01 / READ THE CHANGE
Track differs from heading
Crosswind alters the ground track. Guidance uses a wind-corrected heading target to remove lateral displacement.
ARM. INTERCEPT. CAPTURE.
Localiser & Glideslope Capture
Move the initial aircraft position. Watch lateral and vertical guidance capture a synthetic approach while wind changes the ground track.
3D MODEL + LINKED DIAGRAMB · LIVE
Drag to orbit · right-drag to pan · scroll to zoom. Flight-path height and lateral scales are exaggerated for inspection.
Diagram · drag background to pan
Drag the turquoise handles, or focus a handle and use arrow keys. The sliders provide the same controls.
Preparing the calculation…
A · no saved reference
02 / READ THE CHANGE
Capture is a mode change
The vertical path is armed until the aircraft is close to the beam from below and lateral capture has occurred. Starting above can leave it armed throughout.
03 / READ THE CHANGE
A deliberately bounded model
TAS is held ideally and the bank/flight-path responses represent pre-stabilised inner loops. The experiment ends 300 m before the threshold.
THE SAME MODEL, CONNECTED VIEWS
Follow the calculation
B · solid turquoise A · dashed amber
Compare A and B
| Quantity | A · saved | B · live | B − A | Unit |
|---|
A remains fixed until saved again. Export includes the model version, settings and plotted data.
Equations, assumptions & sources
Read the balance, then connect each symbol to the model. Open a symbol key for definitions and units. Long equations can be scrolled sideways.
01 · Resolve the flight path
The aircraft approaches the runway as x decreases. Crosswind affects ground track.
Symbols & units
- Distance to threshold, lateral displacement and height, m.
- True airspeed and signed crosswind component, m/s.
- Flight-path angle (positive climbing) and heading deviation from the approach axis, rad.
02 · Bank changes heading
The banked-turn kinematics link lateral guidance to aircraft heading.
Symbols & units
- Bank angle, rad; gravitational acceleration 9.80665 m/s².
03 · Follow the reference beam
The illustrative beam passes 15 m above the threshold at a 3° approach angle.
Symbols & units
- Target beam height, m. This geometric model does not provide flare or autoland behaviour.
Synthetic straight 3° path, 9 km start distance, no airport procedure or radio propagation model. Bank limited to 25°, flight-path command −6° to +1°, bank lag 2 s and flight-path lag 4 s. Pitch display uses γ + 3° illustrative incidence. No stall, thrust/energy constraints, terrain, flare or autoland.
MIT · stability and control notes ↗FAA · aviation handbook library ↗Physical relations and teaching sources support the stated concepts. Generic coefficients are explicitly illustrative; they are not measured manufacturer data. Numerical verification is separate from experimental validation. Model version: applied-labs-v1.1.