Seagull simulator
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  Most gulls don't bother to learn more  than  the  simplest  facts  of flight - how to get from shore to food and back again. For most gulls,  it is not flying that matters, but eating. For this gull, though, it was  not eating that mattered,  but  flight.  More  than  anything  else.  Jonathan Livingston Seagull loved to fly.

Richard Bach, Jonathan Livingstone Seagull 

  The aim of this project is to model with some degree of accuracy the flight dynamics of birds and to render it in real-time in a 3D environment. The flight model will be as general as possible in order to be appliable to most winged birds, but I have chosen the Seagull as a bird of choice because I love the way this bird flies. It offers a rich mixture of soaring and flapping capabilities that makes modelling it both interesting and entertaining.

Flight morphology

  This section describes the crucial body parts of a bird allowing it to fly. Most of this section is information selected from a serie of on-line lectures given at the University of Wales, Aberystwyth. Check the original site for a more complete coverage of bird flight physiology.

The wings

  The movement of the wing, although controlled by the muscles, is governed by the bones and the joints that articulate them. In the case of the bird wing, the free movement around the joint of the wrist is curtailed so that there is only movement in one plane, preventing the wing from bending up or down during the forces exerted by flight. In birds the elbow and wrist joints are linked so that extending the elbow automatically extends the wrist. This is possible because unlike in the elbow of humans, in the bird wing both the ulna and the radius have their own condyle (point of articulation) on the distal end of the humerus. The ulna is more distal to the radius on the elbow so that when the elbow is flexed the two bones of the forearm oppose one another. The radius is then pushed into the various carpal bones of the wrist whilst the ulna is withdrawn. This automatically makes the wrist, and thus the hand flex too and the wing is folded. During extension of the wing the opposite movement occurs. In this way the wing is controlled by the flight muscles, decreasing weight and simplifying coordination. 

  The wing is the lifting surface of the bird and as such must have the right shape and profile to provide the airflow to produce this lift. Much of the visible shape of the wing is produced by the covering of feathers, however, there is a narrow flap of skin that is called the propatagium. This is stretched tight along the leading edge between the shoulder and the wrist when the wing is held out. This is an important part of the wing, it is covered in feathers and forms the leading edge of the inner wing where it helps to provide much of the lift developed by the wing. 

  To provide it with the required rigidity against the airflow the bones of the wing tend to run nearer the leading edge, whilst the trailing edge is constructed solely of a rigid line of feathers. Covert feathers also cover the entire wing and at the trailing edge are found the much larger primary (remiges) and secondary feathers (secondary remiges) 

  The alula is formed by digit II, and lies almost at the wrist joint on the leading edge of the wing. generally it has 3-4 short vaned feathers attached to it. It acts in a similar fashion to the slots on an aircraft, naturally raising into the airstream when the wing approaches stall. The alula is prominent in birds such as the corvids and almost absent in some soaring seabirds.

The legs 

  The legs of a bird may not be considered to be an important requirement for flight, however, without the power they provide during take off many birds would be unable to become airborne. The same can be said for landing where the legs are often used to absorb the large amounts of energy that are generated during initial contact with the ground. 

  Starlings and pigeons do not run to gain speed, instead they jump into the air. This jump is powerful enough to supply the initial inertia required to get them fully airborne. Once in the air they are able to use the full movement of their wings to continue their skyward motion. Albatross with their long wings and swans with their high wing loadings normally rely, like aircraft, on increasing their momentum on the ground until they reach a speed that allows them to become airborne, whilst some dabbling ducks, such as the mallard, are able to launch themselves vertically into the air straight from the water, an incredible feat of pure power. 

The tail 

  The wings are not the only lifting surfaces found on birds, the tail also plays an important role in flight. Obviously tail types vary greatly within the birds and some tails are used for display as well as for flight, but like the wing, their shape is often influenced by their lifestyle. 

  The wings of a bird generally lie slightly ahead of the centre of gravity, this means that when a bird flies its posterior trails in the airflow behind it. The tail provides not only the lift required to buoy up the weight of the body but it also helps in flight control, unfortunately it also adds to drag at higher speeds. The tail allows the wing design in birds to be tailored for efficient cruising and high speed flight and under these conditions it is furled to provide minimal drag. At lower speeds, however, or during maneuvers the tail can be quickly unfurled to reduce induced drag (see later) from the wings and provide a surface for enhanced steering, lift or braking. The tail is suspected to play an important part in maintaining balance and stability in flight and it would seem that it is required to generate lift at low speed when the interaction between the wings and the tail can also most effectively reduce drag. 

  The retrices, or tail feathers generally number 10-12, but are found to range between 8 and 24. These are normally straight and bilaterally paired and the bases covered by coverts to produce a smooth surface for airflow. When you look at a birds tail you see the retrices which are controlled by the tail muscles that allow for the various movements that are required for precision flying.

The feathers 

  Feathers make an ideal aerodynamic surface for airflow. They can produce a smooth uninterrupted surface over which air can pass freely and can remain flexible without losing their aerodynamic properties. Further to that, the surface is also somewhat malleable, giving under areas of pressure, thus letting air pass more easily over the body without disrupting flow and causing drag.

  Flight feathers are asymmetrical, with the leading edge vane being narrower, thicker and less flexible than the trailing edge. If the leading edge of the feather was to bend excessively in the airflow it would cause twisting of the feather, leading to a damaging loss of lift. This asymmetry, however, also ensures that the trailing web of the feather bends upward during the downstroke, providing forward momentum and lift. It has also been shown that the outer primary feathers, that is the ones closest to the wing tip, are mechanically stronger than those closer to the wing root (Ennos, Hickson & Roberts, 1995). This is probably to property that helps them withstand the larger aerodynamic forces that these feathers are subjected to. 

Sources for this section:

University of Wales, Aberystwyth:

Flight physics

  In this section are described the mecanics of the flight. Again, most of this section comes from a serie of on-line lectures given at the University of Wales, Aberystwyth ( From them I've selected and made some editing to those parts that were potentially useful for my model. Check the original site for further information. 

Principles of the aerofoil 

  To understand how lift is produced by a wing we must first come to grips with Bernoulli’s principle. Bernoulli’s principle states, in essence, that fast moving air exerts less pressure than slow moving air. Now a birds wing, when outstretched into the air, is held at a slight downward angle to the onflowing air. This means that air passes over the wing faster than it passes under the wing so there will be less pressure above the wing and more pressure below. This change in pressure causes the wing to move toward the lower pressure with a helping push from the higher presssure below it, thus causes lift. 

  The faster air moves across the wing the more lift the wing will produce, so moving it through the air by flapping increases this airflow and thus increases lift. The bird doesn’t paddle air underneath its wing, instead it cuts into the air with the leading edge to obtain the flow over the surface that it requires. 

The wing 


  Air causes drag on a flying bird and it is this drag that is often important in deciding the shape, not only of the wings but also the body and tails of the bird. It has to be remembered though, that without drag, caused by the movement of air across the wing, it would not be possible to gain any lift, so a zero drag situation is not only out of the question, but it would also be highly undesirable. 

  The first thing to note about drag during flight is that for experimental purposes it can be subdivided into three main categories and so we find parasite, profile and induced drag being produced. 

  Parasite drag is the drag produced by the flow of air over the body of the bird and like a car this is influenced by any uneven surfaces or jutting protrusions such as legs. Remember that drag increases with speed and as herons fly much more slowly than ducks or geese this aerodynamic requirement comes secondary to the functional requirement of food gathering. It isn’t just the front of a bird that has to be aerodynamic though , its at the rear end where the greatest energy savings are to be had. It is here that air bleeds off the body and the potential for a great deal of energy sapping turbulence is produced. Most birds have a tail that helps the flow of air leave the body and can be used to increase lift if required. When a bird is flying quickly it furls its tail and tries to emulate the water droplet, which you’ll remember narrows to a fine point at the back and is the shape that is imposed on the fluid by the forces induced by the passage of the air over it. That is why swallows, frigatebirds and an number of other fliers have sharply forked tails and why falcons and nightjars have very narrow ones. 

  The production of lift comes at the expense of an increase in drag, this is termed induced drag. When a wing producing lift passes through the air it leaves circulating air in its wake that represents lost kinetic energy, thus induced drag is the product of lift production and does not include profile drag which we will come to shortly. When calculations of induced drag are made they assume that air has no viscosity, which we all know to be incorrect. Profile drag takes into account the viscosity of the air so that the addition of profile drag values to those of induced give the total drag value of the wing. Profile drag is in effect what it sounds like, that is the drag produced by the profile of the bird as it moves through the air. So if we add the profile drag, the parasite drag and the induced drag together we find the figure for the total drag. Its not only the wings that add to induced and profile drag though, the tail can also act as a lifting body thus causing induced drag. At the same time, because it is unfurled, it will also add to the profile drag too. 

Angle of attack 

  The angle of attack of the wing is one of the main factors that affects the amount of lift produced, it also has important implications on the amount of drag that it develops. The angle of attack is the angle at which the leading edge cuts into the forward flow of air and around 6-15 degrees is often quoted as being the norm. Increasing this angle increases the volume of air diverted over the wing and leads to an increase in lift, but this is at the expense of drag which quickly increases. This can be demonstrated easily by holding your hand out of a car window as it is being driven along. If you hold your hand flat and then gently rotate it into the oncoming airflow you should feel a gradual increase in lift until finally when you turn it too far it will suddenly lose all its lift and your hand will be jerked backward by the airflow, this is called a stall and is due to the loss of a smooth airflow over your hand. 

  A bird can obviously adjust this angle of attack, not just simply by rotating its wing but also by changing the attitude of its entire body with respect to its forward motion. So during slow flight birds and aircraft tend to fly nose up with a fairly high angle of attack, whilst traveling at speed they tend towards nose down, producing a much lower angle of attack. During take off, when there is very little airflow over the wings, birds such as pigeons increase the angle of attack to give the wing greater purchase on the air so that a larger amount of force can be generated. During a stoop on the other hand a falcon will minimize the angle of attack to allow it to slip through the air with a minimum of drag. 

  The shape of wings have also evolved to help produce lift from lower angles of attack. This is accomplished by the use of a cambered wing. Thus the birds wing is not flat in section, but instead is concave. Because of this the leading edge attacks the air with a lower aspect (it faces straight on into the airstream) than the trailing part and thus minimizes drag, bringing with it the bonuses of better stall and lift characteristics. 

Aspect ratio 

  The aspect ratio of a wing is calculated as b2/S, where b is the wingspan and S is the surface area of the wing. The aspect ratio of a wing is important as generally the higher the aspect ratio (longer and narrower wings) the lower the induced drag produced by the wing at a given speed. Wings with a high aspect ratio tend to be found on birds that soar at relatively high speed whilst those with lower aspect ratios (shorter, wider wings) are found on birds that soar at lower speeds. 

  Drag is produced when high pressure air passing under the wing swirls upward into the low pressure area above and behind the wing. As it does the air creates a sheet of eddies that disrupts the movement of air across the wings trailing edge. This phenomenon reduces lift and leads to drag creating turbulence which is most pronounced at the wingtip, where it is called the tip vortex . This phenomena can often be seen in aircraft where vapour trails can be seen emanating from the wingtips, especially during hard maneuvers. This effect can be diminished by increasing the length of the wing and so decreasing the tip to wing length ratio. Incidentally it is this tip vortex that is used by gulls, geese etc when they fly in the V type formations that you often see. The air directly behind the wingtip is the rising part of the vortex and it is this that the formation flying birds exploit. To get the best out of it they must be tucked in closely behind the leading bird or they will fly into the downwash. In this manner they can minimize their energy usage. 

  Many birds have a requirement for shorter wings and so another method of dissipating tip vortex has evolved. In aircraft, vertical winglets are often placed at the end of the wing to dissipate these vortices in a vertical plane. Birds use a similar method, although in this case their winglets are formed by the primary feathers of the wing. This design of wing is often termed, slotted, meaning that there are gaps between the feathers so that each feather acts independently. As I say, this is most pronounced at the wing tip, where, if you watch a bird in flight you will see these feathers bending upward as the air from below the wing gushes up into the low pressure above. This bending of the feathers leads to the displacement of the tip vortices to the vertical dimension, thus spreading it across a greater area of the wing, leading to a decrease in induced drag. It also leads to the production of forward momentum. 

  To understand a little more the important implications of wingspan and aspect ratio on flight, imagine a bird soaring in level flight through the air at a given speed. Now take a snapshot of 1 second of that birds flight. Looking from directly above the bird you could measure the area that it has passed over by measuring the span of the bird by the distance covered in that second. If the bird has a long wingspan the area will be larger than that of a bird with a lesser wingspan. The measurement that you get can be correlated to the amount of air that that bird has passed through in that given time frame. From this we can see that a bird with a longer wingspan is able to move through more air than a bird of shorter wingspan. Now if that bird is gaining its lift from the air that it has passed through we can also see that a bird of the same weight, with a smaller wingspan, will have to gain more lift from that air than the one with a longer wingspan. In other words the bird with the shorter wingspan has to move more of the air (produce more lift from a given amount of air) that it passes through to obtain the lift that it requires to keep it airborne. 

  It is not only the length of the wings that affect the flight characteristics of the bird, so does the chord length or width of the wing. The longer the chord length of the wing, the greater the separation of the air over its surface can be. So birds with wide wings are generally able to derive more lift from the air they pass through than birds with narrow wings. 

  It has been found in the Procellariiforms (petrel and albatrosses) and it is probably a general phenomenon with a number of bird families, that there is a tendancy for larger birds to have the higher aspect ratio wings.

Wing loading 

  This is defined as the weight of the bird/wing area and measured in grams/centimeter square (g/cm2). Wing loadings have an important implication on large birds and explains why there is a limit to their size. As a bird increase in size, its volume, and so its mass will increase by the cube root, whilst the wing surface only increases as a square root, this is often termed scaling. As the bird gets larger its wing loading will increase until it reaches a value that cannot be sustained. The vultures, albatross and swans are very large birds, at the extreme end of the size scale and have solved the problem of size in different ways. Neither the vulture or the albatross is very proficient at powered flight and both birds rely heavily on their environment to produce the lift they require to both take off and to stay in the air. The vulture though, uses high lift wings to keep itself aloft, loitering on thermals as it scans the savanna for carrion, whilst the higher wing loadings of the albatross mean that it must cruise at much higher speeds to stay airborne. This extra speed is important to the albatross as it allows it to hunt over great tracts of ocean for its widely scattered prey items.

  Wing loading is a very important factor in the flight performance of birds. In general it is found that animals with lower wing loadings tend to fly more slowly and are more maneuverable than do those with higher values. 

  Wing loadings will also be affected by other phenomenon, such as the long legs stork and herons. These birds must land carefully to ensure that they do not damage their legs and so they need low wing loadings to allow them to come down very gently. Compare this to the swan that requires a strip of water to land on, here the bird removes the remainder of its airspeed by sticking its feet out and ploughing through the water. 

The alula 

  The faster a wing travels through the air the more air it passes through and so the more lift is produced. This is not a limitless relationship though because as the bird reaches higher velocities the drag induced by the wings increases too. If the bird travels more slowly though, it passes through less air and thus it must gain more lift from that parcel of air. To do this it can either flap its wings to increase the airflow or it can increase the amount of air that it moves by increasing the angle of attack, thus forcing its wing through a greater volume of air. If the air passing over the wing starts to do so too slowly turbulence will be induced over the surface of the wing and it will start to stall. Remember that for a wing to function correctly there has to be a smooth flow of air over the entire surface of the wing. If separation occurs and the air leaves the wing surface before it reaches the trailing edge a field of turbulence will be produced that will destroy the lift production of the wing. To overcome this problem birds use a similar system to that used by aircraft. The second digit forms the alula, a small winglike structure that is drawn into the airflow of the wing, smoothing it and delaying the stall. This is a passive response to the change in airflow that can also be controlled by the bird, giving it greater control of flight parameters. The aspect ratio of a wing and the overall wing shape will has profound consequences on the rate at which this phenomenon occurs. Narrow wings with less camber tend to have less dependence on the alula than short wings with heavy camber, so many passerines will have well developed alulas whilst the sea soarers will have less use for them. 

Moment of inertia 

  During flapping flight, birds invest power to move the air (aerodynamic power) and to move the wings (inertial power). The inertial power required to accelerate and decelerate the wings during each wing stroke increases with the moment of inertia of the wing (Vandenberg & Rayner, 1995). The moment of inertia value (measured in kg m2) is important because, as with the aspect ratio of the wing, it gives us information on flight characteristics. Like most mammals that rely on speed, all of the larger muscles involved in movement of the limb are found ‘in-board’, close to the body and are attached to the bones and joints of the limb by long tendons. This ensures that as little energy as possible is wasted on moving a heavy limb, it also means that the muscles can act on a lever mechanism, maximizing their power output. 

  It is vitally important for a bird to keep the moment of inertia of its wing as low as possible and a close look at the wing highlights that adaptation. The moment of inertia depends upon the distribution of mass along the wing, the more distal the mass, the higher its influence on inertia. Most of the, muscles, blood supply, tendons etc in the wing are fairly proximal and so have less influence on inertia. On the other hand, looking past the wrist it can be seen that the mass is made up predominantly of purely weight bearing material such as bone and feather. 

  At the same time as keeping the moment of inertia low, the wing must also maintain a reasonable resistance against bending or failure and so wing design must reflect a compromise between strength and weight. Long wings will generally have a higher inertial value than shorter wings and so will be more difficult to flap. Gulls with their relatively long wings tend toward a lazy flight gait with a slow rate of flapping whilst sparrows and other small passerines, with their relatively short wings, are considerably more frenetic in their flight. 

Wing types 

Saville (1957) classified wings into 4 main types: 
  • Elliptical
  • High Speed 
  • High aspect-ratio
  • Slotted high-lift 

  Elliptical wings tend to be found on birds adapted to forested, wooded and shrubby habitats where birds require good maneuverability and are generally short with a low aspect ratio. These wings often have a high degree of slotting which is associated with the requirement of slow speed flight. Elliptical wings are found in the passerines, the gallinaceous species as well as woodpeckers and doves.

  High speed wings are possessed by birds that feed in the air or have to make long migratory hauls. They are seen in the swifts, swallows and also the falcons and some shorebirds. These wings have a relatively high aspect ratio and are only slightly cambered, having an almost flat profile and are often swept back. 

  The high aspect wing is found on soaring sea birds such as albatross and can also be seen on gliders. They, like the slotted high-lift wing can provide plenty of lift in the windswept environment in which they live. 

  The slotted high-lift wing is a characteristic of many terrestrial soaring birds, such as the eagles and the vultures. These wings have a moderate aspect ratio with marked slotting and are heavily cambered. This wing design not only allows them to carry heavy loads but also enables them to minimise energy expenditure whilst foraging for food. 

  So why do we have this dichotomy in wing design between the slotted high-lift and the high aspect wing. Well this can probably be answered by looking at their foraging technique and the environment on which they hunt for food. Vultures tend to loiter in the air, gaining lift from thermals that can be small and require tight turning to remain inside. To them the most important factor is remaining aloft so they can continue to scan for carrion. Speed is not particularly important as they cross back and forth across the plains. This is all in marked contrast to the albatross, this is a large bird, with a fast cruising speed. It must cover many miles of ocean in search of food, whilst at the same time gaining its lift from the winds that are constantly blowing. This foraging technique calls for a whole new set of equipment and so to a completely different wing type. 

The Tail 

  The wings of a bird generally lie slightly ahead of the centre of gravity, this means that when a bird flies its posterior trails in the airflow behind it. The tail provides not only the lift required to bouy up the weight of the body but it also helps in flight control. The tail can be adjusted in a number of ways to help balance, steer or brake the body in flight. 

  On the ground, unless being used for display purposes, the tail is furled away and plays no part in movement, although some of the tail muscles are active. It is during take off and landing when the action of the tail can be seen most clearly, next time you are on the sea front watch the pigeons take off. It all happens very fast, so you will need to watch very carefully. As the wings are initially raised prior to the first downstroke the tail is unfurled and as the bird launches itself into the air its retrices (tail feathers) are rapidly spread producing a concave fan that is tucked under its body and flared out further during the first downstroke. The tail is now in an almost vertical position. As the bird makes further progress, its airspeed increases, the tail lifts progressively and the flaring becomes less pronounced until finally as the tail reaches a more horizontal attitude it is furled once more to minimize drag. During landing the whole procedure is re-enacted except this time the tail is used to help with deceleration. 

  It has been shown in studies with swifts that the use of the tail in flight helps the bird initiate much harder turns. However, during non-maneuvering flight the bird keeps its tail furled to minimise drag. 

Soaring Flight 

  There are a number of methods that a bird can use to gain lift without the need for wing flapping. Generally though, this form of flight is not undertaken by smaller birds and is left, instead to the larger species, like the vultures, storks, raptors and a number of sea birds. The reason for this is probably due to the larger speeds that can be generated by bigger birds and also because the large amounts of energy found this way are difficult for smaller birds to control. 

Thermal soaring 

  Thermals are generated by rising columns of warm air that develop over differentially heated surfaces during the day and are the domain of birds with high lift slotted wings. The shorter wings of these birds, give them better turning characteristics that make them better able to stay within the confines of small thermals. This form of soaring is used by a number of larger species during migration where they climb within a thermal to gain altitude before gliding down to the next thermal and climbing once more. As thermals are generally not developed over large water masses birds tend to collect in huge numbers in places like Gibraltar where they try to obtain as much altitude as they can to help them negotiate the straights into Africa beyond. 

  Thermals are commonly used by vultures who do not take to the wing until the sun has heated the ground long enough to allow the production of rising air columns. 

Slope soaring 

  Slope soaring occurs where winds meet an obstruction and are forced to rise over them. This rising air provides the lift for a large number of different bird species and is particularly noticeable when watching Kestrels hunting along the sea cliffs where large amounts of uplift are developed. Normally they have to hover when hunting, but in these conditions they can often remain motionless bouyed up by the rising air.

Dynamic soaring 

  Dynamic soaring is carried out by sea birds over water where no thermals or slopes are available to provide free lift. This is a more complicated affair than the other two forms of soaring and relies on a birds ability to convert momentum into altitude. For this reason birds with high aspect wings are by far the most proficient at this soaring technique and the albatross with its huge wingspan and high weight is the perfect practitioner. 

  Dynamic soaring relies on a gradient of wind speed being produced over the water. This occurs as energy is lost from wind in the production of waves close to the water surface, so close to the water the wind is moving more slowly. 

  The bird starts by gaining altitude, flying against the wind. Once it is high enough it starts to glide downward. With the wind behind it it rapidly picks up speed and when it gets close to the water it turns into the wind. The air near the water is slower than above and it quickly passes through this with the decrease in drag produced by the slower moving air. The bird then rises quickly on the wind which is now head on. The wind increases the airspeed over its wings and so provides lift that the bird exploits until its airspeed comes close to a stall. It then turns smartly and heads down wind once more gaining speed as it goes. Using this technique sea birds are able to cover huge tracts of the ocean.

Wing geometry and fligth stability (by R. Dryden)

  How do birds with small tails - for example seagulls - achieve stable flight? Presumably there must be some aerodynamic features that are giving the bird stability in the three main axes, or is it simply that the brain of the bird is constantly correcting instabilities as they arise? And then the tip panels of the birds' wings droop downwards (anhedral) which would seem to increase the risk of instability - in contrast many conventional aircraft have wings angled upwards (dihedral) to provide lateral stability.

  A clue from hang gliders: The hang glider wing forms two 'billows', one on each side of the midline. The underside of each wing forms a conical surface, the centreline of which is angled towards the nose of the hang glider. This arrangement, together with the low centre of gravity provided by the weight of the pilot, gives the hang glider stability around all three axes (pitch, roll, and yaw).

  In the early 80s I began to wonder whether the wings of birds such as seagulls conformed to a conical geometry like that of hang gliders. A series of models with wings built over conical jigs confirmed that this arrangement imparts stability during gliding flight - no additional surfaces such as a tailplane are required. Furthermore, it became clear that if the joint axes of the skeleton supporting the bird's wing were set perpendicular to the conical form, the wing is able to extend and flex whilst still retaining the conical geometry required for stability. 

Flapping flight 

  The wing can be tentatively separated into two parts, the outer wing or hand and the inner wing or arm. The inner wing acts like an aircraft wing, it is the lift developing part of the wing. When a bird flaps its wing it is the inner wing that moves the smallest distance, thus the lift it generates is due, to a large extent, on the airstream produced by forward momentum. The inner wing is also the most cambered part of the wing and this is made possible by the extensive bones and connective tissue that can hold this shape better than feathers. This means that it can generate more lift per surface area than the outer wing, it also means that it will stall more easily. 

  The outer wing is the powerplant of the wing, it produces lift, but more crucially it produces forward momentum. It is less cambered than the inner wing and more flexible and it is this flexibility that leads to the momentum. As the wing is flapped downward the outer wing tends to twist slightly forwards, this is due to a number of reasons, one being that air passing under the wing tends to well up toward the tip and as it does so it forces its way out under the back of the wingtip, tilting the wing forward.

  To better understand flapping flight, we will make our observations on a bird in stabilized flight, without taking into account takeoffs and landings (which are more complex to analyze). One can consider that during the flight, the bird carries out three essential motions with its wings: 

  • a motion of vertical flap (up and down).
  • a horizontal motion (forward and backward).
  • a torsion motion (twist of the wings).
  In flight, the bird has a regular trajectory, without any jerking motion. Its body does not go up and down when the wings move down and up. It implies that the wings carry the bird at every moment. Thus, the lifting force remains constant. The bird does not use the energy necessary to flap its wings to create a lifting force, but rather to propel itself forwards. The speed obtained by the streamline flow around the winds creates sufficient lifting force to maintain the flight. 

  Generally, the bird does not use its tail during a straight flight phase, but remains retracted most of the time. During a cycle of flaps, the wings exert, alternatively, a propulsion (while going down), and a deceleration (while going up). According to whether they take place below the average plan or not, these forces create an alternative couple on the trim. The bird compensates this by a continuous search for balance, moving its aerodynamic center with respect to its center of gravity (i.e. by moving its wings back and forth alternatively). Both vertical and horizontal motions are combined together to describe eight-shaped kinematics of the wing. 

  In flight, on one hand, the horizontal speed due to the displacement is the same all along the wingspan, but on the other hand, the vertical speed due to the beat is null at the base and increases gradually to the end of the wing. Both speeds combine together and make the angle of attack of the airflows vary according to the position of the wing : horizontal at the base and more vertical near the extremity. But a profile only tolerates a small variation in its angle of incidence. Consequently, the bird adapts its wing twist to keep a nearly constant angle of incidence. This results in a twist of the wings ends, twisting negative while going down, and positive while going up. As the lifting force has a direction perpendicular to the plane of the wing, it will swing the wing forwards during the descent (by the same way that a helicopter rotor swings forwards and propels the aircraft horizontally). Thus it is the flapping, associated with a judicious twist of the wings, that propels the bird and allows him to fly.

Another description:

  There are three important motions in addition to the bird's forward motion: 

1. Flapping                              2. Twisting                                3. Folding 

  By flapping its wings down, together with the forward motion of the body, a bird can tilt the lift of its wings forward for propulsion. Why don't birds simply move their wings up and down, without twisting and folding? Notice that the outer part of the wing moves down much farther than the inner part close to the body. Twisting allows each part of the wing to keep the necessary angle relative to the airflow. If part of the wing is angled lower than the airflow, there might not be enough lift. If part of the wing is pointed too high, there could be a lot of drag. The wings are flexible, so they twist automatically. 

  Wing folding isn't essential - ornithopters fly without it - but it helps birds fly with less effort. To see why it is helpful, think about what happens during the upstroke. Because the wing is going up, the lift vector points backward, especially in the outer portion of the wing. The upstroke actually slows the bird down! By folding its wings (decreasing the wingspan) a bird can reduce drag during the upstroke.

  In addition to the three basic movements described here, birds can do a lot of other things with their wings to allow them to maneuver in the air. Instead of using their tails for flight control, they move their wings forward and backward for balance. To make a turn, they can twist the wings or apply more power on one side. For slow flight, birds can flap their wings almost forward and backward instead of vertically; the upstroke and downstroke produce lift without forward body motion.

Varying flight speed 

  Flying, like any other mode of locomotion can be done at different speeds. Unlike humans that either walk or run though, birds do not have such clear cut gaits in their flight. Generally though it is thought that there are two overall flight strategies used by birds. These have been designated minimum power and maximum range and are derived from power curve produced during flight. These power curves have been made by measuring the power requirements of birds in air tunnels flying at different speeds. The maximum range speed would be the one that a bird would be expected to use if it was migrating or was in a hurry to get somewhere. The minimum power speed on the other hand would be best used when a bird was foraging or had no time requirement to its flight. Measurements taken of migrating birds do suggest that these figures might represent a real phenomenon. The strength of the flight muscles then will obviously set a limit to the birds power output and the bird is able to fly at high speeds for a short bursts or at lower speeds for a longer periods, like a human running. 

Different flight gaits 

  There are a number of different ways that a bird can flap its wings and this is influenced by the musculature, the type of wing and the speed at which the bird wishes to fly. It is also found that some birds also have the ability to extract lift from the wing flip, or upstroke whilst others can only produce power on the downstroke. By flying in this fashion the birds gait is changed, so that if it flies through helium filled bubbles, the wake produced by using the upstroke to generate lift produces what is known as a continuous-vortex gait whilst when only the downstroke is used a vortex-ring gait is produced.

Pigeon vortex-ring wakeGull continunous wake

  Small passerines and some larger birds have another way of flying, instead of continuously flapping their wings they change rhythmically from flapping to gliding (when the wing is extended) or flapping to bounding (when the wing is flexed). In this way they undergo an undulating flight where first using flapping they propel themselves forward on a slightly rising vector, then at the peak of the rise they cease flapping and continue forward by either gliding or closing their wings and bounding. This type of flying is stereotypic for some bird species, with for instance, the woodpecker that undergoes pronounced flap-bounding and the flap-gliding seen in the falcons and be used as a characteristic for field identification. 

  The reasons for this type of flying are still being examined and there are a number of different aspects under discussion. It is thought that this intermittent flying gait, used mainly in small birds such as the passerines may simply be due to the birds flight muscles being unable to perform continuous flapping, so they are rested during the bounding or gliding phase. Another theory, the ‘fixed gear hypothesis,’ suggests that flap-bounding is used to vary the power output of the flight muscles which are otherwise constrained by a fixed muscle contraction and wing motion. The ‘body-lift’ hypothesis suggests that some gliding during flap-bounding could be advantageous in comparison with continuous flapping over most flight speeds (Tobalske, Peacock & Dial, 1999). Small birds are very light and so drag will often have a stronger influence on their flight than gravity. For this reason it has been suggested that birds may bound between flapping to minimise drag.

Sources for this section:

Flight model

  From all the matter exposed above and in other sources, here are the crucial elements I've decided to include into the model:


  The wings are the main source of thrust, lift and attitude control.
  The proximal part ("arm") of the wing achieves the lift.
  The distal part ("hand") of the wing produces the thrust when flapping and attitude control when soaring and flapping.

  Therefore we can simplify it as follows:  Flapping wing hand creates Thrust, which builds up Airspeed, which flows around wing arm and generates Lift.

  Gulls maintain lift all along the flapping cycle. However, most birds cannot generate lift during the flap-up.

  Air density decreases with altitude.

  The flight will be modeled in two modes:

  1. Soaring/gliding mode: It will be basically a glider model. The 3D animation will show how the wings are used to roll and pitch.
  2. Flapping mode: The player will be able to control the power of each flap, each one producing an added thrust.
  The alula decreases stall speed. This feature will be added later as this can be negleted for gulls.

  The precise movements of the wings will not be included into the flight model. However, they will hopefully show accurately in the 3D animation


  Tail is used only at low speed to get additional manoeuvrability, lift and drag.
  Used as airplanes' air-brake and flaps for landings
  At high speed it is furled and acts as a drag reducer

Bird weight and aerodynamism

  Weight will just be used to compute the gravity force.
  Aerodynamism will be modelled by a few parameters controlling the drag as a function of speed, angle of attack, wing and tail posture.

Landing and take-off

  This will be modelled in a second phase. With the first model, a legless bird will be used.

Landscape-dependend wind field

  Once the flight model is correct for still air, wind will be added. Three factors will be considered:
  1. Differential wind speed with altitude: a lower wind speed close to the sea surface will allow the player to reproduce albatross' infinite gliding technique.
  2. Above land, wind will be modelled in a more elaborate way, with upwelling on the windward side of a hill, acceleration at its top, and turbulences on this leeward side.
  3. Thermal effects will generate vertical air movement.

Programming language: Delphi 6
3D-Environment: OpenGL, GLScene library


Nothing yet. Debugging phase.


  The references below provided useful insight and inspiration at various phases of the project. They are sorted in alphabetical order of the first author. Those references which proved paramountly useful are marked by three red stars (***)

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Updated 12.07.2003