A curved-vane rotor presents hollow and convex blade surfaces to moving air. The illustration shows the open rotor described in Hiscox figure 614. The calculator is an equivalent-load comparison: it converts an entered pressure and effective area into assumed tangential force, torque and a clearly labelled 70%-factor power case.
Curved Vane Windmill or Motor Interactive Calculator
Explore an equivalent tangential-load model alongside an open curved-vane rotor. The fixed 70% comparison is an assumption, not measured efficiency; no wind-speed performance is predicted.
Equation Used
- Equivalent uniform pressure reduced to a tangential resultant.
- N equal loads at the same effective moment arm.
- Calculation rpm is independently prescribed.
- 0.70 factor is illustrative and not a rating.
- Rotor proportions and animation speed are explanatory.
No aerodynamic pressure distribution, returning-blade drag, operating rpm or actual wind-power prediction.
Curved sheets around a vertical shaft
The rotor has twelve curved upright sheets connected around a central shaft. Gold sheets mark the number of equivalent loaded vanes selected in the calculator. That highlighting does not identify which vanes a real airflow loads at each position.
Air flows around the exposed curved sheets of this wind-driven rotor. Supports, blade height and the displayed 5 rpm are illustrative.
Compare an equivalent load case
Use the inputs to examine the arithmetic of equivalent pressure, effective area, moment arm, number of loads and calculation speed. The worked example uses a pressure difference of 0.05 kPa. Larger entries represent hypothetical loads; they do not establish a realistic wind-pressure range.
A real curved blade experiences a distributed pressure and a resultant whose direction and moment arm vary. The model assumes those effects have already been reduced to equal tangential resultants and a common perpendicular moment arm.
From equivalent pressure to torque
Convert Δp from kPa to Pa, A from cm² to m² and r from mm to m. The equivalent force per vane is F=Δp A. If N equal tangential loads act at moment arm r, ideal torque is τ=N F r.
The 70% comparison case uses τ₇₀=0.70τ. At calculation speed n in rpm, its corresponding mechanical power is P₇₀=τ₇₀(2πn/60). The fixed 0.70 multiplier is an assumption only, not a measured efficiency or an aerodynamic prediction.
Worked equivalent-load example
At Δp=0.05 kPa and A=12 cm², equivalent force per vane is 0.060 N. Three such loads at a 30 mm moment arm give 0.0054 N·m ideal torque. The 70%-factor case gives 0.00378 N·m and about 0.475 W at 1200 rpm.
Doubling area, equivalent pressure, moment arm or load count doubles torque in this model. Doubling calculation rpm doubles the power comparison without changing torque.
No wind-performance claim
The calculator does not infer pressure from wind speed, predict the resisting torque on returning blades, solve flow through the rotor, or determine the equilibrium rpm. It cannot establish actual shaft output or starting behavior.
The animation is deliberately slowed and independent of the entered calculation rpm. The rotor’s displayed height and radius do not establish the effective pressure area or moment arm. Those inputs describe the assumed load reduction, not a manufactured blade design.
Curved-vane questions
Why are only some vanes gold?
They count the equivalent loads used in the arithmetic. They are not a simulated pressure field.
Is 70% the efficiency of this design?
No. The calculator applies a fixed 0.70 multiplier to compare an assumed reduced torque with the ideal torque.
Does the entered pressure equal ordinary wind pressure?
Not necessarily. It is an equivalent pressure difference supplied by the user; no wind-speed conversion is performed.
Can this size a working windmill?
It can compare assumed loads, but actual aerodynamic and mechanical performance require additional evidence.
References
Hiscox, Mechanical Movements, Powers, Devices and Appliances, printed page 165, figure 614, for the open curved-vane arrangement. NASA Glenn, Torque (Moment), for force times perpendicular moment arm. NASA Glenn, Aerodynamic Forces, for pressure forces acting on surfaces; the equal tangential resultants used here are a stated simplification.
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