How to calculate Strouhal number (St) dimensionless fluid dynamics ratio measuring oscillation frequency (vortex shedding or flutter) relative to convective time: St = f * L / u. f frequency Hz; L characteristic length m (cylinder diameter D, airfoil chord c); u free-stream velocity m/s.

Karman vortex street cylinder Re=u*D/nu: Re<47 stable wake no shedding; 47<Re<200 laminar St=0.212*(1-21.2/Re) Roshko 1954; 250<Re<250000 Karman classic St~0.21; 250k<Re10M post-supercritical St~0.21.

Regime classification: St1 very high extreme.

Vincenc Strouhal (Bohemia 1850-1922) Charles University Prague + Wurzburg 1878 paper Annalen der Physik 5:216 'Uber eine besondere Art der Tonerregung' Aeolian tones cylinder + f=c*u/D pioneering aeroacoustics.

Theodore von Karman (Hungary USA 1881-1963) Caltech GALCIT 1911 paper Gottinger Nachrichten + 1912 alternating staggered double-row vortex shedding pattern + Karman vortex street eponym. Roshko 1954 NACA TN 3169 Caltech + Williamson 1996 Annual Review Fluid Mechanics 28:477.

USA universities + national labs: NASA Langley Research Center Hampton VA 1917 3500 employees wind tunnels + computational fluid dynamics CFD + aerodynamics + thermal protection systems TPS Apollo Mars rovers; NASA Ames Research Center Mountain View CA 1939 2300 supercomputing + arc jet facility 60 MW + thermal protection + aerodynamics; Caltech California Institute Technology Pasadena CA 1891 2300 + GALCIT Graduate Aeronautical Lab + Anatol Roshko legacy + Hans Liepmann; MIT Massachusetts Institute Technology Cambridge MA 1861 11000 students + Aero/Astro + Wright Brothers Wind Tunnel; Stanford University Palo Alto CA 1885 17000 + Aero/Astro + Joint Institute Aeronautics; Princeton Aeronautical 1746 + Schaaf-Chambre legacy 1958 'Flow of Rarefied Gases' + Mechanical Aerospace Engineering; UC Berkeley CA 1868 45000 Mechanical Engineering + Plasma Physics; Cornell Ithaca NY 1865 Mechanical Aerospace Engineering + Cornell High Energy Synchrotron Source CHESS UHV; Texas A&M College Station 1876 Aerospace Engineering + hypersonic + wind tunnel; University Michigan Ann Arbor 1817 Aerospace Engineering + supersonic wind tunnel; Georgia Tech Atlanta 1885 Aerospace + GTRI Georgia Tech Research Institute; Purdue Lafayette IN 1869 Aerospace Engineering;

Penn State University Park 1855 Aerospace Engineering + applied aerodynamics; Notre Dame IN 1842 Aerospace Mechanical Engineering.

USA national labs research: NIST National Institute Standards Technology Boulder CO + Gaithersburg MD 1901 3000 employees thermophysical properties; AEDC Arnold Engineering Development Complex Tullahoma TN Air Force wind tunnels Mach 14 + 16 + arc heated + altitude chambers; CUBRC Buffalo NY hypersonic shock tunnel LENS-X 7-30 km/s; NREL Golden CO 3000 wind energy + National Wind Technology Center NWTC + 5 MW reference turbine; ORNL Oak Ridge TN 5000 + Spallation Neutron Source SNS + UHV beamlines; Sandia National Laboratories Albuquerque NM + Livermore CA 14000 + Wind Energy Sandia Wind Energy Technologies Office; LANL Los Alamos NM 1943 12000 nuclear + materials + UHV; PNNL Pacific Northwest Richland WA 1965 5000 environmental + chemistry; LLNL Lawrence Livermore CA 1952 + High Performance Computing + CFD simulations; INL Idaho Falls 1949 5000 nuclear; Brookhaven NY 1947 + Relativistic Heavy Ion Collider RHIC; Argonne National Laboratory Lemont IL 1946 + Advanced Photon Source APS synchrotron; ARL Army Research Laboratory Aberdeen MD; ONR Office Naval Research Arlington VA + DARPA Defense Advanced Research Projects Agency Arlington VA.

USA aerospace industry: Boeing Chicago IL 1916 156000 employees + commercial 737 747 757 767 777 787 + military F-15 F-18 + B-1 B-2 B-21 + Boeing Commercial Airplanes Renton WA + Everett WA + South Carolina + Boeing Defense Space Security; Lockheed Martin Bethesda MD 1995 116000 + F-22 Raptor + F-35 Lightning II + C-130 Hercules + C-5 Galaxy + Skunk Works Palmdale CA + Sikorsky helicopters; Northrop Grumman Falls Church VA 1994 95000 + B-21 Raider + Joint STARS + Cygnus cargo vehicle; General Dynamics Falls Church VA 100000 + Bath Iron Works + Electric Boat submarines; Raytheon Technologies Waltham MA 1922 180000 + Pratt Whitney engines + Collins Aerospace + Raytheon Missile Defense; Textron Providence RI 33000 + Bell Helicopter + Cessna business jets + Beechcraft + Lycoming engines; Bombardier Canada USA Connecticut subsidiary CRJ regional jets; Embraer Brazil USA Florida subsidiary E-Jets regional.

USA NewSpace: SpaceX Hawthorne CA 2002 13000 + Falcon 9 Falcon Heavy Starship + Raptor methalox engine + Dragon crew + cargo + Starlink 5000+ LEO satellites; Blue Origin Kent WA 2000 Bezos + New Shepard + New Glenn + BE-4 methalox; Virgin Galactic Mojave CA 2004 + SpaceShipTwo suborbital; Sierra Space Lone Tree CO 2021 + Dream Chaser; Rocket Lab Long Beach CA 2006 + Electron + Neutron; Astra Space Alameda CA 2016.

USA naval offshore: General Dynamics Bath Iron Works Bath ME warships + DDG-51 Arleigh Burke; HII Huntington Ingalls Newport News VA + Pascagoula MS + LPD-17 amphibious; Ingalls Shipbuilding Pascagoula MS; Newport News Shipbuilding aircraft carriers Gerald R Ford + nuclear submarines Virginia + Columbia; ExxonMobil Spring TX 62000 + offshore platforms Hibernia Hibernia + Sakhalin-1 Russia; Chevron San Ramon CA 1879 45000 + Tahiti + Big Foot deepwater Gulf of Mexico; ConocoPhillips Houston TX 16000 + Tor Bristow Bay Alaska.

USA bridges + civil engineering wind: Tacoma Narrows Washington WA 1940 disaster aeroelastic flutter Galloping Gertie + 1950 rebuild + Washington State Department Transportation; Verrazzano-Narrows New York 1298 m 1964 vortex shedding analysis; Golden Gate San Francisco CA 1937 1280 m suspension; Mackinac Bridge MI 1957 1158 m suspension + flutter analysis; ARRB Australian Road Research Board collaboration.

USA wind energy: NREL National Renewable Energy Laboratory Golden CO 3000 + National Wind Technology Center NWTC + 5 MW reference turbine; AWEA American Wind Energy Association Washington DC + Sandia Wind Energy Technologies Office; GE Renewable Energy Schenectady NY + Onshore + Haliade-X 14 MW Offshore; Vestas USA Portland OR + Pueblo CO + Brighton CO Manufacturing; Siemens Gamesa USA Hutchinson KS + Fort Madison IA Manufacturing; Senvion + Nordex; Block Island Wind Farm Rhode Island RI 30 MW first US offshore + Vineyard Wind 800 MW Massachusetts.

Strouhal formula

St = f * L / u dimensionless ratio. Karman vortex street cylinder Re 250-250k St~0.21 classic. f frequency Hz; L characteristic m; u m/s.

History and context

Vincenc Strouhal Bohemia 1850-1922 Charles University Prague + Wurzburg 1878 Annalen Physik 5:216 Aeolian tones cylinder + f=c*u/D pioneering aeroacoustics. Theodore von Karman Hungary USA 1881-1963 Caltech GALCIT 1911-1912 alternating staggered vortex shedding pattern + 'Karman vortex street' eponym. Roshko 1954 NACA TN 3169 Caltech + Williamson 1996 ARFM 28:477. USA universities: NASA Langley Hampton VA 1917 3500 + wind tunnels CFD; NASA Ames CA 1939 2300 + arc jet 60 MW + supercomputing; Caltech 1891 2300 + GALCIT Roshko Liepmann legacy; MIT Cambridge 1861 11000 + Aero/Astro Wright Brothers Wind Tunnel; Stanford 1885 17000 + Aero/Astro Joint Institute Aeronautics; Princeton 1746 + Mechanical Aerospace + Schaaf-Chambre legacy; UC Berkeley 1868 45000 Mechanical + Plasma Physics; Cornell 1865 + CHESS UHV; Texas A&M 1876 + hypersonic; Michigan 1817 + supersonic wind tunnel; Georgia Tech 1885 + GTRI; Purdue 1869; Penn State 1855; Notre Dame 1842. USA national labs: NIST 3000 + AEDC Tullahoma Mach 14-16 + CUBRC Buffalo LENS-X 7-30 km/s + NREL Golden 3000 NWTC 5 MW + ORNL 5000 SNS + Sandia 14000 Wind Energy + LANL 12000 + PNNL 5000 + LLNL 1952 HPC + INL Idaho 5000 + BNL 1947 + Argonne APS + ARL ONR DARPA. USA aerospace: Boeing 156000 + Lockheed Martin 116000 + Northrop 95000 + General Dynamics 100000 + Raytheon 180000 + Textron 33000 + Bombardier + Embraer. USA NewSpace: SpaceX 13000 + Blue Origin + Virgin Galactic + Sierra Space + Rocket Lab + Astra.

USA naval: General Dynamics Bath ME + HII Newport News VA + Pascagoula MS + Newport News carriers + ExxonMobil 62000 + Chevron 45000 + ConocoPhillips 16000 deepwater. USA bridges: Tacoma Narrows 1940 Galloping Gertie + Verrazzano-Narrows + Golden Gate + Mackinac. USA wind: NREL NWTC + AWEA + Sandia + GE Schenectady Haliade-X 14 MW + Vestas + Siemens Gamesa + Block Island 30 MW + Vineyard Wind 800 MW.

Strouhal table

• St = f * L / u
• St<0.01: very low quasi-steady
• 0.1<St<0.3: Karman vortex street
• St>1: very high extreme
• Karman cylinder Re 250-250k: St~0.21
• Re<47: no shedding
• Re 47-200: St=0.212*(1-21.2/Re)
• Re 250k-3M: drag crisis
• Re 3M-10M: St~0.30
• Strouhal 1878 Annalen 5:216
• Karman 1911 Gottingen
• Roshko 1954 NACA TN 3169 Caltech
• Williamson 1996 ARFM 28:477
• USA NASA Langley 1917: 3500 wind tunnels
• USA NASA Ames 1939: 2300 arc jet 60 MW
• USA Caltech GALCIT: Roshko Liepmann
• USA MIT Wright Brothers: wind tunnel
• USA AEDC Tullahoma: Mach 14-16
• USA NREL NWTC: 5 MW reference
• USA Tacoma Narrows 1940: Galloping Gertie
• USA Boeing 1916: 156000 commercial
• USA Lockheed 1995: 116000 F-22 F-35
• USA SpaceX 2002: 13000 Starlink Raptor
• USA Newport News: aircraft carriers
• USA ExxonMobil 62000: offshore Hibernia
• USA GE Haliade-X 14 MW: offshore
• USA Vineyard Wind 800 MW: Massachusetts

Numerical examples

Example 1 - User frequency. f=10 Hz, L=0.05 m, u=1.0 m/s. St=0.5 high frequency. USA: Caltech GALCIT wind tunnel Roshko legacy.

Example 2 - Low Re laminar. Re=100, L=0.01 m, u=0.05 m/s. St=0.167 Karman regime. USA: MIT Aero/Astro + Stanford Joint Institute Aeronautics.

Example 3 - Karman classic. Re=5000, L=0.1 m, u=1 m/s. f=2.1 Hz. St=0.21. USA: chimneys ExxonMobil refineries Baytown Beaumont + ConocoPhillips Bay Alaska.

Example 4 - Supercritical. Re=500000, L=1 m, u=10 m/s. f=3 Hz. St=0.30. USA: marine cables ExxonMobil offshore Hibernia + Chevron Big Foot Gulf Mexico.

Example 5 - Chimney wind. f=5 Hz, L=3 m, u=15 m/s. St=1.0 high frequency. USA: chimneys Marathon Petroleum + Phillips 66 + Valero refineries.

Limits

1. Geometry: cylinder St~0.21; square St~0.13; airfoil shape-dependent.
2. Re dependence St(Re) curve.
3. Surface roughness shifts drag crisis.
4. Free stream turbulence Tu intensity.
5. Aspect ratio L/D end effects.
6. Lock-in resonance flutter aeroelastic Tacoma 1940.
7. Multi-cylinder arrays interference.
8. Compressibility M>0.3 transonic.
9. 3D wake Mode A B span-wise.
10. Numerical CFD DNS LES URANS unsteady.

Common errors

L definition: D cylinder, c chord airfoil.

f Hz vs omega rad/s: factor 2*pi.

Re dependence ignored: St(Re) varies subcritical vs supercritical.

Lock-in resonance: Tacoma Narrows 1940 disaster.

3D effects 2D assumption: end effects L/D < 100.

Practical applications

1. Wind engineering chimneys: USA ExxonMobil Baytown 590k bpd + Marathon Petroleum 17000 + Phillips 66 14000 + Valero 10000 refineries.
2. Marine cables offshore: ExxonMobil 62000 + Chevron 45000 + ConocoPhillips 16000 deepwater Gulf Mexico + Tahiti + Big Foot.
3. Bridges + civil structures: Tacoma Narrows 1940 + Verrazzano-Narrows 1964 + Golden Gate 1937 + Mackinac 1957 + WSDOT.
4. Heat exchanger tube banks: Honeywell UOP 13000 catalysts + Trane 35000 + Carrier 56000 HVAC.
5. Airfoil flutter aerospace: Boeing 156000 + Lockheed Martin 116000 + Northrop 95000 + General Dynamics 100000 + Raytheon 180000.
6. Wind turbines: NREL NWTC 5 MW + GE Haliade-X 14 MW Schenectady + Vestas Portland CO + Siemens Gamesa Kansas Iowa + Block Island 30 MW + Vineyard Wind 800 MW MA.
7. Naval shipbuilding: General Dynamics Bath ME + HII Newport News VA Pascagoula MS + Ingalls + cruise liners.
8. Hypersonic aerospace: NASA Langley wind tunnels + Ames 60 MW arc jet + AEDC Mach 14-16 + CUBRC LENS-X.
9. Automotive aerodynamics: Tesla Fremont CA + Ford Detroit + GM Detroit + Stellantis Auburn Hills MI.
10. University research aerodynamics: NASA Langley + Ames + Caltech GALCIT + MIT Aero + Stanford + Princeton + Berkeley + Cornell + Texas A&M + Michigan + Georgia Tech + Purdue + Penn State.

Updated July 2026