This paper evaluates the effectiveness of a variety of flotation methods on a number of properties, including buoyancy, righting capability, and resistance to environmental conditions, and offers an optimal flotation method for water polo goals. This research and analysis is conducted with a focus on these methods’ potential application in the modification of the water polo goals which the Northwestern University Club Water Polo Team currently uses during practices and games. After comparing displacement, air bladder, and various foam flotation methods, a specific combination of two different flotation methods, utilizing the most promising properties of each material, could offer the best solution to these water polo goals’ flotation issues.
Keywords: displacement, air bladder, foam, water polo, flotation, buoyancy
The flotation of an object can be achieved relatively easily, but the particular conditions of a water polo game make for a more challenging set of requirements for the flotation of goals. Potential goal materials must endure movement in and out of the water, a possible reaction with chlorine in pool water, and degradation over time. In the past, the goals have been stored outside – even during the winter – when not in use. This storage method with likely continue from time to time, so the materials should be resistant to any wear that comes with weather. This paper compares the behavior and performance of three main methods of flotation – displacement, air bladder, and a few types of foam – under these conditions. In this paper I propose an effective combination of flotation materials as the best option for flotation modifications to the NU Club Water Polo goals.
The effect of surroundings is a central consideration in the analysis of flotation methods. Firstly, water polo at Northwestern is played in a chlorine water pool. This is an inevitable condition, as the pool itself cannot be altered in any way, and the cost of a water type change would greatly outweigh the benefits of any goal alterations. Thus the flotation method must not react with this chlorine water in any way that causes either degradation of the flotation method or harm to people in the pool.
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Secondly, the process of goal setup and storage before and after practice puts some frictional stress on the underside of the goal as it slides over the edge of the pool. The pool edge consist of the edge of the pool deck, a half-foot drop, and a filtration ledge, at the water level, that extends about a foot horizontally into the pool. At the beginning of practice, team members place the goal on the deck next to the pool and slide it, with motion parallel to its long edges, along the edge structure and into the water. At the end of practice, they perform the same process, but in reverse (see Appendix: Client Interview Notes). The goal is structurally sound given the metal supports strategically positioned throughout the goal, but the flotation method should not react poorly to any very slight bending or twisting that occurs during the setup and storage process (see Appendix: Images).
Finally, the goals occasionally are stored outside the aquatics center. This often happens when spectators need the space around the pool, where the goals are usually placed outside of practice, during competition. Outside storage can occur year-round, but it poses the greatest challenges to the goals’ integrity during the winter, when the wet foam can easily freeze to the concrete ground (see Appendix: Client Interview Notes). The flotation method should be resistant to drastic temperature changes and the harsh conditions of the Evanston winter.
Potential Flotation Methods
The first option in consideration is a displacement hull similar to those that characterize most vessels. According to Archimedes’ Principle, when an object of a certain mass is placed in a liquid, it displaces a certain volume of that liquid. The Greek mathematician Archimedes claimed that this displacement induces a buoyant force, equal to the weight of the displaced liquid, exerted directly upward on the object. Mohazzabi revisits and reaffirms this old and proven physics principle, confirming its verity while applying it in new settings (Mohazzabi, 2017). The object has mass, so the force of gravity acting downward on the object opposes this buoyant force. The object will sink into the water until the gravitational and buoyant forces are equal. If the object weighs more than the water it displaces, the object sinks. If some liquid leaks into the hull, it simply adds to the object’s mass, requiring a greater buoyant force to achieve flotation.
The gravitational and buoyant forces are also responsible for displacement hulls’ righting ability. Assume the boat is symmetric about a plane running its length and height. When a boat rolls, it rotates about an axis running parallel to the length of the boat. As long as the center of mass is positioned below this rotational axis, the boat will right itself for small angles of roll. If the boat rolls clockwise, the center of mass shifts left and the buoyant force, still pointing upward, acts at a point to the right of the center of mass. Thus the buoyant force exerts a counterclockwise moment about the center of mass, causing the boat to rotate counterclockwise and right itself (Center of Gravity and Buoyancy) (see Appendix: Images, Figure 1).
The second option in consideration is an air bladder, or a series of air bladders, installed in the volume under the water polo goals. This method utilizes the difference in density between the air inside the bladder and the water in the pool, ultimately causing flotation through the same principles that make displacement hulls effective. A version of this mechanism can be found in many fish species, but some argue that its central purpose is in other, possibly respiratory, functions (Morris, 1885). Nonetheless, air bladders can be found in other marine applications.
The first consideration is reactivity of the bladder material with chlorine water. Polyurethane-coated nylon airbags in Optimist sailboats keep the dinghy afloat if the open hull fills with water (Airbag, Red High Float 48 litre). Nylon is fairly chemically compatible, satisfactory up to 72℉ with chlorine water, which is found in the Northwestern pool (Nylon Chemical Compatibility [Chart], 2018). Polyurethane, the coating on the bladder, has limited and unsatisfactory chemical compatibility with chlorine water at various temperatures (PVC and Polyurethane Chemical Compatibility [Chart]). Special precaution ought to be taken in selecting the type of polymer used to make the bladder, as chlorine water clearly reacts with certain polymer types, leading to the degradation of the material.
A second consideration is the durability of the bladder material given the frictional wear that comes with the goal setup and removal process. Sliding the bottom of the goal over the pool edge could potentially tear the air bladder, rendering it completely useless. The bladder should be made of a very durable material, or it could be protected from the pool deck by some spacer or a series of bars in a grid formation. A hard displacement hull, in comparison with an air bladder, would likely require no additional protection—this is one advantage of a displacement hull over an air bladder.
Thirdly, if the goal is stored outside during the winter, the air bladder must endure a drastic drop in air temperature from the pool environment to the outdoors. If the air reaches too high a pressure, the bladder might pop and become useless. However, according to the ideal gas law, a drop in temperature would cause a drop in pressure. As long as the bladder is filled with air in a warm pool environment, outdoor winter storage should not present any issues.
The third and most intuitive option in consideration is to simply replace the foam currently in use. Although the current implementation is flawed, as the foam has decayed with time, some improvements could make it a more suitable method of flotation.
In the context of this particular application, foam can be considered a more effective form of an air bladder. Polyurethane foam, the most likely type to be used, is lightweight, strong, and corrosion-resistant (Gadhave, Mahanwar, Gadekar, 2018). It can come in open- or closed-cell forms, but a closed-cell polyurethane foam is likely best in a water polo environment (Open Cell Foam Vs. Closed Cell Foam: Best Definitive Guide). When an air bladder wears or is punctured, it can no longer serve its purpose. Foam’s structure consists of many pockets of gas trapped in cells, so a puncture only affects those cells that it directly touches, and the remaining cells can still cause flotation. Again, buoyancy comes about by the density difference and Archimedes’ Principle, which defines the opposing gravitational and buoyant forces acting on an object suspended in liquid. This makes foam a more durable version of an air bladder, and therefore a more reliable selection for the water polo goals.
Foam has two general physical forms: solid and 2-part liquid. Solid, most common, can be machined down into the needed shape. 2-part foam can fill any shape of volume as long as enough foam is provided. Within these categories, the foams’ compositions can be engineered with to fit specific needs, from flotation to mold prevention to insulation (Foam Series: Comparing Types of Cushion Foam). Some types have been approved by the US Coast Guard for use in marine settings (2 Part Liquid, Expanding Urethane Foam). The two parts, when combined, will expand to fill a volume of shape, as long as there is enough material to fill it. Given the irregular shapes of the volumes for foam storage in the water polo goals that NU Club Water Polo uses, this 2-part polyurethane foam may be a better choice than solid foam (see Appendix: Images, Figure 2).
As described in the air bladder section, reactivity of polyurethane with chlorine water can lead to the degradation of the polyurethane foam. Therefore, if this method is used, it should be protected in some way from the chlorine water in the pool.
Analysis and Potential Solution
Displacement hulls, air bladders, and flotation foams, all by the same principle of displacement, all are effective flotation methods in different settings. Given the conditions of the environments in which NU Club Water Polo goals reside, a particular combination of these options may yield the most effective flotation method for the water polo goals. I propose a combination of closed cell, 2-part polyurethane foam and a watertight, hard polymer, displacement hull, installed underneath each water polo goal. The specific dimensions and shape of this design are dependent on the weight distribution of the water polo goals.
A hard polymer hull would protect the goals from the frictional wear that occurs when they are slid over the pool edge during setup and removal, before and after practice. During winter storage, the hull’s smooth, hard surface would not easily freeze to the ground. In the water, as long as the hull shape is suitable for the goal’s weight distribution, the displacement hull should be buoyant enough and able to right the goal if it rolls due to turbulence in the water. The hull should be watertight to prevent water from adding to its mass and ultimately removing its ability to help the goal to float.
The hull also would be supported, either in specific sections or throughout its entire volume, by 2-part polyurethane foam. By taking up volume and retaining an overall low density, the foam would make the hull resistant to any punctures and subsequent leakages. If whatever causes leakages in the hull also punctures the foam inside, its closed-cell structure would keep it functional by salvaging the surrounding bubbles of trapped gas. For strategic foam positioning, the expanding foam could occupy the possibly irregular volumes within the hull (see Appendix: Images, Figure 3). Again, the specific characteristics of this proposed solution are dependent upon further analysis of the weight distribution and positioned flotation needs of the water polo goals.
Displacement, the general mechanism by which all three flotation methods provide buoyancy, is a function of the volume of water displaced, which depends on the densities of the materials used in the goals and the flotation method. The air bladder utilizes a closed compartment of air, a low density material, to maximize its buoyancy capabilities. Foam’s durability, with its many independent cells of air, proves itself a better option than the air bladder. Finally, the displacement hull provides protection and righting capabilities. The proposed combination of flotation foam and a true displacement hull is likely the best possible solution to the water polo goals’ flotation issues.
- 2 Part Liquid, Expanding Urethane Foam. (n.d.). Retrieved from http://www.uscomposites.com/foam.html
- Airbag, Red High Float 48 litre. (n.d.). Retrieved from http://www.apsltd.com/airbag-red-high-float-48-litre.html
- Center of Gravity and Buoyancy. (n.d.). Retrieved from https://www.engineeringtoolbox.com/centre-gravity-buoyancy-d_1286.html
- Gadhave, R. , Mahanwar, P. and Gadekar, P. (2018) Lignin-Polyurethane Based Biodegradable Foam. Open Journal of Polymer Chemistry, 8, 1-10. doi: 10.4236/ojpchem.2018.81001
- Foam Series: Comparing Types of Cushion Foam. (n.d.). Retrieved from https://www.sailrite.com/Foam-Series-Comparing-Types-of-Cushion-Foam
- Mohazzabi, P. (2017) Archimedes’ Principle Revisited. Journal of Applied Mathematics and Physics, 5, 836-843. https://doi.org/10.4236/jamp.2017.54073
- Morris, C. (1885). On the Air-Bladder of Fishes. Proceedings of the Academy of Natural Sciences of Philadelphia, 37, 124-135. Retrieved from http://www.jstor.org/stable/4061110
- Nylon Chemical Compatibility [Chart]. (2018). In CP Lab Safety. Retrieved from https://www.calpaclab.com/nylon-chemical-compatibility-chart/
- Open Cell Foam Vs. Closed Cell Foam: Best Definitive Guide. (n.d.). Retrieved from https://www.foamtechchina.com/open-cell-foam-vs-closed-cell-foam/
- PVC and Polyurethane Chemical Compatibility [Chart]. (n.d.). In Rittenhouse. Retrieved from https://mkrittenhouse.com/ca/related-info/pvc-and-polyurethane-chemical-compatibility
Figure 1: Displacement hulls have righting ability.
Figure 2: 2-part polyurethane foam can fill oddly shaped volumes.
Figure 3: The abnormal volumes in the water polo goals could be reflected in the foam volumes within the displacement hull.
Appendix: Client Interview Notes
● Slide goal into water – one person in water braces entry
○ Place goal down right before pool, one person in water, one person on deck, and slowly slide goal into pool
● Taking out – unhook and two people drag it out – sometimes rotate 90 degrees (not as difficult as putting it in)
○ Need to be careful to not let it scrape along tile floor
○ Foam pads are expensive to replace ($400)
○ Foam pads they have don’t fit perfectly
○ Trouble making sure kickboards stay in place for maintaining floatation – adjusting them isn’t time productive
○ Big issue if crossbar gets in water – fills and sinks and gets really heavy and hard to get back up
○ Lightweight – need 2 people to carry, but not easy
○ Handles missing – now holding rings
○ Must move hands before dropping goal to avoid hurting fingers
○ Weight distributed towards crossbar side
○ Goals don’t have designated storage; they are often put outside and foam sometimes freezes to ground
○ Line tied to goal goes back around weight on ground to prevent goal from floating away
○ Method of holding goal in place with metal block is sketchy
Our goals / Other notes
● Research types of foam
● No need to be super precise with side to side movement in water
● Same goal used in game but suspended between lane lines – only flotation still an issue
● Consider mounting line using clamp that attaches to drain holes (approximately 5.5 ft from hole – same position as anchoring weight presently)
● Possibly look for foam alternatives
● Look to see where we could add handles
● Lower models not suitable for team
● No higher quality models except custom made (expensive)
● Anti brand goals used