# Degrees of freedom (mechanics)

AI and Robotics

Nov 13, 2013 (4 years and 5 months ago)

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Degrees of freedom (mechanics)

In
mechanics
, the
degree of freedom

(DOF) of a
mechanical system

is the number of
independent parameters that define its configuration. It is the number of parameters that
determine the state of a physical system and is important to the analysis of systems of bodies in
mechanical engineering
,
aeronautical engineering
,
robotics
, and
structural engineering
.

The position of a single car (engine) moving along a track has one degree of freedom, because
the posit
ion of the car is defined by the distance along the track. A train of rigid cars connected
by hinges to an engine still has only one degree of freedom because the positions of the cars
behind the engine are constrained by the shape of the track.

An automob
ile with highly stiff suspension can be considered to be a rigid body traveling on a
plane (a flat, two
-
dimensional space). This body has three independent degrees of freedom
consisting of two components of translation and one angle of rotation. Skidding o
r
drifting

is a
good example of an automobile's three independent degrees of freedom.

The position of a rigid body in space is defined by three components o
f
translation

and three
components of
rotation
, which means that it has six degrees of fre
edom.

The
Exact constraint

mechanical design method manages the degrees of freedom to neither
underconstrain nor overconstrain a device.
[1]

Motions and dimensions

The position of an
n
-
dimensional
rigid body

is defined by the
rigid transformation
, [T]=[A,
d
],
where
d

is an
n
-
dimensional translation and
A

is an
n

x
n

rotation matrix, which has
n

translational degrees of freedom and
n
(
n

-

1)/2 rotational degrees of freedom. The number of
rotational degrees of freedom comes from the dimension of the rotation group
SO(n)
.

A non
-
rigid or deformable body may be thought of as a co
llection of many minute particles
(infinite number of DOFs); this is often approximated by a finite DOF system. When motion
involving large displacements is the main objective of study (e.g. for analyzing the motion of
satellites), a deformable body may be

approximated as a rigid body (or even a particle) in order
to simplify the analysis.

The degree of freedom of a system can be viewed as the minimum number of coordinates
required to specify a configuration. Applying this definition, we have:

1.

For a single
particle in a plane two coordinates define its location so it has two degrees of
freedom;

2.

A single particle in space requires three coordinates so it has three degrees of freedom;

3.

Two particles in space have a combined six degrees of freedom;

4.

If two partic
les in space are constrained to maintain a constant distance from each other,
such as in the case of a diatomic molecule, then the six coordinates must satisfy a single
constraint equation defined by the distance formula. This reduces the degree of freedom

of the system to five, because the distance formula can be used to solve for the remaining
coordinate once the other five are specified.

Six degrees of freedom

Attitude degrees of freedom for an airplane.

The motion of a ship at sea has the
six degrees of freedom

of a rigid body, and is described as:
[2]

Translation:

1.

Moving up and down (heaving);

2.

Moving left and right (swaying);

3.

Moving forward and backward (surging);

Rotation

1.

Tilts forward and backward (
pitching
);

2.

Swivels left and right (
yawing
);

3.

Pivots side to side (
rolling
).

The trajectory of an airplane in flight has three degrees of freedom and its attitude along the
trajectory has three degrees of freedom, for a total of six degrees of freedom.

Mobility formula

The mobility formula counts the number of parameters that define the configuration of a set of
rigid bodies that are constrained by joints connecting these bodies.

Consider a system of
n

rigid bodies moving in space has
6n

degrees of freedom measured
rela
tive to a fixed frame. In order to count the degrees of freedom of this system, include the
ground frame in the count of bodies, so that mobility is independent of the choice of the body
that forms the fixed frame. Then the degree
-
of
-
freedom of the unconst
rained system of
N=n+1

is

because the fixed body has zero degrees of freedom relative to itself.

Joints that connect bodies in this system remove degrees of freedom and reduce mobility.
Specifically, hinges and sliders each impose five constraints and ther
efore remove five degrees
of freedom. It is convenient to define the number of constraints
c

that a joint imposes in terms of
the joint's freedom
f
, where
c=6
-
f
. In the case of a hinge or slider, which are one degree of
freedom joints, have
f=1

and therefo
re
c=6
-
1=5
.

The result is that the mobility of a system formed from
n

j

joints each with
freedom
f
i
,
i=1, ..., j,

is given by

Recall that
N

There are two important special cases: (i
) a simple open chain, and (ii) a simple closed chain. A
single open chain consists of
n

moving links connected end to end by
n

joints, with one end
connected to a ground link. Thus, in this case
N=j+1

and the mobility of the chain is

For a simple closed
chain,
n

-
to
-
end by
n+1

joints such that the
two ends are connected to the ground link forming a loop. In this case, we have
N=j

and the
mobility of the chain is

An example of a simple open chain is a serial robot
manipulator. These robotic systems are
constructed from a series of links connected by six one degree
-
of
-
freedom revolute or prismatic
joints, so the system has six degrees of freedom.

An example of a simple closed chain is the RSSR spatial four
-
e. The sum of the
freedom of these joints is eight, so the mobility of the linkage is two, where one of the degrees of
freedom is the rotation of the coupler around the line joining the two S joints.

Planar and spherical movement

It is common practice to d
esign the

so that the movement of all of the bodies are
constrained to lie on parallel planes, to form what is known as a
. It is a
lso
possible to construct the linkage system so that all of the bodies move on concentric spheres,
forming a
. In both cases, the degrees of freedom of the links in each system is
now three rather than six, and the constraints imposed by j
oints are now
c=3
-
f
.

In this case, the mobility formula is given by

and the special cases become

planar or spherical simple open chain,

planar or spherical simple closed chain,

An example of a planar simple closed chain is the planar
four
-
, which is a
four
-
bar loop with four one degree
-
of
-
freedom joints and therefore has mobility M=1.

Systems of bodies

An
articulated robot

with six DOF in a kinematic chain.

A system with several bodies would have a combined DOF that is the sum of the DOFs of
the
bodies, less the internal constraints they may have on relative motion. A
mechanism

or

containing a number of connected rigid bodies may have more than the degrees of freedom for a
single rigid body. Here the term
degrees of freedom

is

used to describe the number of parameters
needed to specify the spatial pose of a linkage.

A specific type of linkage is the open
kinematic chain
, where a set of rigid links are connected at
joints
; a joint may provide one DOF (hinge/sliding), or two (cylindrical). Such chains occur
commonly in
robotics
,
biomechanics
, and for
satellites

and other space structures. A human arm
is considered to have seven DOFs. A shoulder gives pitch, yaw, and roll, an elbow allows for
pitch and roll, and a wrist allows for pitch and yaw. Only 3 of those movements would be
necessary to move the hand to any point in space, but people would lack th
e ability to grasp
things from different angles or directions. A robot (or object) that has mechanisms to control all
6 physical DOF is said to be holonomic. An object with fewer controllable DOFs than total
DOFs is said to be non
-
holonomic, and an object
with more controllable DOFs than total DOFs
(such as the human arm) is said to be redundant.

In mobile robotics, a car
-
like robot can reach any position and orientation in 2
-
D space, so it
needs 3 DOFs to describe its pose, but at any point, you can move i
t only by a forward motion
and a steering angle. So it has two control DOFs and three representational DOFs; i.e. it is non
-
holonomic. A fixed
-
wing aircraft, with 3

4 control DOFs (forward motion, roll, pitch, and to a
limited extent, yaw) in a 3
-
D space,
is also non
-
holonomic, as it cannot move directly up/down
or left/right.

Longitudinal static stability

Longitudinal static stability

is the stability of an aircraft in the longitudinal, or pitching, plane
-
flight conditions. This characteristic

is important in determining whether a
human
pilot

will be able to control the aircraft in the longitudinal plane without requiring excessive
attention or excessive strength.
[1]

Static stability

Three cases for static stability: following a pitch disturbance, aircraft can be either unstable,
neutral, or stable.

As any vehicle moves it will be sub
jected to minor changes in the forces that act on it, and in its
speed.

If such a change causes further changes that tend to restore the vehicle to its original
speed and orientation, without human or machine input, the vehicle is said to be statically
sta
ble. The aircraft has positive stability.

If such a change causes further changes that tend to drive the vehicle away from its
original speed and orientation, the vehicle is said to be statically unstable. The aircraft has
negative stability.

If such a cha
nge causes no tendency for the vehicle to be restored to its original speed
and orientation, and no tendency for the vehicle to be driven away from its original speed
and orientation, the vehicle is said to be neutrally stable. The aircraft has zero stabil
ity.

For a vehicle to possess positive static stability it is not necessary for its speed and orientation to
return to exactly the speed and orientation that existed before the minor change that caused the
upset. It is sufficient that the speed and orienta
tion do not continue to diverge but undergo at
least a small change back towards the original speed and orientation.

Longitudinal stability

The longitudinal stability of an aircraft refers to the aircraft's stability in the pitching plane
-

the
plane which

describes the position of the aircraft's nose in relation to its tail and the horizon.
[1]

(Other stability modes are
directional stability

and lateral stability.)

If an aircraft is longitudinally stable, a small increase in
angle of attack

will cause the
pitching
moment

on the aircraft to change so that the angle of attack decreases. Similarly, a small
decrease in angle
of attack will cause the pitching moment to change so that the angle of attack
increases.
[1]

The pilot of an aircraft with positive longitudi
nal stability, whether it is a human pilot or an
autopilot
, has an easy task to fly the aircraft and maintain the desired pitch attitude which, in
turn, makes it easy to control the spee
d, angle of attack and
fuselage

angle relative to the horizon.
The pilot of an aircraft with negative longitudinal stability has a more difficult task to fly the
aircraft. It will be neces
sary for the pilot devote more effort, make more frequent inputs to the
elevator control, and make larger inputs, in an attempt to maintain the desired pitch attitude.
[1]

Most successful aircraft have positive longitudinal stability, providing the aircraft's
center of
gravity

lies within the approved range. Some acrobatic and
combat aircraft have low
-
positive or
neutral stability to provide high maneuverability. Some advanced aircraft have a form of low
-
negative stability called
relaxed stabil
ity

to provide extra
-
high maneuverability.

Center of gravity

The longitudinal static stability of an aircraft is significantly influenced by the position of the
center of gravity of the aircraft. Such potential cg adjustments are typically imagined as
incr
ements forward or aft from the "aerodynamic center" of the wing which is a position,
typically near 1/4 chord aft of the leading edge, where changes in angle of attack do not change
pitching moment. The pitching moment is not typically zero there, just con
stant.

As the center of gravity moves forward the longitudinal static stability of the aircraft increases.
The reason is twofold:

the moment arm between the
horizontal stabilizer

increases and

the contribution of the wing's lift to pitching moment is also stabilizing in consequence of
ITS changing moment arm.

Similarly, if the center of gravity is moved aft, the longitudinal static stability of the aircraft
decreases.
[1]

Moving the cg aft far enough will destabilize the airplane, at a point when the
wing's upsetting moment exceeds the restoring moment of the tail
.

Stability boundaries for a particular aircraft include limitations on the most forward and aft
locations permitted for the center of gravity. No attempt should be made to fly an aircraft if its
center of gravity is outside the approved range, or will mov
e outside the approved range during
the flight.

Analysis

Near the cruise condition most of the lift force is generated by the wings, with ideally only a
small amount generated by the fuselage and tail. We may analyse the longitudinal static stability
by co
nsidering the aircraft in
equilibrium

under wing lift, tail force, and weight. The moment
equilibrium condition is called
trim
, and we are generally interested in the longitudinal stability

Trim

The
tailplane

is usual
ly a symmetrical airfoil, so its force is proportional to angle of attack, but in
general, there will also be an
elevator

deflection to maintain moment equilibriu
m (trim). In
addition, the tail is located in the flow field of the main wing, and consequently experiences a
downwash
, reducing the angle of attack at the tailplane.

For a statically stab
le aircraft of conventional (tail in rear) configuration, the
tailplane

force
typically acts downward. In canard aircraft, both fore and aft planes are lifting surfaces. The
fundamental requirement for static stability is that the aft surface have greater leverage in
restoring a disturbance than the forward surface have in ex
acerbating it. This "leverage" is a
product of moment arm from the center of gravity and surface area. Correctly balanced in this
way, the partial derivative of pitching moment, w.r.t changes in angle of attack will be negative:
pitch up to a larger angle
of attack and the resultant pitching moment will tend to pitch the
aircraft back down. (Here, pitch is used casually for the angle between the nose and the direction
of the airflow; angle of attack.) This is the "stability derivative" d(M)/d(alpha), descri
bed below.
Violations of this basic principle are exploited in some high performance combat aircraft to
enhance agility; artificial stability is supplied by electronic means.

Note that for a rear
-
l stabilizer less
than that of the main wing, so the main wing should
stall

before the tail, ensuring that the stall is
followed immediately by a reduction in
angle of attack

on the main wing, promoting recovery
from the stall. (In contrast, in a
can
ard

greater than that of the main wing, so that the horizontal stabilizer stalls before the main wing,
again promoting recovery from the stall.)

There are a few classical cases where this favourabl
e response was not achieved, notably some
early T
-
tail jet aircraft. In the event of a very high angle of attack, the horizontal stabilizer
became immersed in the downwash from the fuselage, causing excessive download on the
stabilizer, increasing the angl
e of attack still further. The only way an aircraft could recover from
this situation was by jettisoning tail ballast or deploying a special tail parachute. The
phenomenon became known as '
deep stall
'.

Static stability

The nature of stability may be examined by considering the increment in pitching moment with
change in angle of attack at the trim condition. If this is nose up, the aircraft is longitudinally
unstable; if nose down it is stable. Differentiating the moment equation with respect to
:

Note: is a
stability derivative
.

It is convenient to treat total lift
as acting at a distance h ahead of the centre of gravity, so that the
moment equation may be written:

Applying the increment in angle of attack:

Equating the two expressions for moment increment:

The total lift is the sum of
and
so the sum in the denomin
ator can be simplified and
written as the derivative of the total lift due to angle of attack, yielding:

Where c is the
mean aerodynamic chord

of the main wing.

The term:

is known as the tail volume ratio. Its rather complicated coefficient, the ratio of the two lift
derivatives, has values in the range of 0.50 to 0.65 for typical configurations, according to
Piercy. Hence the expression for h may be written more

compactly, though somewhat
approximately, as:

h is known as the
static margin
. For stability it must be negative. (However, for consistency of
language, the static margin is sometimes taken as
, so that positive stability is associated
with positive static margin.)

Neutral point

A mathematical analysis of the longitudinal static s
tability of a complete aircraft (including
horizontal stabilizer) yields the position of center of gravity at which stability is neutral. This
position is called the neutral point.
[1]

(The larger the area of the horizontal stabilizer, and the
greater the moment arm of the horizontal stabilizer about the aerodynamic center, the further aft
is the neutral point.)

The static center of gravity margin (c.g
. margin) or
static margin

is the distance between the
center of gravity (or mass) and the neutral point. It is usually quoted as a percentage of the
Mean
Aerodynamic Chord
. The center of gravity must lie ahead of the neutral point for positive
stability (positive static margin). If the center of gravity is behind the neutral point, the aircraf
t is
longitudinally unstable (the static margin is negative), and active inputs to the control surfaces
are required to maintain stable flight. Some combat aircraft that are controlled by
fly
-
by
-
wire

systems are designed to be longitudinally unstable so they will be highly maneuverable.
Ultimately, the position of the center of gravity relative to the neutral point determines the
stability, control forces, and controllability of the v
ehicle.

For a
tailless aircraft
, the neutral point coincides with the aerodynamic center, and so for
longitudinal static stability the center of gravity must lie ahead o
f the aerodynamic center.

Flight control surfaces

,
search

For the systems that operate flight control surfaces, see
aircraft flight control system
.

Flight control surfac
es

Basic aircraft control surfaces and motion.

Aircraft
flight control surfaces

allow a pilot to adjust and control the aircraft's flight
attitude
.

Development of an effective set of flight controls was a critical advance in the development of
aircraft. Early efforts at fixed
-
wing aircraft design succeeded in generating sufficient lift to get
the aircraft off the ground, but once aloft, the aircraft p
roved uncontrollable, often with
disastrous results. The development of effective flight controls is what allowed stable flight.

-
wing aircraft of conventional design.
Other fixed
-
wing aircraft
configurations may use different control surfaces but the basic
principles remain. The controls (stick and rudder) for rotary wing aircraft (
helicopter

or
autogyro
) accomplish the same motions about the
three axes of rotation
, but manipulate the
rotating flight controls (ma
in rotor disk and tail rotor disk) in a completely different manner.

Development

The
Wright brothers

are credited with developing the first practical control surfaces. It i
s a main
part of their patent on flying.
[1]

Unlike modern control surfaces, they used
wing war
ping
.
[2]

In an
attempt to circumvent the Wright patent,
Glen Curtis

. Hinged
control surfaces have the advantage of not causing stresses that are a problem of wing warping
and are easier to build into structures.

Axes of motion

Main article:
Aircraft principal axes

Rotation around the three axes

An aircraft is free to rotate around three axes that are perpendicular to each other and intersect at
its
center of gravity

(CG). To control position and direction a pilot must be able to control

Lateral axis

The lateral axis passes through an aircr
called
pitch
. Pitch changes the vertical direction that the aircraft's nose is pointing. The elevators
are the primary control surfaces for pitch.

Longitudinal axis

The longitudinal axis passes throu
called
roll
. Rolling motion changes the orientation of the aircraft's wings with respect to the
downward force of gravity. The pilot changes bank angle by increasing the lift on one wing and
de
creasing it on the other. This differential lift causes bank rotation around the longitudinal axis.
The ailerons are the primary control of bank. The rudder also has a secondary effect on bank.

Vertical axis

The vertical axis passes through an aircraft fr
yaw
. Yaw changes the direction the aircraft's nose is pointing, left or right. The primary control
of yaw is with the rudder. Ailerons also have a secondary effect on yaw.

It is important to note that
these axes move with the aircraft, and change relative to the earth as
the aircraft moves. For example, for an aircraft whose left wing is pointing straight down, its
"vertical" axis is parallel with the ground, while its "lateral" axis is perpendicular to

the ground.

Main control surfaces

The main control surfaces of a
fixed
-
wing aircraft

are attached to the airframe on hinges or tracks
so they may move and thus defle
ct the air stream passing over them. This redirection of the air
stream generates an unbalanced force to rotate the plane about the associated axis.

Ailerons

Main article:
Aileron

Aileron su
rface

Ailerons

are mounted on the trailing edge of each wing near the wingtips and move in opposite
directions. When the pilot moves the
stick

left, or turns the wheel counter
-
clockwise, the left
aileron goes up and the right aileron goes down. A raised aileron reduces lift on that wing and a
lowered one increases lift, so moving the stick left causes the left wing to drop
and the right wing
to rise. This causes the aircraft to roll to the left and begin to turn to the left. Centering the stick
returns the ailerons to neutral maintaining the
bank angle
. The aircraft will continue to turn until
opposite aileron motion returns the bank angle to zero to fly straight.

Elevator

An
elevator

is a moveable part of the
horizontal stabilizer
, hinged to the back of the fixed part of
the horizontal tail. They move up and down together. When the pilot pull
s the stick backward,
the elevators go up. Pushing the stick forward causes the elevators to go down. Raised elevators
push down on the tail and cause the nose to pitch up. This makes the wings fly at a higher
angle
of attack
, which generates more lift and more
drag
. Centering the stick returns the elevators to
neutral and stops the change of p
itch. Many aircraft use a fully moveable horizontal stabilizer
called
stabilator

or all
-
moving tail. Some aircraft, such as an
MD
-
80
, use a
servo tab

within the
elevator surface to aerodynamically move the main surface into position. The direction of travel
of the control tab will thus be in a direction opp
osite to the main control surface. It is for this
reason that an
MD
-
80

tail looks like it has a 'split' elevator system.

Rudder

The
rudder

is typically mounted on the trailing edge of the vertical stabilizer, part of the
empennage
. When the pilot pushes the left pedal, the rudder deflects left. Pushing the right
pedal
causes the rudder to deflect right. Deflecting the rudder right pushes the tail left and causes the
nose to yaw to the right. Centering the rudder pedals returns the rudder to neutral and stops the
yaw.

Secondary effects of controls

Ailerons

The ailerons primarily control roll. Whenever lift is increased,
induced drag

is also increased.
When the stick is moved left to roll the aircraft to the left, the right aileron is

lowered which
increases lift on the right wing and therefore increases induced drag on the right wing. Using
ailerons causes
, meaning the nose of the aircraft yaws in a
direction opposite to the
aileron application. When moving the stick to the left to bank the wings, adverse yaw moves the
nose of the aircraft to the
right
. Adverse yaw is more pronounced for light aircraft with long
wings, such as gliders. It is counterac
ted by the pilot with the rudder.
Differential ailerons

are
ailerons which have been rigged such that the downgoing aileron deflects less than the upward
-
moving o

Rudder

The rudder is a fundamental control surface, typically controlled by pedals rather than at the
stick. It is the primary means of controlling yaw
--
the rotation of an airplane about its vertical
axis. The rudder may also be c
alled upon to counter
-
act the adverse yaw produced by the roll
-
control surfaces.

If rudder is continuously applied in level flight the aircraft will yaw initially in the direction of
the applied rudder

the primary effect of rudder. After a few seconds th
e aircraft will tend to
bank in the direction of yaw.

This arises initially from the increased speed of the wing opposite to the direction of yaw and the
reduced speed of the other wing. The faster wing generates more lift and so rises, while the other
win
g tends to go down because of generating less lift. Continued application of rudder sustains
rolling tendency because the aircraft flying at an angle to the airflow
-

skidding towards the
forward wing. When applying right rudder in an aircraft with
dihedral

the left hand wing will
have increased angle of attack and the right hand wing will have decreased angle of attack which
will result in a roll to the right. An
aircraft with
anhedral

will show the opposite effect. This
effect of the rudder is commonly used in model aircraft where if sufficient diheral or po
lyhedral
is included in the wing design, primary roll control such as ailerons may be omitted altogether.

Turning the aircraft

Unlike a boat, turning an aircraft is not normally carried out with the rudder. With aircraft, the
turn is caused by the
horizontal component of lift. The lifting force, perpendicular to the wings of
the aircraft, is tilted in the direction of the intended turn by rolling the aircraft into the turn. As
the bank angle is increased, the lifting force, which was previously acti
ng only in the vertical, is
split into two components: One acting vertically and one acting horizontally.

If the total lift is kept constant, the vertical component of lift will decrease. As the weight of the
aircraft is unchanged, this would result in the

aircraft descending if not countered. To maintain
level flight requires increased positive (up) elevator to increase the angle of attack, increase the
total lift generated and keep the vertical component of lift equal with the weight of the aircraft.
This

cannot continue indefinitely. The wings can only generate a finite amount of lift at a given
air speed. As the

) is increased an accelerated
aerodynamic
stall

will occur, even though the aircraft is above its 1G stall speed.

The total lift (load factor) required to maintain level flight is
directly related to the bank angle
.
This means that for a given airspeed, level flight can only be mai
ntained up to a certain given
angle of bank. Beyond this angle of bank, the aircraft will suffer an accelerated stall if the pilot
attempts to generate enough lift to maintain level flight.

Alternate main control surfaces

Some aircraft configurations have
non
-
standard primary controls. For example instead of
elevators at the back of the stabilizers, the
entire tailplane may change angle
. Some aircraft have
a
tail in the shape of a V
, and the moving parts at the back of those combine the functions of
elevators and rudder. Delta wing aircraft may have "
elevons
" at

the back of the wing, which
combine the functions of elevators and ailerons.

Secondary control surfaces

KLM

Fokker 70
, showing
position of flap and liftdumpers
flight controls
. The liftdumpers are
the lifted cream
-
coloured panels on the wing upper surface (in this picture there are five on the
right wing). The flaps are the large drooped surfaces on the trailing edge of the wing.

Spoilers

Main articles:
Spoiler (aeronautics)

and
Spoileron

On low drag aircraft like
sailplanes
,
spoilers

are used to disrupt airflow over the wing and greatly
increase the
amount of drag. This allows a glider pilot to lose altitude without gaining excessive
airspeed. Spoilers are sometimes called "lift dumpers". Spoilers that can be used asymmetrically
are called
spoilerons

and are able to affect an aircraft's roll.

Flaps

Flaps

are mounted on the trailing edge on the inboard section of each wing (near the wing roots).
The
y are deflected down to increase the effective curvature of the wing. Flaps raise the
Maximum Lift Coefficient

of the aircraft and therefore reduce its stalling speed.
[3]

They are used
during low speed, high angle of attack flight including take
-
off and descent for landing. Some
aircraft are equipped with "flapperons", which are more common
ly called "inboard
ailerons"
[
citation needed
]
. These devices function primarily as ailerons, but on some aircraft, will
"droop" when the flaps are
deployed, thus acting as both a flap and a roll
-
control inboard aileron.

Slats

Slats
, also known as
, are extensions to the front of a wing for lift

augmentation, and are intended to reduce the stalling speed by altering the airflow over the wing.
Slats may be fixed or retractable
-

fixed slats (e.g. as on the
Fieseler F
i 156 Storch
) give excellent
slow speed and
STOL

capabilities, but compromise higher speed performance. Retractable slats,
as seen on most airliners, provide reduced stalling speed for take
-
off an
d landing, but are
retracted for cruising.

Air brakes

Air brakes

are used to increase drag. Spoilers might act as air brakes, but are not pure air brakes
as the
y also function as lift
-
dumpers or in some cases as roll control surfaces. Air brakes are
usually surfaces that deflect outwards from the fuselage (in most cases symmetrically on
opposing sides) into the airstream in order to increase form
-
drag. As they ar
e in most cases
located elsewhere on the aircraft, they do not directly affect the lift generated by the wing. Their
purpose is to slow down the aircraft. They are particularly useful when a high rate of descent is
required or the aircraft needs to be reta
rded. They are common on high performance military
aircraft as well as civilian aircraft, especially those lacking reverse thrust capability.

Other control surfaces

Trim

Trimming controls allow a pilot to balance the lift and drag being produced by the win
gs and
control surfaces over a wide range of load and airspeed. This reduces the effort required to adjust
or maintain a desired flight
attitude
.

Elevator trim

Elevator t
rim balances the control force necessary to maintain the aerodynamic down force on
the tail. Whilst carrying out certain flight exercises, a lot of trim could be required to maintain
the desired angle of attack. This mainly applies to
slow flight
, where maintaining a nose
-
up
attitude requires a lot of trim. Elevator trim is correlated with the speed of the airflow over the
tail, thus airspeed changes to the aircraft require re
-
trimmin
g. An important design parameter for
aircraft is the stability of the aircraft when trimmed for level flight. Any disturbances such as
gusts or turbulence will be damped over a short period of time and the aircraft will return to its
level flight trimmed a
irspeed.

Trimming tail plane

Except for very light aircraft, trim tabs on elevators are unable to provide the force and range of
motion desired.

To provide the appropriate trim force the entire horizontal tail plane is made
adjustable in pitch. This allows the pilot to select exactly the right amount of positive or negative
lift from the tail plane while reducing drag from the elevators.

Control h
orn

A control horn is a section of control surface which projects ahead of the pivot point. It generates
a force which tends to increase the surface's deflection thus reducing the control pressure
experienced by the pilot. Control horns may also incorporat
e a
counterweight

which helps to
balance the control and prevent it from "fluttering" in the airstream. Some designs feature
separate anti
-
flutter weights.

In RC model aircraft, a "control horn" is an arm similar to a
bell crank

that connects to a control
rod linkage. Typically one end of each rod connects to one control horn, sometimes c
alled the
servo arm, rigidly attached to the shaft of the
RC servo
, and the other end of the rod connects to
another control horn rigidly attached to the cont
rol surface

Spring trim

In the simplest cases trimming is done by a mechanical
spring

(or
bunge
e
appropriate force to augment the pilot's control input. The spring is usually connected to an
elevator trim lever to allow the pilot to set the spring force applied.

Rudder and aileron trim

Trim often does not only apply to the
elevator
, as there is also trim for the rudder and ailerons in
larger aircraft. The use of this is to counter the effects of slip stream, or to counter the effects of
the
centre of gravity

being to one side. This can be caused by a larger weight on one side of the
aircraft compared to the other, such as when one fuel tank has a lot more fuel in

it than the other.

Aircraft flight mechanics

relies largely or entirely upon a
single source
.
Relevant discussion may be
found on the
talk page

by introducing
citations

to

(November 2012)

may require
cleanup

to meet Wikipedia's
quality standards
.
No
cleanup
reason

if you can.

(October

2010)

In
aeronautics
,
aircraft flight mechanics

is the study of the forces that act on an aircraft in
flight, and the way the aircraft responds to those forces.

Flight mechanics

are relevant to fixed wing (
gliders
,
aeroplanes
) and rotary wing (
helicopters
)
aircraft. An Aeroplane (Airplane in
US

usage), is defined as: (
ICAO

Document 9110).

Straight and level flight of aircraft

In flight an aircraft can be considered as being acted on by four forces:
lift
,
weight
,
thrust
, and
drag
.
[2]

Thrust is the force generated by the engine (jet) or the propeller and acts along the
engine's thrust vector. Lift acts perpendicular to the vector representing the a
ircraft's velocity
(aka power) relative to the atmosphere. Drag acts parallel to the aircraft's velocity vector, but in
the opposite direction because drag resists motion through the air. Weight acts through the
aircraft's centre of gravity
, towards the center of the Earth.

In straight and level
flight
,(or movement in the air) lift is

approximately equal to weight. In
aircraft

is not accelerating, thrust is equal and opposite to drag.
[3]

In straight climbing flight, lift is less than weight.
[4]

At first, this seems incorrect because if an
aircraft is climbing it seems lift must ex
ceed weight. When an aircraft is climbing at constant
speed it is its thrust that enables it to climb and gain extra potential energy. Lift acts
perpendicular to the vector representing the velocity of the aircraft relative to the atmosphere, so
lift is un
able to alter the aircraft's potential energy or kinetic energy. This can be seen by
considering an aerobatic aircraft in straight vertical flight
-

one that is climbing straight upwards
(or descending straight downwards). Vertical flight requires no lift!

When flying straight
upwards the aircraft can reach zero airspeed before falling earthwards
-

the wing is generating no
lift and so does not stall. In straight, climbing flight at constant airspeed, thrust exceeds drag.

In straight descending flight, lift

is less than weight.

In addition, if the aircraft is not accelerating,
thrust is less than drag. In turning flight, lift exceeds weight and produces a

greater
than one, determined by the aircraft's
angle of bank
.

Aircraft control and movement

There are three primary ways for an aircraft to change its orientation
relative to the passing air.
Pitch

(movement of the nose up or down, rotation around the transversal axis),
Roll

(rotation
around the longitudinal axis, that is, the axis which runs along the length of the aircraft) and
Yaw

(movement of the nose to left or

right, rotation about the vertical axis). Turning the aircraft
(change of heading) requires the aircraft firstly to roll to achieve an angle of bank (in order to
balance the centrifugal force); when the desired change of heading has been accomplished the
aircraft must again be rolled in the opposite direction to reduce the angle of bank to zero. Lift
acts vertically up through center of pressure which depends on the position of wings. The
position of the centre of pressure will change with changes in the a
ngle of attack and aircraft
wing flaps setting.

Aircraft control surfaces

Yaw

is induced by a moveable rudder
-
fin. The movement of the rudder changes the size and
orientation of the force the vertical surface produces. Since the force is created at a distance
behind the centre of gravity, this sideways force causes a yawing moment
then a yawing motion.
On a large aircraft there may be several independent rudders on the single fin for both safety and
to control the inter
-

Using yaw alone is not a very efficient way of executing a level turn in an aircraft
and will result
in some sideslip. A precise combination of bank and lift must be generated to cause the required
centripetal forces without producing a sideslip.

Pitch

is controlled by the rear part of the
tailplane
's horizontal stabilizer being hinged to create an
elevator
. By moving the elevator c
ontrol backwards the pilot moves the elevator up (a position of
negative camber) and the downwards force on the horizontal tail is increased. The
angle of attack

on the
wings

increased so the nose is pitched up and lift is generally increased. In micro
-
lights
and
hang gliders

the pitch action is

reversed
-

the pitch control system is much simpler so when
the pilot moves the elevator control backwards it produces a nose
-
down pitch and the angle of
attack on the wing is reduced.

The system of a fixed tail surface and moveable elevators is standard
in subsonic aircraft. Craft
capable of supersonic flight often have a
stabilator
, an all
-
moving tail surface. Pitch is changed
in this case by moving the entire horizontal surface of t
he tail. This seemingly simple innovation
was one of the key technologies that made supersonic flight possible. In early attempts, as pilots
exceeded the
critical M
ach number
, a strange phenomenon made their control surfaces useless,
and their aircraft uncontrollable. It was determined that as an aircraft approaches the speed of
sound, the air approaching the aircraft is compressed and shock waves begin to form at al
l the
leading edges and around the hinge lines of the elevator. These shock waves caused movements
of the elevator to cause no pressure change on the stabilizer upstream of the elevator. The
problem was solved by changing the stabilizer and hinged elevator

to an all
-
moving stabilizer
-

the entire horizontal surface of the tail became a one
-
piece control surface. Also, in supersonic
flight the change in camber has less effect on lift and a stabilator produces less drag
[
citation needed
]
.

Aircraft that need control at extreme angles of attack are sometimes fitted with a
canard

configuration, in which pitching movement is created using a forward foreplane (roughly level
with the cockpit). Such a system produces an immediate increase in pitch authority, and therefore
a better response to pitch controls. This system is c
ommon in delta
-
wing aircraft (deltaplane),
which use a stabilator
-
type canard foreplane. A disadvantage to a canard configuration compared
to an aft tail is that the wing cannot use as much extension of flaps to increase wing lift at slow
speeds due to sta
ll performance. A combination tri
-
surface aircraft uses both a canard and an aft
tail (in addition to the main wing) to achieve advantages of both configurations.

A further design of tailplane is the
V
-
tail
, so named because that instead of the standard inverted
T or T
-
tail, there are two vertical fins angled away from each other in a V (if they're arranged
like a V, at least one of them isn't vertical). To produce yaw like a rudder, the two tr
ailing edge
control surfaces move in the same direction. To produce pitch like an elevator, the surfaces move
in opposite directions.

Roll

is controlled by movable sections on the trailing edge of the wings called
ailerons
. The
ailerons move differentially
-

one goes up as the other goes down. The difference in camber of
the wing cause a difference in lift and thus a rolling movement. As well as ailerons, there are
sometimes also
spoilers

-

small hinged plates on the upper surface of the wing, originally used to
produce drag to slow the aircraft down and to reduce lift when descending. On modern a
ircraft,
which have the benefit of automation, they can be used in combination with the ailerons to
provide roll control.

The earliest powered aircraft built by the
Wright
brothers

did not have ailerons. The whole wing
was warped using wires. Wing warping is efficient since there is no discontinuity in the wing
geometry. But as speeds increased unintentional warping became a problem and so ailerons were
developed.

The actual

linkages within the aircraft are discussed in
aircraft flight control systems
. for more
info go to www.nasa history.com