My 'Pretty Fin' Patent

[Arak Lea]

So, I had this idea about fins. The typical fin is more of a paddle than something more efficient like a foil.
Both have the same purpose, to create lift. And air foils are much the same.

So I studied what I could about fins in the wild. Come to find out, many more of them have more in common with foils than a 'paddle blade'. Tuna and whales for example, both have foils. And in some cases they optimize the profile to enhance to a typical hydrofoil.

A number of current fins offer up as foils, but no, most are not really operating that way. SO this is the basis of my patent.

There are 67 pages of text and drawings, so be patient. But if you must, feel free to comment or question anything at any post. How can we learn if we do not question?

I will add that I have tested an initial version, and it worked as expected, but needs much more adjustment to be any kind of useful to scuba or snorkel diving. It is more than I can hope to do in my current circumstances. So I am giving it to the world, just to see what can happen.

So we start here.

Title

BLADE FOR A SWIM FIN WITH INTERNAL MECHANISUM USED TO ACTUATE BENDING OF A FOIL SHAPE WITH TWIN AXLE MECHANISUM AS A SUPPORT STRUCTURE



Abstract

A blade assembly for each of a bi-peddle swim fin pair where each fin contains one of several internal mechanical means to force each blade into a hydro foil profile resulting from an automatic reaction to forces encountered during a kick stroke. The profile of the foils reshapes to a reverse profile in the opposite stroke, and flattens out as forces reach a zero or neutral force between strokes. The mechanism requires support from a flexible pair of spars and two axles as a support structure that holds the foil at an optimal position relative to the fin boot. Pressure in reaction to the relative flow of water are the only forces required to enact the shaping of the blade. Several different means of shaping are presented as well as optional features for the blade and support structure.

Background

Theory of Operation for Bi-Pedal Fins

The original rubber "Duck Feet" are a recognizable standard for bi-pedal fins and are loosely similar to actual duck feet. Each Duck-Foot consist of a semi-elastic sheet stretched between flexible spars, together as a single blade. These are then attached to a boot as a single unit. The boot is shaped to fit over a swimmer’s foot. This is the first known rubber swim fin for the foot in the modern western world.

Common thinking tends to cast the rubber swim fin (Fig 1-A) as equivalent to caudal fins on a fish (Fig 2-B). However, an actual duck’s foot is mechanically much closer in configuration.

After ‘Duck-Feet’ (Fig 1-A) progressive versions of the rubber swim fin are longer, deviating further from duck feet as well as still deviating from the typical fish fin (Fig 2-B).

Compare the profiles in Fig 1-A versus 2-B. There is a hidden difference. Starting with “duck-feet”, fins often appear to model nature but that concept is actually limited to a 2-dimensional understanding.

Common 2-dimensional thinking often conceptualizes caudal fins (fish tail fins) as a paddle pushing against water, which resists the push. The result pushes the swimmer forward and is viewed as an ‘equal and opposite’ reaction. This represents a shallow observation.

However, many fins on fish and whales have special features with a 3-dimensional aspect. Some of this can be seen in the comparison between the views from the edge of a swim fin (Fig 3-C) versus an actual fish fin (Fig 4-D) during a single stroke. As one can see in the drawing, the curve of the swim-fin is reversed from the particular fish-fin shown.

 

[Arak Lea]

The fish fin as shown has the advantage of tips extending out into unobstructed water. Conversely, the swim fin is narrow and suffers from being completely within the flow-shadow of the human foot. In this case the fish fin at the tips (Fig 4 D) can approximate the form of a low-speed hydro foil or air-foil. The swim fin (Fig 3 C) as it is commonly implemented, cannot.

The implementation of duck-feet as a push type concept is very convenient for simple rubber materials.

It is informative to look at the fin more like a foil (Fig 5-A and B), where lift is a result of the difference between pressures above (Fig 5-A) versus below (Fig 5-B) of the foil or similarly a difference between two sides of the fin blade (Fig 7-A). The difference, Fig 7-4 versus Fig 7-5, results in a force of lift. The reaction to this lift provides motion for the swimmer, or in another case, sustaining the altitude of an air foil.

The fin in Fig 6-C has been rotated (Fig 6-D) to match the same direction of motion and direction of lift. All three forms (A, B, D) are oriented for lift toward the top of the image. And each, when in operation, are moving to the right (x, y, z) relative to the medium it interacts with. Note that in this case (Fig 6-D), the volume of fluid just above the fin is also leeward from the foot due to the given path of flow.

For low speed flows, at a level which a swimmer would generate, the Fig 5-B profile is more efficient than Fig 5-A. A simple bending of a flat foil would be suitable in this case.

Given a flow of fluid medium around an asymmetric foil (Fig 7-A), while laminar flow exists, Bernoulli’s Law states that the upper path (Fig 7-4) is longer and therefore the flow will accelerate to a faster speed. Where that difference of velocity exists, that zone will decompress to a lower pressure. Due to the ‘Coanda Effect’, and while the flow rate stays below some threshold, for a given curve, laminar flow will follow the surface to the trailing edge. This allows a low-pressure zone to exist along the path where laminar flow is still attached. The fastest flow with lowest pressure is nearer the leading edge, and including surfaces just adjacent. A measure of low pressure does continue down-stream along the surface while laminar flow exists.

The flow below the fin (Fig 7-5), which is slowing and compressing, goes to a higher pressure. The difference between upper and lower pressure zones, acting on the surfaces of the foil, and transmitted through its structure, generates lift (Fig 7-3).

The attachment of laminar flow on the convex side is more volatile and easier to interrupt than the concave side, so the outside (low pressure side, Fig7-4) geometry needs to be more carefully preserved than the inside-underside-concave shape (Fig 7-5).

The absolute limits for a ‘low pressure zone’ on both a fin or foil is limited to between ambient and nearly zero ‘pounds per square inch’. The limits for high pressure zones are always from ambient up to whatever power and speed is available from the source. But in a water medium, also while it is below the level of at which cavitation occurs. At ‘Sea Level’ ambient is 15 PPSI. Underwater ambient is an additional 15 PPSI for each 33 feet of depth. Cavitation is a subject beyond this discussion.

It is therefore possible to generate more pressure differential at depth than at ‘Sea Level’. The ability to do so at the speed desired is based on available power and the efficiencies of the fins in those specific conditions. In this case a diver’s legs are the source of power.

 

[Arak Lea]

During the downward ‘kick’ stroke, the common swim fin (Fig 8-C) has a shape that creates non-laminar flow in the upper zone (Fig 8-C4) because it sits in the fluid shadow of the foot. But also, on its own at that aspect angle, the inverted curve shape would cause a stalled, turbulent flow. This turbulent, stalled zone (Fig 8-C 2 thru 4) has a higher pressure than a laminar flow would create. A return upward stroke (not shown) has a reduced shadow but overwise has similar issues.

In the downward kick stroke, the toe of the foot up to the ankle (Fig 8-C1) which first encounters flow creates a frontal stalled zone with no useable lift. Some fins provide a vent between the toe and blade (not shown) to reduce pressure at that zone during the kick stroke.

In comparison, the drag of the fin (Fig 8-C2) is higher than the drag on a foil (Fig 7-A2) and inversely the fin lift (Fig 7-A3) is lower than for the foil (Fig 8-C3). Both differences benefit towards the foil.

It should be obvious that a foil (Fig 7-A) can be better than the common fin blade (Fig 8-C). And one should note, even if the fin-blade curve could be modified to a foil curve, the foot is still in the way. To mitigate the issue, a foil would need to be moved some distance from the toe of the boot.

In the diagram (Fig 9-3) one can see that for ‘Blade Fins’, lift during the up-stroke is in the opposite direction from the down stroke (Fig 8-3). As shown in both images, common ‘Blade Fins’ curve toward the intended direction, automatically reacting to forces and bending from mid-section, increasing toward the tip of the blade.

In that respect, the problem for foils to be used in swim fins, is that the profile of a foil would have to be curved to the reverse as compared to common ‘Blades’. Foils need some other means of curving to the opposite. And again, during the opposite stoke, the geometry would have to be reversible.

 

[Arak Lea]

In the images Fig 10 thru 13, all of the diver postures are intentionally presented in duplicate to each other. But the intention is that the leg motions represented are in opposite strokes in two of them. In Fig 10 and 12, the leg closer to the observer is in a downstroke. But for drawings in Fig 11 and 13 the closer leg is in upstroke. Divers in Fig 10 and 11 are shown with fin blades. The divers in Fig 12 and 13 are shown with foils. But in the case of foils, the foil fins are drawn missing any attachment structure. This is to better expose the curvature of the foil and how it is spaced off from the diver’s foot.

Between the two stoke directions, both blade types need to reverse their curvatures to the opposite stroke. As noted in text above, to allow for un-obstructed flows, the foils will need to be at some distance from the toes of the boots.

There is a small a number of fins in current use that offer a blade profile based on foils. These are all symetrical profiles. Only one fin accomplishes any type of a asymetric foil profile and an opposite stroke re-curve. But that fin uses a thin membrain as a cup shape with a fixed curvature. But, in that case there is little difference in the distance of flow between the convex and concave sides of the blade. See in the references to prior art.

 

[Arak Lea]

Summary of The Invention

In Fig 14 the upper legs (Fig 14-E and F) are in a down stroke with relative water flow Fig 14-1. To better display the shapes involved and lifting forces, it is reoriented in Fig 14-G and H. In the exibition of both E and G, a part of the supporting spars are errased for clairity. Relative flow is labled 1.

For the reasons noted in paragraphs above, a foil could only improve over a common fin blade if the foils are cleanly offset from the foot. To accomplish this offset, spars are needed to locate and support a foil (Fig 15). Keep in mind, foils would have to independently provide the two opposite curvatures for each stroke. Fig 15 shows the downstroke foil curvature.

The shadow zone behind the foot (Fig 15-4), depending on the relative velosity, will be a volume of turbulent flow. The point to notice is that the gap between the leading edge of each foil and the boot is cridicle to allow unobstructed flow. That allows laminar on the convex side of the fin. But if the blade is too far offset, this increases weight and torque on the swimmer’s ankel can become too great for comfort. Both issues unnessarilly increases the swimmers effort.

The dynamics of the down stroke need to apply also to the up stroke, but again inverted. So the blade profile must reverse. This difference is shown between Fig 16-H compared to Fig 17-N and
Fig 16-E compared to Fig17-K.

 

[Arak Lea]

Bi-Pedal Foil Fin Design

A fin blade in this discussion is roughly a flexible sheet, and if supported correctly it is intended that it will bend only in the intended direction.

Common fins integrate with spars at the edges as a single unit the complete structure bends. Having been supported at only the leading end, it will automatically bend in the direction intended. But foils need to bend to the opposite, and when using similar spars (Fig 18) as the fin type blades (Fig 6-D), this foil design (Fig 20) needs to be separate parts for spars (Fig 20-A) and blade (Fig 20-B).

Another issue to address is that without stabilization from an integrated blade, the bending of the spar may deviate from the intended direction. So, the spars need to be designed to self-control to the correct orientation. In Fig 18 and 19 the spars are shown in a correct bent position for the kick stroke, also known as, the down stroke.

For our foil fins, the spars will be attached at the two axel shafts shown in Fig 18(C & D). As water pressure pushing on the foil increases, force at the tip (at the lower axel D) also increases, and the spars will bend. However, the spars are best to bend in the zone (Fig 19-B) only starting just below the leading axis (Fig 18- C).

The spars need to remain stiffer above the axle (Fig 18-C) so as to help fix the leading edge of the foil in a more advantaged position, at a distance from the boot, and a little forward in the kick stroke.

In the Fig 20, the foil has been included (Fig 20-B). It is shown as under a load from a ‘kick’ (downward) stroke. This foil is shown including a fence at the side edges. Fig 21 shows this assembly in profile.
In Fig 22 the foil is shown by itself while at rest. The leading edge is to the left (Fig 22-Leading).

Since the foil body is supported at leading and trailing edges, and responds to pressure more at the middle, the bend of the spar is mirrored in the foil, and not simply duplicated. This reversal provides the required hydrofoil profile and orientation. Both parts will re-curve to the reverse during the counter stroke.

The bends in the two parts regulate each other to the same depth of curve due to the attachment locations. The resulting degree of curve is dependent on the degree of elasticity, its distribution along the length of the part, how much the blade extends beyond the axles, and finally, the level of power applied to the stroke. The square area outside the axles should be less than the area between them. Given that the leading edge needs to extend some distance from the toe of the boot, the trailing is preferred for reduction of square area.

When the foil is not under load and not bending, the leading edge of the foil sits directly between the leading axle (Fig 18-C) and the boot.

The middle of the foil is relatively flexible. The leading edge of the foil nearest the boot, is relatively stiff. The trailing end is also stiffer. Therefore, against water pressure the ends can relate primarily to the changing bend at the middle (see Fig 20-B and Fig 21-D).

As one can see in Image (Fig 21), the distance of the blade from the boot (Fig 21-D) is increased due to the length of the foil before the upper axle moving into the flow coming at the fin. This added distance reaches forward into undisturbed water. This geometry allows the upper axle and foil body to be structured as closer to the foot, with benefits described above.

Fences on the side edges of fin blades are common to most bi-pedal fins. Since these foils are also narrow, as is typical on bi-pedal fins, fences are useful here. The fences are used to maintain a separation between diverse pressure zones by guiding and limiting the direction of water flow. The intent is to keep the flow direction in-line with fin motion. Given that bi-pedal fins are very narrow, the fences also mitigate for that by maintaining the width of the intended pressure zones by restricting lateral flows.

In addition to flexing under force, the spars and foil must resist bending to some degree to accomplish a desired geometry. This is accomplished by adjusting the thickness and elasticity of the materials they are made of. Various densities of Silicone and other rubber plastics are suitable, but must be selected for the performance intended.

For the foil design shown in Fig 22-F, the stiff zones extend roughly two equal distances, one from the forward axle going forward and from the rear axle toward the trailing direction. This first design, and some number of other optional foil designs will be described in detail.

Given that the foil must also have extra stiffness at the leading and trailing edges, and more flexibility toward the middle, it benefits when comprised of more than one section or layer of material. The sizes of these zones also need to vary with respect to the performance intended. For all versions of the foil body described below, the thickness and elasticity can be varied to create the desired profile at the outside as a convex curve. Tradeoffs between measurements of thickness, length and elasticity sets the depth and other geometric features of the foil.

 

[Arak Lea]

Detailed Description of the Invention

Fin Support Structure

Like the vast majority of modern swim fins and SCUBA fins, the whole fin is cast out of one or more elastomeric materials. When multiple layers/densities are used, multiple steps of casting are typical. In this design the spars (Fig 23-B and C) can be included with the boot in the same casting, or alternately co-bonded to the boot in additional castings. This patent does not address the design of the boot itself.

The spars (Fig 23-B and C) have Shafts (Fig 23-D and E) inserted into a hole, then through the foil body, then through the hole in the opposite spar. ‘C’ rings are then slipped into slots at each end. The hole can then be sealed with application of a compatible bonding material. The shafts and ‘C’ clips should be stainless-steel since this is a permanent installation and exposed to natural elements.

 

[Arak Lea]

The width of each the spars are allowed to be as wide as possible with-in the desired overall width of the foil. Featuring ribs with fence ridges (Fig 24-1 & 3) on each spar help limit water cross-flow. Limiting cross-flow is important since the foils are very narrow, and the laminar flow areas have very limited area to exist independently from turbulence.

The height and elasticity of the ribs determine the bend in relation to the power applied. The cross-bar (Fig 24-F2) is of a higher firmness (Shore durometer scale A, 60 to 90), but relatively thin, this combination is meant specifically to help limit off-direction bending. This configuration allows the ribs to have fencing as opposed to a simple box section. The inside fence thickness versus the outside can be used to help compensate for torsional or non-parallel bending.

Image Fig 23 and Fig 24 are drawn as spars of a single elastic material. As was previously noted, that is not the only option. Where the material make-up is mutually compatible to bonding two or more layers with diverse elasticity, such as with silicones, the following design is made possible.

 

[Arak Lea]

In this design option Fig 25, articles B and C are a stiffer material, perhaps using Shore Durometer Scale A, 50 to 90, and are cast first. The articles Fig 25-D and E are then cast over B and C, and also bonded with the boot in one or multiple casting steps. This new spar material is relatively flexible perhaps Shore Durometer Scale A, 30 to 70.

‘cast over’ in this regard means to place a previously formed item into a mold, and inject the second material around it.

In this next design option (Fig 26), a higher performance is possible than the options above. But it is also more complex and more costly. When Fig-A and B are cast, a stiffener (Fig 26-C and D) is first inserted into the mold and fully encapsulated inside. This stiffener is a semi-ridged, bendable material such as a medium density reinforced polyethylene, or a composite such as fiberglass or graphite. Being fully encapsulated allows that it does not need to co-bond with the more elastic material that encapsulates it. Holes in the stiffener increase contact paths and thereby reduce possible separations between upper and lower sections of the elastic material. This also hold the stiffeners in position with-in.

 

[Arak Lea]

Fin Foil Assembly

The foil must accomplish an appropriate bend at a given level of power, in the right places, and with relative stiffness in other sections. Several designs can accomplish this. Each has its own level of performance, complexity and cost.

The actual location of the two axles along the foil will also affect the degree and center of bending. More area between the two axels will give more bend. Moving the trailing-axel forward will favor more bend to the front and less for the rear.

Foil Embodiment #1

This foil design (Fig 27) has up to 4 levels of elasticity in its combined materials. It can be cast in multiple steps either starting at the middle, or starting from one edge to the opposite. The elasticity for each layer depends on the intended use of the fin. Typically, a more powerful or skilled swimmer would prefer to use the firmer materials.

Casting from the middle starts with Fig 27-E, then cast in D and F, then cast C and G, then cast fences A and B.

The height of the fence at the side edges depends on the application and the density of the fence material used. At the highest it can be kept parabolic as shown, or flatter and oval when lower. The ideal performance allows good flexibility but will not fold over during foil bending against forces. And thick enough to not lay down from differential pressure zones produced by fluid flows.

The result would typically appear like Fig 28.

Some suggested ranges in silicone rubbers for these segments are;

A and B - Shore durometer scale A, 30 to 60 (always less than D)
C and G - Shore durometer scale A, 60 to 90 (always more than D)
D and F - Shore durometer scale A, 40 to 70 (always more than E, less than C)
E - Shore durometer scale A, 30 to 60 (always less than D)