# Wings: Design Constraints Related to Flight Behaviors in Birds

## Abstract

A bird’s wings are essential for transportation and mobility. All species of birds have different wings that can differ in many aspects: wingspan, wing color, wing shape, weight, composition and more. These characteristics define each bird species and come from generations of genetic heredity and adaptation to their changing environment. However, birds of all species can be classified by looking at their flight paths and patterns. They can fly efficiently by using their wings in three flight patterns: flapping, soaring (or gliding, the flight method gliders/sailplanes use) and diving. In this report, we mainly focus on flapping and soaring, with a small section featuring diving in peregrine falcons.

## Introduction

What are the specific factors that influence whether birds prefer soaring or flapping? There are many interrelating design constraints at play. The first is the relationship between body mass and the amount of power a bird’s muscles can produce. According to in vivo measures made by Jackson and Dial (2011), maximum mass-specific power output scales slightly negatively with pectoralis muscle mass, suggesting that as a bird becomes larger, their flight performance becomes increasingly limited by their mechanical power output. Thus, bird size and the maximum power output of its primary flight muscles have an impact on flight style, behavior and ecological interactions (Tobalske, “Evolution of avian flight”). A second factor is aerial environment. Many larger soaring birds use air currents and thermal updrafts to conserve energy while flying. For example, strong air currents can be found in places like oceansides, cliffsides, and mountains. A third factor is migration and whether the bird prioritizes saving time or energy during the long flight. Finally, one of the most important considerations for energy conservation is aerodynamic drag reduction, as it is the only source of energy loss in flight. In fact, increasing lift, which is a force produced by the action of air flow on the wing, generates a lift-induced drag force. Another portion of drag is parasitic drag, which includes skin friction drag from the friction between air and body surfaces and form drag from the bird’s frontal area (Merck, 2017). In our report, we explore flapping, soaring, and multiple bird case studies, while discussing how the aforementioned design constraints relate to a bird’s morphology and influence preferred flight styles.

## Flight Patterns

### Flapping in Birds

Flapping wings remains a flight behavior that is hard to replicate by efficient and usable mechanical designs. Yet, all birds and even some mammals like bats flap their wings as it is an imperative part of take-off, landing, and maneuvering in the air when flying. When birds are flapping, two pairs of massive muscles are involved: the pectoralis, which lowers the wing and the supracoracoideus, which raises it. Together, these muscles comprise up to 25 % of a bird’s mass (Gill et al., 2020; Tobalske, “Evolution of avian flight”). The pectoralis of most birds has a uniquely uniform composition of only fast-twitch fibers with limited variation in myosin isoforms; this allows the downstroke to produce most of the work and power generated during flapping (Tobalske, “Evolution of avian flight”). As the wings push down, the angle of attack is increased and the tips of the primary feathers – those on the wing tip – are pushed up and pulled at an angle. When the wing moves up again, it twists to decrease the angle of attack – usually to 0 degrees – to minimize drag, and the primary feathers separate to prevent resistance. A force of lift is generated by flapping: on the downstroke, air is pushed downwards, which according to Newton’s third law, creates a reaction force that lifts the bird in the opposite direction (Dvořák, 2016). Birds flap their wings differently during flight to satisfy its different stages.

When engaging in flight, they tilt their body or their wings forward and start flapping them. This generates a lift perpendicular to the plane of the wings, which corresponds to a force upwards and to the front of the bird, elevating the bird and giving it a flight velocity forward (Chin and Lentink, 2019). Take-off is one of the most energetically demanding aspects of flight (Dvořák, 2016). When birds want to land on the ground or any elevated surface and if their speed is too high for a safe landing, they will tilt their body or wings backwards. This induces a lift upwards and to the back of the bird, perpendicular to its wings. The force it produces has a coordinate x which goes against the thrust of the bird, thus slowing down its velocity for a safe landing.

During flight, birds flap their wings to constantly balance between gravity and drag, while maintaining a positive thrust to travel. Flapping also provides a higher control overturns or any unexpected circumstances, as birds can generate lift in different directions by tilting their wings (Chin and Lentink, 2019). In fact, small birds, which prefer flapping, have evolved to have a much larger ‘hand’ portion that represents around 80 % of their wings to improve their maneuverability in the air (Dvořák, 2016). However, flapping can quickly shorten the duration of the flight, as it is energy consuming.

Despite flapping being more energy consuming than soaring, most small birds, up to 0.3 kg in mass, use flap-bounding as their main style of flight, which is predicted to offer energetic advantages compared to continuous flapping. Flap-bounding is characterized by alternating phases of large-amplitude flapping and flexed-wing bounds (Fig. 3), although species with more pointed, narrow, and long wings will modulate their non-flapping wing position, even gliding with wings fully extended. Small bird species that use flap-gliding tend to do so when flying at slower speeds and switch to flap-bounding at higher speeds. Flap-bounding and flap-gliding are known as intermittent flight styles. The bird does not use any primary flight muscles during the bound, but it produces a small amount of body and tail lift. The power-costs of flap-bounding indicate that the flight style is more energetically efficient than continuous flapping if the body and tail produce enough lift to support about 10-15 % of the bird’s weight (Tobalske, “Evolution of avian flight”). According to analyses by Sachs (“Wind effects on bounding flight”), this only happens when flying into a headwind. Meanwhile, flap-gliding is energetically favorable over a range of flight speeds. Paradoxically, small birds frequently use flap-bounding during slow flight and brief hovering phases despite the high energy cost. Current research has not yet explored the metabolic costs in flap-bounding versus continuous flapping, which could bring more insight into why birds use flap-bounding (Tobalske, “Evolution of avian flight”).

In contrast, the energy cost of flapping is especially impactful for species of large birds that have to provide more lift to balance a much heavier weight. Pennycuick (1972) remarks a clear correlation between the expenditure of energy and body mass with the following equation:

P_{mr} ∝ {7\over 6} M

(1)

where Pmr is the power of maximum speed range and M is the body mass. Flapping vigorously to induce a forward thrust and overpower drag is an energetically costly flying method that is not favorable for larger birds in theory.

### Soaring in Birds

Another flight behavior involves soaring, where birds can sustain their flight over long periods of time without flapping their wings. In contrast to flapping, soaring requires almost no motor power, meaning birds do not need to provide any additional energy to maintain it. This is an energetically inexpensive method of flying because it uses a lesser basal metabolic rate given by the equation:

P_s ∝ {3\over 4}M

(2)

where Ps is the soaring power and M is the body mass (Baudinette and Schmidt-Nielsen, 1974). The relationship between body mass and power may suggest that the soaring method is only favorable for larger birds, but some smaller birds, such as the warbler, also prefer soaring rather than flapping. This flight behavior can generally be observed during the migration of many species of birds, where they can be seen gliding in the air for an extended duration without any movement of their wings or tails.

The aerodynamics of birds’ soaring is explained by the lift force. The cross-sectional shape of the wing while fully extended is such that air is directed downward when the bird flies forward (Tobalske, “Biomechanics of bird flight”); following Newton’s third law, a reaction force with direction opposite of the fluid going downwards is created, which lifts the bird upwards. This can also be explained by another phenomenon: as the air goes above the wing, it accelerates, while the air flowing under the wing decelerates because of how the wing is shaped. Following Bernoulli’s principle, the air flowing under the wing generates a higher pressure than the air flow above it. This difference in pressure lifts the wing, or the body above, perpendicular to the direction of the air flow (“Bernoulli’s Principle” | Flight Safety Foundation | SKYbrary Aviation Safety, 2017) (Fig. 4). Additional net lift may come from airflow around the bird’s body in some species, especially during intermittent flight while the wings are folded or semi-folded.

However, birds cannot stay at a constant height when only soaring, as they are constantly subjected to their weight, drag and air friction which slows them down and lowers their flight altitude over time. In fact, a sink rate can be assigned to each different species of bird (Cutler, 2015). As the name suggests, this measures the rate at which a bird loses altitude per a unit of time while soaring. Both the wing loading, which is the ratio of the bird’s weight to its wings’ surface area, and the wing aspect-ratio, which is the ratio of length to width of the wing, are factors that affect the rate of sinking. A lower wing loading suggests that either the bird is less prone to the force of weight, as its mass is small, or the bird has large wings, which improves the impact of lift on the bird, resulting in a smaller sink rate (Cutler, 2015). In contrast, a low wing aspect-ratio generates greater drag, therefore increasing the rate of sinking. Additionally, high pressure air flowing under the wing of a bird tends to flow upwards at the tip of the wings creating air turbulence around the wing, which disturbs the flow of air above and under the wing, also reducing lift and increasing drag. For broad wings, the volume of high-pressure air is larger, thus increasing the flow disturbance and resulting in a more important drag (Cutler, 2015). Correspondingly, birds with a small wing loading and a high aspect-ratio are usually more favored for soaring and lose altitude at a slower rate.

Even so, birds can use their environment to gain altitude during their flight while only soaring. Birds take advantage of rising columns of hot air present in the atmosphere, referred to as thermal updrafts, or of wind currents flowing upwards over hills and mountains (Akos et al., 2010). Thermal updrafts are caused by solar radiation heating a certain place, which in turn heats up the air around it, causing it to rise. Birds then spread their wings and gain height by circling in those thermal drafts (Fig. 6). The size of those circles depends again on their wing loading and wing aspect-ratio (Akos et al., 2010). The radius of the circle they form when rising in thermals is usually linearly proportional to their wing loading (Fig. 7), which means heavier birds follow a larger circle path. However, some large birds with a low wing aspect ratio rise in smaller circles, granting them more maneuverability over their path (Akos et al., 2010). The altitude gained from circling in thermals also increases the potential energy of the bird, which would increase the maximum velocity that can be attained during a dive. After reaching their desired height, birds then soar, slowly losing their altitude based on their sinking rate until they reach the next thermal updraft or engage in a dive path for different purposes (Akos et al., 2010). Peal (1880) noted that birds, weighing about 20 to 40 lbs, usually flap until they reach an altitude of 100 to 200 feet, where they will start to soar if there exists a breeze or a wind. The principle is to find air that rises faster than the bird sinking so that each lap of the spiraling pattern gives them a 10 to 20 feet rise (Peal, 1880). Following this flight behavior, birds can fly over long distances while using minimal to no energy for transport.

## Case Studies

### Zebra Finches

The zebra finch (Fig. 8) is a bird native to the dry grasslands of Australia. Its flight style is distinct in that it uses flap-bounding when flying at all speeds, compared to many birds that switch between flap-gliding at slow speeds and flap-bounding at fast-speeds. There are two long-standing hypotheses used to explain why some bird species prefer flap-bounding: the ‘fixed-gear hypothesis’ and the ‘body-lift hypothesis’.

The fixed-gear hypothesis suggests that size-related constraints on wing anatomy and on the diversity of fiber types in the pectoralis restrict small birds to a single, fixed level of power output per flap. Consequently, the hypothesis predicts that small birds cannot adapt their wingbeat kinematics or gait to optimize energy costs for different flight speeds and that the only way to vary their mean power output is to use intermittent bounds. In an in-depth study conducted on zebra finches flying at a wide range of speeds, Tobalske and colleagues (“Kinematics of flap-bounding flight in the zebra finches”) found changes in the angular velocity of the wing (Fig. 9), likely indicating that contractile velocity in the pectoralis varies with flight speed. This contradicts the fixed-gear hypothesis. They also note that differences in wingbeat kinematics between species seem to depend more on wing design factors, including aspect ratio and skeletal proportions, rather than pectoralis muscle fiber composition. As a result, they suggest that the fixed-gear hypothesis should be altered to remove muscle physiology and emphasize the constraints due to wing anatomy (Tobalske et al., “Kinematics of flap-bounding flight in the zebra finches”).

The ‘body-lift hypothesis’, on the other hand, says that partial weight-support created by body and tail lift during bounds make flap-bounding more energetically efficient. Body lift is the upward vertical force that can be generated from air flowing over the bird’s body during a flexed wing bound. Tobalske and colleagues (“Kinematics of flap-bounding flight in the zebra finches”) found that the magnitude of body lift in zebra finches depends strongly on flight speed: body lift was generated during bounds at speeds from 4 m/s to 14 m/s (the highest speed that the birds could fly), reaching a maximum of 0.0206 N or 15.9 % of body weight at 10 m/s. In contrast, at 2 m/s, body lift generated approximately 0 N of force (Fig. 10a). The researchers also looked at body lift to drag ratios. This ratio decreased from 3.10 to 0.77 as flight speed increased from 4 m/s to 14 m/s (Fig. 10c). Above 10 m/s, there was also a slight decrease in both body lift and drag. These variations in the ratio of body lift to drag suggest that zebra finches purposefully change the aerodynamic function of their bounds according to flight speed — likely by adjusting their body angle during the bound as evidenced in Fig. 11: — they accentuate body lift around speeds of 4 m/s, but prioritize a reduction in body drag at the slight expense of body lift at speeds over 12 m/s.

The study found that flap-bounding seemingly offered an aerodynamic advantage over continuous flapping between flight speeds of 6 m/s to 14 m/s. Energy costs are highest when hovering and flying at low speeds. As speed increases, the percentage of time spent flapping in a flap-bound cycle decreases as the bird takes greater advantage of body lift. Thus, the mechanical cost of flying is likely lowest at faster flight speeds (about 10 m/s to 14 m/s).

Another key constraint that could explain flap-bounding is the high cost of muscle activation. As Usherwood (2016) proposes, the premise is that small birds will sacrifice many aspects of mechanical efficiency – where the most efficient flight would be level and steady – to increase the duration of muscle contraction and reduce muscle activation demands. This results in a preference for high-amplitude downstrokes during flapping and ‘excessively’ long wings (Usherwood, 2016). Shorter wings would allow for steadier, and thus more aerodynamically efficient flight. However, for shorter wings to produce enough flap velocity and thrust, they would need faster wingbeat cycles, meaning briefer downstrokes, smaller muscle contraction durations, and higher muscle activation costs. On the other hand, flapping with ‘excessively long wings’ and high-amplitude flaps results in an excessive aerodynamic impulse on each downstroke, which then has to be balanced either with aerodynamically inactive upstrokes or with long bounds. As such, the latter method of flight is favorable, probably because it extends the duration of muscle contractions and reduces muscle activation costs (Usherwood, 2016).

### Hummingbirds

One of the key characteristics that make hummingbirds (Fig. 12) so unique is their flying style. Hummingbirds mainly use the hovering method to migrate, incorporated with the forward flying method. Hovering flight (also known as the flapping flight) is done by inducing lift through the action of flapping, which demands a great amount of energy. There are many aspects to consider in understanding their specific flying technique as well as their design constraint that withstands this energetically costly flying method (Altshuler and Dudley, 2003).

Hummingbirds use prolonged hovering methods to fly at a high elevation, where there is less oxygen and air density. This method is utilized by hummingbirds due to their ability to manipulate their wingbeat frequency and their stroke amplitude (Fig. 13). In the laboratory, it was found that hummingbirds increased stroke amplitude and wingbeat frequency to endure lowered air density in constant oxygen partial pressure (Altshuler and Dudley, 2003). In a condition of decreased oxygen partial pressure with constant air density, hummingbirds were able to control the wingbeat frequency and reduce it until they could no longer produce enough vertical forces to counterbalance the body weight. Additionally, in a condition where the air density was decreased with the oxygen increased, the hummingbirds could stabilize the wingbeat kinematics due to the additional oxygen level (Altshuler and Dudley, 2003).

Unlike other birds, hummingbirds can generate lift from both the upstroke and the downstroke using a figure-eight pattern. The type of strokes in hummingbirds is extremely important due to its asymmetry in forces (Tobalske et al., “Three-dimensional kinematics of hummingbird flight”). It was found that hummingbirds generate only 25 % of their weight support during the upstroke and 75 % during the downstroke. This means that the wing kinematics and aerodynamics associated with each type of stroke is asymmetrical, creating disparity in the movement at the wrist of each stroke and the stroke-plane angle (Fig. 14). The upstroke starts with wrist elevation and the downstroke starts with wrist depression (Tobalske et al., “Three-dimensional kinematics of hummingbird flight”). Even though hummingbirds fly with upstrokes and downstrokes in relation to their body, their wings flap sideways in relation to the ground because they typically hold their bodies upright when they are flying. Consequently, they gain lift by inverting their wings moderately, ensuring that the aerofoil points in the appropriate direction (Fig. 15). This flying style resembles large insects greatly and can be achieved in hummingbirds due to their experiences with sustained hovering flight (Warrick et al., 2005).

The size of the bird also cannot be disregarded in hovering, since it is commonly observed that flight performance generally degrades with increases in size. In hummingbirds, most sizes have similar wing stroke velocity despite their differences in body mass. However, an increase in size means that they have relatively longer wings and may induce more muscle power and increase their load-lifting capacity (Chai and Millard, 1997). Size is usually correlated to aerodynamics and wing mechanics, so different bird species can adopt various wing designs and body patterns to accommodate their constraints. Nevertheless, all hummingbirds become potent aerial competitors to compete for the resources they need to survive.

Condor

Condor birds (Fig. 16) are one of the largest flying birds. They are also known as the world’s heaviest soaring birds. In fact, their wingspan is between 2.9 m and 3.2 m. From beak to tail, their body is about 1.2 m long and they can weigh up to 15 kg (Coll, 2016). These birds face limitations in flight performance due to their body weight and their flying design is very energy demanding. Even with their impressive wingspan, condors can have a tough time staying aloft when in flight, because of their massive weight (Coll, 2016). However, condors can sustain soaring across a wide range of wind and thermal conditions like in mountainous regions, where they can glide effortlessly on the air currents of windy areas and on thermal air currents, taking advantage of rising hot air. For instance, Andean Condors can soar up to a height of 5 500 m using air currents. In other words, soaring requires updrafts of air. Indeed, for the largest flying birds, the dependence on soaring is such that their geographical distribution appears to be linked to, and potentially constrained by, the availability of updrafts (Williams et al., 2019).

Large birds tend to mostly soar because the selective pressure to extract kinetic and potential energy from the aerial environment is related to the costs of powered flight, which increase more or less proportionately with body size. Remarkably, condors flap for approximately only 1 % of their flight time, specifically during takeoff and when close to the ground (Williams et al., 2019). Nonetheless, even in winter conditions with weak thermals, condors are only predicted to flap for approximately two seconds per kilometer. Therefore, the overall flight effort in the largest soaring birds appears to be constrained by the requirements for takeoff (Williams et al., 2019). Researchers conclude that take-offs, which require about 3.3 minutes of flapping, use about the same amount of energy as 50 minutes of soaring. Since take-off demands a lot of energy, condor birds are constrained by the location of their landing: landing depends on several factors such as the altitude and environment in which they land, and if the location provides the potential of finding food (Williams et al., 2019).

The disparity between the metabolic costs of soaring and flapping increases with animal mass, so that for large birds, the cost of flapping flight is predicted to be some 30 times greater than resting metabolic costs. Furthermore, birds are likely to modulate their use of flapping flight by simply choosing to not fly in suboptimal conditions. However, the “negative consequence” of gliding is being a relatively slow form of travel (Williams et al., 2019).

## Albatross

Albatrosses (Fig. 17), like seagulls, are also one of the largest species of birds in existence. They also possess the longest wingspan among birds, reaching a length of up to 3.7 m (12 ft) while having relatively narrow wings. This translates to a high aspect-ratio and a high wing loading, which discourages flapping, as the large weight of the albatross induces a higher energy cost for flapping, and encourages soaring, as its slender wings causes less high-pressured air to flow over the wings and form turbulences (Sachs, “Minimum wind strength required for dynamic soaring of albatrosses”).

Remarkably, albatrosses travel immense distances overseas with minimal to zero energy cost related to movement: some wandering albatrosses, one of the species of albatrosses, have been observed to travel more than 5 000 km per week over the seas while looking for a place to land or hunt, relying on wind alone. As thermal updrafts are sometimes rare over the large ocean, albatrosses have developed a different soaring method (Sachs, “Minimum wind strength required for dynamic soaring of albatrosses”).

When thermal soaring is not used, albatrosses can be observed flying following a 4-step pattern around 20 m above sea water level (Sachs, “Minimum wind strength required for dynamic soaring of albatrosses”). The wind shear (wind gradient) next to the sea level is as follows: the wind force and velocity is close to zero at sea level because of the friction with the water and they increase the further they are in altitude from sea level. Initially, the albatross starts climbing upward, facing a direction almost opposite to the wind velocity and starts gaining altitude and speed generated from an increase in lift force. The albatross then turns, keeping his current speed as the constant wind velocity balances out the drag suffered by the bird. The bird then starts its descent: the bird gains kinetic energy as it loses its potential energy, balancing out the slower wind speed next to the water. Lastly, the bird engages in a turn at low altitude, losing a bit of its speed and the loop starts again. This whole process is defined as dynamic soaring, and it can be repeated practically an infinite amount of time if done efficiently (Fig. 18).

We can note that the degree of the turn varies depending on the wind condition. Following Rayleigh’s wind model (Rayleigh, 1883, as cited in Bousquet et al., 2017), where the wind does not follow a gradient, but rather an area where there is wind and one where there is not (next to sea level), the bird takes a 180° half-turn for a zero-energy loss overall travel, following an oscillating trajectory. However, following new research and observations (Bousquet et al., 2017), a wind gradient is created by the friction of the water and the volume of air moved by the waves. This forms a shear layer between the slow or absence of wind layer and the wind stream layer. The overall wind speed in this gradient can be estimated by the following equation:

W(z)={W_0\over (1+exp({-z\over \delta}))}

(3)

where W0 is the typical wind speed in that region, z is the altitude where the wind is measured and δ is the length to scale ratio (Fig. 19). In this case, albatrosses take smaller turns, around 50° to 70°, having a somewhat oscillating trajectory and following a path slightly at angle to the perpendicular direction of the wind velocity (Bousquet et al., 2017). The shape and length of these turns also varies depending on the scale of the wind gradient: larger gradients give room to longer and smoother turns, therefore more controlled dynamic soaring while small wind gradient translates into minimal turns and almost a straight fly path (Fig. 20).

Thus, albatrosses have adapted well to their large aspect-ratio, using their long wings to catch the maximum volume of wind for lifting and their narrow wings to minimize the overall drag during the process. With the alternation of these 2 flight behaviors, thermal soaring and dynamic soaring, albatrosses can roam over immense distances using dynamic soaring to find prey or explore new areas, until they reach a thermal updraft to gain altitude and return to their nests (Bousquet et al., 2017)

### Peregrine Falcon

The peregrine falcon (Fig. 21) is a crow-sized bird of prey. Like eagles, they need to hunt for their food, which can vary from small mammals like rabbits to other smaller birds. As these prey can be very agile and difficult to catch, peregrine falcons, as well as other birds of prey, have been observed to dive at impressive speeds to perform a swift attack or catch their prey. In fact, peregrine falcons are the fastest fliers among birds, with the ability to reach speeds of up to 320 km/h when diving (“Peregrine Falcon” | All About Birds | Cornell Lab of Ornithology, n.d.).

Falcons can achieve those high speeds by changing the overall shape of their wings. This is known as wing morphing. When retracting or contracting their wings and varying their angle, birds achieve different aerodynamics which help them increase their speed (“Peregrine Falcon” | All About Birds | Cornell Lab of Ornithology, n.d.).

To catch their prey, falcons usually start by increasing their altitude. This can be done by either thermal soaring, if a thermal updraft is present, or by flapping their wings when needed. The bird, upon reaching the desired altitude, starts to increase its speed by flapping its wings, where it can reach almost 150 km/h in a horizontal flight (Ponitz et al., 2014). Peregrine falcons then start steepening their angle of descent, reaching an ideal 15° from the vertical line normal to the ground surface, and contracting their wings. As their wings bend in a special V-shape, with the open end next to the head and the tip of it at the tail (Fig. 22), two things happen: the sum of all forces acting on the wings result in a lift normal to the body of the bird, perpendicular to the angle of diving. This translates, during a dive, to a lift force that is 15° up from the ground surface, increasing the velocity of the bird (Ponitz et al., 2014).

What is more, as the wings are cupped, the air flowing under the wings is more pressurized than during soaring, this causes a much greater lift force (Tucker, 1998) (Fig. 23) while also practically negating the effects of air flow turbulences: the highly pressurized air cannot flow over the wings at the tips, as they bend towards the body. The increase in velocity is also explained by the potential and kinetic energy. As the falcon loses its potential energy during a dive due to the gradual loss of altitude, this transforms into kinetic energy, which means an increase in the bird’s velocity (Tucker, 1998).

Falcons keep a relatively great maneuverability over their flight path when diving, as their short wingspan, resulting from bent wings, allows for swift turns. At the end of a dive, falcons can also quickly switch from diving to a steep climb by orienting their bodies and wings upwards and by widening their wings. This rapid change of angles causes a great lift and drag force, carrying the bird upwards. This serves as a way to gain back altitude if the bird’s objective was missed or to slow down its velocity (Tucker, 1998).

## Conclusion

Flapping and soaring are both essential parts of bird flight, and they both have their own advantages, disadvantages, and related design constraints. Some advantages of flapping are the ability to overpower drag as well as induce a forward thrust, making it indispensable for take-off, landing, and maneuverability in the air. However, flapping and producing thrust demands a lot of energy. On the other hand, soaring requires no additional power output and uses a lesser basal metabolic rate (BMR), hence producing energy-saving lift. As a result, in theory, birds can fly much longer distances using soaring compared to continuous flapping.  The disadvantages of soaring are that it depends more on wind currents and thermal updrafts to sustain. In addition, soaring and gliding tend to be slower than flapping.

Flight efficiency is strongly influenced by several factors such as body mass, muscle power-output, and the aerial environment through which animals travel. For instance, body mass can be seen as both an advantage for small flapping birds, like zebra finches and hummingbirds, and a disadvantage for large heavy birds like condor birds and albatrosses, as a larger mass increases the energy demands for flight. Mass, more specifically muscle mass, is also related to the power output of muscles, which affect a bird’s maneuverability in the air, and their preferred flight-style. For example, according to the fixed-gear hypothesis, a small bird’s power output is limited by size-related anatomical and muscle fiber composition constraints that make flap-bounding the only suitable flight style for them. Furthermore, the environment and climate constrain some birds’ location of flight. As previously stated, soaring birds like the albatross and condor prefer areas with strong wind currents and updrafts. Particularly, condor birds mostly fly in warm rising air using thermal soaring while albatrosses use strong winds found over the sea or ocean for dynamic soaring.

Through natural selection, birds have evolved a range of physiological and morphological traits in response to these constraints, including unique anatomy and morphology, the ability to morph their wings, and migration preferences. Anatomy and morphology — shape, size, bone structure — provide inherent aerodynamic and energy advantages. For example, many small birds’ wings have a larger ‘hand’ portion for better maneuverability, and small flap-bounding birds, like the zebra finch have ‘excessively’ long wings to reduce muscle activation costs, and their bodies are shaped such that they can produce lift during flexed-wing bounds. Meanwhile, larger soaring birds, like the condor and albatross have wings with a larger ‘arm’ portion. Regarding the ability to morph their wings, small birds readily morph between flapping, bounding and gliding positions, and larger birds morph between flapping, soaring, and diving positions. Notably, the peregrine falcon changes the shape and angle of its wings to achieve incredible speeds while diving. In terms of migration, flapping is used in time-selected migration, whereas soaring is used in energy-selected migration.

Energy expenditure and drag reduction are, as well, major factors that play a role in all other mentioned constraints. It determines the efficiency of flapping, soaring, take-off and landing methods. Birds adapt and adjust to all these various constraints, streamlining their wing aerodynamics to best fit the situation and the purpose of their flight.

## References

Akos, Z., Nagy, M., Leven, S., & Vicsek, T. (2010). Thermal soaring flight of birds and unmanned aerial vehicles. Bioinspir Biomim, 5(4), 045003. doi:10.1088/1748-3182/5/4/045003

Altshuler, D. L., & Dudley, R. (2003). Kinematics of hovering hummingbird flight along simulated and natural elevational gradients. Journal of Experimental Biology, 206(Pt 18), 3139-3147. doi:10.1242/jeb.00540

Baudinette, R. V., & Schmidt-Nielsen, K. (1974). Energy cost of gliding flight in herring gulls. Nature, 248(5443), 83-84. doi:10.1038/248083b0

Bousquet, G. D., Triantafyllou, M. S., & Slotine, J.-J. E. (2017). Optimal dynamic soaring consists of successive shallow arcs. Journal of The Royal Society Interface, 14(135), 20170496. doi:doi:10.1098/rsif.2017.0496

Chai, P., & Millard, D. (1997). Flight and size constraints: hovering performance of large hummingbirds under maximal loading. Journal of Experimental Biology, 200(Pt 21), 2757-2763.

Chin, D. D., & Lentink, D. (2019). Birds repurpose the role of drag and lift to take off and land. Nature Communications, 10(1), 5354. doi:10.1038/s41467-019-13347-3

Cutler, C. (2015). How Does Aspect Ratio Affect Your Wing? Retrieved from https://www.boldmethod.com/learn-to-fly/aircraft-systems/how-does-aspect-ratio-affect-a-wing/

Dvořák, R. (2016). Aerodynamics of bird flight. EPJ Web of Conferences, 114, 01001. Retrieved from https://doi.org/10.1051/epjconf/201611401001

Foundation, F. S. (2017, 29 Jul 2017). Bernoulli’s Principle. Retrieved from https://www.skybrary.aero/index.php/Bernoulli%27s_Principle

Gill, F., Rand, A. L., & Storer, R. W. (2020). Bird. Retrieved from https://www.britannica.com/animal/bird-animal

Jackson, B. E., & Dial, K. P. (2011). Scaling of mechanical power output during burst escape flight in the Corvidae. Journal of Experimental Biology, 214(3), 452-461. doi:10.1242/jeb.046789

Lau, G. (2017). Faucon pèlerin. In (Vol. 1575 x 1050, pp. Immature. ). Macaulay Library: Cornell Lab of Ornithology. Retrieved from https://macaulaylibrary.org/asset/54334451

Long, L. N., & Fritz, T. E. (2004). Object-Oriented Unsteady Vortex Lattice Method for Flapping Flight. Journal of Aircraft, 41(6), 1275-1290. doi:10.2514/1.7357

Merck, J. (2017). The Biomechanics of Flight. Retrieved from https://www.geol.umd.edu/~jmerck/geol431/lectures/d12wflight.html

Ornithology, C. L. o. (n.d.). Peregrine Falcon. Retrieved from https://www.allaboutbirds.org/guide/Peregrine_Falcon/overview

Pancamo, D. (2011). Float like a Hummingbird. In. Flickr. Retrieved from https://www.flickr.com/photos/pancamo/6174177658/

Peal, S. E. (1880). Soaring of Birds. Nature, 23(575), 10-11. doi:10.1038/023010b0

Pennycuick, C. J. (1972). SOARING BEHAVIOUR AND PERFORMANCE OF SOME EAST AFRICAN BIRDS, OBSERVED FROM A MOTOR-GLIDER. Ibis, 114(2), 178-218. doi:https://doi.org/10.1111/j.1474-919X.1972.tb02603.x

Ponitz, B., Schmitz, A., Fischer, D., Bleckmann, H., & Brücker, C. (2014). Diving-flight aerodynamics of a peregrine falcon (Falco peregrinus). PloS One, 9(2), e86506-e86506. doi:10.1371/journal.pone.0086506

Quintanilla, E. (2016). Condor des Andes. In (Vol. 5456 x 3632, pp. Adult female. ). Macaulay Library: Cornell Lab of Ornithology.

Rayleigh. (1883). THE SOARING OF BIRDS. Nature, 27(701), 534-535. doi:10.1038/027534a0

SACHS, G. (2005). Minimum shear wind strength required for dynamic soaring of albatrosses. Ibis, 147(1), 1-10. doi:https://doi.org/10.1111/j.1474-919x.2004.00295.x

Sachs, G. (2013). Wind effects on bounding flight. Journal of Theoretical Biology, 316, 35-41. doi:10.1016/j.jtbi.2012.08.039

Sullivan, B. (2009). Albatros hurleur (exulans). In (Vol. 2500 x 1500). Macaulay Library: Cornell Lab of Ornithology. Retrieved from https://macaulaylibrary.org/asset/60808561

Tobalske, B. W. (2007). Biomechanics of bird flight. Journal of Experimental Biology, 210(Pt 18), 3135-3146. doi:10.1242/jeb.000273

Tobalske, B. W. (2016). Evolution of avian flight: muscles and constraints on performance. Philosophical Transactions of the Royal Society B: Biological Sciences, 371(1704), 20150383. doi:doi:10.1098/rstb.2015.0383

Tobalske, B. W., Peacock, W. L., & Dial, K. P. (1999). Kinematics of flap-bounding flight in the zebra finch over a wide range of speeds. Journal of Experimental Biology, 202 (Pt 13), 1725-1739.

Tobalske, B. W., Warrick, D. R., Clark, C. J., Powers, D. R., Hedrick, T. L., Hyder, G. A., & Biewener, A. A. (2007). Three-dimensional kinematics of hummingbird flight. Journal of Experimental Biology, 210(13), 2368-2382. doi:10.1242/jeb.005686

Tucker, V. A. (1998). Gliding flight: speed and acceleration of ideal falcons during diving and pull out. Journal of Experimental Biology, 201(Pt 3), 403-414.

Usherwood, J. R. (2016). Physiological, aerodynamic and geometric constraints of flapping account for bird gaits, and bounding and flap-gliding flight strategies. Journal of Theoretical Biology, 408, 42-52. doi:10.1016/j.jtbi.2016.07.003

Warrick, D. R., Tobalske, B. W., & Powers, D. R. (2005). Aerodynamics of the hovering hummingbird. Nature, 435(7045), 1094-1097. doi:10.1038/nature03647

Wiley, C. (2010). Diamant mandarin (castanotis). In (Vol. 3698 x 2465, pp. Adult male. ). Macaulay Library: Cornell Lab of Ornithology. Retrieved from https://macaulaylibrary.org/asset/38358341?__hstc=60209138.2f3f33a24b44870ec4a577029c49e44b.1615766400041.1615766400042.1615766400043.1&__hssc=60209138.1.1615766400044&__hsfp=81092585

Williams, H. J., Shepard, E. L. C., Holton, M. D., Alarcón, P. A. E., Wilson, R. P., & Lambertucci, S. A. (2020). Physical limits of flight performance in the heaviest soaring bird. Proceedings of the National Academy of Sciences, 117(30), 17884-17890. Retrieved from https://www.pnas.org/content/pnas/117/30/17884.full.pdf