Choose wind speed and tip-speed ratio. Watch the candidate RPM, mechanical power and torque respond using the source-derived curve.
Checking geometry evidence…What the paper supports
CANDIDATE SHAFT SPEED
—
rotor RPM · selected TSR
TURBINE SHAFT POWER
—
mechanical W · selected wind and blade length
TURBINE SHAFT TORQUE
—
newton-metres · selected TSR
REFERENCE WIND POWER · ROTOR AREA
—
wind-flux normalisation baseline
◎
Each curve is a family of candidate shaft states. The green marker is the TSR you chose. Actual RPM must later satisfy turbine torque = generator load torque.
Li 2014 resonance: no observations at TSR 0.81–0.92. Dashed bridge across the corresponding RPM gap is illustrative only; the solver still rejects that region.
Positive-output view enlarged for readability; negative aerodynamic torque remains in the source dataset. A freely operating wind turbine is not expected to maintain a negative-power generating state.
MECHANICAL ENVELOPE · P(ω)
Shaft power vs. RPM
CALCULATED
Calculated from measured Cₚ(λ) and wind power.
LOAD-MATCHING INPUT · Q(ω)
Shaft torque vs. RPM
CALCULATED
This curve is what we will match to your generator's braking torque.
SECTION B / WIND-SPEED SCENARIOS
As the wind picks up.
Hold the selected tip-speed ratio fixed and explore how the calculated rotor output scales with changing wind speed.
THE OTHER VIEW · HOLD TSR FIXED
What changes as the wind picks up?
SCENARIO ONLY
At the TSR selected on the left, keep the same digitised Cₚ value and vary wind speed from 3–12 m/s. The dashed vertical line marks your chosen wind speed. This is a constant-TSR operating scenario, not a prediction of loaded generator behaviour; only 6 m/s was tested.
Normal view: 0–12 m/s axis; 3–12 m/s model calculations.
Mechanical power vs. wind speed
Mechanical torque vs. wind speed
At fixed TSR and constant Cₚ: RPM ∝ U; power ∝ U³; torque ∝ U². Wind-speed scaling is a model assumption, not new experimental evidence.
See the calculation at your selected operating point and what the published experiments do—and do not—support.
Σ Worked calculation at your selected TSR
Using the Step 01 rotor selection…
1. Wind power
Pwind = ½ ρ A U³—
2. Aerodynamic shaft power
Pshaft = Cp(λ) × Pwind—
3. Shaft angular speed
ω = λ U / R—
4. Mechanical torque
Q = Pshaft / ω—
! Evidence & boundaries
AERODYNAMIC INPUTWatanabe et al. (2016), Figure 15Digitised graph; chord blends are estimated.
SELECTED ROTOR GEOMETRYD = 0.70 m · H = 0.70 mTested reference geometry. Changed blade length is an estimated scenario shared by Steps 02 and 04; source Cₚ is held unchanged.
WIND-LENS ACCOUNTINGSame rotor reference areaThe wind lens changes measured Cₚ, not the swept-area formula. No extra lens-area multiplier.
NOT A GENERATOR PREDICTION
Changing TSR explores hypothetical loading points. Step 04 will solve the actual operating speed after Step 03 supplies the generator's braking torque.
NO ZERO-RPM TORQUE INFERENCE
Static torque cannot be deduced from P/ω at λ = 0 (0/0). Values near startup and at wind speeds other than 6 m/s have additional uncertainty.
Evidence distinction: A source-supported Cp value is an aerodynamic input. Shaft RPM, power and torque are calculated candidate states; altered wind speed and geometry are hypothetical transfers. Generator losses and electrical loading are not included.