1) A team of students was tasked with designing a sub-assembly for a 12-inch by 12-inch platform that could support nominal and maximum loads while submerged in water. 2) Their final design used corner cubes and connecting rectangular prisms to meet requirements, but water intake caused experimental results to differ from predictions. 3) Upon reflection, the students determined they could improve their design by combining corner pieces and applying tape more carefully to better prevent water intake.

1. To: Professor Goodrich
From: Section 2 Group 9: M. Feigert, T. Tredway, Z. Jones, W. Kudela, M. Sills
Date: 11 December 2014
Subject: Final Memo: Project 2
Introduction
As a team, we were tasked with developing a sub­assembly for a 12­inch by 12­inch
platform that would be able to support at least a nominal load of 2 pounds and a maximum
load of 4 pounds while submerged in water. Implied by this stipulation is that the design must
have a factor of safety of no less than 2.00. As another explicit requirement, upon addition of
the maximum load, the sub­assembly must not sink more than 70% of the change in depth
resulting from the nominal loading case. The project document implicitly requires that the
sub­assembly promote stability while accounting for uncertainty. Finally, the sub­assembly
must fit within a pre­determined testing area and should be constructed using only specified
building materials.
Design Process/Equations
First and foremost, the sub­assembly must hold both the nominal and maximum loads.
In order for the platform to float, the buoyant force acting upwards on the platform must be
greater than the force of gravity due to the weight of the platform and any added load. The
buoyant force, the force exerted by a fluid on a body that is submerged in it, is defined as:
V gFb = ρ fluid (1)
where Fb is the buoyant force in Newtons (N), pfluid is the density of the fluid in which the object
is submerged in kilograms per liter (kg/L), V is the volume of the fluid displaced by the object
in liters (L), and g is the acceleration due to gravity in meters per second squared (m/s2
). The
force of gravity due to the weight of the platform and added load is given by:
gF = m (2)
where F is the force in Newtons (N), m is the mass of the object in kilograms (kg), and g is the
acceleration due to gravity in meters per second squared (m/s2
). As previously mentioned, in
order to float, the force component of equation (1) must be no less than the force component
of equation (2). Since the liquid in question for this project is water and acceleration due to
gravity is constant, equations (1) and (2) can be combined and simplified to form:
≥ mV (3)
where V refers to the total volume of floats necessary measured in centimeters cubed (cm3
)
and m is the mass of the object in grams (g). Thus, to support the maximum load of 4 pounds
or 2,789.39 grams, the sub­assembly must consist of at least 2,789.39 cm3
of floats. Also
important to consider when it came to designing the sub­assembly was stability. We
developed a design in which all added floats were located around the outside edge of the
platform. In doing this, we created a sub­assembly whose average center of buoyancy was

2. located in the center of the platform, directly below the intended center of gravity. Finally, we
had to deal with perhaps the most difficult explicit requirement: the 70% stipulation. To do so,
we decided on a two­tier design in which the total area of floats in contact with the water
increased as more weight was added. After a period of idea pitching and trial­and­error, our
team decided on a design using one cube (of side length 8.2 centimeters) in each corner of
the platform with rectangular prisms (of dimensions 14.08 cm x 8.2 cm x 4.1 cm) connecting
each cube in a picture frame­like manner.
Though this initial design did meet all implicit and explicit requirements, we realized
the change in height between our nominal and maximum loading cases, at 66% of the initial
change in height, was uncomfortably close to failing to meet the 70% stipulation. In order to
increase the robustness of the design, we decided to add a small rectangular prism (of
dimensions 8.2 cm x 8.2 cm x 2.0 cm) to each of the four corner cubes as can be seen in the
mechanical drawings at the end of the memo. This slight adjustment vastly decreased our
projected percent change in height to a value of only 45%. Indirectly, the change also
increased the maximum load our sub­assembly could support, influencing the factor of safety
in a positive way.
Finalized Design and Experimental Results
In designing the sub­assembly, our goal factor of safety was 4.04. Upon testing the
design to failure though, we found our actual factor of safety to be 16.8% larger at 4.72.
Looking back, we attribute this increased factor of safety primarily to the increased buoyancy
created by an “air bubble” located underneath the platform within the perimeter of rectangular
prisms. Less significantly, we slightly overestimated the mass of the building materials and
platform.
To our team, optimization for cost was important. For this reason, the projected cost
of our initial design was relatively low at only $48.21. The actual cost of designing our
sub­assembly was much higher at $171.56. We attribute this miscalculation to several
factors. First, while estimating the cost of the supplies, we planned on cutting the wide
packing tape twice lengthwise to accomplish more with the same length of tape. While
actually applying the tape however, we decided not to cut it lengthwise in order to better
waterproof the pieces. Furthermore, after testing the platform, we noticed that it took on a
significant amount of water, so in efforts to rectify this, we applied a second layer of tape in
several locations. Finally, our initial cost calculation assumed we would use plastic wrap as a
waterproofing material instead of simply using packing tape.
As for the displacement of our sub­assembly in water, our theoretical and experimental
data is captured in Figure 1 located on the following page. As can be seen in the chart, our
theoretical change in height between the unloaded and nominal load conditions was 2.80
centimeters, whereas our theoretical change in height between the nominal and maximum
load conditions was 45% of this value, or 1.25 centimeters. Experimentally, our first change
in height was 2.50 centimeters. Our second change in height was 56% of this value at 1.40
centimeters. There was a 24.4% difference between our experimental and theoretical percent
of change in height.

3.
Figure 1. Plot of Platform Displacement in Water as Weight is Added
Interestingly, although the factor of safety exceeded expectations significantly, the
percent change was severely increased due the sub­assembly’s inability to hold out water.
Although the first test exceeded expectations for height change, by load condition two, the
platform had taken on water and the results were slightly skewed.
Conclusions
Reflecting on these design choices, one obvious change we would make is to combine
the cube and small rectangular prism located in each corner into one part ­ a rectangular
prism of height 10.2 centimeters. In addition, we would cut the poster board with more
precision so that the corners would fit better and thus not take on as much water. Lastly, we
would spend more time in the construction phase in an attempt to correct our largest mistake:
not applying the tape perfectly flat. Our hasty construction techniques created an air bubble
in the tape which allowed water to seep through. Ultimately, the knowledge we learned from
this project has further familiarized us with the continuous nature of the design process and
has made us better equipped to accomplish tasks in a team setting.

4. Mechanical Drawings
Figure 2 below shows a mechanical drawing of one of the four floats located in the
corners of the platform. Each float consists of a cube (of dimensions 8.2 cm x 8.2 cm x 8.2
cm) capped by a rectangular prism (of dimensions 8.2 cm x 8.2 cm x 2.0 cm).
Figure 2. Mechanical Drawing of the Corner Floats
In Figure 3, located below, one of the four rectangular prisms (of dimensions 14.08 cm
x 8.2 cm x 4.1 cm) is shown in the form of a mechanical drawing.
Figure 3. Mechanical Drawing of the Middle Prisms

5.
Shown below, in Figure 4, is a mechanical drawing of the finalized sub­assembly. All
individual parts are connected to each other and to the platform itself using packing tape.
Figure 4. Mechanical Drawing of the Sub­Assembly Attached to the HDPE Platform