Reduced frequency is the

dimensionless number Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into unit of measurement, units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that a ...

used in general for the case of unsteady

aerodynamics Aerodynamics () is the study of the motion of atmosphere of Earth, air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dynamics and its subfield of gas dynamics, and is an ...

and

aeroelasticity Aeroelasticity is the branch of physics and engineering studying the interactions between the inertial, elastic, and aerodynamic forces occurring while an elastic body is exposed to a fluid flow. The study of aeroelasticity may be broadly classi ...

. It is one of the parameters that defines the degree of unsteadiness of the problem. For the case of flutter analysis, lift history for the motion obtained from the Wagner analysis ( Herbert A. Wagner) with varying frequency of oscillation shows that magnitude of lift decreases and a phase lag develops between the aircraft motion and the unsteady aerodynamic forces. Reduced frequency can be used to explain the amplitude attenuation and the phase lag of the unsteady aerodynamic forces compared to the quasi steady analysis (which in theory assumes no phase lag). Reduced frequency is denoted by the letter "k" and given by the expression

k = (\omega \times b)/V

where: * ω = circular frequency * b = airfoil semi-chord * V = flow velocity The semi-chord is used instead of the chord due to its use in the derivation of unsteady lift based on thin airfoil theory. Sears, William R., "Some Aspects of Non-Stationary Airfoil Theory and Its Practical Application," ''Journal of the Aeronautical Sciences'', Vol. 8, No. 3, 1941, pp. 104-108 Based on the value of reduced frequency "k", we can roughly divide the flow into: # Steady state aerodynamics – k=0 # Quasi-steady aerodynamics – 0≤k≤0.05 # Unsteady aerodynamics – k>0.05 >0.2 is considered highly unsteady

References

{{Reflist Dimensionless numbers of fluid mechanics Fluid dynamics