How Computers and Robotics Helped Us Understand Flippers

Table of Contents


The advancement of technology has allowed researchers to develop efficient software which aids in the recognition of animals based on their flippers, conduct experiments to further examine the parameters which define the efficacy of these limbs, and manufacture robots which simulate marine animals and their flippers to deepen the understanding of the behavior and physics behind it. This report begins by detailing several computer-based programs designed to identify various marine animals, including turtles, humpback whales, and sperm whales by their flukes and flippers. Following the description of these software, the effects of tubercles on the flippers of humpback whales is examined through an experiment conducted with artificial flipper models in a low-speed closed-circuit wind tunnel to simulate the underwater environment of these whales. In another study, scientists created a biomimetic fish robot with the goal of determining the effect of an artificial fin on its performance. The report concludes with an examination of an aquatic robot modelled after a turtle, created to understand why many marine animals have two flippers instead of four.

Computer Based Identification of Marine Animals Based on their Flukes and Flippers

Accurate identification of animals is important for mark-recapture, a technique used to count the number of individuals in a given population (“Mark-Recapture” | Northern Arizona University, n.d.). This is important as it can give critical data on the migrating movements of populations and of individual animals (Katona et al., 1979). External and internal tags can be used to re-identify animals. However, external tags can degrade over time or be lost while internal tags can be quite expensive and require a specific reader. An efficient alternative is to use biometric identification (Gatto et al., 2018). The rapid development of databases and IT systems makes this approach increasingly feasible.

Turtle Flipper Identification

Green turtles, loggerhead turtles, and hawksbill turtles are often recognized by the analysis of their facial scales. However, this can disturb the turtles and even become a source of stress. Another way of identifying them is to take and analyze pictures of their flippers. As they have more scales on them, more patterns can be analysed, making them a more reliable way of identification (Gatto et al., 2018).  

In their research, Gatto et al. (2018) proceeded to turtle biometric recognition. Firstly, they took a vast number of photos of different individuals. In each, the whole flipper was photographed, to ensure that the area of interest was captured. Then, only the best pictures were entered in the APHIS database while the fuzzy ones were kept to be used as comparison pictures — among other non-blurry pictures — later in the experiment. Moreover, the same procedure that is used in the Interactive Individual Identification System (Reijns, 2020), a software that can identify animals by their physical characteristics, was used to compare the different photos. This software works by first positioning points of reference that delimitate the area of interest. In each picture, these three points of interest were chosen to be at the positions shown in Fig. 1.

Fig. 1 Reference points on the turtle flipper. [Adapted from Gatto et al., 2018]

Subsequently, other points in the area delimited by the three reference points must be chosen. Gatto et al. (2018) chose these points to be the places where the scales joined, creating a pattern that was considered as the fingerprint. Then, the scientists used the software to evaluate other pictures — comparison pictures — with the ones already entered in the database. Each picture in the database received a score, ranking how closely it matched the image in the database. The results obtained in the research were afterwards verified by the scientists: each turtle pictured was identified with a metal tag to keep track of its identity among each of them and to make sure that the pictures with the highest matching scores were images of the flipper of the same turtle (Gatto et al., 2018). If the best matching picture did not correspond to the correct turtle, the score of the correct corresponding picture was recorded. In their experiment, the APHIS database correctly identified the right individual over ninety percent of the time for olive ridley and green turtles. However, if the comparison pictures were blurry, the percentage of correct identification fell below 90 % for green turtles and under 80 % for olive ridley turtles (Gatto et al., 2018). What they concluded from the study is that, when the reference points were well placed and the pictures were clear, the APHIS software was very reliable. When the pictures were blurry, it was still relatively efficient, but when the reference points were not placed at the right positions, the software identification capacity decreased significantly (Gatto et al., 2018).

Humpback Whale Fluke Identification

Identifying humpback whales by their flukes is also possible. In the study conducted by Mizroch et al. (1990), a computer-based system that does exactly that was described. The software in question has been conceived by a collaboration of the National Marine Mammal Laboratory (NMML) and scientists studying humpback whales in the North Pacific and North Atlantic oceans. It is an advanced version of the one that was first created in 1970 by Balcomb and Katona. In the software, the program user must manually enter information about the fluke pictures based on three different criteria: the pigment pattern, the position of natural marks and scars, and the shape of the gap between the flukes (Mizroch et al., 1990). The pigment pattern comprehends the black and white motifs on the leading and trailing edge of the fluke (Fig. 2), features of the medial line, and the pigmentation of the fluke.

Fig. 2 Example of fluke patterns. [Adapted from Mizroch et al., 1990]

Further, the notches between the flukes can take various shapes such as squared and V-shaped. When the user wants to compare a new fluke photograph, they must indicate the pigment pattern, notch shape, and position of marks and scars of the photograph. There are two functions in the program: the SCAN function and the MATCH function. In the first one, the SCAN function, it only brings up the pictures of the database that have the exact same information recorded (same notch, same pigment pattern, and same natural marks). In the MATCH function, a fluke pattern similarity matrix is coded to account for the chance that a picture will be mismatched due to light contrast or angle. Every photograph gets a grade out of 20 for its similarity to the new picture’s fluke pattern. The pictures are also ranked out of 14 for the number of areas (Fig. 3) that match with specific marks and scars on the comparing picture. An overall score, on a maximum of 34 points, is obtained by adding these two values together. The software then ranks the images in the database based on how close they are to the new picture and shows the best matching pictures with their corresponding matching scores. Since there are countless humpback whales in the ocean, the number of pictures taken and inserted in the database is significant. In addition to that, each year, the number of photographs of humpback whale flukes added to the database varies between 1000 and 2000. Since the photo collection is enormous, the use of such a software greatly reduces the time that is required to compare photographs of humpback whale’s flukes. The software described above can analyse up to 54 000 pictures.

Fig. 3 Specific regions on the fluke. [Adapted from Mizroch et al., 1990]

Computer Identification of Sperm Whales by their Flukes

In his 1990 paper, Hal Whitehead describes a computer system that is very similar to the one described in the previous section. However, this one is used for the identification of sperm whales (Whitehead, 1990, as cited in Hammond et al., 2021). The goal of creating this software was to find an inexpensive method that would diminish the time required to identify sperm whales and minimize human errors throughout the process. In the program, the marks on the trailing edge of the flukes are the comparing criteria. The image of the flukes is first digitized using a scanner. Then, the user must manually enter the location of the marks on the flukes — the distance is measured from left to right — with a code describing the type of each mark encountered (Whitehead, 1990, as cited in Hammond et al., 2021) (Fig. 4).

Fig. 4 Codes for the software. [Adapted from Whitehead, 1990, as cited in Hammond et al., 2021]

In addition, other information such as the date, time and location must be provided. Once the data is fed to the computer, to spot any mistakes, the program checks that there has only been one fluke notch entered and that there is an even number of distinct nicks, waves, scallops, missing portions and invisible areas (Fig. 4). A fluke representation including the points entered by the user is then displayed on the screen (Fig. 5) to make sure that if there was any mistake, the user sees it. The software then asks if the notch is open — the two flukes are tight — or not, and if the end of the flukes are curled or not (Whitehead, 1990, as cited in Hammond et al., 2021).

Fig. 5 Marks on the sperm whale fluke. [Adapted from Whitehead, 1990, as cited in Hammond et al., 2021]   

The correct analysis of a photograph greatly depends on the resolution of the image, its orientation, and its tilt. For the program to assess the likelihood of the values entered by the user to be correct, the values of the tilt, resolution and orientation must be calculated. On the representation of the fluke that is displayed on the screen (Fig. 5), two dashed lines are drawn to indicate the prolongation of the edges of the flukes (Whitehead, 1990, as cited in Hammond et al., 2021). The point P (Fig. 5) represents the intersection of these two lines. The two points that describe the location of each fluke tip and the point P, form a triangle. The user is asked to place the mouse on the point P and right click, which keeps its coordinates in the computer’s memory. Since the values of each vertex of the triangle are known, the orientation angle and the tilt can be calculated by analyzing how much the triangle should be turned and rotated to obtain a symmetrical triangle. The resolution of the image is obtained by dividing the length of the two flukes by the number of pixels that separate them. These values are stored for each image entered so the user has an idea of the quality of the picture that was taken (Whitehead, 1990, as cited in Hammond et al., 2021).

To compare a new photograph with the existing images in the database, a similarity matrix (Fig. 6) is built (Whitehead, 1990, as cited in Hammond et al., 2021). The coordinates of the marks on the flukes of the pictures in the database are compared with the coordinates of the marks of the comparing picture. For each picture in the database, values representing how close the points of the comparing picture are to those of the database, are calculated. These values are stored in the similarity matrix. The number of descriptive information – such as if the flukes are open or closed – that match is calculated. From these values, an overall match coefficient is computed (Whitehead, 1990, as cited in Hammond et al., 2021).  

Fig. 6 Similarity matrix. [Adapted from Whitehead, 1990, as cited in Hammond et al., 2021]

The pictures in the database are compared one by one to the comparing picture and the best match is shown at the top of the screen. If the match is good, the system asks if the user wants to replace the data of the old picture or keep it (Whitehead, 1990, as cited in Hammond et al., 2021). This is decided by looking at the values that describe the quality of the image (the orientation and tilt angles, and its resolution value). As an approximate idea, a user of the interface would be able to analyze 1000 pictures of flukes in about 50 hours instead of the months that it would take if done by hand. The cost of the hardware is little compared to the amount saved by the diminution of the employee working time. The date and time associated with each picture is used to interpret the migratory movements of the whales as scientists can know where and when whales were seen (Whitehead, 1990, as cited in Hammond et al., 2021).

Simulations Examining Effects of Tubercules on the Flippers of Humpback Whales

Aquatic animals must be able to maneuver underwater to catch prey and perform a variety of other functions. To achieve movement, the animals utilize their flippers. The maneuverability and turning performance of aquatic mammals is constrained by morphology and affected by the mobility and flexibility of the animal’s body, along with the hydrodynamic characteristics and position of the control surfaces (Miklosovic et al., 2004).

For large animals, this underwater dexterity does not come easily. Baleen whales (Mysticeti), have a specialized feeding system that restricts their maneuverability and causes most of their bodies to be inflexible. The humpback whale (Megaptera novaeangliae) is unique among other Mysticetes because of its ability to perform acrobatic underwater turning maneuvers to catch prey using their extremely mobile, high-aspect-ratio flippers (Miklosovic et al., 2004). High-aspect-ratio flippers refer to flippers whose length greatly exceeds its width (Cutler, 2015). Morphological structures which further differentiate M. novaeangliae from other baleen whales are its large, rounded tubercles along the leading edge of the flipper, resulting in the scalloped appearance shown in Fig. 7 (Miklosovic et al., 2004).

Fig. 7 Scalloped-edge flipper of a humpback whale. [Adapted from Miklosovic et al., 2004]

Miklosovic et al. (2004) performed experiments to test the hypothesis that these leading-edge tubercles can modify the hydrodynamic characteristics of the flipper to increase its effectiveness in turning.

Researchers constructed two scale models of the humpback whale’s pectoral flipper, depicted in Fig. 8.

Fig. 8 Smooth (left) and scalloped (right) flipper models. [Adapted from Miklosovic et al., 2004]

One of the models possessed leading-edge tubercles while the other did not. The authors report wind tunnel measurements of the lift and drag, along with other parameters, as a function of the angle of attack of the idealized scale models (Miklosovic et al., 2004). Although there is definite variability of the size and shape of tubercles among different whales, leading the researchers to expect that details of the geometry would influence the performance of an individual flipper; the flippers were roughly modelled after the left pectoral flipper of a 9.02 m male humpback whale. The first model flipper had a smooth leading edge while the second model flipper had a scalloped leading-edge profile, approximating the pattern of the specimen flipper. The sinusoidal pattern had a distally decreasing intertubercular spacing and tubercle amplitude which was consistent with the flipper of the 9.02 m humpback whale (Miklosovic et al., 2004).

The authors constructed the flipper models based on a symmetrical NACA 0020 foil section because the cross-sectional profile of the flipper resembles conventional turbulent-flow airfoils with a maximal thickness of approximately 20 %. The model flippers were produced on a CNC mill from 3.81 cm thick clear polycarbonate, with a maximal chord of 16.19 cm and a span of 56.52 cm (Miklosovic et al., 2004).

Miklosovic et al. (2004) conducted their tests at the United States Naval Academy in the low-speed closed-circuit wind tunnel. The tests were performed at incompressible flow conditions, causing the aerodynamics to simulate the hydrodynamics of flow around the flipper. Since flippers do not oscillate during turning maneuvers, the researchers assumed only steady flow conditions in their testing. The maximum Mach number reached during the tests was 0.2 (Miklosovic et al., 2004). The Mach number refers to a dimensionless value used to analyze fluid flow dynamics where compressibility is an important factor and can be expressed by:

M=  {v\over c}


Where Mis the Mach number, v is the fluid flow speed, and c is the speed of sound (“Mach Number” | Engineering ToolBox, 2004). The vented test section had a cross section of 54 x 38 in and a length of 94 in. The experiments in the wind tunnel were performed at uncorrected Reynolds numbers, which are used to describe the viscosity of the flow in fluids, in the range of 5.05 x 105 – 5.20 x 105. The expected value of the Reynolds number (Re) for the whale is around 106 (Miklosovic et al., 2004). Although the Reynolds number applied in the researchers’ experiments is approximately half of the estimated Reynolds number for the animal, it is still well within the operating range of adult animals and close to the maximum for young animals. After conducting the tests on the effect of the Reynolds number on the measured quantities, Miklosovic et al. (2004) found that the lift coefficient was relatively insensitive to Re at moderate incidence angles.

 Both flipper models were mounted in the wind tunnel on a rotating table that changed the local pitch angle, allowing the models to be rotated through an angle of attack, , ranging from -2° to + 20° using a pitch-pause technique (Miklosovic et al., 2004). Aerodynamic forces and moments were transmitted to a platform balance that was underneath the rotating table. The test section was also equipped with pressure transducers and a thermocouple to collect real-time measurements of freestream velocity and air density. The main parameters that described the aerodynamic forces placed on the model flippers by the flow were the drag coefficient is expressed by Eq. 2 below whereas the lift coefficient is expressed by Eq. 3 below.

C_D\equiv 2D*(\rho U^2_\infin A)^{-1}


C_L\equiv 2L*(\rho U^2_\infin A)^{-1}


In the expression for the drag coefficient, D is the drag force, A is the projected planform area, U is the flow speed, and ρ is the air density. In the expression for the lift coefficient, L is the lift force, A is the projected planform area, U is the flow speed, and ρ is the air density (Miklosovic et al., 2004).

Using the smooth flipper model, the Reynolds numbers varied from 135 000 to 550 000 and the lift and drag coefficients were measured at angles of attack of 0° and 5°, and it was concluded that, although both the lift and drag coefficients demonstrate dependence at lower Reynolds numbers, when the Reynolds number did increase, very little Reynolds number dependence was observed (Miklosovic et al., 2004). The lift coefficient proved the least dependency, as it showed no sensitivity to Reynolds numbers higher than 200 000 whereas the drag coefficient approaches a constant value at Reynolds numbers above, but is never truly a constant (Miklosovic et al., 2004). The researchers expected that the stall behavior on the outboard portion of the flipper would be highly dependent on the Reynolds numbers due to its narrow tip, but after the simulation, they concluded that the Reynolds sensitivity can be assumed to be negligibly small.

Fig. 9 Data for smooth whale flipper model: (a) Wind tunnel measurement of lift coefficient as a function of the angle of attack, (b) Wind tunnel measurement of the drag coefficient as a function of the angle of attack, (c) Aerodynamic efficiency as a function of the angle of attack, (d) profile of the smooth flipper model (solid line) compared to actual flipper model (dotted line). [Adapted from Miklosovic et al., 2004]

Fig. 9a depicts the lift curve for the smooth model and shows a linear relation between the lift coefficient, CL, and the angle of attack, α, for angles below 12°. The constant slope implies that the flow is attached to the surface of the model flipper and stall is absent during this flow state (Miklosovic et al., 2004). Stall refers to a reduction in the lift coefficient generated by a foil as the angle of attack increases and exceeds the critical angle of attack (Crane, 1997). For the smooth flipper model, the critical angle of attack is 12°, and the reduction in the lift coefficient is only 13 %, which is a smaller drop than would be expected with complete leading-edge flow separation. Flow separation near distal region before flow separation near the proximal region may be the reason for the partial loss of lift. As α is increased from 12.1° to 18.5°, the lift coefficient decreases from 0.78 to 0.38 (Miklosovic et al., 2004). Fig. 9b shows the drag curve for the smooth model and indicates that stall occurs when drag increases from 0.0485 to 0.0821 over a change in the angle of attack of approximately 0.5°. Subsequently, CDDD increases more gradually from 0.0821 to 0.2226, suggesting a progression to total flow separation over the entire flipper at a larger angle of attack (Miklosovic et al., 2004). Fig. 9c illustrates the curve of aerodynamic efficiency, or the L/D ratio. The graph identifies the drag cost of producing lift, with the maximum value of L/D being 22.5 at α = 7.5°, which is considered efficient for a section having 20 % maintains L/D values greater than 20 through incidence angles of 5-10° (Miklosovic et al., 2004).     

Next, Miklosovic et al. (2004) focused on the scalloped flipper model in the wind tunnel to measure the aerodynamic performance and compare the measurements of the scalloped model to those of the smooth model.

Fig. 10 Data for scalloped whale flipper model (data points) compared to data for smooth whale flipper model (solid lines): (a) Wind tunnel measurement of lift coefficient as a function of the angle of attack, (b) Wind tunnel measurement of the drag coefficient as a function of the angle of attack, (c) Aerodynamic efficiency as a function of the angle of attack, (d) profile of the scalloped flipper model (solid line) compared to actual flipper model (dotted line). [Adapted from Miklosovic et al., 2004]

Fig. 10a shows that the lift curve for both flippers is relatively similar, although the slope of the scalloped flipper is shallower from α= 8.5° to 14.5°. Another important discovery is that the critical angle of attack, or α stall, is 16.3°, which is 40 % higher than α stall for the smooth flipper model. Further, it is important to note that CLmax is 0.93, a 6 % increase from the smooth model, which means the scalloped model has a higher range of operation, suggesting higher lift at higher incidence angles (Miklosovic et al., 2004). The drag curve of the scalloped flipper in comparison to the smooth flipper is pictured in Fig. 10b, which shows that, at low angles, the drag is similar to that of the smooth model. However, between the angles of attack of 10.3° and 11.8°, the drag of the scalloped model exceeds the drag of the smooth flipper. Nonetheless, at angles higher than 11.8° the drag of the scalloped model is consistently lower than the drag of the first model (Miklosovic et al., 2004). This discovery implies that there is a significant reduction in drag, which enables the maneuvers of the whale to be more energy efficient i.e., less energy can be used to create a greater force with the flipper. The aerodynamic efficiency of the second flipper model in comparison to the first model is pictured in Fig. 10c. As a result of the characteristics of lift and drag described above, the L/D ratio of the scalloped model is greater for most of the angles, indicating that the second flipper performs better than the first, especially at higher angles (Miklosovic et al., 2004).

To summarize the findings of the researchers, the flipper model with the scalloped leading edge delays stall by supplying greater lift at higher angles of attack and maintains higher lift with lower drag after stall. This characteristic would improve the maneuverability of the humpback whale and be very useful for feeding. Vortex generators, which are small tabs placed on the leading edge of an aircraft wing serve the purpose of energizing the flow over the wing of an aircraft to maintain or increase lift by preventing stall, may be considered structures that are analogous to tubercles as the hydrodynamic performance capabilities of flippers with tubercles correspond to vortex generators (Miklosovic et al., 2004).

Effect of an Artificial Caudal Fin on the Performance of a Fish Robot

The unique way in which fish move around is studied for various applications. Recently, the results of studies conducted on mimicking fish locomotion are being used for designing underwater vehicles. Along with electric motors and linkage systems, these vehicles are modelled on the swimming characteristics of fish. For instance, the morphology and kinematics of tuna are mimicked by a hydraulic actuator-driven fish robot, the Vorticity Control Unmanned Undersea Vehicle, developed in the Draper Laboratory of Cambridge, Massachusetts (Heo et al., 2007).

A mechanical noise and/or electromagnetic signature is produced by the electric motor of the robots. Their purpose is to facilitate detection of the robot’s location in water. Along with these signatures, increasing the size of the robot due to the bulky mechanical joint system or the weight of the electric motor, raises its possibility of recognition (Heo et al., 2007). Considering this, smart materials are preferred when creating the actuating system in these small underwater systems as they enhance the actuation performance without leaving behind a distracting noise signature. For example, a lamprey fish robot is actuated using a shape memory alloy, a small underwater robot is actuated using a flexible conducting polymer called ICTF, an underwater vehicle is propelled using piezoceramic actuators, and a fish robot is actuated using a unimorph piezoceramic type called lightweight piezocomposite actuator (Heo et al., 2007).

A group of researchers created a new biomimetic fish robot to assess its efficiency. This robot consists of a body, an actuate system, an artificial caudal fin and a central fin, as seen in Fig. 11 (Heo et al., 2007). The waterproof body encloses an actuate system that uses two piezoceramic unimorph actuators. Additionally, a four-bar linkage system is also set up. The oscillating caudal fin is attached to the end of the body whereas the ventral fin is strategically located on the posterior side of the body to decrease its yawing motion. Altogether, their robot, weighing 550 g, is 27 cm long, 5 cm wide, and 6.5 cm high. However, of this total mass, 450 g is auxiliary, for the sake of matching the buoyancy force and gravity typically experienced by a fish (Heo et al., 2007).

Fig. 11 Final assembly of biomimetic fish robot, with each part labeled. [Adapted from Heo et al., 2007]

The two piezoceramic actuators endure a bending motion that produce limited displacement; hence the actuation system developed to amplify and transform the energy into substantial caudal fin motion. Fig. 12 illustrates the key elements of the robot’s actuation system. These include, the fixture structure, lightweight piezocomposite actuator previously mentioned, rack-pinion system, two cranks, and two couplers (Heo et al., 2007). These actuators can create a bending motion through electric excitation and are enveloped between a glass/epoxy layer and a carbon/epoxy later. Moreover, the rack-pinion system has two racks, each attached at the centre of its corresponding actuator. The pinion joined to the two racks produces a rotational motion from the racks moving up and down from the actuators creating a bending motion. As this motion happens, the long crank, connected to the pinion, rotates in a push-pull motion, subsequently rotating the short crank, controlling the artificial caudal fin as it starts an oscillating motion (Heo et al., 2007).

Fig. 12 Breakdown of actuation system of fish robot with labeled parts. [Adapted from Heo et al., 2007]

While designing the artificial caudal fin, the thickness distribution of a real mackerel caudal fin was considered. The fin is split into 16 different regions as seen in Fig. 13, and each measured in millimeters. As supported by Table 1, the thickness of the fin generally decreases when following from the peduncle to the end of the fin (Heo et al., 2007).

Fig. 13 Real mackerel caudal fin and measuring points. [Adapted from Heo et al., 2007]
LocationThickness (mm)LocationThickness (mm)
Table 1 Recorded thickness of real mackerel caudal fin for 16 sections, mm. [Adapted from Heo et al., 2007]

Despite the difficulty to reproduce an exact replica of the fin regarding its thickness distribution, this assessment provides helpful guidance. Made from a sheet of polypropylene plastic, an artificial fin with variable thickness is shown in Fig. 14 (Heo et al., 2007). Although it is only split into five sections, the general pattern is maintained as the fin displays a gradient thickness. Additionally, three more fins are made with exact shape and area as the previous, except with uniform thicknesses, thin (TNF), medium (MDF), and thick (THF). The thinner fin is chosen to produce the same force while moving, yet with increased flexibility. The medium fin is chosen to represent an average stiffness similar to the variable thickness fin (VTF). The thick fin is chosen to simulate a stiffer fin (Heo et al., 2007).

Fig. 14 Mimicking caudal fin. [Adapted from Heo et al., 2007] (a) Variable thickness. (b) Uniform thickness.

Next, the four fins are put through a swimming test to assess how the thickness affects the performance of the fish robot while swimming. This simulation is done in a water tank measuring 100 cm by 50 cm by 40 cm and a 15 cm water level. The five parameters that are measured are the swimming speed, Strouhal number, Froude number, Reynolds number, and the net forward force (Heo et al., 2007).

To begin, the swimming speed of the fish robot is increased until the excitation frequency reaches approximately 0.9 Hz. Above this frequency, the swimming speed decreases, largely because of the larger tail beating amplitude. This suggests that the actuators produce the largest actuation displacement and force at 0.9 Hz. Moreover, Fig. 15 shows that the fastest swimming speed is attained by the VTF, followed by the MDF, TNF, and then THF. This shows that, among the uniform thickness fins, the MDF is most effective (Heo et al., 2007).

Fig. 15 Swimming speed vs. Frequency of the fish robot. [Adapted from Heo et al., 2007]

To continue, the swimming performance of the fish robot can be compared to real fish using the Strouhal number. It is a ratio of unsteady force to inertial force in flow to measure the efficiency of thrust (Heo et al., 2007). Strouhal’s number is expressed as:

St={fA\over U}


where f is the tail beat frequency, A is the trap beat peak-to-peak amplitude, and U is the swimming speed. The swimming test shows that Strouhal’s number decreases as the frequency increases. This is because at frequencies lower than 0.9 Hz, the tail beat amplitude is relatively larger whereas at frequencies greater than 0.9Hz, there is a significant reduction in this tail beat amplitude. The Strouhal numbers of the fish robot are all greater than 0.795 across the VTF, TNF, MDF, and THF as seen in Fig. 16. Typically, the range for a fast swimmer is 0.25 < St < 0.4, suggesting these fish robots suffer from inefficient thrust (Heo et al., 2007).

Fig. 16 Strouhal Number vs. Frequency of fish robot. [Adapted from Heo et al., 2007]

Furthermore, Froude number is a ratio of inertial force to gravity force in the flow, to measure the maneuverability of the fish. This is expressed as:

 Fr={U\over √gL}


where U is the swimming speed, g is the gravity constant, 9.8 m/s2, and L is the length of the fish, previously mentioned as 27 cm (Heo et al., 2007). The swimming test shows that the Froude number increases for higher tail beat frequencies, reaching a maximum at 0.9 Hz. Despite the largest Froude number found is for the VTF at 0.0155 as shown in Fig. 17, it is still very low as it is less than 1. This suggests that the fish robot has poor maneuverability because its inertial force is much less dominant than its gravity force (Heo et al., 2007).

Fig. 17 Froude Number vs Frequency of fish robot. [Adapted from Heo et al., 2007]

Moreover, Reynolds number is a ratio of inertial force to viscous force in the flow, to measure the cruise of the fish. It is expressed as:

R={UL\over v}


where U is the swimming speed, L is the length of the fish, and v is the kinematic viscosity of the water. The swimming test shows that Reynolds number reached a maximum at 0.9 Hz, similar to the swimming speed and the Froude number. As shown in Fig. 18, the lowest Reynolds number is found at 5116 for THF while the highest is found at 6802 for VTF. As these are in the range of 103 < R < 105, it can be concluded that the water flow around the fish robot is in the transition from laminar flow to turbulent flow (Heo et al., 2007).

Fig. 18 Reynold’s Number versus Frequency of fish robot. [Adapted from Heo et al., 2007]

Lastly, the net forward force is the difference between the thrust force generated by the caudal fin and the drag force of the fish robot. Assuming that the swimming acceleration is constant throughout, the net forward force can be approximated using the impulse-momentum relation expressed as:

∫F dt=m(U_2-U_1) 


Fig. 19 shows again that maximum net forward force is attained at 0.9 Hz. VTF shows the highest at 0.71 mN, suggesting that it is the best thruster while THF shows the lowest at 0.62 mN, suggesting that it is the poorest (Heo et al., 2007).

Fig. 19 Net Forward Force vs. Frequency of fish robot. [Adapted from Heo et al., 2007]

An Aquatic Robot to Explain the Behavior of Flippers

To understand flippers more thoroughly and why most aquatic animals have two flippers instead of four, Long et al. (2006) designed an aquatic robot named Madeleine (Fig. 20). The design of the robot’s flippers was modelled after the flippers of aquatic vertebrates. Experiments conducted with Madeleine led to insights on the parameters for efficiency of flippers such as that having four flippers doubles energy costs with no noticeable improvements to acceleration or top speed.

Fig. 20 Madeleine, the aquatic robot. [Adapted from Long et al., 2006]

Firstly, Kemp et al. (2005) found that a non-symmetrical swimming apparatus (e.g., one flipper on one side and two on the other) was extremely efficient. Despite this, it would not be helpful in modeling the efficiency parameters of animal flippers as all vertebrates possess bilateral symmetry. Therefore, they designed Madeleine to have a bilaterally symmetric swimming apparatus (Kemp et al., 2005).

Madeleine’s flippers had to be made of a material that correctly mimicked a vertebrate’s flipper. By treating them as a composite, Koob and Long (2000) found that the overall structure of a vertebrate’s flipper had a Young’s modulus — measure of the amount of force it takes to stretch a material; it varies widely among different materials (Editors of Encyclopedia Britannica, “Young’s modulus”) — of 0.9 MPa (Koob and Long, 2000, as cited in Long et al., 2006). Madeleine’s flippers were made of a material with the same property.

The movement patterns of Madeleine’s flippers had to be analogous to those of aquatic animals, which happen in an oscillating vortex-shedding mechanism. This means the flipper flowing through water creates alternating low-pressure zones behind it as it oscillates (Fig. 21). This type of movement shares hydromechanical properties with the flapping of the flippers of a turtle (Wyneken, 1997, as cited in Long et al., 2006).

Fig. 21 “Vortex street” left behind by a vortex-shedding mechanism. Photographed by Jürgen Wagner in 2014. [Adapted from “Kármán vortex street” | Wikimedia Commons, n.d.]

Madeleine had a dry weight of 24.4 kg, including her flippers, which weigh in at 1.1 kg each, similar to the weight of an average sea turtle flipper (Long et al., 2006).

Finally, the power density of the robot was 5 W/kg during cruising and 10 W/kg during acceleration. This means that Madeleine was consuming 5 W of power for each kg she weighed during cruising and double the power during acceleration. In 1999, Alexander et al. found that these were the power densities found in vertebrate aerobic muscles (Alexander et al., 1999, as cited in Long et al., 2006).

Fig. 22 Power draw and acceleration of Madeleine during swimming tests. [Adapted from Long et al., 2005]


All in all, this study aims to describe the particular uses of computers to achieve information storage and processing related to flippers. The use of large databases has, among other things, allowed scientists to more easily analyse parameters describing the efficiency of flippers, and the processing power of computers has proven to be an important asset in techniques such as mark recapture. The above analysis explains some of these efficiency parameters and gives insight on results that were found by water and wind tunnel simulations of flippers. Apart from being efficient locomotion organs, flippers were also found to be useful for biometric recognition. Biometric recognition is helpful to study a specific individual in a population, regardless of whether the goal is scientific discovery or conservation. Computer simulations modeling the way bumps on whales’ flippers delay stall to increase the overall hydrodynamic efficiency were also covered. To conclude, an example of the advances that were done using the power of computer processing was shown. The scientific community has designed a variety of robots, including one modeled after a fish and one modeled after a turtle to study the properties of flippers as well as the effects of various changes to an animal’s swimming apparatus.


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