Airplane Performance and Dynamics


  • A draft of the exam has been uploaded on WeBeep, and is accessible through this link.
  • The lectures and labs of the current edition of the course (2023-24) are now over.
  • This page is related to both modules of the graduate course of Airplane Performance and Dynamics for the Academic Year 2023-24.
  • Please check out the exam dates and indications at the end of the page.

Schedule of lectures and exercise classes

Lectures and labs for this module will be offered in classrooms only.

The weekly schedule for the fall semester of 2023 is as follows.

Monday Wednesday Thursday
14.30-16.00 Lecture (B8.1.1) 9.30-11.00 Lecture (B8.0.7) 14.30-16.00 Lecture (BL27.08)
11.30-13.00 Lab (B8.0.7)

The available time frames will be exploited according to the day-by-day situation and the actual evolution of the course. Please check the calendar on the WeBeep page of the course for updates on this matter.

Classroom papers

Classrooms papers from lectures and labs will be listed and linked here. Access is through Politecnico server, therefore it will possibile only for Politecnico users.


Entry ID Document link
Wed., Sep. 13rd Lecture 1 – Aircraft modeling: types of analysis and models. Reference systems: motivation, descriptions of different references for aeronautics. Presentation (course intro)
Wed., Sep. 13rd Lecture 2 – Reference systems (conclusions). Three-dimensional rotations: motivation, types of modeling. Tait-Bryan sequenc (theoretical approach). Tensorial definition of rotation of a vector. Representation of rotation tensor. Change of reference of a vector.
Thu., Sep. 14th Lecture 3 – Properties of rotations. Change of reference of tensors. Composition of rotations: tensor calculus and matrix representation. Application to the Tait-Bryan sequence: complete rotation tensor, representation of the rotation tensor via multiplication of planar rotation matrices. Lectures 1-2-3
Mon., Sep. 18th Lecture 4 – Kinematics: Poisson’s rule, moving axes theorem. Definition of position: composition of position vectors. Velocity and acceleration by differentiation with respect to inertial reference.
Wed., Sep. 20th Lecture 5 – Acceleration with respect to inertial systems. Errors associated to inertial system hypothesis for references employed in aircraft dynamics.
Wed., Sep. 20th Lecture 6 – Application of the Tait-Bryan sequence to selected couples of references. Attitude angles. Aerodynamic angles. Flight path angles. Euler angles rates and relationship with body rotational speed vector.
Thu., Sep. 21st Lecture 7 – Dynamics. Newton’s second principle for a point mass and for a rigid body. Mass and static moment. Skew-symmetric form of vectors. Moment of momentum theorem for a point mass and for a rigid body. Inertia tensor. Lectures 4-5-6-7
Mon., Sep. 25th Lab 1 – Rotations, integration of kinematic equations. [Dr. Jayanna] Lab 1
Thu., Sep. 28th Lecture 8 – Generalized form of balance equations. Notes on validity of the agnostic formulation. Hypotheses: body reference in CG, geometry and mass symmetry. Representation of the equations of motion in body frame: definition of scalar components of vector projections, scalar form of the balance equations. Unknowns vs. equations balance, need for kinematic equations. Lecture 8
Mon., Oct. 2nd Lecture 9 – Comments on non-linear equations. Generalized static equilibrium. General solution of static trim problem. Example of trajectories compatible with static trim. Equations vs. unknowns balance for a static trim condition, parameterized solution. Generalities on linearization of the dyanamic equations.
Wed., Oct. 4th Lecture 10 – Linearization of equations of motion. Inertial terms. Gravity forcing term. Aerodynamic force and moments.
Wed., Oct. 4th Lecture 11 – Coefficients appearing in aerodynamic forcing terms, dependencies. Hypothesis of linear aerodynamics: stability and control derivatives. Introduction to non-dimensional form of linearized balance equations: definitions of non-dimensional and scaled terms, variables in vector form in body reference. Lectures 9-10-11
Mon., Oct. 9th Lecture 12 – Non-dimensional form of linearized balance equations. Target variables. Inertial term (momentum/moment of momentum). Aerodynamic force and moment: stability derivatives with respect to non-dimensional quantities. Gravity term. Momentum balance in terms of target variables.
Wed., Oct. 11th Lecture 13 – Moment of momentum balance in terms of target variables. Complete linearized equations in control form. Linearization of kinematic relationships. Uses of linearized systems for aircraft dynamics. Qualitative exploration of most intense stability and control derivatives.
Wed., Oct. 11th Lecture 14 – Simplification of negligible aerodynamic derivatives. Hypothesis of symmetric flight in the vertical plane: effect on kinematic and dynamic reference values. Decoupling of linearized dynamics.
Thu., Oct. 12th Lecture 15 – Decoupled linearized equations in states-space form. Final remarks on linearized systems. Estimation of coefficients in dynamic equations: methods for estimation. Listing of coefficients required for longitudinal dynamics. Lectures 12-13-14-15
Mon., Oct. 16th Lecture 16 – Two-dimensional aerodynamics of aerofoils. Lift, drag and moment coefficients. Zero-lift condition. Aerodynamic center (focus). Introduction to finite lifting surfaces.
Wed., Oct. 18th Lecture 17 – Coefficients in longitudinal aerodynamics: equivalence wind vs. body axes. Wing geometry. Lift coefficient estimation for a lifting surface. Two-surfaces model.
Wed., Oct. 18th Lab 2 – Theory of linear systems. [Dr. Jayanna] Lab 2
Thu., Oct. 19th Lecture 18 – Lift coefficient for an aircraft. Pitching moment coefficient for an lifting surfaces and slender bodies on board, total value for an aircraft. Effect of high angle of attack on swept-back wings. Lectures 16-17-18
Mon., Oct. 23rd Lecture 19 – Suitability of models for specific flight conditions (remarks). Drag coefficient and derivatives. Derivatives with respect to longitudinal velocity. Derivatives with respect to pitch rate. Acceleration derivatives in the longitudinal plane.
Wed., Oct. 25th Lecture 20 – Control derivatives: elevator. Reference values in longitudinal dynamics. Stability derivatives in lateral-directional dynamics: side force.
Wed., Oct. 25th Lecture 21 – Stability derivatives with respect to sideslip: yawing and rolling moment.
Thu., Oct. 26th Lecture 22 – Rotary derivatives in lateral-directional dynamics. Control derivatives with respect to rudder deflection. Lectures 19-20-21-22
Mon., Oct. 30th Lecture 23 – Control derivatives with respect to aileron deflection. Control derivatives related to propulsion. Equilibrium in forward flight: from body to wind reference. Static stability in the longitudinal plane.
Thu., Nov. 2nd Lecture 24 – Longitudinal static stability on two-surfaces model. Neutral point. Trimmability and stability. Drag penalty and relaxed static stability. Equilibrium control solution (elevator): effect of trim lift coefficient and center of gravity. Excursion limits of the center of gravity. Lectures 23-24
Mon., Nov. 6th Lecture 25 – Stick-free equilibrium and static stability: floating elevator deflection, hinge moment, effect on static stability, comparison with stick-fixed stability. Technological solutions for elevator design. Trim tab: effect on equilibrium and hinge moment. Procedure for in-flight neutral point identification (stick-fixed).
Wed., Nov. 8th Lecture 26 – Procedure for in-flight neutral point identification (stick-free). Stick force on elevator: relationship with hinge moment. Stick force in trim: dependencies on tab deflection, velocity. Derivative of stick force and regulation requirements. Stick-fixed stability in longitudinal maneuvers: pull-up. Lectures 25-26
Wed., Nov. 8th Lab 3 – Static stability in steady horizontal flight (1) [Dr. Song] Lab 3
Thu., Nov. 9th Lab 4 – Static stability in steady horizontal flight (2) [Dr. Song] Lab 4
Mon., Nov. 13rd Lecture 27 – Directional static stability criterion and directional equilibrium. Rudder hinge moment and pedal force. Stick-fixed and stick-free conditions. Lateral static stability.
Wed., Nov. 15th Lecture 28 – Eigenanalysis on LTI systems: general concepts. Eigenanalysis of the longitudinal dynamics of a traditional aircraft. Eigenanalysis of lateral-directional dynamics of a traditional aircraft (up to presentation of modes).
Wed., Nov. 15th Lab 5 – Maneuvering stability [Dr. Song] Lab 5
Thu., Nov. 16th Lecture 29 – Effect of stability derivatives on lateral-directional dynamics. Longitudinal and lateral-directional dynamics: mode break-down, relationship with static stability levels. Flying qualities. Lectures 27-28-29
Mon., Nov. 20th Lecture 30 – Introduction to flight control systems. General concepts on modeling and logics for control. Modeling for longitudinal stability augmentation system. Possible control scheme.
Wed., Nov. 22nd Lab 6 – Simplified models longitudinal dynamics [Dr. Jayanna]
Wed., Nov. 22nd Lab 7 – Simplified models lateral-directional dynamics [Dr. Jayanna] Labs 6-7
Thu., Nov. 23rd Lecture 31 – Analytical development of longitudinal SAS. Effect of filters and elevator dynamics. States-space form, with or without filters and actuators. Control gains and short period dynamics: conditioning effects. Lectures 30-31
Mon., Nov. 27th Lab 8 – Longitudinal and lateral-directional response [Dr. Jayanna]
Wed., Nov. 29th Lecture 32 – Roll-yaw damper: concepts. Flight performance: static equilibrium in horizontal flight. Elevator control for pitch equilibrium. Trimmed lift, drag, polar: effect of CG position. Thrust required: dependence on velocity. Effect of weight, altitude.
Wed., Nov. 29th Lab 9 – Lab on longitudinal and lateral-directional response [Dr. Jayanna] Lab 8-9
Thu., Nov. 30th Lecture 33 – Penaud analysis in power. Climb performance: equilibrium in aerodynamic reference. Penaud analysis and climb performance. Optimal climb conditions. Flight envelope. Lectures 32-33
Mon., Dec. 4th Lab 10 – Non-linear simulation [Dr. Jayanna] Lab 10
Wed., Dec. 6th Lecture 34 – Performance in cruise. Basic of aircraft sizing: requirements and sizing loop. Goal of preliminary and detailed sizing. Lecture 34
Wed., Dec. 6th Lab 11 – Flight performance computations [Dr. Song] Lab 11
Mon., Dec. 11th Lecture 35 – Preliminary weight sizing. Weight break-down. Historical regressions of weight data. Fuel fractions method.
Wed., Dec. 13th Lecture 36 – Sizing matrix plot. Lectures 35-36
Wed., Dec. 13th Lab 12 – Flight performance computations [Dr. Song] Lab 12
Thu., Dec. 14th Seminar by Dr. Chimetto, Borroni – Leonardo Velivoli Presentation
Mon., Dec. 18th Lab 13 – Preliminary weight sizing [Dr. Song] Lab 13
Wed., Dec. 20th Lab 14 – Sizing matrix plot [Dr. Song]

Disclaimer: lecture papers are not revised following lectures, and may contain errors and inaccuracies.

Exercise classes

Exercise classes will be held by

  • Dr. Dharani Jayanna

Dept. of Aerospace Science and Technology – Building B13 (control systems laboratory)


  • Dr. Wenxuan Song

Dept. of Aerospace Science and Technology – Building B19 (wind tunnel)


Meeting by prior appointment only.

Exam terms

Exams of both modules of the Aircraft Performance and Dynamics course will always take place together in a single session. The written exam consists of a collection of short questions related to the topics presented throughout the course lectures and labs. At the teacher’s discretion, it may be required to complete the assessment through an additional oral exam.

Exam sessions will be five – two in the Winter term (January-February 2024), two in the Summer term (June-July 2024), one in the Fall term (September 2024).

1st Session 2nd Session 3rd Session 4th Session 5th Session
January 12th, 2024 February 7th, 2024 TBD TBD TBD
9.00 9.00

A draft of the exam for the current edition of the course can be found at this link.


Prof. Carlo E.D. Riboldi
Tel.: +39 02 2399 8342
Office: Department of Aerospace Science and Technology (building B12, top floor)
Reception by prior appointment only (in person or via MS Teams). Please contact the teacher to schedule a meeting.