This calculator compares static drag on isolated concave and convex hemispherical cup faces. It does not predict rotor torque, RPM, power, starting behavior or structural loads.
Hemispherical Cup Windmill Interactive Calculator
Compare stationary isolated-face drag using entered coefficients, wind speed and cup-opening projected area.
Equation Used
- Stationary isolated cup face normal to uniform free-stream flow.
- Air density fixed at 1.225 kg/m^3 and user-entered drag coefficients treated as compatible with projected area.
- No arm radius, azimuthal relative velocity, cup interaction, shielding, Reynolds-number effect, rotor speed or torque model.
- The 1.1 multiplier is not established as a gust, fatigue or structural design factor.
Static drag comparison only. The projected reference area is the circular cup opening πd²/4, not the hemisphere curved surface area. The final 1.1× force-sum output is an illustrative arithmetic comparison, not a verified peak cyclic load.
Static face-drag comparison
For a stationary isolated body normal to uniform flow, drag is F=½ρV²CdA. The calculator applies that expression separately to entered concave- and convex-face coefficients using the circular cup-opening projected area A=πd²/4.
A rotating cup rotor experiences changing relative velocity, azimuth, interference and wake effects. Those are not represented by two static force calculations.
Use as a limited comparison
The calculator can show sensitivity to wind speed, cup diameter and user-entered coefficients. It cannot select a wind rotor, anemometer, pump, generator, shaft, arm, bearing or foundation.
Projected-area drag equation
Dynamic pressure is q=½ρV² and isolated-face drag is F=qCdA. With cup diameter d, projected frontal area is A=π(d/2)². The calculator fixes ρ at 1.225 kg/m³.
The coefficient ratio is Cd,concave/Cd,convex. It is not a rotor torque or power coefficient.
Transparent example
For V=12 m/s and d=200 mm, A≈0.03142 m² and q=88.2 Pa. With entered coefficients 1.42 and 0.38, the static comparisons are about 3.94 N and 1.05 N, with coefficient ratio 3.74.
The illustrative 1.1× sum is about 5.49 N. It has no established relationship to a rotor’s peak cyclic load.
Scope and limitations
Rotor performance needs arm radius, cup count and orientation, angular speed, relative flow at each azimuth, wakes, overlap/interference, Reynolds number, losses and load torque. Structural design additionally needs gust criteria, material properties, connections, fatigue spectrum and applicable wind-load requirements.
Frequently asked questions
Why is projected area used?
Drag coefficients are paired with a defined reference area. This tool uses the circular cup opening, so the entered coefficients must use that area too.
Does the drag difference equal shaft torque?
No. Torque also requires arm radius and the azimuth-dependent forces on every moving cup.
Is the 1.1× sum a design load?
No. It is an illustrative sum multiplied by 1.1, without a verified gust, fatigue or structural design basis.
Why does changing wind speed not change rotation speed?
The rotor illustration plays at a fixed speed. Wind speed changes the static drag calculation; rotor dynamics are not modeled.
Calculation basis
NASA Glenn: Drag Equation explains the relationship between drag coefficient, reference area, density and velocity. Its drag-coefficient discussion explains why the numerical coefficient depends on the chosen reference area.
The preset coefficients are illustrative inputs, not measured performance data for a specified cup or rotor. The illustration has fixed dimensions and a fixed playback speed; it does not solve the forces or motion of a windmill.
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