Free · Physics models
Ideal Rotating-Cylinder Lift
Relate signed spin, circulation, fluid density and cross-flow speed for an ideal rotating cylinder.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
The ideal example uses a one-meter radius and span, one revolution per second, one-meter-per-second cross-flow and nominal density of 1.225 kilograms per cubic meter. Its signed lift is about 48.36 newtons.
Circumferential speed = 2πradius×rotations per second; circulation = 2πradius×circumferential speed; signed force = density×circulation×free-stream speed×length.
Worked example
Enter these known values and leave the other values blank.
- Radius (r)
- 1 m
- Length (ℓ)
- 1 m
- Rate of rotation (f)
- 1 revs/s
- Free stream velocity (v==free==)
- 1 m/s
- Angular velocity (ω)
- 6.283 rad/s
- Rotational speed (v==r==)
- 6.283 m/s
- Vortex strength (G)
- 39.48 m²/s
- Density (ρ)
- 1.225 kg/m³
- Magnus force
- 48.36106 N
Assumptions and limitations
- The cylinder rotates about its lengthwise axis in a uniform cross-flow. Positive radius and length are required; signed spin or flow reverses the modeled force direction.
- The fluid menu retains captured numerical density examples without a specified temperature, pressure or phase. These are scenario inputs, not a certified property database.
- This is an ideal two-dimensional circulation model. Viscosity, boundary layers, flow separation, finite-end effects and unsteady lift are omitted.
- Clear the unknown numeric field before solving a supported inverse.
Common questions
What does this scenario assume?
The cylinder rotates about its lengthwise axis in a uniform cross-flow. Positive radius and length are required; signed spin or flow reverses the modeled force direction.
What does the result leave out?
This is an ideal two-dimensional circulation model. Viscosity, boundary layers, flow separation, finite-end effects and unsteady lift are omitted.
References
Model input requirements: Model fluid density must be nonnegative.