Introduction: why vortex shedding frequency matters
Vortex shedding is a common source of periodic loading on chimneys, masts, cables, heat-exchanger tubes, and other bluff bodies. The hard part is rarely finding a formula—it is turning a real situation into inputs you can measure, validating that the inputs make sense, and interpreting the result in a way that supports a decision. This Vortex Shedding Frequency Calculator helps you do that quickly and consistently.
Use it for early screening: estimate the shedding frequency and compare it to a structure’s natural frequencies. If the values are close, resonance and vortex-induced vibration may be possible and a more detailed assessment is warranted.
What problem does this calculator solve?
This calculator estimates the dominant vortex shedding frequency f (in Hz) behind a bluff body using the Strouhal relationship. It is most useful for quick checks such as: “Is the shedding frequency near my structure’s natural frequency?” and “How does changing velocity or diameter shift the shedding frequency?”
How to use this calculator
- Enter Flow Velocity (m/s) (U).
- Enter Characteristic Width (m) (D)—often the cylinder diameter.
- Enter Strouhal Number (St)—dimensionless (typical values are often ~0.1–0.3 depending on shape and Reynolds number).
- Select Compute Frequency to calculate f.
Inputs: how to pick good values
- Units: enter SI units (m/s and m). The result is in Hz.
- Velocity: use the free-stream velocity relative to the body (wind speed, current speed, etc.).
- Characteristic width: use the projected dimension normal to the flow (diameter for a circular cylinder).
- Strouhal number: choose a value appropriate to your geometry and flow regime; if unsure for a circular cylinder in subcritical flow, 0.2 is a common starting estimate.
Formula used
The Strouhal number is defined as:
Rearranging to solve for shedding frequency:
f = St × U / D
Worked example
Example: a circular chimney with D = 2.0 m in wind U = 25 m/s, using St = 0.2:
f = 0.2 × 25 / 2.0 = 2.5 Hz
If a structural mode is near 2.5 Hz, vortex-induced vibration may be possible and mitigation (strakes, spoilers, damping, or geometry changes) may be considered.
Limitations and assumptions
- Empirical coefficient: accuracy depends on how representative your chosen St is for the actual geometry and Reynolds number.
- Uniform flow assumption: strong turbulence, shear, or interference from nearby structures can broaden or shift the shedding response.
- Frequency only: this tool estimates frequency, not vibration amplitude, fatigue, or lock-in response.
Strouhal Number and Vortex Shedding Frequency
The key non-dimensional parameter governing regular vortex shedding behind bluff bodies is the Strouhal number, typically written as St. It relates the shedding frequency to the body size and flow velocity. For a uniform flow past a stationary body, the standard definition is:
where:
- St is the Strouhal number (dimensionless)
- f is the vortex shedding frequency (Hz)
- D is the characteristic width of the body normal to the flow (m)
- U is the free-stream flow velocity (m/s)
For many practical ranges of Reynolds number in subcritical flow regimes, the Strouhal number for a given shape is approximately constant. This allows engineers to treat St as a known coefficient taken from experiments or design references and then solve for the unknown shedding frequency.
Formula Used by This Calculator
The calculator rearranges the Strouhal relation to solve directly for the shedding frequency f. Starting from:
St = (f × D) / U
we obtain:
f = St × U / D
- The shedding frequency increases linearly with flow velocity.
- The shedding frequency decreases as the characteristic width increases.
- For a fixed geometry and flow regime, the Strouhal number sets the proportionality between velocity and frequency.
The calculator assumes consistent SI units: velocity in metres per second (m/s), width or diameter in metres (m), and it returns frequency in hertz (Hz). If you use other units, convert them to SI before entering them.
Typical Strouhal Numbers by Shape
The Strouhal number depends on the body geometry, Reynolds number, surface roughness, and sometimes on turbulence level in the incoming flow. However, for many engineering cases there are well-established approximate ranges. The following typical values can be used as starting points when detailed experimental data are not available.
| Geometry | Typical Strouhal Number Range |
|---|---|
| Circular cylinder | 0.18 – 0.22 (0.2 is a common design estimate) |
| Square prism | 0.12 – 0.15 |
| Triangular prism | 0.13 – 0.18 |
| Flat plate (edge-on to flow) | 0.14 – 0.17 |
These bands are indicative only. For safety-critical design, consult wind tunnel data, model tests, standards, or high-quality CFD studies specific to your geometry, Reynolds number range, and surface condition.
How to Use This Calculator
The inputs correspond directly to the Strouhal relation:
- Flow velocity (m/s): Use the free-stream velocity relative to the body. For wind-exposed structures, this may be a reference wind speed at a given height; for offshore applications, use the current speed or towing speed.
- Characteristic width (m): For circular cylinders, enter the outside diameter. For non-circular cross-sections, use the projected dimension normal to the main flow direction (for example, the face width of a square prism facing the flow).
- Strouhal number: Choose a value appropriate to your shape and flow regime. If you are unsure for a circular cylinder in moderate Reynolds number range, 0.2 is a common initial estimate.
Reasonable numeric ranges are:
- Velocity: positive and typically greater than about 0.5 m/s for well-defined shedding in air or water.
- Width or diameter: positive; for large civil structures this may range from 0.05 m (small rods) up to several metres (large stacks).
- Strouhal number: positive and often between about 0.1 and 0.3 for many isolated bluff bodies; unusual geometries or flow conditions can fall outside this range.
After entering these values, the calculator returns the estimated vortex shedding frequency in hertz. You can then compare this frequency with structural natural frequencies from a separate analysis or from a natural frequency calculator.
Worked Example Calculation
Consider a steel chimney with an outside diameter of 2.0 m exposed to a design wind speed of 25 m/s. For a circular cylinder in air at moderate Reynolds number, an initial Strouhal number estimate of 0.2 is reasonable.
Inputs:
- Flow velocity U = 25 m/s
- Characteristic width D = 2.0 m
- Strouhal number St = 0.2
Using the formula:
f = St × U / D
Compute:
St × U = 0.2 × 25 = 5.0f = 5.0 / 2.0 = 2.5 Hz
The estimated vortex shedding frequency is therefore 2.5 Hz. If a structural dynamics model indicates that the chimney’s first lateral natural frequency is, for instance, 2.3 Hz, there is potential for resonance. In such a case, further aeroelastic analysis and mitigation measures (for example, helical strakes, spoilers, tuned mass dampers, or geometry modifications) may be required.
Interpreting the Results
The output from the calculator is a single frequency value in hertz. In engineering design, this number is usually not the final answer but an input to a broader vibration assessment. Typical uses include:
- Resonance screening: Compare the shedding frequency with the natural frequencies of the structure. If the ratio of shedding frequency to a natural frequency is close to 1 (or, in some cases, a low-order fraction), there is a higher risk of resonance and large-amplitude vortex-induced vibrations.
- Parametric studies: Quickly see how changes in diameter or flow speed shift the shedding frequency. For example, increasing the diameter lowers the frequency for a fixed velocity, potentially moving it away from a critical mode.
- Design envelope checks: Evaluate shedding frequency across a range of operating velocities. This helps identify speed ranges where resonance is most likely, so operating procedures or mitigation strategies can be designed around them.
If the computed frequency lies near one of the dominant natural modes, you should either adjust the structural properties (stiffness, mass distribution, damping) to move its natural frequency or introduce aerodynamic modifications to disrupt coherent shedding. The Strouhal-based estimate provides an efficient way to identify which cases need deeper analysis.
Comparison With More Detailed Approaches
The Strouhal formula is simple and fast. The table below compares it qualitatively with more advanced analysis methods often used in design offices.
| Method | Key Features | Typical Use Case |
|---|---|---|
| Strouhal number calculator (this tool) | Uses a single empirical Strouhal value; very fast; requires only velocity and width. | Preliminary screening, early design, educational purposes, quick sensitivity checks. |
| Design codes / standards formulas | Often provide bands of Strouhal number, amplitude limits, and partial safety factors. | Routine design of chimneys, stacks, masts, and similar structures within code scope. |
| Wind tunnel or water channel testing | Directly measures shedding behaviour and dynamic response under controlled conditions. | Critical or unusual structures where higher accuracy and physical validation are required. |
| Computational fluid dynamics (CFD) | Simulates unsteady flow and vortex shedding; may capture complex geometries and interference. | Research, advanced design studies, and configurations not well covered by empirical data. |
In most workflows, the simple Strouhal estimate is used first to flag possible issues, and more detailed methods are applied only where justified by risk and cost.
Assumptions and Limitations
The results from this calculator are approximate and rely on several important assumptions:
- Isolated bluff body: The formula assumes a single body not strongly influenced by neighbouring structures, cross-bracing, or complex cross-wind interference.
- Moderate Reynolds number regime: The Strouhal number ranges provided are most applicable to subcritical flows where the shedding pattern is well organized. Near critical or supercritical regimes, St can deviate significantly.
- Quasi-steady, uniform flow: The approach assumes a reasonably steady upstream velocity. Strong turbulence, shear, or gustiness can broaden the frequency content around the nominal shedding frequency.
- Empirical Strouhal value: The accuracy of the result depends directly on how representative your chosen Strouhal number is for the actual geometry, Reynolds number range, and surface roughness.
- No structural dynamics coupling: The calculator estimates only the fluid forcing frequency. It does not compute vibration amplitudes, stresses, or fatigue life.
Because of these limitations:
- Treat the output as a screening-level estimate.
- For critical infrastructure (such as tall stacks, major bridges, offshore platforms, or risers), always confirm results using appropriate design standards, specialist analyses, and, where needed, physical or numerical modelling.
- This tool is not a substitute for a full aeroelastic or vortex-induced vibration design.
The content is informed by standard fluid mechanics and bluff-body aerodynamics references commonly used in engineering education and practice. It is intended for engineers, researchers, and students who need a quick computational aid, rather than a comprehensive design code.