TU Delft
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2016/2017 Aerospace Engineering Master Aerospace Engineering
Stochastic Aerospace Systems
Responsible Instructor
Name E-mail
Prof.dr.ir. M. Mulder    M.Mulder@tudelft.nl
Name E-mail
Dr.ir. D.M. Pool    D.M.Pool@tudelft.nl
Contact Hours / Week x/x/x/x
Education Period
Start Education
Exam Period
Course Language
Required for
Expected prior knowledge
AE2235-I Aerospace System and Control Theory
AE2235-II Instrumentation and Signals
AE4301 Automatic Flight Control Systems Design
Week arrangement
See Detailed Description of Course
1. Introduction
2. Chapter 2 of the lecture notes.
3. Chapter 3.
4. Chapter 3.
5. Chapter 4.
6. Chapter 4.
7. Chapter 5.
Course Contents
The contents of the course follows from eight chapters of the lecture notes as below. Chapter 9 (Etkin's 4 point model) serves as background reading.

1. Introduction (aircraft do respond to atmospheric turbulence, effects on flight path, attitude, passenger comfort, safety, fatigue).

2. Scalar stochastic processes (probability theory, joint probability density functions, covariance and correlation functions, stochastic processes, ergodic processes).

3. Spectral analysis of stochastic processes in continuous time (Fourier analysis, power spectral densities, analysis of dynamic linear system responses in frequency domain).

4. Spectral analysis of stochastic processes in discrete time (discrete time Fourier transform, Fast Fourier Transform, spectral estimates-smoothing).

5. Multivariable stochastic processes (covariance function matrix and spectral density matrix, multi-variable system responses in the frequency and in the time domain).

6. Description of atmospheric turbulence (physical mechanisms, stochastic models of atmospheric turbulence, the two fundamental correlation functions, von Karman en Dryden spectra, models in the time domain).

7. Symmetric aircraft response to atmospheric turbulence (symmetrical aerodynamic forces and moments due to turbulence, gust derivatives, equations of motion of aircraft
flying in symmetrical atmospheric turbulence).

8. Asymmetric aircraft response to atmospheric turbulence (elementary two-dimensional fields of turbulence, asymmetrical aerodynamic forces and moments, asymmetrical gust derivatives, equations of motion).
Study Goals
Introduction to stochastic processes, spectral analysis, understanding the physics of aircraft responses to atmospheric turbulence, derivation of equations of motion of symmetrical and asymmetrical responses to atmospheric turbulence.
Education Method
Literature and Study Materials
J.A. Mulder, J.C. van der Vaart, W.H.J.J. van Staveren, M. Mulder: Aircraft responses to atmospheric turbulence, Lecture notes AE4304 , October 2015.
All lecture slides will be made available electronically via the Blackboard.
Written (with formula page)
The written examination (on probability and stochastic processes, chapters 1-5 of the lecture notes) is followed by the assignment ae4304P (related to the theories of chapters 6-8 of the lecture notes).
Lectures, MATLAB/PYTHON demonstrations.