Recently Lucile wondered if hydrodynamic interactions, such as the ones ongoing in a fish school that allow each fish to spend less energy when compared swimming alone, existed up in the air, upon groups of bird... Yes Lucile ! And bird flocks (collective flying bird groups) - right image - behave in a very similar way to fish schools - left image -, to defend against predators, feed more efficiently and optimise their global energy ! An interesting - and very short ! - article about this phenomenon, [14], discusses the case of great white pelicans, Pelecanus onocrotalus, flying in a uniform speed of 48 km/h, and compares their energy ‘expenditure’ (consumption) when flying alone or ‘in formation’ (in a group) ‘V’ shaped. The authors simply measured the wing-beat frequency from videos they recorded, and the heart rate of the pelicans with an electronic heart-rate logger. Their graph is presented just below: x axis are the different flying modes/altitudes and y axis is the heart rate (for the colored columns) and wing-beat frequency (for the dots). Numbering of dots indicates the position in the group: ‘1’ for being the leader, etc, etc. Evidently, the pelicans save a significant amount of effort/energy by flying in formation, compared when flying alone ! Also, the same results regarding the difference of wing-beat frequencies between individuals of different positions in the group are observed in the first graph of my last post [15], for fish’ tail-beat frequencies: individuals at the front of a group seem to spend more energy than those located at the back or middle of it. This is because each pelicans, or birds from any other bird flocks, uses the air movement and vortex wakes generated from their adjacent neighbours; each wing moves in an upwash field that is generated by the wings of the other birds in the formation. Isn't this extraordinary ?? This energy saving advantage is probably a principal reason for the evolution of flight formation in large birds that migrate in groups (since they’re heavy…). REF: [14] Article: Weimerskirch, Martin, Clerquin, Alexandre & Jiraskova - 2001 - Energy saving in flight formation - Nature, Vol. 413, pages 697-698 [15] Blog Post: Hanaé (me) - 2016 - SCHOOLING TO OPTIMISE HYDRODYNAMIC INTERACTIONS - Weebly: http://stagelfdv.weebly.com/home/schooling-to-optimise-hydrodynamic-interactions Oh no WAIT ! You’re not done with this post yet ! Since reading gets boring, watch this nice TED-Ed video on ‘How do schools of fish swim in harmony ?’ and ‘How do the tiny cells in your brain give rise to the complex thoughts, memories, and consciousness that are you ?’
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Just a quick video to show Hanaé's lab and experimental procedure with 3 fish: Hey fellers ! Moonfish school speaking ~ So Maryam asked us to describe a bit more the hydrodynamic interactions ongoing while we swim in a school and why swimming together allows us to spend less energy than swimming alone ? Hydrodynamic interactions describe the interplays between the fish, or any other particles, and the water, or fluid, they are immersed in. Red nose tetra fish, from Hanaé’s experiment, move in response to water flow velocity, which thus creates new perturbations in their environment. By generating and reacting to this local flow velocity, each fish experiences hydrodynamic interactions with the other school’s fish and attempt to benefit from them to save energy. So schooling, like we do, is very good way to optimise hydrodynamic interactions between individuals: each one of us uses the flow ‘patterns’ from adjacent swimming fish of the group to save energy, and so the global school’s energy ! Also, there has been evidence that fish located at the back of a school spend less energy than those swimming in the front. Check out these two studies with schools of juvenile and grey mullet Liza aurata: [10] & [11]. Below we pasted the most interesting figure of [10], showing the comparison of tail-beat frequencies (TBF), so the ‘swimming effort’, as we say, of 1 fish swimming alone, this same fish swimming in the first school’s row (at the front) and this same fish again swimming in the further rows, for 3 different swimming velocities; 10, 20 and 30 cm/s. In this study, 15 schools of eight fish were used and for each school, one of the members was chosen to be tested while swimming alone. As in Hanaé’s experiment, vidéos were analysed to estimate the TBF: Can’t we clearly see that the solitary fish puts much more effort into swimming alone compared when swimming in a school ?? This is fascinating ! Hanaé and her project team also managed to draw results of that sort. They compared the Strouhal number: St = fA / U (dividing the amplitude A and frequency f of the tail beating by the swimming speed U), of 1 solitary fish swimming alone, with this same fish swimming in a pair (2 fish) school, and in a trial (3 fish) school, for 4 different swimming velocities; 2.7, 6.8, 11 and 13.7 cm/s. The Strouhal number is therefore also related to the fish’ swimming efficiency ! Hence, they obtained this next graph: x axis is the swimming speeds U, in m/s and y axis is the Strouhal numbers for the different fish groups.
Studies, such as [12] and [13], on swimming and propulsive efficiency demonstrated that they are much higher over a low and narrow range of Strouhal number, between 0,2 and 0,4. In Hanaé’s graph above, we can definitely conclude that the solitary fish swims less efficiently compared when swimming with another or two other fish ! In addition to that observation, it is interesting to see that Strouhal number, for all different groups’ size, decreases as the swimming fish’ speed increases. But this is another story Dory ! REF: [10] Article: Marras et al. - 2014 - Fish swimming in school save energy regardless of their spatial position - Behavioral Ecology and Sociobiology, Pages 1-8 [11] Article: Killen et al. - 2012 - Aerobic capacity influences the spacial position of individuals within fish schools - Proceedings Biology Science, Vol. 279, Pages 357-364 [12] Article: K. Taylor, L. Nudds & L. R. Thomas - 2003 - Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency - Nature, Vol. 425, Pages 707-711 [13] Article: G.S. Triantafyllou, M.S. Triantafyllou & M.A. Grosenbaugh - 1993 - Optimal Thrust Development in Oscillating Foils with Application to Fish Propulsion - Journal of Fluids and Structures, Vol. 7, Issue 2, Pages 205-224 Hello ! Yup, it's us again ! If you're into maths, this post might interest you; it is about the DLT method. Wait, what is the DLT method you say ? Why do we want to discuss about it ? DLT stands for Direct Linear Transformation method. It is used to calibrate cameras, such as the ones Hanaé is handling during her internship, to convert 2D positions from 2D frames back into real 3D positions, and so track precisely the red nose tetra fish in her experiment. This technical report [7] and this website [8], explain it clearly. But we still think it is complex to understand... Therefore, here, we will report simply the DLT method demonstrated in [7] and [8], by applying it to Hanaé's experiment.
The DLT method uses this set of control points, whose 2D image space coordinates are known, to calculate the mapping between them and the 3D object space coordinates.
Considering [u0, v0, 0], the principal point’s coordinates, the image reference coordinates of C become then [u0, v0, d], and the vector V2 drawn from C to I is then [u-u0, v-v0, -d]. Since O, I and C are collinear, vector V1 and V2 form a single straight line and V2 = cV1. (with c a scaling scalar). Note here that vectors V1 and V2 were originally described in the object-space reference frame and in the image-plane reference frame respectively. In order to directly relate the coordinates, the DLT method necessary describes them in a common reference: so vector V1 is then transformed to the image-plane reference frame. Now the system can replace V1 and V2 in the expression: V2 = cV1, regarding the vectors in the image-plane reference frame: Which is then used to substitute c in the first two above expressions: Coefficients L1 to L11 are the two side DLT cameras’ parameters Hanaé obtains with the calibration MATLAB code, that reflect the relationships between the object-space reference and the image-plane reference. Thanks to them, 2D image-space coordinates, can be projected into 3D object-space coordinates, and vise versa, when the points considered are visible from both cameras. This is called reconstruction using DLT method. REF: [7] Article: Bardsley & Li - 3D Reconstruction Using the Direct Linear Transform with a Gabor Wavelet Based Correspondence Measure: http://bardsley.org.uk/wp-content/uploads/2007/02/3d-reconstruction-using-the-direct-linear-transform.pdf [8] Website: Kwon - 1998 - DLT Method - website: http://www.kwon3d.com/theory/dlt/dlt.html [9] Article: Abdel-Aziz & Karara - 1971 - Direct linear transformation into object space coordinates in close range photogrammetry - ASP Symposium on Close-Range Photogrammetry in Illinois, Pages 1-18. Hey you ! Here is a riddle !: How do we organise ourselves, in a school (a group) ? And why do we swim in this or that configuration ? Yes, we know you can answer part of the question. You will say that we do so to defend against predators, by diluting the chance of individual capture [1], and to boost the group’s foraging (feeding) success [2], because we have a lot of eyes looking for food and when one fish shows feeding behaviour, we follow. In fact, these motions and reactions of the school are the result of complex social interactions, depending on our needs and way of living. What you might not know, is that we swim together also to optimise hydrodynamic interactions, so we spend less energy compared to swimming alone. [3] [4] [5]. It is exactly like team cyclists who want look to minimise wind resistance ! Although these kind of cohesive organisations have been discussed since years and many observations, models and simulations have been performed, none of you guys understands exactly the formation of swimming fish groups, like ours. Héhé ! But wait… Actually, there is someone from FDV studying the question… Hanaé ! She is working in one of the ESPCI’s labs, with a Phd student named Intesaaf. They study the basic mechanisms of the formation of stable swimming groups with 4 to 5 red nose tetra fish Hemigrammus bleheri. How ? With this specific and ‘’home made’’ setup, below. They place gently a group of 4 or 5 fish in the channel / test section, with specific and different uniform water flows corresponding to different swimming velocities (speeds) of the fish, and they capture films from 3 cameras; one on each side and another on top : With these videos, they are able to track the fish using MATLAB, to measure the distances and angles of each fish to nearest neighbours, and observe synchronisation. So far, Intesaaf and Hanaé have only performed experiments, and have not started to analyse their data. Experiments with our cousins, the red nose tetra fish, are not easy because they get stressed and tired easily ! Here is a video, from the top camera, showing a group of 5 swimming together in the channel, in a relatively stationary position: Before Hanaé arrived in the lab, Intesaaf has been working on the phase locking and pattern formation of 2 swimming red nose tetra fish, using the same setup and tracking analysis. He concluded that 2 fish synchronise more at higher swimming velocities (they look synchronised when they swim in phase IP or out of phase OP - see image bellow) and that they do so to save energy and communicate efficiently. Check out his poster about this study ! [6]:
REF: [1] Article: An individual based model of fish school reactions: predicting antipredator behaviour as observed in nature - Published October 1997: http://onlinelibrary.wiley.com/doi/10.1046/j.1365-2419.1997.00037.x/full [2] Article: Fish in larger shoals find food faster - Published December 1981: http://link.springer.com/article/10.1007/BF00300175 [3] Article: Energy savings in sea bass swimming in a school: measurements of tail beat frequency and oxygen consumption at different swimming speeds - Published August 1998: http://onlinelibrary.wiley.com/doi/10.1111/j.1095-8649.1998.tb00986.x/full [4] Article: Burst-and-coast swimming in schooling fish (Notemigonus crysoleucas) with implications for energy economy - Published in 1991: http://www.sciencedirect.com/science/article/pii/030096299190382M [5] Article: Hydromechanics of Fish Schooling - Published in January 1973: http://www.nature.com/nature/journal/v241/n5387/abs/241290a0.html [6] Poster: Phase locking and pattern formation in tandem fish swimming - 2016: http://nonlineaire.univ-lille1.fr/SNL/media/2016/resumes/ASHRAF_intesaaf.pdf |