-lane highway through open terrain with higher operating speeds

bruce-highway-qldprinces-highway-vicgreat-western-highway-nsw
Parameter ranges
design_speed_km_h
80 – 110
max_superelevation_pct
6 – 7
side_friction_factor
0.13 – 0.22

Motorway

motorway

High-speed divided motorway with grade-separated interchanges

m1-pacific-motorwaym2-hills-motorwaywestern-ring-road-melbourne
Parameter ranges
design_speed_km_h
100 – 130
max_superelevation_pct
5 – 6
side_friction_factor
0.09 – 0.16

Example task

sydney-parramatta-road-suburban-arterial-preview — hard difficulty, some inputs hidden.

Suburban arterial road with moderate traffic and signalised intersections. sydney-parramatta-road. Required outputs: min_radius_m, desirable_min_radius_m

The model sees

Scenario context and visible inputs.

design_speed_km_h
60 to 80 km/h
max_superelevation_pct
5 to 6 %

Executable tool: min-curve-radius_calc.py

The model must infer

Inputs withheld at this difficulty.

  • Side friction factor

    side_friction_factor

Stand-in text in the prompt

The road is a {{ archetype.description }} ({{ archetype.site_context }}). Determine the appropriate side friction factor from AGRD Table 7.5 for the given design speed.

The model must produce

The scored JSON answer schema.

{
  "min_radius_m": <number>,
  "desirable_min_radius_m": <number>
}
  • min_radius_m · scored within ±3%
  • desirable_min_radius_m · scored within ±3%