•  The stability and buoyancy of the boat was studied in order to maximize the stability and buoyancy and minimize the weight of the boat."

•  In order for the boat to float, the buoyancy force has to be greater than the weight of the boat itself. The magnitude of this force (FB) is the weight of the liquid displaced by the boat:"

FB = γwater∀disp "

•  The stability of the boat is dependent of the metacenter (mc) of the boat: The metacenter must be above the center of gravity (CG) of the boat in order to achieve stability."

•  When the metacenter is above the CG of the boat, a righting moment is produced; an overturning moment is produced when it is below (Figure 1)."

""

"

Figure 1. Metacenter, Center of Buoyancy, and Center of Gravity and Stability of Boat (Heuzé, 2014).

"

•  The metacenter of the boat represents the intersection of the buoyancy force line-of-action that passes through the center of buoyancy (CB) and the object’s vertical line-of-symmetry that passes through the center of gravity (Course Notes)."

•  The mc of the boat can be calculated by adding the MB of the boat to the CB. This MB value is dependent on the moment of inertia of the boat and the volume of the liquid displaced by the boat:"

MB = Io∀disp "

•  Maximizing the moment of inertia of the boat and minimizing the volume displaced can achieve a maximum mc, thus giving a maximum stability when coupled with a low CG of the boat."

•  The boat could not be longer than 40 centimetres (cm) in length, and both its width and depth could not be greater than half of its length."

•  The boat had to be constructed only from the provided cardboard and duct tape, and had to have openings to accept a 3.5-kilogram (kg) concrete cylinder that has a 10-cm diameter and is 20-cm in length, as well as steel balls of 0.5-inch diameter."

"

"

•  A flat base was used for most stability as opposed to a V-Shaped Bottom (Washington College, n.d.)."

•  A triangular tip was added to the boat to reduce the fluid drag as the boat travels in water."

•  The triangle at the front of the boat was used to reduce the surface area in contact with the water, since a large contact surface area yields greater fluid resistance experienced by the boat (Science Fair Projects, n.d.)."

•  The rectangular base with maximum possible dimensions was constructed."

•  A cube has the largest volume; hence a shape as close to a cube was selected to gain the maximum amout of volume displacement in water."

•  A hull of 39.5 cm long, 19.5 cm wide, and 10 cm deep was used to increase the maximum buoyant force the boat could withstand without sinking. This allowed for more mass to be loaded onto the boat."

•  The top view of the boat can be seen in Figure 2."

""

Figure 2. Top view of design with dimensions of openings for concrete cylinder and steel balls. All units are in cm.

"

•  An additional prism was added beneath the hull to lower the center of gravity so the metacenter was above the center of gravity."

•  To obtain a stable object which produces a righting moment during the even keel test (Basic Stability Test), it was essential that the metacenter of the boat was above the center of gravity."

•  The locations of the concrete cylinder and the compartments for maximum load test were designed for optimal balance."

•  Cylinder compartment was placed on the centroid of the base shape. Compartments for additional masses were divided so that there was equal used and unused area on both sides of the cylinder."

•  Each piece of cardboard was covered with layers of duct tape on all sides to minimize any potential leaks."

•  During the construction, any bends or folds in the cardboard were avoided to ensure overall structural strength."

BACKGROUND

EXAMINATION OF BUOYANCY THROUGH CONSTRUCTION

AND TESTING OF CARDBOARD BOAT

Alyssa Carr, Navan Chawla, Patricia Klemp, Michelle Liu, Heidi Vanheule "

DESIGN RESULTS

•  The finished boat was tested put through a level deck test, a basic stability test, a channel movement test, and a maximum load test. The physical characteristic of the finished boat were recorded before the testing and are located in Table 1."

•  Level Deck Test: This test involved simply placing the boat in the water with the load of the concrete cylinder (3.5kg) and using levels placed at the top of the cylinder to determine whether or not the boat floated completely level. Although the deck was level bow to stern, it listed slightly to the portside (shown in Figure 3)."

"""

Figure 3. Photo of boat listing slightly to the portside upon entering water.

"

•  Basic Stability Test: The basic stability test involved pushing both the port and starboard side of the boat, and the bow and stern of the boat to the water level to see if the boat would right itself. The boat righted itself without a problem after every basic stability test."

•  Channel Movement Test: The channel movement test consisted of pushing the boat though the water to determine how streamlined it was. The more streamlined a boat design is, the straighter it travels. The boat was initially travelling straight, but eventually curled to the portside."

•  Maximum Load Test: The maximum load test involved loading the boat until failure. The weight to strength ratio was then determined by dividing the weight the boat carried by the weight of the boat itself. The boat was able to withstand a load of 7.54 before sinking. The weight to strength ratio of 9.64 was calculated as follows:"

"

Weight" 782.40g "

Length" 39cm"

Width" 19.5cm"

Depth " 16.5cm"

RECOMMENDATIONS

•  The boat carried a maximum load of 7.34 kg, which translated into a weight ratio of 9.63."

•  The boat’s main fault lies in its heaviness. The mass of the boat lowered the overall weight ratio. A heavy boat resulted in an inefficient design."

•  One recommendation is to lower the boat’s weight by using less tape. Both the inside and outside of the boat are covered in tape in order to protect against water damage and leaks."

•  For future designs, the amount of tape used for the interior of the boat should be minimized. Only the vital and weak parts, such as the corners and the seams, should be taped. The dividers that were installed in the boat should not be taped. By concentrating the tape to only select areas, the boat’s weight should significantly decrease thus increasing its weight ratio."

•  Another recommendation is to increase the amount of usable volume inside of the boat. The boat’s current design includes six dividers. Two dividers are used to separate the steel ball compartments from the concrete cylinder. Two dividers are used to separate the tip of the boat and the back of the boat from the steel ball compartments. Two dividers are used to separate the steel ball compartments into four sections. "

•  Removing the dividers from both the back and the front of the boat, the tip and back of the boat can be used for storage. This added storage means that the weight from the steel balls can be more evenly distributed. Removing the dividers will also decrease the overall weight of the boat. "

•  A final recommendation to improve the boat design is to increase the depth of the boat. Increase the boat height so that it can sustain more weight before it sinks. Currently the boat walls are 15 cm. "

•  It is recommended for future designs that the wall heights are maximized to 19.5 cm."

REFERENCES

Heuzé, C. (October 30, 2014). Sinking on the Seven Seas. Climatesnack. Retrieved from http://www.climatesnack.com/2014/10/30/sinking-on-the-seven-seas/ (Retrieved on July 11, 2015)."

Science Fair Projects, (n.d.). How does the bow of a ship influence water resistance?. Retrieved from http://www.all-science-fair-projects.com/print_project_1210_141 (Retrieved on July 11, 2015)."

Washington College,(n.d.). Cardboard Boat Building Tips. Retrieved from https://www.washcoll.edu/centers/ces/cardboard-boat-building-tips.php (Retrieved on July 11, 2015)."

CIVE280 | Group 20 | Presented to Dr. S. Pagsuyoin | July 14th, 2015