Aerodynamics is the branch of science devoted to study the motion of air flow past the solid objects. The field that studies the motion of air, particularly its interactions with the aircraft, is known as aircraft aerodynamics. However, the scope of aerodynamics is not just limited to the aircraft, rather it comprises all those phenomena where the air flow past a structure whether stationary or in motion, in the earth’s sensible atmosphere. The word aerodynamics is made of two Greek words: aer (aero) means air \(+\) dynamikós (dynamics) refers to power. Essentially, the study of aerodynamics revolves around estimating the forces and moments acting on an airborne vehicle. From the very beginning, we were interested to emulate a bird and while thinking of human flight centered on the imitation of birds, several attempts have been made to bring such a device into reality. But even today it seems unachievable with existing technologies. In a bird’s flight, the flapping wings perform a dual role; they serve the purpose of both propulsive and aerodynamic devices. Any manmade device which imitates the flight of a bird is known as ornithopter.
The aircraft is a flying object that operates in the sensible atmosphere. Depending upon the mission requirement, aircraft varies in shapes and sizes. The whole aircraft has a median plane of symmetry, dividing the machine into two halves. Basically, these parts are mirror image of each other, if this plane of symmetry is considered as a mirror.
The aircraft requires lift to fly in the air, and thus a pair of wings is attached to the long cylindrical section, known as fuselage. Although each component of an aircraft contributes in generating the lift, the major portion comes from wings only. That is, the wings are main lifting surfaces which contributes maximum to the lift. The wing fixed at the right side of fuselage is termed as starboard wing, and the wing located at the left is called the port wing. To produce lift, the aircraft must be pushed through the air. When the aircraft flies, its motion is retarded by an opposing force called drag. In turbinepowered aircraft, to generate thrust and overcoming the drag, engines are mounted beneath the wings.
To control and maneuver the aircraft, wings of smaller sizes are attached at the rear end, commonly referred to as tail section. A pair of smallsize fixed wings mounted horizontally is called horizontal stabilizer, and a vertically placed fixed part is known as vertical stabilizer. As the name suggests, both stabilizers provide stability to the aircraft. In case of a sudden gust, nose of the aircraft uses to swing sideways from the original direction of motion, called yaw. Likewise, the upanddown motion of the nose is known as pitch. The horizontal stabilizer prevents the pitching motion, whereas the vertical stabilizer is responsible for preventing the yawing motion of the nose.
The property of a fluid due to which the fluid layer has shearing stresses between them is known as coefficient of viscosity
\(\mathrm {\left( \mu \right) }\). With increase of temperature, viscosity of liquid decreases. Empirically, viscosity of a liquid is expressed in the following form:
$$\begin{aligned} \mathrm {\ln \left( \frac{\mathrm {\mu }}{\mathrm {\mu }_{0}}\right) }&\,\mathrm { =\mathrm {a}+\mathrm {b}\left( \frac{\mathrm {T}_{0}}{\mathrm {T}}\right) +\mathrm {c}\left( \frac{\mathrm {T}_{0}}{\mathrm {T}}\right) ^{2}} \end{aligned}$$
where the coefficients
\(\mathrm {a}\),
\(\mathrm {b}\), and
\(\mathrm {c}\) are arbitrary constants;
\(\mathrm {T_{0}}\) is the reference temperature; and
\({\mathrm {\mu }_{0}}\) is the viscosity of liquid at the temperature
\({\mathrm {T}_{0}}\).
In contrast, the viscosity of a gas increases with temperature as shown by the following relations:
$$\begin{aligned} \mathrm {\frac{\mathrm {\mu }}{\mathrm {\mu }_{0}}}&\,\mathrm { ={\left\{ \begin{array}{ll} \left( \frac{\mathrm {T}}{\mathrm {T}_{0}}\right) ^{n} &{} \text {Power law}\\ \left( \frac{\mathrm {T}}{\mathrm {T}_{0}}\right) ^{\frac{3}{2}}\left[ \frac{\mathrm {T}_{0}+\mathrm {S}}{\mathrm {T}+\mathrm {S}}\right] &{} \text {Sutherland law} \end{array}\right. }} \end{aligned}$$
where
\({\mathrm {\mu {}_{0}}}\) is the known viscosity at a known absolute temperature
\(\mathrm {T}_{0}\); and
\({\mathrm {S}}\) is called the Sutherland constant. For air,
\(\mathrm {n=}\) 0.7 and
\(\mathrm {S=\text {110 }\, K}\); a more useful form of Sutherland formula is given below:
$$\begin{aligned} {\mathrm {\mu }}&= \,\text {1.46}\times \ 10^{6}\left( \frac{\mathrm {T}^{\frac{3}{2}}}{\mathrm {T}+\text {111}}\right) ; \\&\text {for}, {\left\{ \begin{array}{ll} \text {0.01}\,\mathrm{atm}<p_{\text {static}}<\text {100}\,\mathrm{atm};&\text {0}\,\mathrm{K}<T<\text {3000}\,\mathrm{K}\end{array}\right. } \end{aligned}$$
According to the Archimedes principle, an object will be buoyed up by a force equal in magnitude to the weight of fluid displaced by the object. Similarly, an aircraft flying in the air experiences a buoyant force equal in magnitude to the weight of displaced air. The forces acting on the flying aircraft are known as aerodynamic forces. The aerodynamic force is resolved into horizontal and vertical components. The horizontal component acting in the direction of freestream is termed drag, and the vertical component, perpendicular to the freestream direction, is known as lift.
In a threedimensional body, if a section is cut with a plane (parallel to the plane of symmetry), the intersection of the body surface with that plane is termed as profile. For an aircraft wing, this profile is better known as airfoil. When the flow past an airfoil, then the latter produces the aerodynamic forces, namely, lift and drag. Alternatively, for a given area, the profile which generates a maximum amount of lift is called an airfoil. The shape and orientation of an airfoil section sliced at various locations on the wing usually depend on its distance from the plane of symmetry.
At conventional angles of incidence, in comparison with freestream static pressure, the suction (upper) surface experiences a decrease in pressure over a large portion of it, whereas a lesser decrease in pressure is felt by the lower (pressure) surface. This uneven pressure acting on upper and lower surfaces leads to the nonuniform pressure distribution around the airfoil, due to which lift and drag are produced on the airfoil.
The aerodynamic forces on an airfoil section may be represented by lift, drag, and pitching moment. At each value of the lift coefficient, there will be a particular point about which the pitching moment coefficient is zero. The aerodynamic effects on the airfoil section may be represented by the lift and the drag alone acting at that point, termed as the center of pressure.
The aerodynamic center is the reference point about which the pitching moment coefficient does not change with changes in the angle of attack.
The essential requirement to establish physical similarity between two flows is that the physics behind them must be same. That is, the flow in a horizontal pipe is quite different from the flow in an open channel. This is because the pipe flows are governed by the viscous and pressure forces, whereas the openchannel flows are predominately influenced by gravity force. Thus, the flows which are governed by the same physical principle, but operating under different conditions, will be called similar if there are some specified physical quantities whose ratios between these flows are found constant everywhere. If the specified quantities are related to geometrical dimensions, then the similarity is called geometric similarity; if the quantities are associated to the motion, then it is termed as kinematic similarity; and if the quantities refer to forces, then the similarity is known as dynamic similarity. Note that the two flows will be called similar only if all these similarities exist simultaneously.
In investigations of physical similarity, the full size or actual scale systems are called prototypes, while the laboratoryscale systems are known as models. It should be noted that the use of same fluid with both prototype and model is not necessary, and also the model need not be smaller than the prototype always.
Whenever a substance is compressed by applying the pressure, its density changes. The gases undergo a large change in density whenever pressure is applied, whereas liquid shows relatively lower density change. In contrast, when solids are compressed, virtually no change in density is noticeable. The amount by which a substance can be compressed is measured in terms of a specific property, known as compressibility. If the pressure is increased by an infinitesimal amount
\(\mathrm {dp}\), and the corresponding infinitesimal decrease in specific volume of the fluid element is
\(\mathrm {d\forall '}\), then the compressibility
\(\mathrm {\left( \mathrm {\beta }\right) }\) of the fluid element will be given by
$$\begin{aligned} {\mathrm {\beta }}&\,\mathrm { =\frac{1}{\forall '}\frac{d\forall '}{dp}} \end{aligned}$$
When a gas is compressed by increasing the pressure, temperature of the gas increases and thus, the heat transfer through the system (gas) boundary is inevitable. If the gas temperature is held constant by some suitable heat transfer mechanism, then
\({\mathrm {\beta }}\) is referred to as isothermal compressibility
\(\mathrm {\left( \mathrm {\beta }_{T}\right) }\), given by
$$\begin{aligned} {\mathrm {\beta }_{T}}&\,\mathrm { =\frac{1}{\rho }\left( \frac{d\rho }{dp}\right) _{T}} \end{aligned}$$
However, if the system is made insulated, i.e., no exchange of heat with the surrounding is possible, then the compression takes place isentropically. Thus,
\({\mathrm {\beta }}\) is termed as isentropic compressibility
\(\mathrm {\left( \mathrm {\beta }_{s}\right) }\), defined as
$$\begin{aligned} {\mathrm {\beta }_{s}}&\mathrm {=\frac{1}{\rho }\left( \frac{d\rho }{dp}\right) _{s}} \end{aligned}$$
The fluid molecules are free to move in random fashion within the fluid boundaries. The movement of these molecules causes the transport of mass, momentum, and energy from one location to another in the fluid. Essentially, this transport of matter at microscopic scale gives rise to the phenomena of mass diffusion, viscosity, and thermal conduction. All real fluid flows which manifest the effects of these transport phenomena are called viscous flows. Contrarily, a flow which does not have viscosity, thermal conduction, or diffusion is termed as inviscid flow.
Among all the criteria of categorizing and describing different aerodynamic flows, the classification based on the Mach number is presumably the most ubiquitous. If
\(\mathrm {M}_{\mathrm {a}}\) is the freestream Mach number at an arbitrary point in a flow field, then using
\({\mathrm {\mathrm {M}_{\mathrm {a}}}}\) as the criterion we can define the following speed regimes:

If \({\mathrm {\mathrm {M}_{\mathrm {a}}<\text {1}}}\), the flow is called subsonic.

If \(\mathrm {\text {0.8}<\mathrm {M}_{\mathrm {a}}<\text {1.2}}\), the flow is called transonic.

If \({\mathrm {M}_{\mathrm {a}}>\text {1}}\), the flow is termed as supersonic.

If \({\mathrm {M}_{\mathrm {a}}>\text {5}}\), the flow is known as hypersonic.
Hodograph is a vector diagram, also known as velocity diagram, which shows the changes in velocity with respect to position or time. It was first used by James Bradley, but the practical development of Hodograph was later carried out by Sir William Rowan Hamilton (1805–1865). The Hodograph transformation finds vast applications in aerodynamics, as it can transform the nonlinear equations to the linear ones.