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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.

inputs

5 fields

context

4 archetypes

engine

with-tool

outputs

3 scored fields

contract fields

Parameter Map

5 inputs to 3 scored outputs

  • design_speed_km_h

    float

    Design operating speed V

    20 to 250km/h

  • curve_radius_m

    float

    Horizontal curve radius R

    150 to 5000m

  • actual_cant_mm

    floatfrom archetypehidden in hard

    Applied (actual) cant E_a

    0 to 150mm

  • max_cant_deficiency_mm

    floatfrom archetypehidden in hard

    Maximum allowable cant deficiency C_d_max

    50 to 110mm

  • gauge_type

    enumoptional

    Track gauge classification

    standardnarrow
equilibrium_cant_mmtol 0.03

Equilibrium cant E_eq (mm)

cant_deficiency_mmtol 0.03

Cant deficiency C_d = E_eq - E_a (mm)

maximum_speed_km_htol 0.03

Maximum allowable speed V_max (km/h)

visibility contract

Difficulty Ladder

all_giveneasy

All parameters given, gentle curves on mainline or branch

all fields visible
all_givenmedium

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

all fields visible
partialhard

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

actual_cant_mmmax_cant_deficiency_mm

scenario bands

Archetype Atlas

urban_metro

3 contexts

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

curve_radius_m150 to 400
design_speed_km_h40 to 80
actual_cant_mm40 to 100
max_cant_deficiency_mm50 to 75

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

mainline_freight

3 contexts

Mainline freight corridor with gentle curves and heavy axle loads

curve_radius_m800 to 3000
design_speed_km_h60 to 115
actual_cant_mm30 to 80
max_cant_deficiency_mm50 to 75

artc-hunter-valley-coal / artc-north-south-corridor / pilbara-iron-ore-wa

high_speed_passenger

3 contexts

High-speed passenger rail corridor with sweeping curves

curve_radius_m1500 to 5000
design_speed_km_h130 to 250
actual_cant_mm80 to 150
max_cant_deficiency_mm75 to 110

sydney-melbourne-hsr / brisbane-gold-coast-fast-rail / perth-bunbury-fast-rail

branch_line

3 contexts

Regional branch line with moderate curves and mixed traffic

curve_radius_m200 to 800
design_speed_km_h20 to 80
actual_cant_mm20 to 80
max_cant_deficiency_mm50 to 75

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

rendered task

Generation Preview

sydney-metro-northwest-urban-metro-preview

difficulty
hard
visibility
partial
archetype
urban_metro
site context
sydney-metro-northwest
instruction excerptcant-calculation_calc.py

visible fields

  • design_speed_km_h40 to 80 km/h
  • curve_radius_m150 to 400 m
  • gauge_typestandard

withheld schema

max_cant_deficiency_mmactual_cant_mmequilibrium_cant_mmcant_deficiency_mmmaximum_speed_km_h
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