
Aeroelasticity is the branch of
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which rel ...
and
engineering
Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...
studying the interactions between the
inertial,
elastic, and
aerodynamic
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 dyn ...
forces occurring while an elastic body is exposed to a
fluid flow. The study of aeroelasticity may be broadly classified into two fields: ''static aeroelasticity'' dealing with the static or
steady state
In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties ' ...
response of an elastic body to a fluid flow; and ''dynamic aeroelasticity'' dealing with the body's
dynamic (typically
vibrational) response.
Aircraft are prone to aeroelastic effects because they need to be lightweight and withstand large aerodynamic loads. Aircraft are designed to avoid the following aeroelastic problems:
# divergence where the aerodynamic forces increase the angle of attack of a wing which further increases the force;
# control reversal where control activation produces an opposite aerodynamic moment that reduces, or in extreme cases, reverses the control effectiveness; and
# flutter which is the uncontained vibration that can lead to the destruction of an aircraft.
Aeroelasticity problems can be prevented by adjusting the mass, stiffness or aerodynamics of structures which can be determined and verified through the use of calculations, ''ground vibration tests'' and ''flight flutter trials''. Flutter of
control surfaces is usually eliminated by the careful placement of ''mass balances''.
The synthesis of aeroelasticity with
thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws o ...
is known as ''aerothermoelasticity'', and its synthesis with
control theory
Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a ...
is known as ''aeroservoelasticity''.
History
The second failure of
Samuel Langley's prototype plane on the Potomac was attributed to aeroelastic effects (specifically, torsional divergence).
An early scientific work on the subject was
George Bryan
George Bryan (1731January 27, 1791) was an Irish/American Pennsylvania businessman, and politician of the Revolutionary era. He served as the first vice-president of Pennsylvania (analogous to lieutenant governor) and its second president (g ...
's ''Theory of the Stability of a Rigid Aeroplane'' published in 1906.
Problems with torsional divergence plagued aircraft in the
First World War
World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fig ...
and were solved largely by trial-and-error and ad hoc stiffening of the wing. The first recorded and documented case of flutter in an aircraft was that which occurred to a
Handley Page O/400
The Handley Page Type O was a biplane bomber used by Britain during the First World War. When built, the Type O was the largest aircraft that had been built in the UK and one of the largest in the world. There were two main variants, the Hand ...
bomber during a flight in 1916, when it suffered a violent tail oscillation, which caused extreme distortion of the rear fuselage and the elevators to move asymmetrically. Although the aircraft landed safely, in the subsequent investigation
F. W. Lanchester was consulted. One of his recommendations was that left and right elevators should be rigidly connected by a stiff shaft, which was to subsequently become a design requirement. In addition, the
National Physical Laboratory (NPL) was asked to investigate the phenomenon theoretically, which was subsequently carried out by
Leonard Bairstow and
Arthur Fage.
In 1926,
Hans Reissner published a theory of wing divergence, leading to much further theoretical research on the subject.
The term ''aeroelasticity'' itself was coined by
Harold Roxbee Cox and
Alfred Pugsley at the
Royal Aircraft Establishment
The Royal Aircraft Establishment (RAE) was a British research establishment, known by several different names during its history, that eventually came under the aegis of the UK Ministry of Defence (MoD), before finally losing its identity in me ...
(RAE),
Farnborough Farnborough may refer to:
Australia
* Farnborough, Queensland, a locality in the Shire of Livingstone
United Kingdom
* Farnborough, Hampshire, a town in the Rushmoor district of Hampshire, England
** Farnborough (Main) railway station, a railw ...
in the early 1930s.
In the development of
aeronautical engineering
Aerospace engineering is the primary field of engineering concerned with the development of aircraft and spacecraft. It has two major and overlapping branches: aeronautical engineering and astronautical engineering. Avionics engineering is sim ...
at
Caltech
The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...
,
Theodore von Kármán started a course "Elasticity applied to Aeronautics". After teaching the course for one term, Kármán passed it over to
Ernest Edwin Sechler, who developed aeroelasticity in that course and in publication of
textbook
A textbook is a book containing a comprehensive compilation of content in a branch of study with the intention of explaining it. Textbooks are produced to meet the needs of educators, usually at educational institutions. Schoolbooks are textboo ...
s on the subject.
In 1947,
Arthur Roderick Collar
Arthur Roderick Collar CBE FRS FREng (22 February 1908 – 12 February 1986) was an English scientist and engineer who made significant contributions in the areas of aeroelasticity, matrix theory and its applications in engineering dynamics.A.G ...
defined aeroelasticity as "the study of the mutual interaction that takes place within the triangle of the inertial, elastic, and aerodynamic forces acting on structural members exposed to an airstream, and the influence of this study on design".
Static aeroelasticity
In an aeroplane, two significant static aeroelastic effects may occur. ''Divergence'' is a phenomenon in which the elastic twist of the wing suddenly becomes theoretically infinite, typically causing the wing to fail. ''Control reversal'' is a phenomenon occurring only in wings with
aileron
An aileron (French for "little wing" or "fin") is a hinged flight control surface usually forming part of the trailing edge of each wing of a fixed-wing aircraft. Ailerons are used in pairs to control the aircraft in roll (or movement arou ...
s or other control surfaces, in which these control surfaces reverse their usual functionality (e.g., the rolling direction associated with a given aileron moment is reversed).
Divergence
Divergence occurs when a lifting surface deflects under aerodynamic load in a direction which further increases lift in a positive feedback loop. The increased lift deflects the structure further, which eventually brings the structure to the point of divergence.
Control reversal
Control surface reversal is the loss (or reversal) of the expected response of a control surface, due to deformation of the main lifting surface. For simple models (e.g. single aileron on an Euler-Bernoulli beam), control reversal speeds can be derived analytically as for torsional divergence. Control reversal can be used to aerodynamic advantage, and forms part of the
Kaman servo-flap rotor Kaman may refer to:
* Kaman (surname)
* Kamein (Kaman), an ethnic group in Burma
* Kaman Aircraft, an American aerospace company and helicopter manufacturer
* Kaman Music Corporation, a company of several musical instrument manufacturers
* Kaman Ro ...
design.
Dynamic aeroelasticity
Dynamic aeroelasticity studies the interactions among aerodynamic, elastic, and inertial forces. Examples of dynamic aeroelastic phenomena are:
Flutter
Flutter is a dynamic instability of an elastic structure in a fluid flow, caused by
positive feedback
Positive feedback (exacerbating feedback, self-reinforcing feedback) is a process that occurs in a feedback loop which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in th ...
between the body's deflection and the force exerted by the fluid flow. In a
linear system
In systems theory, a linear system is a mathematical model of a system based on the use of a linear operator.
Linear systems typically exhibit features and properties that are much simpler than the nonlinear case.
As a mathematical abstracti ...
, "flutter point" is the point at which the structure is undergoing
simple harmonic motion—zero net
damping—and so any further decrease in net damping will result in a
self-oscillation and eventual failure. "Net damping" can be understood as the sum of the structure's natural positive damping and the negative damping of the aerodynamic force. Flutter can be classified into two types: ''hard flutter'', in which the net damping decreases very suddenly, very close to the flutter point; and ''soft flutter'', in which the net damping decreases gradually.
In water the mass ratio of the pitch inertia of the foil to that of the circumscribing cylinder of fluid is generally too low for binary flutter to occur, as shown by explicit solution of the simplest pitch and heave flutter stability determinant.
Structures exposed to aerodynamic forces—including wings and aerofoils, but also chimneys and bridges—are generally designed carefully within known parameters to avoid flutter. Blunt shapes, such as chimneys, can give off a continuous stream of vortices known as a
Kármán vortex street, which can induce structural oscillations.
Strakes are typically wrapped around chimneys to stop the formation of these vortices.
In complex structures where both the aerodynamics and the mechanical properties of the structure are not fully understood, flutter can be discounted only through detailed testing. Even changing the mass distribution of an aircraft or the
stiffness of one component can induce flutter in an apparently unrelated aerodynamic component. At its mildest, this can appear as a "buzz" in the aircraft structure, but at its most violent, it can develop uncontrollably with great speed and cause serious damage to the aircraft or lead to its destruction,
[.] as in
Northwest Airlines Flight 2 in 1938,
Braniff Flight 542
Braniff International Airways Flight 542, a Lockheed L-188 Electra, registration N9705C, was a scheduled domestic flight from Houston, Texas, bound for New York with scheduled stops in Dallas and Washington, D.C. On September 29, 1959, 23 minutes ...
in 1959, or the prototypes for Finland's
VL Myrsky fighter aircraft in the early 1940s. Famously, the original
Tacoma Narrows Bridge was possibly destroyed as a result of aeroelastic fluttering.
[The adequacy of comparison between flutter in aircraft aerodynamics and Tacoma Narrows Bridge case is discussed and disputed in Yusuf K. Billah, Robert H. Scanian]
"Resonance, Tacoma Bridge failure, and undergraduate physics textbooks"
Am. J. Phys. 59(2), 118–124, February 1991.
Aeroservoelasticity
In some cases, automatic control systems have been demonstrated to help prevent or limit flutter-related structural vibration.
Propeller whirl flutter
''Propeller whirl flutter'' is a special case of flutter involving the aerodynamic and inertial effects of a rotating propeller and the stiffness of the supporting
nacelle structure. Dynamic instability can occur involving pitch and yaw degrees of freedom of the propeller and the engine supports leading to an unstable precession of the propeller. Failure of the engine supports led to whirl flutter occurring on two Lockheed L-188 Electra aircraft, in 1959 on
Braniff Flight 542
Braniff International Airways Flight 542, a Lockheed L-188 Electra, registration N9705C, was a scheduled domestic flight from Houston, Texas, bound for New York with scheduled stops in Dallas and Washington, D.C. On September 29, 1959, 23 minutes ...
and again in 1960 on
Northwest Orient Airlines Flight 710
Northwest Orient Airlines Flight 710, a Lockheed L-188 Electra, disintegrated in-flight and crashed near Cannelton, Indiana (10 miles east of Tell City, Indiana) on March 17, 1960. The flight carried 57 passengers and six crew members. There wer ...
.
Transonic aeroelasticity
Flow is highly non-linear in the
transonic regime, dominated by moving shock waves. Avoiding flutter is mission-critical for aircraft that fly through transonic Mach numbers. The role of shock waves was first analyzed by
Holt Ashley
Holt Ashley (January 10, 1923May 9, 2006) was an American aeronautical engineer notable for his seminal research of aeroelasticity.[Langley Research Center
The Langley Research Center (LaRC or NASA Langley), located in Hampton, Virginia, United States of America, is the oldest of NASA's field centers. It directly borders Langley Air Force Base and the Back River on the Chesapeake Bay. LaRC has f ...](_blank)
.
Buffeting
Buffeting is a high-frequency instability, caused by airflow separation or shock wave oscillations from one object striking another. It is caused by a sudden impulse of load increasing. It is a random forced vibration. Generally it affects the tail unit of the aircraft structure due to air flow downstream of the wing.
The methods for buffet detection are:
# Pressure coefficient diagram
# Pressure divergence at trailing edge
# Computing separation from trailing edge based on
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 = \ ...
# Normal force fluctuating divergence
Prediction and cure

In the period 1950–1970,
AGARD
The Advisory Group for Aerospace Research and Development (AGARD) was an agency of NATO that existed from 1952 to 1996.
AGARD was founded as an Agency of the NATO Military Committee. It was set up in May 1952 with headquarters in Neuilly sur Sei ...
developed the ''Manual on Aeroelasticity'' which details the processes used in solving and verifying aeroelastic problems along with standard examples that can be used to test numerical solutions.
Aeroelasticity involves not just the external aerodynamic loads and the way they change but also the structural, damping and mass characteristics of the aircraft. Prediction involves making a
mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...
of the aircraft as a series of masses connected by springs and dampers which are tuned to represent the
dynamic characteristics of the aircraft structure. The model also includes details of applied aerodynamic forces and how they vary.
The model can be used to predict the flutter margin and, if necessary, test fixes to potential problems. Small carefully chosen changes to mass distribution and local structural stiffness can be very effective in solving aeroelastic problems.
Methods of predicting flutter in linear structures include the ''p-method'', the ''k-method'' and the ''p-k method''.
For
nonlinear system
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...
s, flutter is usually interpreted as a
limit cycle
In mathematics, in the study of dynamical systems with two-dimensional phase space, a limit cycle is a closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinit ...
oscillation (LCO), and methods from the study of
dynamical system
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water i ...
s can be used to determine the speed at which flutter will occur.
Media
These videos detail the
Active Aeroelastic Wing two-phase
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, succeedi ...
-
Air Force
An air force – in the broadest sense – is the national military branch that primarily conducts aerial warfare. More specifically, it is the branch of a nation's armed services that is responsible for aerial warfare as distinct from an ar ...
flight research program to investigate the potential of aerodynamically twisting flexible wings to improve maneuverability of high-performance aircraft at transonic and
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 ...
speeds, with traditional control surfaces such as
aileron
An aileron (French for "little wing" or "fin") is a hinged flight control surface usually forming part of the trailing edge of each wing of a fixed-wing aircraft. Ailerons are used in pairs to control the aircraft in roll (or movement arou ...
s and leading-edge flaps used to induce the twist.
Image:Active Aeroelastic Wing time lapse.ogv, Time lapsed film of Active Aeroelastic Wing (AAW) Wing loads test, December, 2002
Image:F-18A Active Aeroelastic Wing flight test.ogg, F/A-18A (now X-53) Active Aeroelastic Wing (AAW) flight test, December, 2002
Notable aeroelastic failures
*The original
Tacoma Narrows Bridge was destroyed as a result of aeroelastic fluttering.
*Propeller whirl flutter of the
Lockheed L-188 Electra
The Lockheed L-188 Electra is an American turboprop airliner built by Lockheed. First flown in 1957, it was the first large turboprop airliner built in the United States. Initial sales were good, but after two fatal crashes that led to expensi ...
on
Braniff Flight 542
Braniff International Airways Flight 542, a Lockheed L-188 Electra, registration N9705C, was a scheduled domestic flight from Houston, Texas, bound for New York with scheduled stops in Dallas and Washington, D.C. On September 29, 1959, 23 minutes ...
.
*
1931 Transcontinental & Western Air Fokker F-10 crash
On March 31, 1931, a Fokker F-10 belonging to Transcontinental and Western Air crashed near Bazaar, Kansas after taking off from Kansas City Municipal Airport, Kansas City, Missouri.
The scheduled flight was from Kansas City to Los Ange ...
.
* Body freedom flutter of the
GAF Jindivik
The GAF Jindivik is a radio-controlled target drone produced by the Australian Government Aircraft Factories (GAF). The name is from an Aboriginal Australian word meaning "the hunted one". Two manually-controlled prototypes, were built as the GAF ...
drone.
See also
*
Adaptive compliant wing
*
Aerospace engineering
Aerospace engineering is the primary field of engineering concerned with the development of aircraft and spacecraft. It has two major and overlapping branches: aeronautical engineering and astronautical engineering. Avionics engineering is s ...
*
Kármán vortex street
*
Mathematical modeling
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...
*
Oscillation
Oscillation is the repetitive or Periodic function, periodic variation, typically in time, of some measure about a central value (often a point of Mechanical equilibrium, equilibrium) or between two or more different states. Familiar examples o ...
*
Parker Variable Wing
*
Vortex shedding
In fluid dynamics, vortex shedding is an oscillating flow that takes place when a fluid such as air or water flows past a bluff (as opposed to streamlined) body at certain velocities, depending on the size and shape of the body. In this flow, vo ...
*
Vortex-induced vibration
*
X-53 Active Aeroelastic Wing
References
Further reading
* Bisplinghoff, R. L., Ashley, H. and Halfman, H., ''Aeroelasticity''. Dover Science, 1996, , 880 p.
* Dowell, E. H., ''A Modern Course on Aeroelasticity''. .
* Fung, Y. C., ''An Introduction to the Theory of Aeroelasticity''. Dover, 1994, .
* Hodges, D. H. and Pierce, A., ''Introduction to Structural Dynamics and Aeroelasticity'', Cambridge, 2002, .
* Wright, J. R. and Cooper, J. E., ''Introduction to Aircraft Aeroelasticity and Loads'', Wiley 2007, .
* Hoque, M. E., "Active Flutter Control",
LAP Lambert Academic Publishing
Omniscriptum Publishing Group, formerly known as VDM Verlag Dr. Müller, is a German publishing group headquartered in Riga, Latvia. Founded in 2002 in Düsseldorf, its book production is based on print-to-order technology.
The company publis ...
, Germany, 2010, .
* Collar, A. R., "The first fifty years of aeroelasticity", Aerospace, vol. 5, no. 2, pp. 12–20, 1978.
* Garrick, I. E. and Reed W. H., "Historical development of aircraft flutter", Journal of Aircraft, vol. 18, pp. 897–912, Nov. 1981.
* {{cite magazine , url= http://aviationweek.com/business-aviation/low-speed-buffet-high-altitude-transonic-training-weakness-continues , title= Low-Speed Buffet: High-Altitude, Transonic Training Weakness Continues , date= Aug 23, 2018 , author= Patrick R. Veillette , magazine= Business & Commercial Aviation , publisher= Aviation Week Network
External links
Aeroelasticity Branch – NASA Langley Research CenterDLR Institute of AeroelasticityNational Aerospace LaboratoryThe Aeroelasticity Group – Texas A&M UniversityNACA Technical Reports – NASA Langley Research CenterNASA Aeroelasticity Handbook
Aerodynamics
Aircraft wing design
Aerospace engineering
Solid mechanics
Elasticity (physics)
Articles containing video clips