Aeronautical engineering

GUIDO DE MATTEIS
GUIDO DE MATTEIS

Aircraft Flight Dynamics describes the science and mathematics of aircraft motion in a three-dimensional space and links the aerodynamic, propulsion and structural sciences with the applied technologies of systems and avionics.

Specific learning objectives:
- Understanding the dynamics and control of aircraft with respect to design requirements
- Ability to calculate, having understood the physical sense, the stability and control derivatives from the geometric and aerodynamic parameters of the plane
- Understanding how and being able to use the mathematical description of the rigid body of aircraft
- Ability to determine and understand the stability and control response characteristics of aircraft
- Demonstrating of teamwork ability
- Ability to solve problems with computational tools through knowledge, application and development of software codes and/or modern flight simulation codes.

Knowledge and understanding;
Upon completion of the course, the student will be able to:
- Describe the Newtonian approach to formulating the mathematical model of rigid aircraft and its components
- Describe the static stability and controllability of aircraft and their relationship to the aeromechanical characteristics of the vehicle and operating conditions
- Illustrate the physical and mathematical significance of aerodynamic derivatives
- Illustrate and explain methodologies for aircraft mathematical model linearization and dynamic stability analysis
- Illustrate the characteristics of aircraft dynamics and control with reference to the specifications of Flight Qualities
- Describe the response to major flight controls and methods for its determination
- Illustrate aspects of the human-machine interface with respect to controls, cockpit layout, and motion perception
- Describe and compare different flight simulation techniques
- Describe the main architectures of aircraft control systems.

Applying knowledge and understanding
Upon completion of the course, the student will be able to:
- Analyze and solve preliminary design problems with reference to static stability and controllability
- Determine dynamic stability and command-response characteristics of aircraft models having calculated stability and control derivatives from the aerodynamic, geometric, and inertial parameters of the aircraft
- Identify and use appropriate computational tools, including modern applications and toolboxes (Matlab, Simulink), for flight simulation (model/software/hardware/pilot-in-the-loop).

Making judgments
Upon completion of the course, the student will be able to:
- Independently address and solve problems assigned in exercises
- Tackle problems of greater complexity that require planning and coordinating activities, using appropriate computational tools and experimental methods, and writing technical reports within set deadlines.

Communication skills
Upon completion of the course, the student will be able to:
- Conduct collaborative activities as part of group work
- Expose the results of activities both conducted individually and in groups in the form of presentations and/or technical reports.

Learning skills
By the end of the course, the student will have acquired general and introductory level skills in the management of design processes that are strongly interdisciplinary and cross-cutting with respect to different areas of aeronautical engineering and information engineering, where the tools of simulation and modern techniques of prototyping and validation of control systems are used.

Fundamental concepts of dimensional analysis; measurement units, International System of Units (SI), United States customary units. Principal features of standard atmosphere. Formulation of the fundamental equations of rigid body. The basic performance of the aircraft in straight horizontal flight and maneuvering flight. Basic concepts on profile, wing, and complete aircraft aerodynamics in subsonic, transonic, and (hints) supersonic flows. Learn the basics of linear algebra, eigenvalues and eigenvectors, Laplace transform. Fundamentals of linear and stationary, continuous-time, dynamical systems: transfer function, impulse and step responses, frequency response.

The Flight dynamics course is intended to introduce students to description and prediction of aircraft motions. Attention is given to mathematical models and techniques for controllability and stability analyses, and evaluation of flying qualities with brief discussion of control augmentation systems. Topics include equations of motion, configuration
aerodynamics, analysis of linear systems, and longitudinal/lateral-directional motions.

Definitions, principal flight control system, reference frames.(4 h)

Nonlinear equations of motion of rigid aircraft. Transformation matrices, Euler angles. Attitude and trajectory determination. (3 h)

Longitudinal static stability, pitch stiffness, stick-fixed neutral point. Longitudinal control, hinge moment. Stick-free stability. Trim tabs, control force and control force gradient. Use of tabs. Maneuverability, elevator and control force per g. (12 h)

Lateral-directional static stability. Yaw stiffness, roll stiffness. Directional and lateral control. (5 h)

Linearized equations of motion for small excursions from nominal flight conditions. Bryan formulation, definition of stability and control derivatives. Decomposition in longitudinal and lateral-directional equations. Equations in state-space form, Laplace transform. Longitudinal modes. General theory of static stability. Simple approximations of short period and phugoïd characteristic motions. Response to longitudinal controls. Effects of center of gravity position and density gradient on longitudinal stability.
Lateral-directional modes. Simple approximations of Dutch Roll, spiral mode and roll mode characteristic motions. The lateral stability diagram for the Dutch Roll and spiral modes. Response to aileron and rudder controls. (22 h)

Flying and handling qualities, pilot opinion rating, flying qualities requirements. Stability augmentation. (11 h)

In class exercises (18 h)

Team/homework assignments (final report required) (11 h)

Official textbook
- B. Etkin, L.D. Reid, Dynamics of Flight, Stability and Control, John Wiley & Sons, New York, 1996.

• R.F. Stengel, Flight Dynamics, Princeton University Press, Princeton 2014
• M.V. Cook, Flight Dynamics Principles: A Linear Systems Approach to Aircraft Stability and Control, Butterworth-Heinemann, 2013
• B.N. Pamadi, Performance, Stability, Dynamics and Control of Airplanes, AIAA Education Series, 1998
• M.J. Abzug, E.E. Larrabee, Airplane Stability and Control, Cambridge University Press, Cambridge, 1997.

The course is divided into lectures, exercises that involve the resolution of numerical problems and exercises during which problems of greater complexity are solved in small groups.
There will also be seminars on applications of the knowledge acquired in the course to technical problems specific to the labour market.

Although not compulsory, attendance at classes and participation in activities in small groups of students is recommended.

TESTING TOOLS
The assessment is carried out through a written and oral exam, and assignment reports written by teams of students. The written part of the exam consists of two sections, the first on theoretical questions and the second with exercises. The first section, which lasts about 40 minutes, includes questions on all topics of the course, while the second deals with the solution of one or more problems. The duration of the second section is between 30 and 60 minutes, depending on the number of exercises. In the second section textbooks, notes and manuals can be used. The final grade is expressed as follows
- Assignments 15%
- First section written exam 20%
- Second section written exam 20%
- Oral exam 45%

ASSESSMENT METHODS
In addition to asking to “prove that” and, for the part of exercises, to require variations on problems solved in class, the exam requires that the student is able to integrate the skills acquired in the course and apply them in more complex, open-ended problems. A typical exam consists of: verifying conceptual understanding of course topics; verification of the ability to analyze the stability and command responses of the aircraft; verification of the ability to mathematically model the aero-mechanics characteristics of an aeronautical system; verifying the knowledge of methods of stability analysis, of the effects of the main inertial and aerodynamic parameters on the vehicle stability; verifying the knowledge of rationale and main requirements on flight qualities; verifying the knowledge and comprehension of flight dynamics at high incidence. The assessment is supported by the evaluation of the reports on assignments where problems of greater complexity are faced (development and application software codes, simple testing exercises), with wide autonomy and with a work organization defined by the students within each team.

GRADINGS
For the first section of the written exam and for the oral exam: minimum knowledge (rated between 18 and 20); average knowledge (21-24); good ability to apply knowledge (25-27); ability to apply knowledge to problems of some complexity, to demonstrate in-depth comprehension of the course arguments, ability to reason logically, also proposing original solutions (28-30 with honors)
For the second section: the ability to solve only partially the problems, having identified the solution procedure (18-23); the ability to satisfactorily solve the problems, exposing with adequate clarity the method of solution, and deriving, in part or completely, the expected results (24-27); ability to solve the exercises without any error, exposing with excellent clarity procedure and results, even for complex problems (28-30 with honors).
For the assignments (each member of each team receives the same grade as the others): minimum ability (18-20), average (21-24), good (25-27): to structure and solve problems of a certain complexity having identified the appropriate solution methodology, to work in a team, to draw up a technical report. Ability to propose and apply original methodologies for finding the solution, ability to develop in-depth analyzes, and think independently (28-30 with honors).

ORAL TEST.
- Explain the meaning of the stick-force trim condition
- Demonstrate the relationship between stick force and flight speed
- Describe the longitudinal dynamics of the aircraft
- Express the aileron angle-roll rate transfer function
- Illustrate the purpose of the Cooper-Harper diagram
- What does pitch stiffness represent and how is it evaluated?


WRITTEN TEST
With reference to trimmability and longitudinal stability, consider a motor-propeller with constant revolutions (∂(TV)/∂V=0) with the axis of traction in the upper position relative to the center of gravity:
- express the contribution of the propulsion apparatus to the coefficients C_(m_0 ) and C_(m_α )
- having formulated the trim problem and expressed the solution for the balancer angle discuss the effect of the thruster on δ_(E_trim ) as flight speed varies
- express the coefficients C_(T_e ) and C_(T_u ) in a stationary and symmetric flight condition at a nonzero climb angle.

Exercise No. 1
The stability and control derivatives relative to the longitudinal axis take the following values for an aircraft in stationary flight on a straight and horizontal trajectory at the speed V_e=860 ft/s:
X_(δ_E )=14.50 ft s-2 rad-1 X_u=-0.0054 s-1 X_α=-5.08 ft s-2 rad-1
Determine:
- the instantaneous longitudinal acceleration produced by a step command on the balancer ∆δ_E=1.2 deg;
- the speed of flight when the system returns to a stationary condition where, due to the effect of the command, incidence, and pitch angle are varied as ∆α=-0.15 deg, ∆θ=-0.25 deg.

Exercise No. 2
Determine the aerodynamic load in the horizontal tail plane (L_t) for a rectangular-wing sport aviation aircraft in level steady-state flight at Mach=0.22 and an altitude of 1,200 m. Problem data:
W=8,900 N S=25 m2 b=6.5 m C_(m_(〖ac〗_wb )=-0.013 l ̅_t=6.8 m
The aerodynamic center of the wing-fuselage configuration is 0.35 m in front of the center of gravity.