The University of Southampton
Courses

# SESA2025 Mechanics of Flight

## Module Overview

This module further develops the fundamental concepts underpinning aircraft flight, stability, and control. The focus is initially on capturing the aerodynamic behaviour of lifting and control surfaces within simple mathematical models leading to simple 3-DOF equations of motion for a rigid aircraft. Ideas of equilibrium and trim are captured by determining the steady control inputs needed to fly simple steady trajectories, including feasibility, conditional static stability, and drag optimality. These concepts are extended into three-dimensions using ideas of motion as a geometric transformation leading to the full 6-DOF dynamical systems, state space formulation, and flight simulators; linearization about a steady trajectory leads to linear state space models, characteristic motions and dynamic stability, response to gusts, stability augmentation, and linear control. The lectures are complemented by two formative coursework with relevance to the taught material.

### Aims and Objectives

#### Module Aims

To develop further a range of core concepts in mechanics of flight, stability, and control of aircraft, including simple aerodynamic modelling, 3-DOF and full 6-DOF equations of motion for a rigid aircraft, Euler angles and rates, equilibrium and trim, drag, static and dynamic stability, flight simulation, characteristic motions and eigenmodes, response to disturbances, control inputs for simple steady trajectories, stability augmentation.

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Aerodynamic and control forces acting on aircraft, including high-lift devices, origins of drag.
• Aircraft equilibrium, control/trim inputs required for steady trajectories, static stability, optimality.
• Description of motion in three-dimensions, Euler angles and rates, full 6-DOF equations for rigid symmetrical aircraft, state space formulation, solution in the time domain and flight simulation.
• Linearised state space equations for small disturbances about a steady trajectory, aerodynamic derivatives, longitudinal and lateral characteristic motions, eigenmodes, dynamic stability.
• Control inputs for steady sideslip, coordinated turns. Linear response to control inputs and wind gusts. Simple state feedback and autopilots.
##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Perform simple calculations of aircraft trim, lift and drag, static stability.
• Perform simple calculations and computations of aircraft characteristic motions in both timedomain and in terms of eigenmodes
• Analyse aircraft lift/drag/moment data.
##### Transferable and Generic Skills

Having successfully completed this module you will be able to:

• Study and learn independently.
• Communicate work in written reports.
• Demonstrate study and time management skills.
• Solve problems systematically.
##### Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Study and learn both independently.
• Communicate work in written reports.
• Demonstrate study and time management skills.
• Solve problems.
• Appreciate some of the technical issues associated with aerospace vehicle design.

### Syllabus

Introduction Aerodynamic forces and moments: Nomenclature, aircraft axes, lifting and control surfaces, high-lift devices, aerodynamic derivatives, aerodynamic centre, induced flow and downwash, aerodynamic derivatives and neutral point for complete aircraft. Thrust, drag, stall, compressibility effects, wing sweep, trim tabs. Aircraft equilibrium and static stability: Control and trim inputs for steady equilibrium level flight, steady climb, manoeuvring in steady verticalacceleration. Stick-fixed and stick-free static stability, static margins, lateral static stability. Effects of high-lift devices, optimal trim configurations and minimum drag. Aircraft motion in three-dimensions: Motion as geometric transformation, aircraft body and Earth axes, rotation matrices, Euler angles, Euler rates and angular velocity, transformation of vector quantities, inertial time derivative, gravitation effects. Estimation of orientation from inertial sensors, autopilots. Full 6-DOF equations for a rigid aircraft, state space formulation. Solution in the time domain, flight simulators. • Small disturbance equations Linearization about steady equilibrium flight, wind axes, stability and control derivatives, matrix representation, eigenvalues and eigenvectors of characteristic motions, dynamic stability, linear state space formulations, decoupling of longitudinal and lateral motions for symmetric aircraft. Longitudinal dynamic stability: Wind axes and aerodynamic derivatives, gravitational effects. Stick-fixed dynamic stability, Routh–Hurwitz criterion, eigenvalues and eigenvectors of characteristic motions. Phugoid and short period oscillations. Reduced order models and longitudinal approximations. Handling qualities. Lateral dynamic stability: Eigenvalues and eigenvectors of characteristic motions. Dutch roll, spiral mode and roll subsidence. Reduced order models. Handling qualities. State space formulation for response and control applications. Estimation of lateral aerodynamic derivatives. Reduced order models and lateral approximations. Steady sideslip and correctly-banked turn. Control and Response: Control inputs to achieve a given trajectory, stability augmentation and state feedback, autopilots and flight control. Response to wind gusts. Tutorials, Revision and Examples.

### Learning and Teaching

#### Teaching and learning methods

Teaching methods : lectures, including several tutorial sessions. Learning activities include directed reading and problem solving, report writing.

TypeHours
Teaching32
Independent Study118
Total study time150

#### Resources & Reading list

J.D. Anderson (2011). Introduction to Flight.

Raymer, D. (2012). Aircraft Design: A Conceptual Approach.

Cook, MV. (1997). Flight Dynamics Principles.

Cook, MV. (2012). Flight Dynamics Principles: A Linear Systems Approach to Aircraft Stability and Control.

McCormick, BW. (1979). Aerodynamics, Aeronautics and Flight Mechanics.

Phillips, W.F. (2009). Mechanics of Flight.

### Assessment

Coursework

#### Summative

MethodPercentage contribution
Exam  (120 minutes) 100%

#### Referral

MethodPercentage contribution
Exam 100%

#### Repeat Information

Repeat type: Internal & External