Aerodynamics, from grc, ἀήρ ''aero'' (air) + grc, δυναμική (dynamics), is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of
fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) a ...
and its subfield of
gas dynamics. The term ''aerodynamics'' is often used synonymously with gas dynamics, the difference being that "gas dynamics" applies to the study of the motion of all gases, and is not limited to air.
The formal study of aerodynamics began in the modern sense in the eighteenth century, although observations of fundamental concepts such as
aerodynamic drag
In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding ...
were recorded much earlier. Most of the early efforts in aerodynamics were directed toward achieving
heavier-than-air flight, which was first demonstrated by
Otto Lilienthal in 1891. Since then, the use of aerodynamics through
mathematical analysis, empirical approximations,
wind tunnel
Wind tunnels are large tubes with air blowing through them which are used to replicate the interaction between air and an object flying through the air or moving along the ground. Researchers use wind tunnels to learn more about how an aircraft ...
experimentation, and
computer simulation
Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be deter ...
s has formed a rational basis for the development of heavier-than-air flight and a number of other technologies. Recent work in aerodynamics has focused on issues related to
compressible flow,
turbulence
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between ...
, and
boundary layers and has become increasingly
computational in nature.
History
Modern aerodynamics only dates back to the seventeenth century, but aerodynamic forces have been harnessed by humans for thousands of years in sailboats and windmills, and images and stories of flight appear throughout recorded history, such as the
Ancient Greek
Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic pe ...
legend of
Icarus
In Greek mythology, Icarus (; grc, Ἴκαρος, Íkaros, ) was the son of the master craftsman Daedalus, the architect of the labyrinth of Crete. After Theseus, king of Athens and enemy of Minos, escaped from the labyrinth, King Minos sus ...
and
Daedalus
In Greek mythology, Daedalus (, ; Greek: Δαίδαλος; Latin: ''Daedalus''; Etruscan: ''Taitale'') was a skillful architect and craftsman, seen as a symbol of wisdom, knowledge and power. He is the father of Icarus, the uncle of Perdi ...
. Fundamental concepts of
continuum,
drag, and
pressure gradients appear in the work of
Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ...
and
Archimedes
Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientis ...
.
In
1726,
Sir Isaac Newton became the first person to develop a theory of air resistance, making him one of the first aerodynamicists.
Dutch-
Swiss
Swiss may refer to:
* the adjectival form of Switzerland
*Swiss people
Places
* Swiss, Missouri
*Swiss, North Carolina
* Swiss, West Virginia
*Swiss, Wisconsin
Other uses
* Swiss-system tournament, in various games and sports
* Swiss Internation ...
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
Daniel Bernoulli
Daniel Bernoulli FRS (; – 27 March 1782) was a Swiss mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family from Basel. He is particularly remembered for his applications of mathematics to mecha ...
followed in 1738 with ''Hydrodynamica'' in which he described a fundamental relationship between pressure, density, and flow velocity for incompressible flow known today as
Bernoulli's principle, which provides one method for calculating aerodynamic lift. In 1757,
Leonhard Euler
Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries ...
published the more general
Euler equations which could be applied to both compressible and incompressible flows. The Euler equations were extended to incorporate the effects of viscosity in the first half of the 1800s, resulting in the
Navier–Stokes equations
In physics, the Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician Geo ...
. The Navier–Stokes equations are the most general governing equations of fluid flow but are difficult to solve for the flow around all but the simplest of shapes.
In 1799,
Sir George Cayley became the first person to identify the four aerodynamic forces of flight (
weight
In science and engineering, the weight of an object is the force acting on the object due to gravity.
Some standard textbooks define weight as a vector quantity, the gravitational force acting on the object. Others define weight as a scalar qua ...
,
lift,
drag, and
thrust
Thrust is a reaction force described quantitatively by Newton's third law. When a system expels or accelerates mass in one direction, the accelerated mass will cause a force of equal magnitude but opposite direction to be applied to that ...
), as well as the relationships between them,
[''Cayley, George''. "On Aerial Navigation]
Part 1
Part 2
Part 3
''Nicholson's Journal of Natural Philosophy'', 1809–1810. (Via NASA
The National Aeronautics and Space Administration (NASA ) is an independent agency of the US federal government responsible for the civil space program, aeronautics research, and space research.
NASA was established in 1958, succeedin ...
)
Raw text
Retrieved: 30 May 2010. and in doing so outlined the path toward achieving heavier-than-air flight for the next century. In 1871,
Francis Herbert Wenham constructed the first
wind tunnel
Wind tunnels are large tubes with air blowing through them which are used to replicate the interaction between air and an object flying through the air or moving along the ground. Researchers use wind tunnels to learn more about how an aircraft ...
, allowing precise measurements of aerodynamic forces. Drag theories were developed by
Jean le Rond d'Alembert
Jean-Baptiste le Rond d'Alembert (; ; 16 November 1717 – 29 October 1783) was a French mathematician, mechanician, physicist, philosopher, and music theorist. Until 1759 he was, together with Denis Diderot, a co-editor of the '' Encyclopéd ...
,
Gustav Kirchhoff, and
Lord Rayleigh
John William Strutt, 3rd Baron Rayleigh, (; 12 November 1842 – 30 June 1919) was an English mathematician and physicist who made extensive contributions to science. He spent all of his academic career at the University of Cambridge. A ...
. In 1889,
Charles Renard
Charles Renard (1847–1905) born in Damblain, Vosges, was a French military engineer.
Airships
After the Franco-Prussian War of 1870-1871 he started work on the design of airships at the French army aeronautical department. Together with A ...
, a French aeronautical engineer, became the first person to reasonably predict the power needed for sustained flight.
Otto Lilienthal, the first person to become highly successful with glider flights, was also the first to propose thin, curved airfoils that would produce high lift and low drag. Building on these developments as well as research carried out in their own wind tunnel, the
Wright brothers flew the first powered airplane on December 17, 1903.
During the time of the first flights,
Frederick W. Lanchester
Frederick William Lanchester LLD, Hon FRAeS, FRS (23 October 1868 – 8 March 1946), was an English polymath and engineer who made important contributions to automotive engineering and to aerodynamics, and co-invented the topic of operations ...
,
Martin Kutta, and
Nikolai Zhukovsky independently created theories that connected
circulation of a fluid flow to lift. Kutta and Zhukovsky went on to develop a two-dimensional wing theory. Expanding upon the work of Lanchester,
Ludwig Prandtl is credited with developing the mathematics behind thin-airfoil and lifting-line theories as well as work with
boundary layers.
As aircraft speed increased designers began to encounter challenges associated with air
compressibility at speeds near the speed of sound. The differences in airflow under such conditions lead to problems in aircraft control, increased drag due to
shock wave
In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a me ...
s, and the threat of structural failure due to
aeroelastic flutter. The ratio of the flow speed to the speed of sound was named the
Mach number
Mach number (M or Ma) (; ) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.
It is named after the Moravian physicist and philosopher Ernst Mach.
: \mathrm = \f ...
after
Ernst Mach
Ernst Waldfried Josef Wenzel Mach ( , ; 18 February 1838 – 19 February 1916) was a Moravian-born Austrian physicist and philosopher, who contributed to the physics of shock waves. The ratio of one's speed to that of sound is named the Mach n ...
who was one of the first to investigate the properties of the
supersonic
Supersonic speed is the speed of an object that exceeds the speed of sound ( Mach 1). For objects traveling in dry air of a temperature of 20 °C (68 °F) at sea level, this speed is approximately . Speeds greater than five times ...
flow.
Macquorn Rankine and
Pierre Henri Hugoniot independently developed the theory for flow properties before and after a
shock wave
In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a me ...
, while
Jakob Ackeret led the initial work of calculating the lift and drag of supersonic airfoils.
Theodore von Kármán and
Hugh Latimer Dryden introduced the term
transonic
Transonic (or transsonic) flow is air flowing around an object at a speed that generates regions of both subsonic and supersonic airflow around that object. The exact range of speeds depends on the object's critical Mach number, but transoni ...
to describe flow speeds between the
critical Mach number and Mach 1 where drag increases rapidly. This rapid increase in drag led aerodynamicists and aviators to disagree on whether supersonic flight was achievable until the
sound barrier was broken in 1947 using the
Bell X-1
The Bell X-1 (Bell Model 44) is a rocket engine–powered aircraft, designated originally as the XS-1, and was a joint National Advisory Committee for Aeronautics–U.S. Army Air Forces–U.S. Air Force supersonic research project built by Be ...
aircraft.
By the time the sound barrier was broken, aerodynamicists' understanding of the subsonic and low supersonic flow had matured. The
Cold War
The Cold War is a term commonly used to refer to a period of geopolitical tension between the United States and the Soviet Union and their respective allies, the Western Bloc and the Eastern Bloc. The term '' cold war'' is used because t ...
prompted the design of an ever-evolving line of high-performance aircraft.
Computational fluid dynamics
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate ...
began as an effort to solve for flow properties around complex objects and has rapidly grown to the point where entire aircraft can be designed using computer software, with wind-tunnel tests followed by flight tests to confirm the computer predictions. Understanding of
supersonic
Supersonic speed is the speed of an object that exceeds the speed of sound ( Mach 1). For objects traveling in dry air of a temperature of 20 °C (68 °F) at sea level, this speed is approximately . Speeds greater than five times ...
and
hypersonic
In aerodynamics, a hypersonic speed is one that exceeds 5 times the speed of sound, often stated as starting at speeds of Mach 5 and above.
The precise Mach number at which a craft can be said to be flying at hypersonic speed varies, since ind ...
aerodynamics has matured since the 1960s, and the goals of aerodynamicists have shifted from the behaviour of fluid flow to the engineering of a vehicle such that it interacts predictably with the fluid flow. Designing aircraft for supersonic and hypersonic conditions, as well as the desire to improve the aerodynamic efficiency of current aircraft and propulsion systems, continues to motivate new research in aerodynamics, while work continues to be done on important problems in basic aerodynamic theory related to flow turbulence and the existence and uniqueness of analytical solutions to the Navier–Stokes equations.
Fundamental concepts
Understanding the motion of air around an object (often called a flow field) enables the calculation of forces and
moments acting on the object. In many aerodynamics problems, the forces of interest are the fundamental forces of flight:
lift,
drag,
thrust
Thrust is a reaction force described quantitatively by Newton's third law. When a system expels or accelerates mass in one direction, the accelerated mass will cause a force of equal magnitude but opposite direction to be applied to that ...
, and
weight
In science and engineering, the weight of an object is the force acting on the object due to gravity.
Some standard textbooks define weight as a vector quantity, the gravitational force acting on the object. Others define weight as a scalar qua ...
. Of these, lift and drag are aerodynamic forces, i.e. forces due to air flow over a solid body. Calculation of these quantities is often founded upon the assumption that the flow field behaves as a continuum. Continuum flow fields are characterized by properties such as
flow velocity
In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the f ...
,
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...
,
density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
, and
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
, which may be functions of position and time. These properties may be directly or indirectly measured in aerodynamics experiments or calculated starting with the equations for conservation of mass,
momentum
In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass ...
, and energy in air flows. Density, flow velocity, and an additional property,
viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the int ...
, are used to classify flow fields.
Flow classification
Flow velocity is used to classify flows according to speed regime. Subsonic flows are flow fields in which the air speed field is always below the local speed of sound. Transonic flows include both regions of subsonic flow and regions in which the local flow speed is greater than the local speed of sound. Supersonic flows are defined to be flows in which the flow speed is greater than the speed of sound everywhere. A fourth classification, hypersonic flow, refers to flows where the flow speed is much greater than the speed of sound. Aerodynamicists disagree on the precise definition of hypersonic flow.
Compressible flow accounts for varying density within the flow. Subsonic flows are often idealized as incompressible, i.e. the density is assumed to be constant. Transonic and supersonic flows are compressible, and calculations that neglect the changes of density in these flow fields will yield inaccurate results.
Viscosity is associated with the frictional forces in a flow. In some flow fields, viscous effects are very small, and approximate solutions may safely neglect viscous effects. These approximations are called inviscid flows. Flows for which viscosity is not neglected are called viscous flows. Finally, aerodynamic problems may also be classified by the flow environment. External aerodynamics is the study of flow around solid objects of various shapes (e.g. around an airplane wing), while internal aerodynamics is the study of flow through passages inside solid objects (e.g. through a jet engine).
Continuum assumption
Unlike liquids and solids, gases are composed of discrete
molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and b ...
s which occupy only a small fraction of the volume filled by the gas. On a molecular level, flow fields are made up of the collisions of many individual of gas molecules between themselves and with solid surfaces. However, in most aerodynamics applications, the discrete molecular nature of gases is ignored, and the flow field is assumed to behave as a
continuum. This assumption allows fluid properties such as density and flow velocity to be defined everywhere within the flow.
The validity of the
continuum assumption
Fluid mechanics is the branch of physics concerned with the mechanics of fluids ( liquids, gases, and plasmas) and the forces on them.
It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical an ...
is dependent on the density of the gas and the application in question. For the continuum assumption to be valid, the
mean free path
In physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as ...
length must be much smaller than the length scale of the application in question. For example, many aerodynamics applications deal with aircraft flying in atmospheric conditions, where the mean free path length is on the order of micrometers and where the body is orders of magnitude larger. In these cases, the length scale of the aircraft ranges from a few meters to a few tens of meters, which is much larger than the mean free path length. For such applications, the continuum assumption is reasonable. The continuum assumption is less valid for extremely low-density flows, such as those encountered by vehicles at very high altitudes (e.g. 300,000 ft/90 km)
or satellites in
Low Earth orbit
A low Earth orbit (LEO) is an orbit around Earth with a period of 128 minutes or less (making at least 11.25 orbits per day) and an eccentricity less than 0.25. Most of the artificial objects in outer space are in LEO, with an altitude never m ...
. In those cases,
statistical mechanics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic b ...
is a more accurate method of solving the problem than is continuum aerodynamics. The
Knudsen number can be used to guide the choice between statistical mechanics and the continuous formulation of aerodynamics.
Conservation laws
The assumption of a
fluid continuum allows problems in aerodynamics to be solved using
fluid dynamics conservation laws. Three conservation principles are used:
;
Conservation of mass: Conservation of mass requires that mass is neither created nor destroyed within a flow; the mathematical formulation of this principle is known as the
mass continuity equation.
;
Conservation of momentum: The mathematical formulation of this principle can be considered an application of
Newton's Second Law
Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows:
# A body remains at rest, or in mo ...
. Momentum within a flow is only changed by external forces, which may include both
surface forces, such as viscous (
friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction:
*Dry friction is a force that opposes the relative lateral motion of ...
al) forces, and
body force
In physics, a body force is a force that acts throughout the volume of a body.
Springer site - Book 'Solid mechanics'preview paragraph 'Body forces'./ref>
Forces due to gravity, electric fields and magnetic fields are examples of body forces. ...
s, such as
weight
In science and engineering, the weight of an object is the force acting on the object due to gravity.
Some standard textbooks define weight as a vector quantity, the gravitational force acting on the object. Others define weight as a scalar qua ...
. The momentum conservation principle may be expressed as either a
vector equation or separated into a set of three
scalar equations (x,y,z components).
;
Conservation of energy
In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means tha ...
: The energy conservation equation states that energy is neither created nor destroyed within a flow, and that any addition or subtraction of energy to a volume in the flow is caused by
heat transfer
Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy ( heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conducti ...
, or by
work into and out of the region of interest.
Together, these equations are known as the
Navier–Stokes equations
In physics, the Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician Geo ...
, although some authors define the term to only include the momentum equation(s). The Navier–Stokes equations have no known analytical solution and are solved in modern aerodynamics using
computational techniques. Because computational methods using high speed computers were not historically available and the high computational cost of solving these complex equations now that they are available, simplifications of the Navier–Stokes equations have been and continue to be employed. The
Euler equations are a set of similar conservation equations which neglect viscosity and may be used in cases where the effect of viscosity is expected to be small. Further simplifications lead to
Laplace's equation
In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties. This is often written as
\nabla^2\! f = 0 or \Delta f = 0,
where \Delta = \na ...
and
potential flow theory. Additionally,
Bernoulli's equation is a solution in one dimension to both the momentum and energy conservation equations.
The
ideal gas law
The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first s ...
or another such
equation of state
In physics, chemistry, and thermodynamics, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or intern ...
is often used in conjunction with these equations to form a determined system that allows the solution for the unknown variables.
["Understanding Aerodynamics: Arguing from the Real Physics" Doug McLean John Wiley & Sons, 2012 Chapter 3.2 "The main relationships comprising the NS equations are the basic conservation laws for mass, momentum, and energy. To have a complete equation set we also need an equation of state relating temperature, pressure, and density..." https://play.google.com/books/reader?id=_DJuEgpmdr8C&printsec=frontcover&pg=GBS.PA191.w.0.0.0.151]
Branches of aerodynamics
Aerodynamic problems are classified by the flow environment or properties of the flow, including
flow speed
In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the f ...
,
compressibility, and
viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the int ...
. ''External'' aerodynamics is the study of flow around solid objects of various shapes. Evaluating the
lift and
drag on an
airplane
An airplane or aeroplane (informally plane) is a fixed-wing aircraft that is propelled forward by thrust from a jet engine, propeller, or rocket engine. Airplanes come in a variety of sizes, shapes, and wing configurations. The broad ...
or the
shock wave
In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a me ...
s that form in front of the nose of a
rocket
A rocket (from it, rocchetto, , bobbin/spool) is a vehicle that uses jet propulsion to accelerate without using the surrounding air. A rocket engine produces thrust by reaction to exhaust expelled at high speed. Rocket engines work entir ...
are examples of external aerodynamics. ''Internal'' aerodynamics is the study of flow through passages in solid objects. For instance, internal aerodynamics encompasses the study of the airflow through a
jet engine
A jet engine is a type of reaction engine discharging a fast-moving jet (fluid), jet of heated gas (usually air) that generates thrust by jet propulsion. While this broad definition can include Rocket engine, rocket, Pump-jet, water jet, and ...
or through an
air conditioning
Air conditioning, often abbreviated as A/C or AC, is the process of removing heat from an enclosed space to achieve a more comfortable interior environment (sometimes referred to as 'comfort cooling') and in some cases also strictly controlling ...
pipe.
Aerodynamic problems can also be classified according to whether the
flow speed
In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the f ...
is below, near or above the
speed of sound
The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as we ...
. A problem is called subsonic if all the speeds in the problem are less than the speed of sound,
transonic
Transonic (or transsonic) flow is air flowing around an object at a speed that generates regions of both subsonic and supersonic airflow around that object. The exact range of speeds depends on the object's critical Mach number, but transoni ...
if speeds both below and above the speed of sound are present (normally when the characteristic speed is approximately the speed of sound),
supersonic
Supersonic speed is the speed of an object that exceeds the speed of sound ( Mach 1). For objects traveling in dry air of a temperature of 20 °C (68 °F) at sea level, this speed is approximately . Speeds greater than five times ...
when the characteristic flow speed is greater than the speed of sound, and
hypersonic
In aerodynamics, a hypersonic speed is one that exceeds 5 times the speed of sound, often stated as starting at speeds of Mach 5 and above.
The precise Mach number at which a craft can be said to be flying at hypersonic speed varies, since ind ...
when the flow speed is much greater than the speed of sound. Aerodynamicists disagree over the precise definition of hypersonic flow; a rough definition considers flows with
Mach number
Mach number (M or Ma) (; ) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.
It is named after the Moravian physicist and philosopher Ernst Mach.
: \mathrm = \f ...
s above 5 to be hypersonic.
The influence of
viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the int ...
on the flow dictates a third classification. Some problems may encounter only very small viscous effects, in which case viscosity can be considered to be negligible. The approximations to these problems are called
inviscid flow
In fluid dynamics, inviscid flow is the flow of an inviscid (zero-viscosity) fluid, also known as a superfluid. The Reynolds number of inviscid flow approaches infinity as the viscosity approaches zero. When viscous forces are neglected, suc ...
s. Flows for which viscosity cannot be neglected are called viscous flows.
Incompressible aerodynamics
An incompressible flow is a flow in which density is constant in both time and space. Although all real fluids are compressible, a flow is often approximated as incompressible if the effect of the density changes cause only small changes to the calculated results. This is more likely to be true when the flow speeds are significantly lower than the speed of sound. Effects of compressibility are more significant at speeds close to or above the speed of sound. The
Mach number
Mach number (M or Ma) (; ) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.
It is named after the Moravian physicist and philosopher Ernst Mach.
: \mathrm = \f ...
is used to evaluate whether the incompressibility can be assumed, otherwise the effects of compressibility must be included.
Subsonic flow
Subsonic (or low-speed) aerodynamics describes fluid motion in flows which are much lower than the speed of sound everywhere in the flow. There are several branches of subsonic flow but one special case arises when the flow is
inviscid
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the in ...
,
incompressible and
irrotational. This case is called
potential flow and allows the
differential equations
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
that describe the flow to be a simplified version of the equations of
fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) a ...
, thus making available to the aerodynamicist a range of quick and easy solutions.
In solving a subsonic problem, one decision to be made by the aerodynamicist is whether to incorporate the effects of compressibility. Compressibility is a description of the amount of change of
density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
in the flow. When the effects of compressibility on the solution are small, the assumption that density is constant may be made. The problem is then an incompressible low-speed aerodynamics problem. When the density is allowed to vary, the flow is called compressible. In air, compressibility effects are usually ignored when the
Mach number
Mach number (M or Ma) (; ) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.
It is named after the Moravian physicist and philosopher Ernst Mach.
: \mathrm = \f ...
in the flow does not exceed 0.3 (about 335 feet (102 m) per second or 228 miles (366 km) per hour at 60 °F (16 °C)). Above Mach 0.3, the problem flow should be described using compressible aerodynamics.
Compressible aerodynamics
According to the theory of aerodynamics, a flow is considered to be compressible if the
density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
changes along a
streamline. This means that – unlike incompressible flow – changes in density are considered. In general, this is the case where the
Mach number
Mach number (M or Ma) (; ) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.
It is named after the Moravian physicist and philosopher Ernst Mach.
: \mathrm = \f ...
in part or all of the flow exceeds 0.3. The Mach 0.3 value is rather arbitrary, but it is used because gas flows with a Mach number below that value demonstrate changes in density of less than 5%. Furthermore, that maximum 5% density change occurs at the
stagnation point (the point on the object where flow speed is zero), while the density changes around the rest of the object will be significantly lower. Transonic, supersonic, and hypersonic flows are all compressible flows.
Transonic flow
The term Transonic refers to a range of flow velocities just below and above the local
speed of sound
The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as we ...
(generally taken as
Mach 0.8–1.2). It is defined as the range of speeds between the
critical Mach number, when some parts of the airflow over an aircraft become
supersonic
Supersonic speed is the speed of an object that exceeds the speed of sound ( Mach 1). For objects traveling in dry air of a temperature of 20 °C (68 °F) at sea level, this speed is approximately . Speeds greater than five times ...
, and a higher speed, typically near
Mach 1.2, when all of the airflow is supersonic. Between these speeds, some of the airflow is supersonic, while some of the airflow is not supersonic.
Supersonic flow
Supersonic aerodynamic problems are those involving flow speeds greater than the speed of sound. Calculating the lift on the
Concorde
The Aérospatiale/BAC Concorde () is a retired Franco-British supersonic airliner jointly developed and manufactured by Sud Aviation (later Aérospatiale) and the British Aircraft Corporation (BAC).
Studies started in 1954, and France an ...
during cruise can be an example of a supersonic aerodynamic problem.
Supersonic flow behaves very differently from subsonic flow. Fluids react to differences in pressure; pressure changes are how a fluid is "told" to respond to its environment. Therefore, since
sound
In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid.
In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by ...
is, in fact, an infinitesimal pressure difference propagating through a fluid, the
speed of sound
The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as we ...
in that fluid can be considered the fastest speed that "information" can travel in the flow. This difference most obviously manifests itself in the case of a fluid striking an object. In front of that object, the fluid builds up a
stagnation pressure as impact with the object brings the moving fluid to rest. In fluid traveling at subsonic speed, this pressure disturbance can propagate upstream, changing the flow pattern ahead of the object and giving the impression that the fluid "knows" the object is there by seemingly adjusting its movement and is flowing around it. In a supersonic flow, however, the pressure disturbance cannot propagate upstream. Thus, when the fluid finally reaches the object it strikes it and the fluid is forced to change its properties –
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
,
density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
,
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...
, and
Mach number
Mach number (M or Ma) (; ) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.
It is named after the Moravian physicist and philosopher Ernst Mach.
: \mathrm = \f ...
—in an extremely violent and
irreversible fashion called a
shock wave
In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a me ...
. The presence of shock waves, along with the compressibility effects of high-flow velocity (see
Reynolds number
In fluid mechanics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be dom ...
) fluids, is the central difference between the supersonic and subsonic aerodynamics regimes.
Hypersonic flow
In aerodynamics, hypersonic speeds are speeds that are highly supersonic. In the 1970s, the term generally came to refer to speeds of Mach 5 (5 times the speed of sound) and above. The hypersonic regime is a subset of the supersonic regime. Hypersonic flow is characterized by high temperature flow behind a shock wave, viscous interaction, and chemical dissociation of gas.
Associated terminology
The incompressible and compressible flow regimes produce many associated phenomena, such as boundary layers and turbulence.
Boundary layers
The concept of a
boundary layer is important in many problems in aerodynamics. The viscosity and fluid friction in the air is approximated as being significant only in this thin layer. This assumption makes the description of such aerodynamics much more tractable mathematically.
Turbulence
In aerodynamics, turbulence is characterized by chaotic property changes in the flow. These include low momentum diffusion, high momentum convection, and rapid variation of pressure and flow velocity in space and time. Flow that is not turbulent is called
laminar flow
In fluid dynamics, laminar flow is characterized by fluid particles following smooth paths in layers, with each layer moving smoothly past the adjacent layers with little or no mixing. At low velocities, the fluid tends to flow without lateral mi ...
.
Aerodynamics in other fields
Engineering design
Aerodynamics is a significant element of
vehicle design, including
road cars and
truck
A truck or lorry is a motor vehicle designed to transport cargo, carry specialized payloads, or perform other utilitarian work. Trucks vary greatly in size, power, and configuration, but the vast majority feature body-on-frame constructi ...
s where the main goal is to reduce the vehicle
drag coefficient
In fluid dynamics, the drag coefficient (commonly denoted as: c_\mathrm, c_x or c_) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It is used in the drag e ...
, and
racing cars, where in addition to reducing drag the goal is also to increase the overall level of
downforce.
Aerodynamics is also important in the prediction of forces and moments acting on
sailing vessels. It is used in the design of mechanical components such as
hard drive
A hard disk drive (HDD), hard disk, hard drive, or fixed disk is an electro-mechanical data storage device that stores and retrieves digital data using magnetic storage with one or more rigid rapidly rotating platters coated with mag ...
heads.
Structural engineers resort to aerodynamics, and particularly
aeroelasticity, when calculating
wind
Wind is the natural movement of air or other gases relative to a planet's surface. Winds occur on a range of scales, from thunderstorm flows lasting tens of minutes, to local breezes generated by heating of land surfaces and lasting a few ...
loads in the design of large buildings,
bridge
A bridge is a structure built to span a physical obstacle (such as a body of water, valley, road, or rail) without blocking the way underneath. It is constructed for the purpose of providing passage over the obstacle, which is usually someth ...
s, and
wind turbines
The aerodynamics of internal passages is important in
heating/ventilation,
gas piping, and in
automotive engines where detailed flow patterns strongly affect the performance of the engine.
Environmental design
Urban aerodynamics are studied by
town planners and designers seeking to improve
amenity
In property and land use planning, amenity (lat. ''amoenitās'' “pleasantness, delightfulness”) is something considered to benefit a location, contribute to its enjoyment, and thereby increase its value.
Tangible amenities can include t ...
in outdoor spaces, or in creating urban microclimates to reduce the effects of urban pollution. The field of environmental aerodynamics describes ways in which
atmospheric circulation and flight mechanics affect ecosystems.
Aerodynamic equations are used in
numerical weather prediction.
Ball-control in sports
Sports in which aerodynamics are of crucial importance include
soccer
Association football, more commonly known as football or soccer, is a team sport played between two teams of 11 players who primarily use their feet to propel the ball around a rectangular field called a pitch. The objective of the game is ...
,
table tennis
Table tennis, also known as ping-pong and whiff-whaff, is a sport in which two or four players hit a lightweight ball, also known as the ping-pong ball, back and forth across a table using small solid rackets. It takes place on a hard table div ...
,
cricket
Cricket is a bat-and-ball game played between two teams of eleven players on a field at the centre of which is a pitch with a wicket at each end, each comprising two bails balanced on three stumps. The batting side scores runs by st ...
,
baseball
Baseball is a bat-and-ball sport played between two teams of nine players each, taking turns batting and fielding. The game occurs over the course of several plays, with each play generally beginning when a player on the fielding t ...
, and
golf
Golf is a club-and-ball sport in which players use various clubs to hit balls into a series of holes on a course in as few strokes as possible.
Golf, unlike most ball games, cannot and does not use a standardized playing area, and coping wi ...
, in which most players can control the trajectory of the ball using the "
Magnus effect".
See also
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Aeronautics
Aeronautics is the science or art involved with the study, design, and manufacturing of air flight–capable machines, and the techniques of operating aircraft and rockets within the atmosphere. The British Royal Aeronautical Society identif ...
*
Aerostatics
*
Aviation
Aviation includes the activities surrounding mechanical flight and the aircraft industry. ''Aircraft'' includes airplane, fixed-wing and helicopter, rotary-wing types, morphable wings, wing-less lifting bodies, as well as aerostat, lighter- ...
*
Insect flight – how bugs fly
*
List of aerospace engineering topics
This is an alphabetical list of articles pertaining specifically to aerospace engineering. For a broad overview of engineering, see List of engineering topics. For biographies, see List of engineers.
A
* Ablative laser propulsion —
*Absolute ...
*
List of engineering topics
The following outline is provided as an overview of and topical guide to engineering:
Engineering is the scientific discipline and profession that applies scientific theories, mathematical methods, and empirical evidence to design, create, and ...
*
Nose cone design
*
Fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) a ...
*
Computational fluid dynamics
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate ...
References
Further reading
General aerodynamics
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Subsonic aerodynamics
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* Obert, Ed (2009). . Delft; About practical aerodynamics in industry and the effects on design of aircraft. .
Transonic aerodynamics
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Supersonic aerodynamics
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Hypersonic aerodynamics
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History of aerodynamics
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Aerodynamics related to engineering
''Ground vehicles''
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''Fixed-wing aircraft''
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''Helicopters''
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''Missiles''
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''Model aircraft''
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Related branches of aerodynamics
''Aerothermodynamics''
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''Aeroelasticity''
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''Boundary layers''
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''Turbulence''
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External links
NASA Beginner's Guide to AerodynamicsAerodynamics for StudentsAerodynamic Related Projects
Application of Aerodynamics in Formula One (F1)Aerodynamics in Car Racing
{{Authority control
Dynamics
Energy in transport