FLIGHT CONTROL & AUTOPILOT / CHAPTER 04

Route Capture & Waypoint Sequencing

Turn an intended route into a continuous flight path.

Synthetic navigation legs · coordinated-turn guidance · original synthetic teaching example · ideal airspeed and altitude hold

02 / LIVE B · 3D ATTITUDE

0 s

North reference · body direction (amber) · ground track (turquoise)

A · no saved case

CONTROL → RESPONSE → FEEDBACK

Preparing the model

03 / THE CALCULATED TRAJECTORY

Capture the line. Watch the active leg change.

A · dashed amber B · solid turquoise

Equal-scale map. Drag waypoint P2; arrow keys move it by 100 m (Shift + arrows changes northing). The bank response remains finite at corners.

Air + wind = motion over the ground

Vectors use one common velocity scale. The ground-velocity arrow is the vector sum. The 3D direction arrows above indicate direction only; their lengths are decorative.

Measure a signed error

Cross-track error is measured perpendicular to the active leg. Positive is right of its direction of travel. The controller requests an intercept course.

Sequence transparently

This teaching rule advances when the aircraft crosses the leg-end plane. It does not prove the aircraft passed through the waypoint. Each crossing distance is reported below.

A route is not a sharp turn

Roll lag and the bank limit round the aircraft trajectory. There is no fly-by anticipation, terrain, traffic, airspace or navigation-database constraint.

04 / ONE PLAYBACK CLOCK

Follow the whole response

A · dashed amber / B · turquoise
Dotted: command. Click or use arrow keys to scrub.

Compare A and B

Quantity	A · saved	B · live

A stays fixed for this page session. Export includes settings and sampled histories.

Leg-end-plane crossings

These are sequencing events, not certified waypoint passage. Crossing distance is shown for every event.

Equations, assumptions and sources

Model contract

Level-turn motion with uniform wind

\dot{E} = V \sin (ψ) + w_{E}

\dot{N} = V \cos (ψ) + w_{N}

\dot{ψ} = \frac{g \tan (φ)}{V}

L = \frac{m g}{\cos (φ)}

Ideal airspeed and altitude hold; zero sideslip. Bank lag represents a pre-stabilised inner loop, not an aerodynamic actuator.

Symbols & units

$E, N$: East and north coordinates, m; these are not energy or force symbols.
$ψ, φ$: True heading clockwise from north and bank to the right, rad.
$w_{E}, w_{N}$: Wind towards east and north, m/s. The input is a towards bearing, not the meteorological from bearing.
$V, L$: Ideal constant true airspeed, m/s; required lift, N. Available thrust, stall and roll inertia are not solved.

Model context and notation

The aircraft is a reduced-order level coordinated-turn model. True airspeed and altitude are held ideally; sideslip is zero. The bank controller has first-order lag and a 15°/s rate limit. With constant wind: Ė = V sin ψ + wE, Ṅ = V cos ψ + wN, ψ̇ = g tan φ / V. Lift is mg/cos φ. Available thrust, stall, roll inertia and Dutch roll are outside this model. Bank lag represents a pre-stabilised inner loop; it is not an aerodynamic actuator model.

Capture a leg, compensate for wind, then bank

χ_{c} = χ_{leg} - atan (\frac{e_{cross}}{L_{look}})

w_{cross} = w_{E} \cos (χ_{c}) - w_{N} \sin (χ_{c})

ψ_{c} = χ_{c} - asin (\frac{w_{cross}}{V})

φ_{c} = clip (atan (\frac{V 0.08 R wrap (ψ_{c} - ψ)}{g}); - φ_{limit}, φ_{limit})

\dot{φ} = clip (\frac{φ_{c} - φ}{τ_{roll}}; - 15 ° /s, 15 ° /s)

A leg advances at its end plane; this does not certify waypoint passage. The final reference leg continues straight.

Symbols & units

$R$: Dimensionless heading-response multiplier; 0.08R has units s⁻¹.
$φ_{limit}, τ_{roll}$: Selected command limit, rad; first-order bank time constant, s. Roll rate is limited to ±15°/s.
$wrap / clip$: wrap selects the principal heading error in [−π, π]. clip bounds a command to the stated lower and upper limits.
$χ_{c}, ψ_{c}$: Ground-track and nose-direction targets, rad. Heading mode selects ψc directly; the wind triangle applies to track guidance.
$e_{cross}, L_{look}$: Signed perpendicular error and lookahead, m. Positive error is to the right of the active leg.

Model context and notation

Limits and sources

Bank command limited to the selected 10–35°; uniform wind 0–25 m/s and TAS 45–85 m/s. No vertical wind, turbulence or geodetic Earth model. The route is a local synthetic plane, not an operational airport procedure.

Teaching connections: reference frames, turning performance, flight control and flight management systems. Original extension with synthetic parameters.

MIT OCW · lateral autopilots supports the control concepts; its aircraft coefficients are not used.

Numerical verification does not establish flight-test validity.