Ability to determine the aerodynamic forces acting on the aircraft and to evaluate their dependence on geometric and fluid dynamics parameters that characterize a given configuration.

Elements of differential and integral calculus, basics of physics.

1) Fluid as a continuous medium. Balance equations in integral, differential, conservative and non-conservative form. Normal and shear stresses. Normalized equations. The speed ​​of sound. Reynolds, Froude, Mach and Prandtl numbers. The entropy transport equation. The Crocco equation. 2) The ideal fluid approximation. Entropy in an ideal fluid. Streamlines, pathlines, streaklines and timelines. The Bernoulli equation. The Laplace equation. The vorticity equation. Stagnation quantities in compressible flows. 3) Two-dimensional flows of an ideal fluid. Steady and incompressible flow conditions. Steady, incompressible and irrotational flow conditions. The velocity potential. The stream function. Elementary flows: uniform flow, source, vortex, doublet. Freestream + doublet: the flow on a non-lifting cylinder. Pressure coefficient. The d'Alembert 's paradox. Freestream + doublet + vortex: the flow on a lifting cylinder. The Kutta-Joukowski theorem. Airfoils: nomenclature and aerodynamic forces. The pressure center. The stall. The Buckingham Pi theorem. Low speed flow on airfoils: the vortex surface concept, circulation distribution, Kutta condition, Kelvin's theorem and initial vortex. Thin airfoil theory: basic hypotheses, distributions of sources and vortices and their use, tangency condition and linearization of the pressure coefficient. Flow on a flat plate with non-zero angle of attack: calculation of the circulation distribution and verification of the result; thin airfoils theory applied to a flat plate: verification of the Kutta condition, calculation of lift, lift coefficient and slope of the cl:alpha plot, moment and moment coefficient, center of pressure position and aerodynamic center. Symmetrical airfoils. Airfoils with curved mean line: calculation of lift and moment coefficients, ideal angle of attack, center of pressure and aerodynamic center. Distribution of sources. Airfoil stall, effect of thickness. High-lift devices. 4) Introduction to viscous flows, effect of viscosity, dynamic and kinematic viscosity and their dependence on temperature, effect of thermal conductivity, dependence of thermal conductivity on temperature. No-slip condition, separation, form drag and skin friction drag, thermal boundary layer, turbulence, transition to turbulence, effect of turbulence on skin friction and form drag. Boundary layer equations, derivation of the boundary layer equations for compressible flows: mass balance, momentum and energy equations. Kinematic and thermal boundary layers. Boundary layer properties: boundary layer thickness, displacement thickness, momentum thickness, form factor, skin friction, local and average skin friction coefficient, drag coefficient. Boundary layer equations for incompressible flows, boundary layer on a flat plate at zero angle of attack, Blasius transformation, Blasius equation, self-similar velocity profile and Blasius solution, properties of the boundary layer on a flat plate at zero angle of attack. Boundary layer transition, factors that influence the transition. the Reynolds-averaged Navier-Stokes equations, properties of the time averaging operator, derivation of the Reynolds stresses. The closure problem. Boussinesq model for the Reynolds stresses. Hierarchy of turbulent flow models: overview of DNS, LES and RANS. Velocity profile in the turbulent boundary layer. Boundary layer equations for turbulent flow. Turbulent boundary layer on a flat plate: formulas for the various coefficients. Transition Reynolds number and calculation of drag on a flat plate with transition. The thermal boundary layer. Prandtl number interpretation. Kinematic and thermal boundary layer thickness ratio as a function of the Prandtl number. Recovery enthalpy, recovery temperature and recovery factor. Reference temperature method for the analysis of compressible boundary layers or cold/hot wall boundary layers. The von Karman integral boundary layer equation. Thwaites method for the solution of the integral von Karman equation for laminar boundary layers. Head method for the solution of the integral von Karman equation for turbulent boundary layers. Michel's criterion for laminar / turbulent transition. 5) The wing: geometric definitions, tip vortices, downwash and induced angle of attack. Induced drag. Profile drag. Biot-Savart law for a curved vortex. Velocity ​​field induced by an infinite straight vortex. Velocity ​​field induced by a semi-infinite vortex. Helmholtz's theorems. Prandtl theory: horseshoe vortex. Velocity ​​distribution induced by a single horseshoe vortex. The horseshoe vortex system. Continuous distribution of horseshoe vortices: downwash velocity and induced angle of attack, effective angle of attack, Prandtl's integro-differential equation and its meaning, evaluation of lift, induced drag and related coefficients. Elliptical distribution of lift: evaluation of downwash, induced angle of attack, lift, induced drag and related coefficients. Induced angle of attack and induced drag coefficient as a function of lift coefficient and wing aspect ratio. Shape of a wing with elliptical lift distribution. General solution of the Prandtl's integral-differential equation: calculation of lift, induced angle of attack and induced drag coefficient. General lift distribution on a wing: efficiency factor of the wing, slope of the lift / angle of attack curve for a wing with finite aspect ratio. 6) Definition and derivation of the speed of sound. Definition and physical meaning of the Mach number. Shock waves: definition and examples. derivation of jump conditions through a normal shock wave, derivation of the jump conditions through an oblique shock wave. Thin airfoils with small angle of attack in compressible flows: remarks on the governing equations and their approximations. The Prandtl-Glauert correction. Transonic flow and critical Mach number. Calculation of the critical Mach number. Effect of thickness. The drag rise phenomenon. Supercritical airfoils. Swept wings and critical Mach number. Slope of the cL / angle of attack curve in compressible regime and for swept wings. Linearized supersonic flow: basics, lift, drag and moment coefficients, position of the aerodynamic center, lift and drag coefficients for airfoils and wings (review). Mach number effects. 7) Forces on a complete aircraft. Contribution of the different aircraft parts. Induced and parasite drag. Parasite drag breakdown and empirical formulas. Wave drag and area rule. The Sears-Haack's body. Wave drag for bodies with area distribution different from the Sears-Haack body.

Tutorials will be carried out both in the classroom and in the laboratory and will focus on the following topics: Venturi tube. Pitot tube in an incompressible subsonic flow and in a supersonic flow. Calculation of velocity profiles in laminar and turbulent boundary layers. Friction drag calculation on a flat plate with laminar, turbulent and transitional boundary layer. Friction drag calculation on flat plates in compressible flows. Calculation of the laminar boundary layer around a NACA 0012 airfoil: application of the Thwaites method. Application of the Michel criterion for estimating transition on an airfoil. Drag calculation for bluff bodies. Calculation of the critical Mach number and drag rise Mach number for a NACA 0012 airfoil. Calculation of the drag rise Mach number as function of the maximum thickness for NACA 4 digits airfoils. Calculation of angular lift coefficient as function of the Mach number. Calculation of the critical Mach number and drag rise Mach number for the wing. Calculation of wave drag. Study of the drag polar for the complete aircraft: application of empirical methods for the determination of the drag polar for a typical aircraft. Determination of the critical Mach number and drag rise Mach number for the complete aircraft. Laboratories: Measurement of the pressure distribution around the NACA 0015 airfoil at different angles of attack. Calculation of the aerodynamic characteristics Cl-alfa, Cm-alfa and the center of pressure. In some tutorials, calculations will be carried out using MATLAB.

Reference books: - J. Anderson, Fundamentals of Aerodynamics (any edition can be used), McGraw-Hill - G. Iuso, F. Quori, Gasdinamica. Problemi risolti e richiami di teoria, Levrotto & Bella For additional informations: - D.P. Raimer, Aircraft Design: A Conceptual approach, AIAA Educational Series - Barners W. McCormick, Aerodynamics, Aeronautics, and Flight Mechanics, John Wiles & Sons

Exam: Written test; Compulsory oral exam;

The adequate knowledge and understanding of the course topics will be checked and the ability to use such a knowledge for the quantitative evaluation of the aerodynamic characteristics and for the interpretation and description of problems related to the subject will be verified. During the session (appello) that takes place immediately after the end of the lessons, the exam will be a written test consisting of two parts: the first part is a questionnaire without the possibility of using teaching materials, while the second part consists in the solution of 2 or 3 exercises. The written test will last for 1 hour and a half or 2 hours. In the remaining sessions, the exams will be oral at this time, but the students will also be asked to solve an exercise. The oral exam will last for about 30/45 minutes. It is possible that, in case the number of students would increase significantly in the future, the written text will be extended to some exam sessions past the first one.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.