# Analyses of Aircraft Responses to Atmospheric Turbulence by W.H.J.J. Van Staveren

By W.H.J.J. Van Staveren

It is a Ph.D. dissertation. The reaction of airplane to stochastic atmospheric turbulence performs an incredible position in, for instance, plane layout (load calculations) and flight simulation (handling features study and pilot training). with the intention to simulate those plane responses, a correct mathematical version is needed. classical versions might be mentioned during this thesis that's the Delft college of expertise (DUT) version and the 4 element plane (FPA) version. even supposing they're good demonstrated, their constancy is still imprecise. The reason lies in a single of the necessities for approach identity; it has constantly been essential to relate inputs to outputs to figure out, or determine, procedure dynamic features. From experiments, utilizing either the measured enter and the measured output, a mathematical version of any approach may be obtained.When contemplating an input-output approach reminiscent of an airplane subjected to stochastic atmospheric turbulence, an immense challenge emerges. in the course of flight exams, no sensible hassle arises measuring the aircraft-system's outputs, corresponding to the angle-of-attack, the pitch-angle, the roll-angle, and so forth. even though, an immense challenge arises whilst the enter to the aircraft-system is taken into account; this enter is stochastic atmospheric turbulence during this thesis. at present, it nonetheless continues to be tremendous tough to spot the complete flowfield round an aircraft's geometry subjected to a turbulent box of circulate; an unlimited volume of sensors will be required to spot the atmospheric turbulence speed component's distribution (the enter) over it. therefore, it truly is tough, if now not very unlikely, to spot atmospheric turbulence versions from flight exams.

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16) with for a covariance function matrix element, Cui uj (ξ) = Cui uj (ξ1 , ξ2 , 0) = E {ui (0, 0, 0)uj (ξ1 , ξ2 , 0)} Note that the atmospheric turbulence covariance matrix is symmetrical, therefore C u1 u2 (ξ) = Cu2 u1 (ξ), Cu1 u3 (ξ) = Cu3 u1 (ξ) and Cu2 u3 (ξ) = Cu3 u2 (ξ). 6 is presented. This figure shows the atmospheric turbulence velocity components at origin OE , u1 (0, 0, 0) and u2 (0, 0, 0), and at P (ξ1 , ξ2 , 0), u1 (ξ1 , ξ2 , 0) and u2 (ξ1 , ξ2 , 0), decomposed in a direction along the OE P connection line and decomposed perpendicular to the connection line OE P .

7) with ∇Φ the airflow’s velocity components and n the configuration’s local normal vector (both given in the frame Faero ). 8) with Q∞ = [U∞ , V∞ , W∞ ]T , the vector of undisturbed velocity components at infinity. 1: The Aerodynamic Frame of Reference Faero , including the undisturbed velocity components [U∞ , V∞ , W∞ ]T of Q∞ . [11, 12, 8, 9]. 9) 4π r r SB +SW +S∞ SB +SW +S∞ with SW containing both the upper and lower wake-surfaces, or SWupper and SWlower , respectively. 9) hold for a sphere at infinity (S∞ ), the configuration submerged in the airflow (SB ) and the configuration’s wake (SW = SWupper + SWlower ).

The flow equations to be solved are based on Linearized Potential Flow (LPF) formulations, see also references [11, 12]. These formulations only hold for inviscid, irrotational, incompressible flow. In estimating the aerodynamic forces and moments, however, the Computational Aerodynamics approach does have its limitations, they are governed by the fluid flow model. Starting at the highest level of fluid flow modeling, the basic equations of motion describing a fluid flow are the so-called Navier-Stokes equations.