01 / READ THE CHANGE
The force has a lever arm
Moving the engines outboard increases the yawing moment for the same thrust imbalance. Left thrust loss produces a negative yawing moment in the stated axes.
THRUST HAS A MOMENT ARM.
Engine-out Asymmetry & Control
Reduce left-engine thrust and balance the yawing moment. Follow sideslip, yaw rate and the resulting attitude in a bounded lateral model.
3D MODEL + LINKED DIAGRAMB · LIVE
Drag to orbit · right-drag to pan · scroll to zoom. Attitude follows the calculated lateral response; force arrows indicate thrust.
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
Aerodynamic authority scales
The synthetic aerodynamic force and moment derivatives scale with dynamic pressure. Their balance with engine moment changes with airspeed.
03 / READ THE CHANGE
Power loss affects climb
The separate climb estimate uses excess thrust power. It is not a minimum-control-speed demonstration or a simulated engine-out climb trajectory.
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 · Lateral force changes sideslip
This is the model’s small-angle lateral-motion balance.
Symbols & units
- Sideslip and bank angle, rad.
- Side force, N; aircraft mass, kg; true airspeed, m/s.
- Yaw rate, rad/s.
02 · Balance aerodynamic and asymmetric yaw
The thrust imbalance adds a yawing moment that the aerodynamic response and rudder must oppose.
Symbols & units
- Yaw moment of inertia, kg m².
- Illustrative yaw-moment derivatives. Nβ and Nδ: N m/rad; Nr: N m/(rad/s).
- Rudder deflection, rad; engine thrusts, N; lateral engine moment arm, m.
03 · Integrate yaw rate to heading
Heading change is the accumulated yaw response in this small-angle teaching model.
Symbols & units
- Heading change, rad; angular controls and plots may display degrees.
Synthetic 6000 kg aircraft, Iz = 40000 kg m², right-engine thrust 4000 N. Linear side-force/yaw derivatives and ideal pre-stabilised bank servo; constant TAS. Playback stops at |β| > 15°, |φ| > 25° or |ψ| > 45°. No propeller windmilling model, control-speed certification, large-angle recovery or pilot procedure.
FAA · Airplane Flying Handbook ↗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.