Longitudinal static stability

From Wikipedia, the free encyclopedia

Longitudinal static stability is important in determining whether an aircraft will be able to fly as intended.

Contents 1 Static stability 2 Longitudinal stability 3 The pilot's task 4 Center of gravity 5 Analysis 5.1 Trim 5.2 Static stability 6 Neutral point 7 See also 8 References

Static stability

As any vehicle moves it will be subjected 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 stable. 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 change 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 stability.

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 orientation 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, including an unmanned aerial vehicle, 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. (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.

The pilot's task

The pilot of an aircraft with positive longitudinal 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 speed, 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 necessary 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.

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 stability 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. As the center of gravity moves forward the moment arm between the horizontal stabilizer increases and the longitudinal static stability of the aircraft also increases. As the center of gravity moves aft, the longitudinal static stability of the aircraft decreases.

The limitations specified for an aircraft type and model include limitations on the most forward position, and the most aft position, 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 move outside the approved range during the flight.

Analysis

Near the cruise condition most of the lift 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 considering the aircraft in equilibrium under wing and tail lift, and weight. The moment equilibrium condition is called trim, and we are generally interested in the longitudinal stability of the aircraft about this trim condition.

Equating forces in the vertical direction:

W = L_w + L_t

where W is the weight, L_w is the wing lift and L_t is the tail lift.

For a symmetrical airfoil at low angle of attack, the wing lift is proportional to the angle of attack:

where S_w is the wing area C_L is the (wing) lift coefficient, α is the angle of attack. The term α₀ is included to account for camber, which results in lift at zero angle of attack. Finally q is the dynamic pressure:

where ρ is the air density and v is the speed.

Trim

The tailplane is usually a symmetrical airfoil, so its lift is proportional to angle of attack, but in general, there will also be an elevator deflection to maintain moment equilibrium (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 stable aircraft of conventional (tail in rear) configuration, the tailplane lift typically acts downward. In canard aircraft, both fore and aft planes are lifting surfaces. The fundamental requirement for static stability is that the coefficient of lift of the fore surface be greater than that of the aft surface; but even this general statement obviously does not apply to tailless aircraft. Violations of this basic principle are exploited in some high performance combat aircraft to enhance agility; artificial stability is supplied by electronic means.

The tail lift is, therefore:

where S_t is the tail area, C_l is the tail lift coefficient, η is the elevator deflection, and ε is the downwash angle.

Note that for a rear-tail configuration, the aerodynamic loading of the horizontal stabilizer (in N.m ^{− 2}) is 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 canard configuration, the loading of the horizontal stabilizer is 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 favourable 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 angle 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'.

Taking moments about the center of gravity, the net nose-up moment is:

M = L_wx_g − (l_t − x_g)L_t

where x_g is the location of the center of gravity behind the aerodynamic center of the main wing, l_t is the tail moment arm. For trim, this moment must be zero. For a given maximum elevator deflection, there is a corresponding limit on center of gravity position at which the aircraft can be kept in equilibrium. When limited by control deflection this is known as a 'trim limit'. In principle trim limits could determine the permissible forwards and rearwards shift of the centre of gravity, but usually it is only the forward cg limit which is determined by the available control, the aft limit is usually dictated by stability.

In a missile context 'trim limit' more usually refers to the maximum angle of attack, and hence lateral acceleration which can be generated.

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 α:

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:

M = h(L_w + L_t)

Applying the increment in angle of attack:

Equating the two expressions for moment increment:

The denominator of the second term is dominated by the wing lift, so the tail lift term can be ignored, 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, according to Piercy, has values in the range 0.5 to 0.65 for typical configurations. Hence the expression for h may be written more compactly, though somewhat approximately, as:

h = x_g − 0.5cV

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 − h, so that positive stability is associated with positive static margin.)

Neutral point

A mathematical analysis of the longitudinal static stability 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. (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 (negative static margin). If the center of gravity is behind the neutral point, the aircraft is longitudinally unstable (the static margin is positive), and active inputs to the control surfaces are required to maintain stable flight. Ultimately, the position of the center of gravity relative to the neutral point determines the stability, control forces, and controllability of the vehicle.

For a tailless aircraft V = 0, the neutral point coincides with the aerodynamic center, and so for longitudinal static stability the center of gravity must lie ahead of the aerodynamic center.

See also

• Directional stability
• Flight dynamics

References

• Clancy, L.J. (1975), Aerodynamics, Chapter 16, Pitman Publishing Limited, London. ISBN 0 273 01120 0
• Hurt, H.H. Jr, (1960), Aerodynamics for Naval Aviators Chapter 4, A National Flightshop Reprint, Florida.
• Irving, F.G. (1966), An Introduction to the Longitudinal Static Stability of Low-Speed Aircraft, Pergamon Press, Oxford, UK.
• McCormick, B.W., (1979), Aerodynamics, Aeronautics, and Flight Mechanics, Chapter 8, John Wiley and Sons, Inc., New York NY.
• Perkins, C.D. and Hage, R.E., (1949), Airplane Performance Stability and Control, Chapter 5, John Wiley and Sons, Inc., New York NY.
• Piercy, N.A.V. (1944), Elementary Aerodynamics, The English Universities Press Ltd., London.

• All text is available under the terms of the GNU Free Documentation License. (See Copyrights for details.)
  

Principles of Flight

From Wikipedia, the free encyclopedia

Flight is the process by which an object achieves sustained movement either through the air (or movement beyond earth's atmosphere, in the case of spaceflight) by aerodynamically generating lift, propulsive thrust or aerostatically using buoyancy.


The physics of flight

Lighter-than-air aircraft are able to fly without any major input of energy
Main article: Aerodynamics
There are different approaches to flight. If an object has a lower density than air, then it is buoyant and is able to rise and float in the air without using energy; a lighter than air craft is known as an aerostat. A heavier than air craft, known as an aerodyne, includes flighted animals and insects, fixed-wing aircraft and rotorcraft. Because the craft is heavier than air, it must use the force of lift to overcome its weight. The wind resistance caused by the craft moving through the air is called drag and is overcome by propulsive thrust except in the case of gliding.
Some vehicles also use thrust for flight, for example rockets and Harrier Jump Jets.

Forces for flight

Main forces on a heavier-than-air aircraft
Main article: Aerodynamics
Forces relevant to flight are[1]
Propulsive thrust: (except in gliders)
Lift: created by the reaction to an airflow
Drag: created by aerodynamic friction
Weight: (created by gravity)
Buoyancy: for lighter than air flight
These forces must be balanced for stable flight to occur.
The stabilization of flight angles (roll, yaw and pitch) and the rates of change of these can involve horizontal stabilizers (i.e. 'a tail'), ailerons and other movable aerodynamic devices which control angular stability i.e. flight attitude (which in turn affects altitude, heading).

Lift to drag ratio

Speed and drag relationships for a typical flight article
Main article: Lift to drag ratio
When lift is created by the motion of an object through the air, this deflects the air, and this is the source of lift. For sustained level flight lift must be greater than weight.
However, this lift inevitably causes some drag also, and it turns out that the efficiency of lift creation can be associated with a lift/drag ratio for a vehicle; the lift/drag ratios are approximately constant over a wide range of speeds.
Lift to drag ratios for practical aircraft vary from about 4:1 up to 60:1 or more. The lower ratios are generally for vehicles and birds with relatively short wings, and the higher ratios are for vehicles with very long wings, such as gliders.

Thrust to weight ratio
Main article: Thrust-to-weight ratio
If thrust-to-weight ratio is greater than one, then flight can occur without any forward motion.
If the thrust-to-weight ratio is greater than the lift-to-drag ratio then takeoff is possible.

Energy efficiency
To create thrust to push through the air to overcome the drag associated with lift takes energy, and different objects and creatures capable of flight vary in the efficiency of their muscles, motors and how well this translates into forward thrust.
Propulsive efficiency determines how much thrust propeller and jet engines gain from a unit of fuel

Power to weight ratio
Main article: power-to-weight ratio
All animals and devices capable of sustained flight need relatively high power to weight ratios to be able to generate enough lift and/or thrust to achieve take off.

Mechanical flight
Main article: Aviation

Mechanical flight: A Robinson R22 Beta helicopter

A Bombardier Global 5000 business jet takes off
Mechanical flight is the use of a machine to fly. These machines include airplanes, gliders, helicopters, autogyros, airships, balloons, ornithopters and spacecraft. Gliders provide unpowered flight. Another form of mechanical flight is parasailing where a parachute-like object is pulled by a boat. In an airplane, lift is created by the wings; the shape of the wings of the airplane are designed specially for the type of flight desired. There are different types of wings: tempered, semi-tempered, sweptback, rectangular, and elliptical. An aircraft wing is sometimes called an airfoil, which is a device that creates lift when air flows across it.

The study of flight
In 8th century Cordoba, Ibn Firnas studied the dynamism of flying and carried out a number of experiments. After one of his flights he fell on his back and he commented that he now understands the role played by the tail when birds alight on the ground, telling his close friends that birds normally land on the root of the tail which did not happen in that occasion, hence a reference to the missing tail[4]. Durant in his book “the story of Civilisation”, quoting Al-Makkari who mentioned that Ibn Farnas indeed constructed a flying machine[5]. However, he does not elaborate on how the machine works nor whether it was the one Ibn Farnas used nor on its destiny.
Leonardo da Vinci is one of the best-known early students of flight. He made many prototypes of parachutes wings and ornithopters.
Supersonic flight
Main article: supersonic
Supersonic flight is flight faster than the speed of sound. Supersonic flight is associated with the formation of shock waves that form a sonic boom that can be heard from the ground, and is frequently startling. This shockwave takes quite a lot of energy to create and this makes supersonic flight generally less efficient than subsonic flight at about 85% of the speed of sound.

Hypersonic flight
Main article: hypersonic
Hypersonic flight is very high speed flight where the heat generated by the compression of the air due to the motion through the air causes chemical changes to the air. Hypersonic flight is achieved by reentering spacecraft such as the Space Shuttle and Soyuz.

Religion, mythology and fiction
In religion, mythology and fiction, human or anthropomorphic characters sometimes have the ability to fly. Examples include angels in the Hebrew Bible, Daedalus in Greek mythology, and Superman in comics. Two other popular examples are Dumbo, the elephant created by Disney who use his ears to fly, and Santa Claus whose sleigh is pulled by flying reindeers. Other non-human legendary creatures, such as some dragons and Pegasus, are also depicted with an ability to fly.
The ability to fly may come from wings or other visible means of propulsion, from superhuman or god-like powers, or may simply be left unexplained.

See also

Wikimedia Commons has media related to:
Category:Flight

Look up flight in Wiktionary, the free dictionary.
Aerodynamics
Aviation
Flying and gliding animals
Aviation history
Levitation
Transvection (flying)
Aircraft

References
^ Four forces on an aeroplane
^ Averof, Michalis. "Evolutionary origin of insect wings from ancestral gills." Nature, Issue 385, volume 385, February 1997 pp. 627–630.
^ The Trumpeter Swan Society - Swan Identification
^ Al-Makkari, ed. Nafh Al-Teeb Volume 4. Dar Al-Fikre, Egypt, 1986, pp. 348–349.
^ Durant, Will. The Story of Civilisation vol. 13. New York: Simon and Schuster, 1967.

External links
See how it flies: a new spin on the perceptions, procedures, and principles of flight
'Birds in Flight and Aeroplanes' by Evoluntionary Biologist and trained Engineer John Maynard-Smith Freeview video provided by the Vega Science Trust.
The First Try of Human Flight

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