Aircraft dynamics develops the equations of motion, treating a fixed-wing flying vehicle as a rigid body. The special attention is placed on the aerodynamic impact that makes solving the equations challenging due to the strong interactions with aircraft motion. In flight mechanics, the treatment is suggested through some engineering approximations. Aircraft equations of motion are governed by rigid-body dynamics, where the expression in body-fixed frame provides an opportunity of solving 6DOF motion variables through six sets of differential equations. Further, we shall recognize that the applying inputs of forces and moments are interacting with aircraft motion due to aerodynamic effect. Therefore, we use Taylor series expansion to approximate perturbed aerodynamics through the aerodynamic and control derivatives. By connecting these derivatives to the nondimensional parameters that are assumed to be available, we are ready to conduct dynamic analysis.

Static flight stability and control addresses the stability concepts in flight, and impact of flight control effectors on attributions of flight characteristics. Based on static force and moment equations in steady flight conditions, the stability and control trends are revealed without going through dynamic modes or solving dynamic equations. The representative longitudinal stability is the pitch stiffness and the longitudinal control is through the control surface of elevator. The representative lateral stability are addressed by the directional yaw stiffness and the roll stiffness, correspondingly, the yaw control is through the rudder, while the roll control is through the aileron. It is noteworthy that aircraft is treated as a system, that we need to integrate component contributions. In that sense, the wing-horizontal tail configuration is considered for longitudinal analysis, while the body-wing-vertical tail configuration is taken into account for lateral analysis. Stability and control derivatives are estimated and identified as key parameters for the static stability analysis.

This is the first chapter of a new part, “state-space based aircraft dynamics and control,” where a so-called state-space description based modern control is introduced and applied to solve flight dynamics and control problems. We will first officially introduce the concept of state-space model, followed by a model-based design method to systematically calculate feedback control gains to place representative characters to their desired positions, in order to achieve the desired dynamic performance. The placement in flight control introduces two design approaches. In terms of Learning Objectives, the pole placement calculates state (or output) feedback control gain K to place the closed-loop poles to desired positions. For a scalar input, there are various formulas to calculate the control gain vector. For an MIMO system, the placement leads to algebraic matrix manipulation, illustrated by a two-dimensional flight control example. On the other hand, the eigenstructure assignment enables closed-loop desired eigen values and eigenvectors to be placed simultaneously, where eigenvalues are the same as the closed-loop poles, and eigenvectors represent desired modes.

State space based modern flight control has the distinctive feature of systematic design depending on the linearized aircraft flight dynamics model and measurement of feedback state or output signals. In this chapter, we present basic concepts addressing the model uncertainty or disturbance challenges by introducing state estimation (observer) as well as sensitivity in flight control. In the presence of external disturbance (for example, the gust), measurement or process noises, or uncertainty in modelling (linearization approximation, variations of models, or un- modelled modes), the follow-up discussions associated with state-based design address the estimation and robustness in flight control. The linear observer design becomes a companion tool similar to the linear quadratic control design that guarantees the convergence of estimation to the ground truth. Further, the linear quadratic Gaussian design (LQG), based on stochastic process concepts, shows that control and observer design can be decoupled according to the separation principle, each will deal with control performance and estimation performance, respectively.

The basic geometric parameters that define airfoil and wing shapes are presented prior to the basic aerodynamic forces and moments, as well as the nondimensional coefficients, that are used for airfoils and wings. A general description of the impact of airfoil geometry on the resulting aerodynamics, including the effects of camber and thickness, is presented. This includes how flow around a wing is different from flow around an airfoil, as well as methods to estimate the impact of wing geometry on lift and drag. Finally, the chapter concludes with the contributing factors to airplane drag and the methods to estimate zero-lift drag. coefficient of an airplane

Analysis capabilities are developed that include the impact of compressibility on the derivation of equations that govern subsonic compressible and transonic flows, including the relations to transform incompressible experimental data or geometry to subsonic compressible Mach numbers. Transonic flow is defined, including explanations for the flow characteristics that distinguish this flow regime from other flow regimes. Estimation techniques are developed for the critical and drag-divergence Mach numbers. The impact of transonic flow on aircraft design is discussed, including the impact of wing sweep on airplane aerodynamics and the role of supercritical airfoils. Finally, the transonic area rule is discussed, including the impact on transonic and supersonic aircraft.

Understand the physical concepts that apply to supersonic wing aerodynamics, such as knowing the difference between a subsonic and supersonic leading edge and how that impacts the airfoils used for the wing. Information is also presented that expands on why subsonic and supersonic drag-due-to-lift components are caused by different physical phenomenon. Supersonic 2D and 3D flow theories can then be used to analyze the forces and moments acting on a supersonic wing, including conical flow theory for calculating wing-tip effects. The reader should then be able to explain how supersonic airplanes make a compromise between subsonic and supersonic aerodynamic performance, and how that impacts airfoil and wing design parameters. Fuselage shapes then use slender body theory for analysis, and details about how boattails are used for reducing base drag.

Aerodynamic design decisions are rarely made without considering multidisciplinary design factors, which leads to compromises between aerodynamics and other disciplines. Readers will learn how to increase lift on an airplane, and how to modify an airplane in order to achieve aerodynamic improvements. Drag reduction will then be discussed, including ways to reduce drag and the impact of drag reduction on aircraft design. The chapter ends with a study of aircraft from the past and how aerodynamic considerations were included in their design.