Fa2004 16.33312-5 Atmospheric Turbulence Can develop the best insight to how aircraft will behave with gust disturbances if we treat the disturbances as random processes What is a random process? Something(signal) that is random so that a deterministic description is not practical But we can often describe the basic features of the process(e. g mean value. how much it varies about the mean Atmospheric turbulence is a random process, and the magnitude of the gust can only be described in terms of statistical properties For a random process f(t), talk about the mean square 尸2(t)=lim T f(t)dt as a measure of the disturbance intensity (how strong it is) Signal f(t) can be decomposed into its Fourier components, so can use that to develop a frequency domain measure of disturbance strength (w)a that portion of f2(t)that occurs in the frequency band +d (w) is called the power spectral density Bottom line: For a linear system y=G(s w,then 重(u)=a(u)G(j) Given an input disturbance spectral density(e. g gusts), quite si ple to predict expected output (e.g. ride comfort, wing loadia m-Fall 2004 16.333 12–5 Atmospheric Turbulence • Can develop the best insight to how aircraft will behave with gust disturbances if we treat the disturbances as random processes. – What is a random process? Something (signal) that is random so that a deterministic description is not practical!! – But we can often describe the basic features of the process (e.g. mean value, how much it varies about the mean). • Atmospheric turbulence is a random process, and the magnitude of the gust can only be described in terms of statistical properties. – For a random process f(t), talk about the mean square � T 1 f 2(t) = lim f 2 (t) dt T 0 T→∞ as a measure of the disturbance intensity (how strong it is). • Signal f(t) can be decomposed into its Fourier components, so can use that to develop a frequency domain measure of disturbance strength – Φ(ω) ≈ that portion of f 2(t) that occurs in the frequency band ω ω → + dω – Φ(ω) is called the power spectral density • Bottom line: For a linear system y = G(s)w, then Φy(ω) = Φw(ω)|G(jω) 2 | ⇒ Given an input disturbance spectral density (e.g. gusts), quite sim￾ple to predict expected output (e.g. ride comfort, wing loading)