Figure 11: Flume tank with carriage system on top

​​​​​​​​​​​​​Engineering


After the geometry and limits of motion of the flippers have been found, the engineering aspect of the project started. Models that are based on what is known from the paleontology and that therefore represent the plesiosaurs as accurately as possible must be used to determine how they used their flippers. These models can be computational (computer simulations), or experimental  (robotic plesiosaur model). Both of these enable me to find the motions that give the highest thrust and the best efficiency. It is likely that the plesiosaur would have used these optimum motions to swim because evolution tends to make things as efficient as they can be, especially in an aquatic environment.


But how does a wing create thrust? There are many ways of describing this but the most useful for this work is the production and shedding of vortices. A vortex is just an area of rotating fluid, like the whirlpool that is formed when you pull the plug out of the sink. Vortices are formed on the surface of a flapping wing, and if they are shed at the right time during the flapping cycle then they can create thrust. Consider figure 7 which shows the vorticity generated by a flapping wing. Here the fluid is moving from left to right and red indicates clockwise vorticity whilst blue indicates anticlockwise vorticity. There are many vortices behind the wing, but the strongest ones are at the outer edge of the wake. This is called a 'Von Karman vortex street' as the vortices are like the lampposts alternating either side of the street. 














The tandem-wing arrangement is special because the hind wing is moving in the wake of the fore wing, and therefore interacts with this vortex street. Depending on the spacing and phase shift between the wings, this can either increase or decrease the efficiency and thrust. Because the strength of the vortices is proportional to the amount of thrust produced, it is easy to see from the vorticity fields which cases give higher thrusts. For example, figures 8 and 9 show exactly the same thing as figure 7, but now there are two wings instead of one. The only difference between these two cases is the phase difference between the foils.  Figure 8 shows a wide wake with weak vorticity, and therefore produces a low thrust, whereas figure 9 has much stronger and well-organised vortices in the wake and so produces a much higher thrust. So it can be seen from this brief explanation that the phase difference between the wings can have a huge effect on the thrust produced by the hind wing. This project aims to determine what  phase differences plesiosaurs would have used to give them the best performance... and evolutionary advantage. 



















​​

The simulations are run using 'Lily Pad', which is an open-source Computational Fluid Dynamics (CFD) solver developed by Dr Gabriel Weymouth. This solves each case very quickly compared to many other CFD solvers so enables a large parameter space to be investigated. ​​​​

Figure 12: In-phase motion of flippers

Figure 13: Out of phase motion of flippers

Figure 6: Pelvis and femur showing approximate upper limit of motion of limb

​​Additional Materials


This project is in collaboration with the vertebrate paleontology research group at the National Oceanography Centre in Southampton (NOCS), lead by Gareth Dyke.   ​http://sotonvp.com/


   Outreach Poster:                                                             Three Minute Thesis video:








Flipper

Pelvis

Pelvis

​Flipper

Figure 5: Hip joint of a plesiosaur

Figure 4: CAD model of Collard flipper

Figure 3: X-Ray of the Collard specimen, courtesy of Argos Inspection

     ​​Limits of Motion 


The limits of motion of the flippers refers to how much movement the animal would have been able to achieve. How far would the plesiosaurs be able to move their flippers up, down, front and back, and how much would they be able to rotate their flippers? ​These limits of movement of the flippers can be estimated by looking at the shoulder and hip-joints of the plesiosaurs, and the specimen chosen for this was the Muraenosaurus leedsi, NHM R2428, as the bones are preserved in 3D, rather than being flattend on a substrate. The shape of the surfaces of the bones, along with the cartilage gives an indication of these limits. The V-shaped joints of the plesiosaurs show that they could have moved their flippers up and down quite a lot, but not forward and backwards much. 






Figure 1: Rhomaleosaurus victor, redrawn from (Romer, 1966)

Figure 2: Image by Rodrigo Vega


​​References

Romer, A. S. 1966. Vertebrate Paleontology. University of Chicago Press, Chicago. 

Rodrigo Vega. Deviant Art




​​​​Paleontology 


In order to set up an experiment about the swimming method of plesiosaurs, two pieces of information must be obtained from fossil evidence: the  geometry and the limits of motion of the flippers.

Plesiosauria is a large group of animals with diverse characteristics, and it is therefore a huge task to analyse  the subtle differences between all of their swimming techniques. Instead, general characteristics about plesiosaurs have been established using two main specimens: one to give the geometry of the flippers and another to give the limits of motion. 


     Geometry


The specimen used to obtain the geometry of the flippers is called the 'Collard Specimen', which was found in 2010 in Bridgwater Bay in Somerset, and is a good choice as it is preserved in the substrate and the providence is exceptional, meaning that the geometry of the flippers can be relied upon. More details about the specimen can be found here. There is one problem with all plesiosaur fossils however: there is no soft-tissue preservation. The flippers of extant animals which use flippers to swim have been used to estimate the extent of the soft tissue on the plesiosaur flippers, and the result is shown below. 




​To run the experiment, the flume tank is turned on,  the flippers are set flapping by the robot, the forces on the flippers are measured, and dye is used to visusalise the flow. 


As seen with the simulations, different phase shifts between the flippers means that the hind flipper interacts with the wake of the front flipper in different ways, and the experiment confirms this. Lets compare figures 12 and 13 below, where the water is moving from left to right and everything about the motion is the same apart from the phase of the flippers. In figure 12, the flippers are moving up and down together (in-phase), and in figure 13 the hind flipper is moving down as the front flipper moves up.  In figure 12 it can be seen that the hind wing is not in the wake of the front wing for very long, and only crosses through it, whereas in figure 13 the hind flipper is constantly in the wake of the front flipper. Therefore the phase of the flippers is extremely important and affects how much thrust the hind flipper can produce. 

















Implications for the plesiosaur 


The fact that the phase of the flippers is such an important parameter that governs the thrust production of the hind flipper means that the phase would have needed to be accurately controlled by the plesiosaur. For a particular plesiosaur swimming at a particular speed there is a motion that gives the highest thrust, and another that gives the highest efficiency. However, if the plesiosaur swims at a different speed, changes the frequency of the flap, or the spacing between the flippers, then these optimum motions change. In other words, there is no fixed motion that gives the best performance over all conditions, and it really depends on the other characteristics of the swimming. This means that each plesiosaur would have its own motions that it would use for different speeds, and it would learn these as it grew up. 


Applications


It is easy to see that a swimming motion that is good for the pleiosaur would also be good for an underwater vehicle that uses four flippers rather than a propeller.  Such a vehicle could potentially be quieter, more maneouverable, and potentially more efficient than a propeller-driven vehicle. 


Flapping wings can also be used to generate power, rather than thrust, by extracting energy from a flow of water or air. Renewable energy systems that use tandem flapping wings could be developed for use in tidal streams and rivers which could be quieter and better for the environment compared to conventional turbines. 




​​​Introduction


Millions of years ago when the dinosaurs were walking around on the earth, there was a type of marine reptile called a plesiosaur that was swimming in the seas. Plesiosaurs were reptiles that had evolved to live in the ocean, and had four big flippers that they used to swim with. These flippers were similar to the flippers of a turtle or sea lion, but whereas these creatures only really use their front two for propulsion, plesiosaurs used all four. 













Each flipper of the plesiosaur would have moved primarily up and down, which is called ‘underwater flight’ because it is very similar to how a bird flaps its wings.   So we know how each flipper moves on its own, but how do the flippers move in relation to one another? How does the hind flipper move with respect to the fore flipper?  Do they both go up and down together? Does one go up as the other goes down? Or is it something in between the two?  


Finding the relative motion of all four flippers is the main focus of this research, and is approached from both palaeontological and engineering perspectives. 



Project leader : Luke Muscutt

Supervisors: Prof GanapathisubramaniDr Gareth DykeDr Gabriel Weymouth, Colin Palmer

The Hydrodynamics of Plesiosaurs

Figure 7: Vorticity field around a flapping wing

Figure 10: Manufactured plesiosaur flipper for use in the experiments. 

Figure 8: Vorticity field around tandem flapping wings for low thrust.

Phase = 3*PI/4


​​Acknowledgements

This work is being funded by EPSRC and Ginko Investments Ltd




Figure 9: Vorticity field around tandem flapping wings for high thrust.

Phase = 7*PI/4

Experiment


​​​The simulations are great for looking at a large parameter space and for finding general rules that describe the interaction of the flippers. However, they are limited to two-dimensions and low Reynolds numbers (Re), and experiments are necessary to determine what happens with the 3D flipper shape at higher Re. This experiment consists of a 'robotic plesiosaur' that flaps two of the reconstructed plesiosaur flippers in water - within the limits of motion given found from the fossils. This 'robotic plesiosaur' doesn't look a lot like a plesiosaur - in fact it looks more like a CNC machine - but it flaps the flippers accurately so this is what is important for a scientific investigation.