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built templatetrack-geometrywith-tool

Vertical Curve Design

Computes the minimum vertical curve radius and length required at railway grade transition points using R_v = V^2 / (12.96 * a_v) and L_v = (A/100) * R_v. Ensures vertical acceleration remains within passenger comfort and rolling stock safety limits per ARTC ETS-05-00 and AREMA Chapter 5.

inputs

4 fields

context

4 archetypes

engine

with-tool

outputs

3 scored fields

contract fields

Parameter Map

4 inputs to 3 scored outputs

  • initial_grade_pct

    float

    Initial longitudinal grade g1 (positive = uphill)

    -5 to 5%

  • final_grade_pct

    float

    Final longitudinal grade g2 (positive = uphill)

    -5 to 5%

  • design_speed_km_h

    float

    Design operating speed V

    20 to 300km/h

  • max_vertical_acceleration_m_s2

    floatfrom archetypehidden in hard

    Maximum acceptable vertical acceleration a_v for passenger comfort

    0.01 to 0.1m/s²
algebraic_grade_difference_pcttol 0.01

Algebraic grade difference A = |g1 - g2| (%)

min_vertical_curve_radius_mtol 0.03

Minimum vertical curve radius R_v (m)

min_vertical_curve_length_mtol 0.03

Minimum vertical curve length L_v (m)

visibility contract

Difficulty Ladder

all_giveneasy

All parameters given, moderate gradients on mainline or freight corridors

all fields visible
all_givenmedium

All parameters given, any corridor type including steep metro grades

all fields visible
partialhard

Vertical acceleration hidden — agent must infer from corridor type and passenger comfort requirements

max_vertical_acceleration_m_s2

scenario bands

Archetype Atlas

mainline_passenger

3 contexts

Mainline passenger rail corridor with moderate speeds and comfort requirements

initial_grade_pct-2 to 2
final_grade_pct-2 to 2
design_speed_km_h100 to 160
max_vertical_acceleration_m_s20.03 to 0.05

artc-north-south-corridor / sydney-central-west / melbourne-geelong-mainline

heavy_haul_freight

3 contexts

Heavy haul freight corridor with low speeds and relaxed comfort limits

initial_grade_pct-1.5 to 1.5
final_grade_pct-1.5 to 1.5
design_speed_km_h60 to 100
max_vertical_acceleration_m_s20.05 to 0.07

artc-hunter-valley-coal / pilbara-iron-ore-wa / qld-north-coast-freight

urban_metro

3 contexts

Urban metro or commuter rail with tight gradients and frequent grade transitions

initial_grade_pct-3.5 to 3.5
final_grade_pct-3.5 to 3.5
design_speed_km_h40 to 80
max_vertical_acceleration_m_s20.03 to 0.05

sydney-metro-northwest / melbourne-metro-tunnel / brisbane-cross-river-rail

branch_line

3 contexts

Regional branch line with moderate gradients and mixed traffic

initial_grade_pct-2.5 to 2.5
final_grade_pct-2.5 to 2.5
design_speed_km_h20 to 80
max_vertical_acceleration_m_s20.04 to 0.07

nsw-north-coast-line / vic-geelong-warrnambool / qld-western-line

rendered task

Generation Preview

artc-north-south-corridor-mainline-passenger-preview

difficulty
hard
visibility
partial
archetype
mainline_passenger
site context
artc-north-south-corridor
instruction excerptvertical-curve-design_calc.py

visible fields

  • initial_grade_pct-2 to 2 %
  • final_grade_pct-2 to 2 %
  • design_speed_km_h100 to 160 km/h

withheld schema

max_vertical_acceleration_m_s2algebraic_grade_difference_pctmin_vertical_curve_radius_mmin_vertical_curve_length_m
Mainline passenger rail corridor with moderate speeds and comfort requirements. artc-north-south-corridor. Required outputs: algebraic_grade_difference_pct, min_vertical_curve_radius_m, min_vertical_curve_length_m