01 / READ THE CHANGE
Mass moments determine CG
The empty aircraft, payload and remaining fuel each contribute mass × position. The same total mass can have a different centre of gravity.
MOVE MASS. REBALANCE THE AIRCRAFT.
Payload, Fuel & Centre of Gravity
Drag the payload along the cabin and choose which tank empties first. Follow centre-of-gravity travel, tail force and elevator demand.
INTERACTIVE CALCULATED DIAGRAMB · LIVE
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
Trim is a moment balance
Wing lift and tail force must support weight and cancel pitching moment. A tail can carry upward or downward load depending on the balance.
03 / READ THE CHANGE
Fuel moves the balance
Each time sample recomputes trim after fuel use. Static margin is a property of the declared wing–tail model, not an aircraft loading approval.
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 · Locate the centre of gravity
Payload position and fuel distribution change the mass-weighted balance point.
Symbols & units
- Mass of item i, kg; longitudinal position from the datum, m.
- Centre-of-gravity position, m. Position increases aft.
02 · Support the weight
Tail lift is signed. A downward tail load requires the wing to carry more than the aircraft weight.
Symbols & units
- Forces, N. Wing/tail lift is positive upwards; weight is a positive magnitude.
03 · Balance pitching moments
A change in loading alters the tail force required for steady trim.
Symbols & units
- Wing and tail force locations, m from the same datum.
- Wing pitching moment, N m, with the sign convention in this balance.
Synthetic empty mass 6000 kg at x = 12 m; wing/tail aerodynamic centres 12/20 m, areas 30/8 m², mean chord 3 m, Cm₀ = −0.02. Lift slopes 5.5/4 rad⁻¹, downwash gradient 0.3 and elevator effectiveness 0.6. Fuel tanks at 10/16 m; burn 400 kg/h. Linear attached-flow steady trim; excessive angles are flagged. No fuel slosh or transient pitch response.
MIT · stability and control notes ↗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.