Airside manoeuvre simulation

The science of airside motion.

Tractrix simulates how aircraft and ground vehicles really move on an apron or taxiway — swept paths, pushback, turning, jet blast, stands and fillets — and checks every result against ICAO, FAA and EASA clearances. The algorithms are open and every number can be traced to its source.

388 aircraft types, FAA ACD ICAO Doc 9157 kinematics Open source, GPL-2.0-or-later
Plan view: Airbus A320 taxiing through a 45 m, 90° taxiway turn The cockpit follows the taxiway centreline while the main gear traces the tractrix inside the curve. Swept envelope, clearance envelope, main-gear and wingtip tracks computed by the OpenAirside engine. Minimum outer-tyre edge margin 0.20 m against 3.00 m required; maximum nose-wheel angle 16.8°. R 45 m ℄
Fig. 1 — A320, cockpit over centreline, 45 m turn, 15 m code C taxiway s198.7m δ0.4° (limit 75°) min edge0.20m (req. 3.00)
388aircraft types from the FAA Aircraft Characteristics Database
44types with manufacturer steering limits, each entry cited
14ground vehicles: tugs, baggage train, loaders, fuel, bus, ARFF
34automated tests: 20 engine unit tests, 14 QGIS integration tests

02 Capabilities

Each check tied to the clause it implements.

Clearance envelopes are the simulated swept envelope plus the distance the selected standard requires. Values are listed with their source on the standards reference.

Table 1 Capabilities, standard basis and availability. ● available · ○ planned (protocol v1.1) · — not planned
CapabilityStandard basisQGISCloudAutoCADRevit
Aircraft path and group path
nose-gear, cockpit or custom tracking
ICAO Doc 9157 Pt 2 App. 1●●●●
Pushback and towing
towbar and towbarless tugs
Nose-wheel tow limit●●●●
Turning radii R1–R6 and 180° turnManufacturer APM method●●●●
Jet blast contours and intake hazardICAO Doc 9157 Table A2-1●●●●
GSE and trailer trainsSteering lock, jack-knife > 90°●●●●
Wingtip and edge clearancesAnnex 14 Table 3-1 · AC 150/5300-13B●●●●
Stand design and conflictsAnnex 14 §3.13.6●○○○
Taxiway fillet / required pavementDoc 9157 Table 1-1 · FAA TESM●○○○
Envelope separation checkUser-defined separation●———

03 Open science

Evidence before assertion.

Commercial swept-path tools ask you to trust a black box. Tractrix publishes the model, the data and the tests, so a reviewer can reproduce any figure you put in a report.

  • Every algorithm is in the open-source OpenAirside engine, with the equations on the methodology page.
  • Aircraft dimensions come from the public-domain FAA Aircraft Characteristics Database; steering limits cite the manufacturer document.
  • Every output carries a note of what was estimated rather than published.
  • No vendor library, data file or software was used or reverse-engineered.

See the full validation

Table 2 Checked live in QGIS 4.0 on the demo airport.
CheckResultExpected
A320 minimum edge margin, 45 m turns4.39 m≥ 3 m
B777-300ER, same turns6.6 m off, 2 breachesNeeds fillets
Fillet track-in, A3202.63 m2.7 m by hand
Fillet track-in, B777-300ER11.6 m—
Pushback nose-wheel angle17.8°17.5° analytic
Stand conflict S2/S30.18 m4.5 m required
A320 breakaway 56 km/h contour48 mICAO: 48 m

04 Workflow

Draw. Simulate. Verify. Report.

The same four steps in every product. Your drawing stays the source of truth; Tractrix adds analysis layers and never edits your geometry.

  1. Draw

    Draw the centreline, lead-in or pushback route as a line in the direction of travel, on your own drawing or GIS layer.

    in: polyline · pavement · obstacles

  2. Simulate

    Pick aircraft or vehicles from the library. The engine integrates the no-slip kinematics in 5 cm steps.

    engine: tractrix/1 request

  3. Verify

    Steering-limit exceedances, pavement-edge breaches, obstacle and stand conflicts are flagged where they occur.

    out: issues with value, limit, position

  4. Report

    Envelopes, tracks and time-stamped footprints for animation, plus an HTML report and a JSON summary.

    out: GeoJSON · layers · HTML · JSON

A tractrix: the nose point moves along the straight line while the trailing point, at fixed distance, follows the tractrix curve. R main gear P nose gear d = |P − R|
Fig. 2 The exact tractrix x = d(t − tanh t), y = d sech t. Each segment has the same length d and is tangent to the curve: the trailing point always moves towards the leading one.

05 The name

Named after the curve at the heart of the engine.

When a nose gear is steered along a line, the main gear does not follow the line. It cuts inside, tracing a curve that mathematicians have called the tractrix since the seventeenth century — the path of a load dragged on a rope of fixed length.

ICAO Doc 9157, Part 2, Appendix 1 describes aircraft ground manoeuvres with exactly this mathematics. Tractrix integrates it directly, rather than approximating it with circular arcs.

The mathematics, step by step →

Start with the free QGIS plugin today.

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