01 / READ THE CHANGE
Pitch is not incidence
Local incidence is blade angle minus the inflow angle. Rotation, forward speed and induced flow all change the relative wind.
A ROTATING WING, SECTION BY SECTION.
Propeller Pitch & Efficiency
Change pitch and twist, then inspect the local incidence. Couple blade-element forces to the axial momentum of the slipstream.
3D MODEL + LINKED DIAGRAMB · LIVE
Drag to orbit · right-drag to pan · scroll to zoom. Rotation is slowed; blade geometry follows the selected pitch and twist.
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
The shaft pays for thrust
Torque multiplied by angular speed is shaft power. Useful propulsive power is thrust multiplied by forward speed.
03 / READ THE CHANGE
Close the momentum balance
The induced velocity is solved so integrated blade thrust equals the actuator-disc axial momentum increase.
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 · Pitch and inflow set blade incidence
The blade sees both forward flow and rotational motion.
Symbols & units
- Section angle of attack, local blade pitch and inflow angle, rad.
- Forward and induced speeds, m/s; angular speed, rad/s; radial position, m.
02 · Each blade element adds thrust
The section lift and drag are resolved into axial thrust.
Symbols & units
- Relative section speed, m/s; number of blades; local chord, m.
- Air density, kg/m³; dimensionless section lift and drag coefficients.
03 · Match induction and account for power
The blade-element thrust is matched to a uniform actuator-disc inflow.
Symbols & units
- Total thrust, N; propeller disc area, m².
- Shaft torque, N m; useful propulsive power divided by shaft power. At static V = 0, this efficiency is zero.
60 radial elements from 0.2R to R; uniform axial induction, no swirl induction or tip loss. Constant chord 0.09R. Synthetic smooth polar CL = 1.2tanh(2πα/1.2), CD = 0.015 + 0.02CL². Positive-powered solutions only. Large local incidence is flagged; this polar is not measured stall data. Rotation is slowed for inspection.
NASA · propeller geometry ↗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.