Continuous gusts

Continuous gusts or stochastic gusts are winds that vary randomly in space and time. Models of continuous gusts are used to represent atmospheric turbulence, especially clear air turbulence and turbulent winds in storms. The Federal Aviation Administration (FAA) and the United States Department of Defense provide requirements for the models of continuous gusts used in design and simulation of aircraft. Continuous gusts or stochastic gusts are winds that vary randomly in space and time. Models of continuous gusts are used to represent atmospheric turbulence, especially clear air turbulence and turbulent winds in storms. The Federal Aviation Administration (FAA) and the United States Department of Defense provide requirements for the models of continuous gusts used in design and simulation of aircraft. A variety of models exist for gusts but only two, the Dryden and von Kármán models, are generally used for continuous gusts in flight dynamics applications. Both of these models define gusts in terms of power spectral densities for the linear and angular velocity components parameterized by turbulence length scales and intensities. The velocity components of these continuous gust models can be incorporated into airplane equations of motion as a wind disturbance. While these models of continuous gusts are not white noise, filters can be designed that take a white noise input and output a random process with the Dryden or von Kármán models. The models accepted by the FAA and Department of Defense represent continuous gusts as a wind linear and angular velocity field that is a random process and make a number of simplifying assumptions in order to describe them mathematically. In particular, continuous gusts are assumed to be: These assumptions, while unrealistic, yield acceptable models for flight dynamics applications. The last assumption of a velocity field that does not vary with time is especially unrealistic, since measurements of atmospheric turbulence at one point in space always vary with time. These models rely on the airplane's motion through the gusts to generate temporal variations in wind velocity, making them inappropriate for use as inputs to models of hovering, wind turbines, or other applications that are fixed in space. The models also make assumptions about how continuous gusts vary with altitude. The Dryden and von Kármán models specified by the Department of Defense define three different altitude ranges: low, 10 ft to 1000 ft AGL; medium/high, 2000 ft AGL and above; and in between. The turbulence intensities, turbulence scale lengths, and turbulence axes depend on the altitude. The Department of Defense also provides models for the gust angular velocity but gives criteria based on airplane stability derivatives for when they can be omitted. The Dryden model is one of the most commonly used models of continuous gusts. It was first published in 1952. The power spectral density of the longitudinal linear velocity component is Φ u g ( Ω ) = σ u 2 2 L u π 1 1 + ( L u Ω ) 2 {displaystyle Phi _{u_{g}}(Omega )=sigma _{u}^{2}{frac {2L_{u}}{pi }}{frac {1}{1+(L_{u}Omega )^{2}}}} where ug is the gusts' longitudinal linear velocity component, σu is the turbulence intensity, Lu is the turbulence scale length, and Ω is a spatial frequency. The Dryden model has rational power spectral densities for each velocity component. This means that an exact filter can be formed that takes white noise as an input and outputs a random process with the Dryden model's power spectral densities.