From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> VII. MORPHOLOGY OF TAILS <s> 1. 1. The centre of area of the wings of a Harris' hawk gliding freely in a wind tunnel moved forward 0.09 wing chord lengths when the hawk increased its wing span from 0.68 to 1.07 m. The movement of the centre of area probably produces a positive pitching moment that, if unopposed, would cause the bird's head to rise. The tail remained folded until wing span reached 87% of maximum and then began to spread. This behaviour is also typical of gliding birds in nature, which spread their tails when the wings are near maximum span. Tail spreading probably produces a negative pitching moment that compensates for the forward movement of the wings at maximum span. ::: ::: 2. 2. As the tail spread, its centre of area moved backwards. This movement, together with the increase in tail area, can keep the centre of area of the combined wings and tail from moving forward, even at maximum wing span. ::: ::: 3. 3. The tail can generate an estimated 10% of the hawk's total lift at maximum wing span and 5 % or less at shorter wing spans. ::: ::: 4. 4. I moved the centre of area of the hawk's wings forward experimentally by clipping 76 mm from primary feathers 6–10 and 38 mm from primary feather 5. The effect of this operation on the hawk's behaviour indicated that the forward movement of the centre of area of the wings caused a positive pitching moment. The hawk pitched up more in flight. It held its wings at shorter than normal spans, which partially compensated for the effects of clipping by moving the centre of area of the wings backwards. It also spread its tail at shorter than normal spans, which would compensate for an increase in the pitching moment of the wings. <s> BIB001 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> VII. MORPHOLOGY OF TAILS <s> The aerodynamic properties of a bird’s tail, and the forces produced by it, can be predicted by using slender lifting surface theory. The results of the model show that unlike conventional wings, which generate lift proportional to their area, the lift generated by the tail is proportional to the square of its maximum continuous span. Lift is unaffected by substantial variations in tail shape provided that the tail initially expands in width along the direction of flow. Behind the point of maximum width of the tail the flow is dominated by the wake of the forward section. Any area behind this point therefore causes only drag, not lift. The centre of lift is at the centre of area of the part of the tail in front of the point of maximum width. The moment arm of the tail, about its apex, is therefore more than twice the moment arm of a conventional wing about its leading edge. The drag of the tail is a combination of induced drag proportional to lift, and profile drag proportional to surface area. Induced drag can be halved by drooping the outer tail feathers to generate leading edge suction. This may be used for control, particularly in slow flight when both wings and tail are generating maximum lift. The slender lifting surface model is very accurate at angles of attack below about 15°. At higher angles of attack vortex formation at the leading edge can stabilize the flow over the tail and thereby generate increased lift by a detached vortex mechanism. Asymmetry in the orientation of the leading edges with relation to the freestream (either in roll, yaw or caused by asymmetry in the planform) is amplified in the flow field and leads to large rolling and yawing forces that could be used for control in turning manoeuvres. The slender lifting surface model can be used to examine the effect of variations in tail shape and tail spread on the aerodynamic performance of the tail. A forked tail that has a triangular planform when spread to just over 120° gives the best aerodynamic performance and this may be close to a universal optimum, in terms of aerodynamic efficiency, for a means to control pitch and yaw. However, natural selection may act to optimise the performance of the tail when it is not widely spread. The tail is normally only widely spread during manoeuvres, or at low speeds, selection may act to improve the efficiency of the tail when it is spread to only a relatively narrow angle - for example to maximize the bird’s overall lift to drag ratio - the optimum shape at any angle of spread is that which gives a straight trailing edge to the tail. This will always give a slightly forked planform, but fork depth will depend on how widely the tail is spread when selection acts, and this depends on the criteria for optimization under natural selection. A forked tail is more sensitive to changes in angle of attack and angle of spread, than other tail types. Forked tails are more susceptible to damage than other tail morphologies, and suffer a greater loss of performance following damage. Forked tails also confer less inherent stability than any other type of tail. Aerodynamic performance may not be an im portant optimization criterion for birds that fly in a cluttered environment, or do not fly very much. Natural selection, under these conditions, may favour tails of other shapes. The aerodynamic costs of sexually selected elongated tails can be predicted from the model. These predictions can be used to distinguish between the various models for the evolution of elongated tails. Elongated graduated tails and pintails could have evolved either through a Fisherian or H andicap mechanism. The evolution of long forked tails can be initially favoured by natural selection, the pattern of feather elongation seen in sexually selected forked tails is predicted by the Fisher hypothesis (Fisher 1930) but not by any of the other theories of sexual selection. <s> BIB002 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> VII. MORPHOLOGY OF TAILS <s> Variation with tail spread of the lift generated by a bird tail was measured on mounted, frozen European starlings (Sturnus vulgaris) in a wind tunnel at a typical air speed and body and tail angle of attack in order to test predictions of existing aerodynamic theories modelling tail lift. Measured lift at all but the lowest tail spread angles was significantly lower than the predictions of slender wing, leading edge vortex and lifting line models of lift production. Instead, the tail lift coefficient based on tail area was independent of tail spread, tail aspect ratio and maximum tail span. Theoretical models do not predict bird tail lift reliably and, when applied to tail morphology, may underestimate the aerodynamic optimum tail feather length. Flow visualization experiments reveal that an isolated tail generates leading edge vortices as expected for a low-aspect ratio delta wing, but that in the intact bird body-tail interactions are critical in determining tail aerodynamics: lifting vortices shed from the body interact with the tail and degrade tail lift compared with that of an isolated tail. <s> BIB003 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> VII. MORPHOLOGY OF TAILS <s> Using three-dimensional infrared high-speed video, we captured the wing and body kinematics of free-flying fruit flies as they performed rapid flight maneuvers. We then “replayed” the wing kinematics on a dynamically scaled robotic model to measure the aerodynamic forces produced by the wings. The results show that a fly generates rapid turns with surprisingly subtle modifications in wing motion, which nonetheless generate sufficient torque for the fly to rotate its body through each turn. The magnitude and time course of the torque and body motion during rapid turns indicate that inertia, not friction, dominates the flight dynamics of insects. <s> BIB004 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> VII. MORPHOLOGY OF TAILS <s> Abstract Bird tails, which are an aerodynamic surface in the horizontal plane, are treated with regard to their effects on yaw stability. Reference is made to wings of very small aspect ratio similar to the values of bird tails in order to identify features which are significant for the aerodynamic yawing moment characteristics due to sideslip. It is shown that there are yawing moments of considerable magnitude for this aspect ratio region. Furthermore, the lift coefficient, which also exerts an influence, is included in the treatment of yaw stability. To show more concretely the addressed effects for birds, the yawing moment characteristics of the wing–tail combination of a pigeon, which is considered as a representative example, are treated in detail. For this purpose, a sophisticated aerodynamic method capable to deal with the mutual flow interactions between the tail and the wing is used to compute results of high precision. The yawing moment characteristics of the pigeon wing–tail combination with respect to the sideslip angle and the lift coefficient are determined, with emphasis placed on the contribution of the tail. It is shown that there is a significant contribution of the tail to yaw stability. The findings of this paper on the contribution of the tail to the yawing moment characteristics are supported by an evaluation of existing experimental data. Furthermore, the physical mechanisms are considered which are the reasons for the stabilizing role of the tail. These effects concern the contribution of the drag acting at the tail to the yawing moment. In addition, it is shown that extended legs and feet, when exposed to the airflow, can contribute to yaw stability. <s> BIB005 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> VII. MORPHOLOGY OF TAILS <s> Flying animals exhibit remarkable capabilities for both generating maneuvers and stabilizing their course and orientation after perturbation. Here we show that flapping fliers ranging in size from fruit flies to large birds benefit from substantial damping of angular velocity through a passive mechanism termed flapping counter-torque (FCT). Our FCT model predicts that isometrically scaled animals experience similar damping on a per-wingbeat time scale, resulting in similar turning dynamics in wingbeat time regardless of body size. The model also shows how animals may simultaneously specialize in both maneuverability and stability (at the cost of efficiency) and provides a framework for linking morphology, wing kinematics, maneuverability, and flight dynamics across a wide range of flying animals spanning insects, bats, and birds. <s> BIB006 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> VII. MORPHOLOGY OF TAILS <s> Micro Air Vehicles (MAVs) with flapping wings try to mimic their biological counterparts, insects and hummingbirds, as they can combine high agility manoeuvres with precision hovering flight. Near-hovering flapping flight is naturally unstable and needs to be stabilized actively. We present a novel mechanism for pitch moment generation in a robotic hummingbird that uses wing twist modulation via flexible wing root bars. A custom build force balance, sensitive enough to measure the cycle averaged pitch moment as well as lift force, is also presented. The introduced prototype mechanism generates pitch moment of up to ± 0.5 mNm. Finally we integrate a Shape Memory Alloy (SMA) wire to actuate the wing root bar ends. We present achievable displacement versus bandwidth as well as generated pitch moment. <s> BIB007 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> VII. MORPHOLOGY OF TAILS <s> Animal fliers frequently move through a variety of perturbed flows during their daily aerial routines. However, the extent to which these perturbations influence flight control and energetic expenditure is essentially unknown. Here, we evaluate the kinematic and metabolic consequences of flight within variably sized vortex shedding flows using five Anna's hummingbirds feeding from an artificial flower in steady control flow and within vortex wakes produced behind vertical cylinders. Tests were conducted at three horizontal airspeeds (3, 6 and 9 m s−1) and using three different wake-generating cylinders (with diameters equal to 38, 77 and 173% of birds' wing length). Only minimal effects on wing and body kinematics were demonstrated for flight behind the smallest cylinder, whereas flight behind the medium-sized cylinder resulted in significant increases in the variances of wingbeat frequency, and variances of body orientation, especially at higher airspeeds. Metabolic rate was, however, unchanged relative to that of unperturbed flight. Hummingbirds flying within the vortex street behind the largest cylinder exhibited highest increases in variances of wingbeat frequency, and of body roll, pitch and yaw amplitudes at all measured airspeeds. Impressively, metabolic rate under this last condition increased by up to 25% compared with control flights. Cylinder wakes sufficiently large to interact with both wings can thus strongly affect stability in flight, eliciting compensatory kinematic changes with a consequent increase in flight metabolic costs. Our findings suggest that vortical flows frequently encountered by aerial taxa in diverse environments may impose substantial energetic costs. <s> BIB008 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> VII. MORPHOLOGY OF TAILS <s> Hovering flapping flight is inherently unstable and needs to be stabilized actively. We present a control mechanism that modulates independently the wing flapping amplitude and offset by displacing joints of a flapping linkage mechanism. We demonstrate its performance by high speed camera recordings of the wing motion as well as by direct measurements of pitch moment and lift force. While flapping at 17 Hz the prototype produces 90 mN of lift and generates pitch moments from -0.7 N.mm to 1.1 N.mm. The mechanism shows low level of cross-coupling in combined pitch and roll commands. <s> BIB009 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> VII. MORPHOLOGY OF TAILS <s> Airflow conditions close to the Earth's surface are often complex, posing challenges to flight stability and control for volant taxa. Relatively little is known about how well flying animals can contend with complex, adverse air flows, or about the flight control mechanisms used by animals to mitigate wind disturbances. Several recent studies have examined flight in the unsteady von Karman vortex streets that form behind cylinders, generating flow disturbances that are predictable in space and time; these structures are relatively rare in nature, because they occur only the immediate, downstream vicinity of an object. In contrast, freestream turbulence is characterized by rapid, unpredictable flow disturbances across a wide range of spatial and temporal scales, and is nearly ubiquitous in natural habitats. Hummingbirds are ideal organisms for studying the influence of freestream turbulence on flight, as they forage in a variety of aerial conditions and are powerful flyers. We filmed ruby-throated hummingbirds ( Archilochus colubris ) maintaining position at a feeder in laminar and strongly turbulent (intensity ∼15%) airflow environments within a wind tunnel and compared their mean kinematics of the head, body, tail and wing, as well as variability in these parameters. Hummingbirds exhibited remarkably stable head position and orientation in both smooth and turbulent flow while maintaining position at the feeder. However, the hummingbird's body was less stable in turbulent flow and appeared to be most sensitive to disturbances along the mediolateral axis, displaying large lateral accelerations, translations and rolling motions during flight. The hummingbirds mitigated these disturbances by increasing mean wing stroke amplitude and stroke plane angle, and by varying these parameters asymmetrically between the wings and from one stroke to the next. They also actively varied the orientation and fan angle of the tail, maintaining a larger mean fan angle when flying in turbulent flow; this may improve their passive stability, but probably incurs an energetic cost as a result of increased drag. Overall, we observed many of the same kinematic changes noted previously for hummingbirds flying in a von Karman vortex street, but we also observed kinematic changes associated with high force production, similar to those seen during load-lifting or high-speed flight. These findings suggest that flight may be particularly costly in fully mixed, freestream turbulence, which is the flow condition that hummingbirds are likely to encounter most frequently in natural habitats. <s> BIB010 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> VII. MORPHOLOGY OF TAILS <s> Flapping wing micro air vehicles (MAVs) take inspiration from natural fliers, such as insects and hummingbirds. Existing designs manage to mimic the wing motion of natural fliers to a certain extent; nevertheless, differences will always exist due to completely different building blocks of biological and man-made systems. The same holds true for the design of the wings themselves, as biological and engineering materials differ significantly. This paper presents results of experimental optimization of wing shape of a flexible wing for a hummingbird-sized flapping wing MAV. During the experiments we varied the wing 'slackness' (defined by a camber angle), the wing shape (determined by the aspect and taper ratios) and the surface area. Apart from the generated lift, we also evaluated the overall power efficiency of the flapping wing MAV achieved with the various wing design. The results indicate that especially the camber angle and aspect ratio have a critical impact on the force production and efficiency. The best performance was obtained with a wing of trapezoidal shape with a straight leading edge and an aspect ratio of 9.3, both parameters being very similar to a typical hummingbird wing. Finally, the wing performance was demonstrated by a lift-off of a 17.2 g flapping wing robot. <s> BIB011 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> VII. MORPHOLOGY OF TAILS <s> An insect-like tailless flapping wing micro air vehicle (FW-MAV) without feedback control eventually becomes unstable after takeoff. Flying an insect-like tailless FW-MAV is more challenging than flying a bird-like tailed FW-MAV, due to the difference in control principles. This work introduces the design and controlled flight of an insect-like tailless FW-MAV, named KUBeetle. A combination of four-bar linkage and pulley-string mechanisms was used to develop a lightweight flapping mechanism that could achieve a high flapping amplitude of approximately 190°. Clap-and-flings at dorsal and ventral stroke reversals were implemented to enhance vertical force. In the absence of a control surface at the tail, adjustment of the location of the trailing edges at the wing roots to modulate the rotational angle of the wings was used to generate control moments for the attitude control. Measurements by a 6-axis load cell showed that the control mechanism produced reasonable pitch, roll and yaw moments according to the corresponding control inputs. The control mechanism was integrated with three sub-micro servos to realize the pitch, roll and yaw controls. A simple PD feedback controller was implemented for flight stability with an onboard microcontroller and a gyroscope that sensed the pitch, roll and yaw rates. Several flight tests demonstrated that the tailless KUBeetle could successfully perform a vertical climb, then hover and loiter within a 0.3 m ground radius with small variations in pitch and roll body angles. <s> BIB012 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> VII. MORPHOLOGY OF TAILS <s> Hovering flapping wing flight is intrinsically unstable in most cases and requires active flight stabilization mechanisms. This paper explores the passive stability enhancement with the addition of top and bottom sails, and the capability to predict the stability from a very simple model decoupling the roll and pitch axes. The various parameters involved in the dynamical model are evaluated from experiments. One of the findings is that the damping coefficient of a bottom sail (located in the flow induced by the flapping wings) is significantly larger than that of a top sail. Flight experiments have been conducted on a flapping wing robot of the size of a hummingbird with sails of various sizes and the observations regarding the flight stability correlate quite well with the predictions of the dynamical model. Twelve out of 13 flight experiments are in agreement with stability predictions. <s> BIB013
As we known, wing shape is remarkable essential since the wing shapes are directly related to flight modes. Also, the bird's tails play an important role in maintaining stability over a range of flight speeds and in generating lift and drag to help roll, pitch and yaw turning and slow flight. Bird's tails vary as much as their wings, or even more BIB002 . The tail shapes and morphology of birds are naturally selected by gender. The birds' tails have intricate and distinct shapes particular in sexually dimorphic species. Many birds have a long and elaborate tail as a sexual ornament since long and elaborate tails can enhance mating success for female choice  . However, flight performance might be constraint such ornamental diversity  . Universally, different birds select different tail shape, but they have a common feature, namely, the tails play an aerodynamic role in flight BIB001 - BIB003 , as the birds' tail directly affects stable flight, and they can use their tails to operate body turns BIB006 - BIB004 . Also, hummingbirds may use tail spreading to stabilize their posture BIB008 , BIB010 . In this section, hummingbird tail morphology and tail design and manufacture will be introduced. The detail of tails will be studied in the future. All hummingbirds have five bilateral pairs of rectrices (the tail feathers are called rectrices) that individually vary in length and shape  . The number of rectrices is marked from medial 1 to lateral  , seen in Fig. 13 . From such figure, outer tail feathers are longer than the middle pair in the forked tail, and feathers increase in length from the central pair to the outer pair. That is, 5 is the longest of rectrice, whereas 1 is the shortest one. By contrast, as for graduated tails, 1 is the longest and 5 is the shortest rectrix. All rectrices in rounded tails are of almost the same length, feathers increase in length from the outer pair to the middle pair. The length of the longest rectrix is 20% more than that of the shortest one. The maximum continuous span (MCS) is the widest distance of the unbroken surface area of a tail, from 5 to 5 on both lateral sides. The spread angle is the angle between the outermost rectrices presented by β, seen in Fig. 13 . When this angle is above a critical value, the gap between individual tail feathers has appeared. By contrast, the edges of neighbouring tail feathers overlap when this angle is smaller than the critical angle. Therefore, the tail's surface (SA)  can be roughly approximated as where, n is the average length of the tail feather. Fork ratio (FR) is an important parameter to shape the bird's tail, which is defined as defined as the 5 length divided by the 1 length, which is presented as FR = 5 length 1 length When fork ratio is higher than 2 (FR > 2), the tail shape can be roughly defined as an elongated fork tail. The optimal fork ratio is FR = 2 at β = 120 • [92], BIB002 , but this spread angle is not general. After that, it is also explored that the optimal fork ratio is 1.2 when β = 67 • . When fork ratio is in the range of 1.2 < FR < 2, the tail shape can be regarded as a moderate fork. As for the rounded tail, the fork ratio is in 0.83 < FR < 1.2, whereas the graduated tail may be achieved at FR < 0.83. Tail aspect ratio BIB005 , similar wing aspect ratio, is a measure of the shape of the tail and impacts on the aerodynamic performance. It is defined as the square tail span divided by the tail surface, which is given by where, b t is the tail span which can be calculated by b t = 2 5 sin β 2 and S t is the tail surface. Combination of Equation (11) and (13), the tail aspect ratio can be rewritten as To compare morphologies, the spread angle is hypothesized to be constant, whereas the spread angle actually varies with flight posture. To investigate the tail's aerodynamic performance, a family of the tail was built  and an experimental setup consisting of a force balance, voltage amplifiers, and a digital signal processing system (DSP) was constructed BIB011 . Its overview is illustrated in Fig. 14. In Nan's study  , the designed tail based on the mimicking hummingbird's tail is made of the balsa wood with 1 mm thickness. The tail with a maximum tail length of 70 mm is made. The designed-tails were handmade, as is shown in Fig. 15 . In total, three kinds of tails were built and tested, and the parameters are presented in Table 3 . Via studying the experiment, results show that tails VOLUME 7, 2019 can be used to stabilize the posture of birds by generating a moment  , which is similar to the presented result in BIB008 , BIB002 , so it can be applied to the FWMADs to balance the posture. This means that the posture of FWMAD can be performed via adjusting the position of the tail. In the previous study of twin-wing hovering FWMADs, however, the wing twist modulators BIB012 ,  ,  , BIB007 , BIB009 were universally applied to produce pitch and roll moment then achieved the stability of FWMADs. In addition, recent study of tail BIB013 is successfully used on passive stability of FWMADs.