THEORY OF the ASYMMETRIC FIN by Giorgio Dapiran

Premised:

This study as the ballistic one proposed on arabaletes in the elastic guns section, tries to investigate the functioning of the bi-fin.
For all I could find out, there is no specific scientific study in this direction and as every first treatise this required a big intellectual effort.
In agreement with my firm principal of sharing knowledge I place in disposal this information to friends and competitors. This study can obviously be improved and will surly be reviewed and corrected. Whoever would like to share his suggestions or comments can feel free to contact us at info@dapiran.it
All suggestions will be considered and, if pertinent, included with the citation of the author.
Currently the study is conducted with the help Eng Filippo Anglani and Eng Maurizio Filograno

The physical principle of underwater swimming:

When fins did not exist the first Skin spare fishing was conducted by advancing with scissoring or breast stroke movements of the legs and using the arms to assist the swimming action. A typical example of this technique was the swimming stile of the oriental pearl fishers.

The propulsion area of legs and feet was not sufficient to move a big mass of water and the effectiveness of this technique was very scarce. Therefore in the 1950’s the diver* has equipped himself systematically with extended feet prosthesis to enlarge the propulsion area and increase the mass of water involved in the forward movement.

The physical principle of underwater swimming is: movement and resulting response, which means movement after having pushed water in the opposite direction (Third Dynamics Principle).

“At every action corresponds an even reaction in opposite direction.”

The thrust that the sub receives is sustained by the Second Dynamics principle

F = m x a

Thrust = water mass x acceleration of water mass

From this simple equation it’s obvious that the thrust increases at the growth of two factors: The mass of water involved in the thrust, and its acceleration.

The efficiency of underwater swimming = Kinetic energy of the body in forward movement / Muscular work-out.

It is very low for two reasons:

1) The direction component of the thrust produced by the swimmer is minimal.

2) The Hydrodynamic resistance that the body encounters with movement is elevated.

Our body has not evolved to support swimming, but for walking. The synchronized movement of arms and legs, that pushes water in surface swimming, is way less effective than the structural modifications applied for propulsion in the fish’s evolution.

Professional swimmers cover 100m breast stroke in around 58sec and in crawl stile in 46sec. It’s easy to see that the breast stroke is less effective and that can be explained by the reduction of hydrodynamics this stile involves. Consequently, in bi-finned*underwater swimming, the stile applied is the less energetically expensive.

The maximum speed a man can touch in surface swimming is around 1.7/2.2m/s.

In underwater swimming it unlikely goes beyond 1m/s, nothing compared to the 10m/s that many fish can perform.

Underwater swimming with the help of bi-fins

The swimming action of a diver using bi- fins is called Crawl. It requires an alternate movement of both legs that can be divided in four stages:
1) The water in front of the fin is pushed by the articulated movement of the lower limbs that bend in bow like position flexing the knee back and fourth. Simultaneously the fin deforms its surface and accumulates potential elastic energy.

Neglecting the dissipated energy, the equation that applies to this phase is

Muscular workout = Kinetic energy transferred to water + potential elastic power of the fin.

2) At the end of the “kick”, when the leg is at rest, the water increases for the second time it’s speed for the elastic return of the fin in it’s original resting position. This movement contribution is given without any energy use by the swimmer.

3) When the leg is extended the thrust of the fin finishes off.

4) Back stroke of the leg in extension

The first two stages of the crawl are not separated. The end of the first matches/is synchronized with the second. The swimmer advances in dashes with one leg that applies the push and the other back stroking in extension. The mass of the diver work functions as an inertial volano

We can say that the first stage of the thrust is developed the same way in humans and fish: the body bends and with a muscular effort moves the water around its fins.

A human’s leg is not structured with the same muscles a fish has, and can not communicate the same motion and acceleration as an animal that has evolved its aquatic movement for thousands of years.

Man has tried to fill this fiscal gap by wearing a flexible prosthesis, a flat spring!

The flexibility of the material applied in the fin’s manufacture is essential to gain the maximum acceleration possible before the entire mass of water is pushed of the functional surface of the fin.

It is possible to assert that the fin’s evolution tries to optimize the yield between the elastic energy transferred from the fin and the energy required for its deformation.

At the beginning fins were manufactured using primarily a rubber mix material that proved ideal for water use offering comfort and durability to the shoe but returning a inadequate elastic yield, and a large energy take in, during the deformation of the polymers that compose its structure.

In synthesis the rubber fins absorbed part of the muscular energy produced for its deformation but returned only a part of it (rubber is a material that tends to absorb solicitations). Therefore the necessity to develop materials that could transfer major part of the muscular energy from the flexible structure to the water we care to accelerate.

So we passed from the less reactive rubber fins to rigid ones first build in techno polymers then in composite materials.

Lately the best material is proven to be a carbon fiber composite.

Analyzing this energetically the feature that defines the various types of fins is the capability to absorb muscular energy in the form of potential elastic energy and the aptitude to transform it in forward movement. This potential elastic energy is:

A = ½ Ff Were F is the thrust (in kg) and f is the deformation (in cm)

The Yield of the fins

As yield of the fins you intend the ratio between the potential elastic energy (A in the previous formula) and the energy actually transferred to the water.

This concept is very important and afterwards I will have the chance to explain that the best yield or utilization coefficient of the fin is achieved in a well defined configuration.

Other than material and shape of the fin it’s important to emphasize that:

The movement of every solid body that advances in water is directed by the forces that tend to shift it and by those that tend to decelerate it. The thrust is given by the movement of the limbs and the loss of speed is caused by inertial resistance of the body and of the water.

That means that in the swimming action is not sufficient to optimize propulsion but it’s essential to reduce resistance.

I have introduced two very important concepts that will follow us in our discussion: The thrust in the direction of movement (it’s important to underline that only the component that follows the body axel facilitates movement) and the hydrodynamic resistance that, along the same axel obstructs movements.

Using the prosthesis “fins “occupied in crawl swimming, with the alternate movement of both legs you can increase the mass of water moved and eliminate the arm movement. This increases the hydrodynamics or the diver’s body and reduces the resistance in water.

When the legs start there motion they move a negligible amount of water and it is presumable that only the fin provides the thrust.

The fin accelerates an amount of water labeled as “gained mass” the order of magnitude of the gained mass is approximately equal to the mass of water contained in a cylinder having the diameter equivalent to the length of the fin.

To optimize thrust it is necessary to increase the contact area of the fin as much as possible as long as it is not interfering with the alternated movement of the legs in crawl swimming.

On a first analysis of the propulsion movement with fins, you can understand that for the particular anatomy of the human leg, a diver can easily perform a back kick clockwise (figure 1a) accelerating the mass of water by the synchronized movement of femur tibia and foot. Since he can’t bend his knee in an anti-clockwise direction it can accelerate the mass of water only through the movement of the foot and a wearing movement of the femur (figure 1b).

The natural anatomy of the knee, a juncture with only one direction of movement, significantly influences underwater swimming technique using fins.

The propulsive yield of stage 1a is undoubtedly better of the one of stage1b.This is understandable analyzing the mass of the muscles that are involved in the action: the femoral quadricepses are the most powerful muscles of the human body…

Nevertheless stage 1b is not to be considered completely passive even if in this phase the diver tries to find the leg position that offers the lowest hydrodynamic resistance. This is important considering the other factors that occur in apnea like the muscular workout in oxygen deficiency. Therefore it is less energetically expensive focusing the thrust in stage 1a were the anatomy and the muscles of the leg offer a superior propulsive yield.

Analyzing the dynamics of the femur and tibia that rotate clockwise is even more fascinating (figure 1a). Comparing them with two jointed rods and theorizing the fixed juncture as the hip –femur one it’s possible to analyze the velocity diagrams of the two rods.

Synchronizing the relative rotation of femur-tibia it’s possible to accelerate the ankle movement: adding up the knee speed, generated from the contraction of the femoral quadriceps, and the tibia one, generated from the anterior tibia muscle***, it is possible to gain great velocity.

The same thing happens in football when the efficiency of the kick is given by the synchronized movement of the leg (femur-tibia) that gives the maximum speed to the kicking foot. This process is often applied in javelin throwing, when the coordinate movement of humerus and radius speeds up the wrist at its maximum acceleration.

Why does the foot reach a great speed of thrust?

The acceleration that the water can reach pushed by the fin is dependent from the speed that the foot can accomplish in a unit of time witch we know is dependent from the resistance the water performs. If we wear fins with great “thrusting surface” we will never reach great speeds no matter the effort. Otherwise if we use fins that are narrow and don’t exceed in thrust surface the efficiency will be higher and the speed will be resulting.

It is easy to comprehend the tendency of constructors to manufacture narrow fins: to speedup the movement of the foot and the thrusting surface, but we will learn to understand that this trend presents its negative sides too.

This last thought underlines the tendency in increasing the thrust witch is proportional to the two multiplication factors, acceleration and mass. It has to determine a compromising value of the two. If we aim at moving great mass of water we can’t hope in great acceleration and if we need a big acceleration we can’t reach it by moving a great amount of water.

I hope not to induce the divers with big muscles in trying to reach great accelerations with big surfaced fins, the swimming action is mostly based on agility were the good neuron-muscular coordination is more important than the actual strength. This without considering the great oxygen consume that is resulting to a great muscular workout witch greatly reduces the diving period.

Did I forget about the rotation of the foot?

In the first dynamic study I did no want to refer to the function of the foot to shorten a complicated composite movement. Actually the rods shown on the diagram referred to the diver’s legs are three. Actually with the introduction of the bi-fins the last rod, witch is referred two the foot, is the most important of them all.

It is important to reach a high absolute value of speed*in the moment in witch the water rolls over the edge of the fin.

At this point the importance of the simultaneous movement of femoral quadriceps femoral quadriceps anterior tibia and in the last stage the rotation of the foot induced by the gastrocnemius

Last thing to underline is that during the set off from a standstill position the water is initially accelerated from the femoral quadriceps and afterwards from the tibia and from the gemellus that control the rotation of the foot giving the last thrust to the mass of water already in motion. It’s in this last stage the bent fin requests muscular workout, charges like a spring, and returns potential elastic energy that furthermore speeds up the water.

Comparative study on fishes swimming motion

Since there is no organic theoretic and experimental study on the underwater swimming technique with bi-fins the correct approach to understand the best movement and to manufacture a functional prosthesis is to try figure out and duplicate the specific structures that fishes have selected in thousands of years of evolution.

Just as it happens for divers, the movement of fish is lead by the forces produced by swimming movements that tend to shift him forwards, and from those that slow down the action: inertial hydrodynamic and viscose resistance.

The shape and the mass of the fishes’ body produce different thrusts and resistances. Therefore some fish are more indicated to comprehend accelerated swim and others give a clearer idea of maneuvered swim or cruising swim techniques.

The barracuda for example has a long and tapering outline ideal to produce great accelerations thanks to the undersized hydrodynamic resistance but is not modeled to conduct a cruising or a maneuvered swim.

The tuna on the other hand has a great cruising action but is deficient in maneuvered movement.

The trigger fish with his tall and compressed body is structured to have good maneuvering properties but is scarce in acceleration and cruising.

Usually the fish with a specialist type of swim are outnumbered by the “generic” ones that have a body structure witch allows good performances in all three types of swimming style, without excelling in any of them.

On the base of its morphologic structure the swimming stiles for fish are divisible in two classes:

undulatory movement and oscillatory movement.


The propulsive element struck by the miotoms ( metameric skeletric muscular system) of the fish thrusts the water witch starts the third dynamic principle. The water exercises a thrust equal in force but contrary in direction on the propulsive factor.

As already mentioned in previous paragraphs the value of this relation is obtained by multiplying the acceleration of the water to the mass of water moved.

The reaction of the water on the fish’s body is perpendicular to the surface of the propulsive factor and can be divided in two different components: one in the direction of the overall movement of the fish, the real forward thrust, and a tangential force perpendicular to the direction of movement.

The resultant of the thrust in the direction of movement of all the propulsive elements, determines the entire thrust forwards that the fish accomplishes from his undulatory movement. Meanwhile the resultant of all the lateral thrusts determines a rotation of the fish’s body around its center of mass. This brings in a condition in witch if the tail fin sways one way the head swings to the other and vice versa.

As you can see on the picture the propulsive elements positioned close to the tail produce stronger thrust than the ones by the head. This for two reasons:

1) The section next to the tail can be inclined at a better angle. The maximum speed can be accomplished when the tail’s movement is perpendicular to the direction of movement.

2) Every propulsive structure accelerates the water coming from the previous one. So for the tail gives the major contribution in the acceleration and speed.

Oscillatory movement:

The principle of physics that guides this process is based on a third type lever in with the fulcrum placed on the juncture between fin and body wile the applied force initiates closely, were the motion muscles bond. The lever is inconvenient and accelerates water at a modest rate (ratio between water resistance and applied force < 1).

The structure of the fins.

The undulatory fins and the caudal ones evolved differently in the different species but have a similar structure witch includes bony or cartilaginous herring-bones enclosed in an epidemic membrane.

The shape of the bones is generally conical.

The body structure of the fish is flexible to obtain the most efficient curvature to generate a thrust thorough the contraction of the miotomy but the tail does not have muscles, other than the ones that insert of the herring-bones in the caudal peduncle**, and bends thanks to the flexibility of the structure sustained by the conical herring-bones (similar configuration has been used in manufacturing the Bi-Fins.

The thickness or the outer edge of the caudal fin is very thin if related to the one of the rest of body, this to give maximum flexibility to the tail (fundamental to generate thrust), and to create a structure with variable decreasing thickness ideal to gain elasticity (a “flat” spring). This structure with herring-bone spreading out fan-wise canalizes the accelerated water flow from the fishes’ body preventing the loss of water from the lateral margins of the tail with a consequential loss of water mass.

This solution determines a substantial structural difference between the fish’s fins and the bi-fins used by divers witch are elastic plane surfaces.

The body structure is flexible but not sufficiently to collect potential elastic energy wile the caudal fin proves to have good flexibility even if not comparable to the one in carbon fiber that is actually used in Bi-Fins manufacturing.

The hydrodynamic inconvenient caused by a flat surface is the skimming of the accelerated water flow of the lateral margins. All the water that rolls off the edge determines an energy loss in the terms of forward thrust. Further on we will see some possible solutions to this problem.

Purpose of the caudal peduncle.

What is the purpose of the narrowing of the fish’s body right before the tail?
This distinctive anatomical feature been adopted by aquatic mammals in a converging evolving process.
If different species have adopted the same anatomical solution obviously there is a valid physics explanation…

One of the explanations is to find in the lateral force, witch is not useful for the forward propulsion, but sways the head of the fish back and forth, and in cursing movement involves a grate energy loss (larger hydrodynamic resistance).

The lateral force decreases if the height of the thrusting surface narrows down in the body fragment that remains inclined at a 45° angle during undulatory motion.

In that body section the fish gains highest acceleration, therefore the propulsive elements gains the highest reaction forces from the water (perpendicular force) and the largest values of lateral thrust.

The second explanation involves viscous resistance, witch depends from the viscosity of the water that runs on the body surface and gains grate importance in protracted swim.

The viscous resistance is proportional to the square of the flow speed and to the fish’s body surface extension. Towards the tail the water reaches the higher flowing speed, therefore, reducing the surface directly in contact with the water reduces viscous resistance. The better the fish are in cruising swimming the smaller is there caudal peduncle!

The exit edges of the fins

The caudal fin has a different shape in relation to the swimming specialization the fish adopts.

Tail Type 1) high and slim connected to the body with a narrow peduncle, used by tuna fish, generates a strong thrust with low viscous resistance.

Tail Type 2) evolved by butterfly fish.With it’s circular shape it is functional for slow maneuvering that includes rotations with narrow angles around a vertical axel working as center of mass

This type of tail has a movement that is similar to the one used in the oscillatory fin rather than the undulatory motion that the caudal fin provides.

The two shapes represent the diametrically opposite movement solutions. 1) For speed 2) For maneuvering. Between the two solutions there are numerous other types of fins adapted to transitional types of swim. In any case all fins that are structured with a concave exit edge are prearranged for speed and the ones with a convex margin are specialized for low speed maneuvering.

What are the advantages of a concave sickle like exit edge?

The shape of the exit edge of the fin influences the direction of the water flow previously accelerated from muscular movement.

Placing along the exit edge of a fin a series of propulsive elements, we could observe that the resultant of all the thrusts gained from the propulsive structures (placed perpendicularly to the surface) is oriented along the longitudinal axel of the fish and generates a thrust that is perfectly in axel. This type of tail also produces a flow of water converging on the thrust axis of the fish and does not waist water mass that has been accelerated by previous muscular movement.

In tail type 2) the flow of water produced by the singular propulsive elements, placed along the exit edge of the fin is divergent from the longitudinal axis of the fish’s body.

This because the water is ducted through canal bends that formed between herring-bones membrane. A flow that is divergent from direction of movement decreases speed but increases stability.

The swimming technique of some terrestrial mammals such as the otter.

Asking ourselves if the swimming technique with Bi-Fins isn’t closer to the one adopted by some aquatic mammals like the otter is reasonable. These mammals have limbs that are comparable to ours and in the ages have evolved an epidermis membrane between the fingers.

The swimming action of these animals is way more complicated than the fish’s one because they add to the undulatory movement of the body a rowing movement of front and hind limbs that are not equipped with any flexible propulsive structure and developed differently from ours, witch are designed for erect posture.

Substantially using Bi-Fins with the Crawl technique, and in even bigger mater using the Mono-fin in dolphin stile, the diver has adapted his body at a remunerative swimming stile based on the flexibility of the fin that with a coordinated movement of the leg charges elastic energy and releases it the most appropriate moment to gain a thrust wave.

The fish with the undulatory movement of there body and of the caudal fin generate a wave that travel’s along there body faster than there progression in the water. In the undulatory movement every half wave span that travels from the head down, is accelerated from the next body flexion. The eel for example can create two contiguous thrust waves. The diver with Bi-Fins generates a single wave, very similar to the one produced by the undulatory movement of the fish. This makes an effective comparison possible.

Here is another brief note regarding other types of swimming adaptations used by animals that were not born aquatic but evolved into this stage: like the penguin. These birds, that spend half there life on dry land, but forage in the sea, do not employ the undulatory movement as most aquatic animals do (this suggests us the efficacy of the motion). Their underwater swimming stile is oaring: the atrophied wings, moved back and forth, push the water in the opposite direction of advancement, gaining a thrust for reaction (similar to the oscillatory fins). No man, till now, has ever tried to emulate this type of swim using a couple of rigid prosthesis for the arms (similar to the structure present on the penguin’s wings) and a mono-fin for the legs, synchronizing the undulatory movement of thorax, legs and fin with the oscillatory one performed by the arm prosthesis.

Our adaptation to underwater swimming with technological prosthesis is just at the beginning!

First comparative considerations on fish’s swimming techniques.

The movement of the structure “leg-fin” can be similar to the undulatory motion of fish.

The bending and longitudinal straightening of the fish’s body that advances (in thrusting stage)is consequential to a coordinate contraction of the miotoms (of the scheletric muscles) of the fish: every propulsive structure close to the tail has to move faster than the one that comes first if it aims at accelerating the water!

The same coordination is required from the femoral biceps and the gastronomies* that move femur and tibia. Imagine a soccer player that kicks a penalty tiring to give the highest acceleration possible to the ball: he will coordinate his movement so that his ankle-foot gains the largest speed possible. In impact position the kinetic energy of the instep of the foot (1/2MV) will pass on to the ball and will be proportional to the speed (V) reached by the foot. This comparison can be extended to a tennis player that strikes the ball with the racket: he will synchronize the movement of the arm to reach the maximum speed possible with the hand.

In conclusion: the fining movement is the coordinated action of the leg that speeds up the ankle to its greatest velocity (see diagram of leg articulation speed, page 6).

In nature the propulsive structures used in undulated swimming are very flexible, therefore the thrusting surface of the Bi-Fins has to have great flexibility mostly near the exit edge were the water is accelerated. I would like to emphasize the fact that some divers that employ rigid fins are not able to accelerate the water and there movement is very similar to the one of a cyclist that pushes on the pedals of his bike. This because the fin offers a great hydrodynamic resistance, too big for the divers muscles witch is not able to swing his leg as in kicking motion.

The fish’s anatomy has in great consideration the lateral thrust generated from the undulatory movement witch requires a great energetic consume not finalized for forward propulsion. In the divers swim this event occurs when:

a) The fin is too flexible and loops up on its self. Under water weight.

b) When the fin is too wide near the shoe, witch corresponds to the caudal peduncle of the fish.

Let’s pretend to divide the thrusting area of a Bi-Fin in the totality of the propulsive elements with unitary sizes: the entire amount of thrust of the fin will be generated from the vector addition*of the thrust of the single propulsive elements.

This simplification allows an easier theoretic study on the fin’s thrust. The water reaction to the stroke of the thrusting surface on the single thrusting element is perpendicular to the surface, this time it’s possible to split the thrust in the direction of motion of the diver and in a direction witch is perpendicular to the thrust (lateral force).

From this introduction it’s easy to see that not all the propulsive elements give an equal amount of thrust in the direction of movement. Everything depends on their position in relation to the bend of the fin.

The component of the lateral force does not produce any thrust but only energy dispersion.

Therefore from this first analysis we can formulate two fundamental conclusions:

-The propulsive elements witch are perpendicular to the direction of movement offer the greatest thrust,

- The less the fin bends the less will be the thrusting component.

-The magnitude of the thrust of the single propulsive elements increases near the exit edge of the fin.

The fin generates a propulsive wave: wile the fin moves the propulsive elements glide longitudinally along the fin’s axel and accelerate the water upcoming from the previous propulsive elements.

Substantially every propulsive element accelerates the water approaching from the previous one until the highest speed is accomplished near the exit edge of the fin.

The swimming rate and the shape of the fin.

The performance of a diver in underwater swimming depend on the difference between the thrust that he accomplishes with the fin and the resistance his body encounters in water during motion.

The resistances (intended as forces that are in opposition to forward movement), considering the same size and mass of the diver’s body, depend on the swimming rate.

Starting the dive from a standstill, for example, the hydrodynamic resistances ads up to the inertial resistance. On the other hand, in cruising swim, the reduction of speed is operated entirely from the hydrodynamic resistance.

The partition of swimming rates is important because to every swimming rate matches an optimal fin shape.

A fin that is manufactured to give better performances in surface swimming is very different from the one built for underwater swimming with stand still position start.

It is necessary to clarify this concept with some examples:

1) Ascending from the bottom, the diver has to fight against the inertia of his body mass and against his own weigh (witch doesn’t influence the horizontal swim). Gaining a certain depth he has to struggle against another resistance caused from the compressing of the wetsuit’s neoprene that reduces the floating thrust but not the weight of the ballast. In this occasion the thrust of the fin has to overcome a resistance that is approximately double the one the diver would have horizontally.

For the theoretical reasons exposed at the beginning of this document, the increase of thrust necessary for this occupation can bee reached by an enlargement of the water mass involved in the thrust or by adding a higher acceleration to the water.

Therefore the fin will have to be wider and the shape will have to allow great accelerations on the exit border (this structural debate will be held later). The finning technique will also be different in horizontal swimming: the propulsive movements will have to be wide and as rapid as possible.

2) For the divers that uses the ARA the swimming conditions are different: the hydrodynamic resistance in this case, is a lot higher than the one encountered by apnea divers, that due to the bigger mass to shift. The inertia that has to be won is bigger too. The additional mass of the diver’s gear, significantly influences the swim, even superiorly than a gain of weight by the diver (the volume of water moved creates a floating thrust). This can be explained considering that the specific weight of the gear is a lot higher than the one of a human body.

In this case too the fin is wider than the one used in surface swimming but the diver equipped with ARA does not need fast ascending since his GAV can provide a sufficient thrust. Therefore he uses shorter fins made of a less reactive material live rubber and plastic. The choice of such material is functional for improper uses of the fins too, such as walking and skipping on the sea bottom of on walls of rocks.

These examples introduce the concept that a fin that is ideal for all purposes does not exist and that the choice of the diver has to aim at the prosthesis suitable for its use.

Even the manufacturers of these products differentiate only a few category of employment: Diving with ARA surfaced finned swimming, snorkeling, and skin sparefishing.

Even if every company manufactures different models I have to admit that the market is still young: each producer for example sells his fins emphasizing the thrust performances but exclude every comment on agility and versatility.

The optimal structure of the fin used in transitory swim

In this paragraph I analyze a specific type of fin employed in skin sparefishing starting from a standstill. This fin is ideal for skin diving at great depths.

The fin’s best configuration involves a fairly flexible structure able to generate a wave of a certain width (1), but not flexible enough to produce a lateral component as would happen in configuration (2).

In configuration (2), as you can see on the sketch, the thrusting margin of the fin is not perpendicular to the direction of movement of the diver.

The obvious observation that comes to mind is that the configuration of the fin under

Bending stress could depend on the muscular strength possessed by the diver.

This belief induced some companies in marketing fins with different “flexibility”. I bracketed this word because used improperly we should be talking about resistance to bending. Actually the fin doesn’t push on a rigid surface (as in a plunge from a diving board) but on a liquid that isn’t even thick/dense that if accelerated moves generating a vortex (I will investigate this concept further on).

Even a very powerfully built diver couldn’t in any case bend a fin that under stress stands in position (1) and shift it in position (2).This because the water glides of the surface before creating a sufficiently rigid support to reach the (2) position.

The configuration of the fin under stress is more related to the structure of the fin than to muscular strength applied.