01 / READ THE CHANGE
Geometry changes loading
Taper and twist redistribute circulation. A narrow tip does not automatically make every design more efficient.
LIFT HAS A SPANWISE STORY
3D Wing Design & Downwash
Shape a wing. Watch the load move. Compare the induced-drag cost of carrying the same lift.
3D MODEL + LINKED DIAGRAMB · LIVE
Drag to orbit · right-drag to pan · scroll to zoom. Lift arrows use relative load; wake lines are schematic extensions of lifting-line downwash.
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
Compare equal lift
At fixed incidence, geometry also changes total lift. Hold lift to compare the induced-drag penalty fairly.
03 / READ THE CHANGE
Follow the downwash
The induced angle reduces the section incidence. Downwash arrows come from the solved lifting-line series; the wake mesh is a schematic extension.
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 · Solve the spanwise loading
The coefficients describe the circulation distribution. Local twist varies from zero at the root to the selected value at the tip.
Symbols & units
- Full wing span and local chord, m.
- Root incidence and local geometric twist, rad.
- Section lift slope: 2π rad⁻¹. Aₙ are dimensionless Fourier coefficients; the solver retains 19 odd terms.
- Spanwise angular coordinate; y = −(b/2) cos θ.
02 · Lift and induced drag
The lift term depends on A₁. Higher harmonics also contribute to induced drag.
Symbols & units
- Aspect ratio b²/S; S is wing area, m².
- Dimensionless coefficients. Profile drag is excluded.
03 · Circulation connects the views
The same solved series supplies the loading and downwash views.
Symbols & units
- Section circulation, m²/s.
- True airspeed, m/s.
Steady, unswept, symmetric lifting line with 79 odd Fourier terms, a₀ = 2π rad⁻¹, zero-lift angle 0°, ρ = 1.225 kg/m³. Profile drag, viscous separation, stall, winglets and compressibility are excluded. The view is actual planform geometry; downwash is calculated at the lifting line only.
NASA · induced drag ↗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.