Spaghetti Tower Lab Report

An Nguyen and Nikola Skerl

Post-Calculus 6 October 2017

TABLE OF CONTENTS

Abstract …………………………………………………………………………………...... pg. 3

Introduction ……………………………………………………………………………....… pg. 4

Materials …………………………………………………………………………………… pg. 4

Methods ………………………………………………………………………………. pgs. 4 - 11

Analysis ………………………………………………………………………………….... pg. 12

Conclusion ………………………………………………………………………………... pg. 13

References ……………………………………………………………………………….... pg. 14

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ABSTRACT

The goal of this study was to construct a spaghetti tower at least 40 cm tall that could support 2.6

kg of weight. For this end, six different designs were tested; this trial-and-error provided lessons

in theoretical engineering both general, such as triangles are the most stable shape and lots of

points of connection between parallels help reduce strain on any given point and thus is more

stable, and more specific to the materials on hand, such as the best way to reduce bending is

either to increase thickness or decrease length. It also gave practical lessons, such as how best to

account for imprecisions inherent in transferring a design to reality and how best to troubleshoot

during construction when those inaccuracies do arise. The study culminated into an eight-layered

tower with an equilateral triangle as a base. On each side of every layer, struts linked opposite

corners and a vertical strut was placed down the center. The final tower fell short, supporting

only 2 kg before collapsing due to practical error - the top of the tower was not level, making it

impossible to balance even a clipboard on top, much less evenly distribute weight. The 2.6kg

textbook thus exerted more force on one side of the building, causing the entire tower to bend

and eventually snap. The tower should have been constructed layer by layer to better account for

variations in height arising from construction.

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INTRODUCTION

The overarching goal of this study was to construct a tower out of spaghetti, with limits

on the amount of material, that was at least 40 cm tall and could support 2.6 kg of weight; the

process and analysis thereof was intended to teach further lessons about engineering, both in

theoretical design and practical construction, as well as technical writing.

As those lessons were meant to arise organically from experimentation, research

specifically pertaining to spaghetti structures was prohibited. However, inspiration was taken

from real-life engineering examples; one of the most ambitious designs tested was based not on a

tower but a bridge. In addition, already-established truss designs like Howe, Pratt and Warren,

were studied and used (“Truss”).

MATERIALS

30 pieces of spaghetti were allotted to each group, each approximately 25 cm long, and

an unlimited supply of hot glue, though the latter could be used only to connect pieces of

spaghetti at key points; coating spaghetti in hot glue was not allowed. A sheet of paper or a thin

piece of cardboard was allowed for use as a base. The spaghetti pieces were able to handle a

surprising amount of vertical force before snapping; however, before the break itself the pieces

had a tendency to bend, with the snap occurring at the vertex of the curve. The shorter the pieces

were, the less they bent and thus could handle more force before breaking. The hot glue served

as an effective connector, but also added a thickness that could throw off calculations and

de-align precisely cut pieces of spaghetti.

METHODS

Throughout the course of this study, six different designs for the spaghetti tower were

trialled.

The first consisted of tetrahedrons stacked on top of one another, connected at the vertex.

Each layer of two tetrahedrons was approximately 15cm tall; a total of three layers were planned

in order to surpass the 40cm height requirement. The bases of the tetrahedrons were to be

connected by pillars. In addition, the first two layers were planned to have buttresses

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perpendicular to the sides of the tetrahedrons that connected to the paper base; the buttresses

were to connect to the main structure at the vertex in the middle of each layer. One layer of this

design (see figure 1.1) was built before abandoning it. Imprecisions resulting from cutting

spaghetti and hot glue adding unaccounted for height meant the tetrahedrons did not connect at

the vertex, with about a 0.5cm gap between them.

Figure 1.1. First layer of initial design.

Given how much force would be directed towards the vertices and the inevitable inaccuracies in

construction that would mean aligning those points properly would be nigh impossible, the

design was deemed impractical.

To alleviate the problem of the design resting on a few key points of weakness, the next

design featured several connection points in the form of struts within layers. Triangles were

chosen to be the basic shape made by the struts, as they did not deform under pressure like

squares, which had a tendency to cave in or tilt. Also, a square base was used as triangles had

been difficult to construct precisely without encasing the vertices in glue to make up for any

variation in spaghetti length. To save on spaghetti as well as make the base stronger in

comparison to the rest of the layers, the layers were designed to shrink in base from top to

bottom, while staying at a constant height (see figure 2.1). This design never made it past the

blueprint phase, as a combination of rough sketches and indecision of how to lay out the trusses

in each layer and exactly how much the base should shrink each time made it impossible to

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calculate whether the design was feasible. In addition, while the shrinking bases made sense in

2D, in 3D one of the side lengths of the base would have to remain constant in order for the

layers to actually touch the layer below, further complicating calculations as different sides of

the layer would require different amounts of spaghetti.

Figure 2.1. Blueprint of second design.

To eliminate uncertainty, the next design was drawn to scale on a large whiteboard. The

basic plan was a giant trapezoidal prism, divided into four, 10cm layers. Trusses were again laid

out to make triangles, while this time staggering the points of connection to the layer below and

thus distributing the weight to different areas; a central, vertical tie was meant to prevent any

bending in the center by horizontal spaghetti that were not connected to a truss because of that.

The main shell was to consist of doubled-up spaghetti to increase strength (see figure 3.1).

Figure 3.1. Diagram of third design, trapezoidal side.

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Existing rectangular trusses such as Pratt, Warren, Howe, and a unique X-design were researched

to serve as the basis for the rectangular sides of the design (see figure 3.2). The Pratt design was

chosen as it had the horizontal layers that matched the trapezoidal layout and was

spaghetti-efficient. For both theoretical and practical reasons, the design was abandoned.

Because the design was drawn to scale, the lengths of the diagram could be measured and

multiplied by the number of sides to determine how much spaghetti was used.

Figure 3.2. Options for trusses for

rectangular sides of third design.

Figure 3.2. Existing truss designs.

(Source: “Truss”)

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Figure 3.3. Initial construction of rectangular side, where folding issue was discovered.

Calculations showed that the frame and rectangular sides would require over half of the allotted

spaghetti, 410 cm out of 750cm, leaving little for the horizontal chords and almost nothing for

our planned trusses. In addition, as construction of the rectangular sides began, a structural flaw

quickly appeared: the truss, clearly meant for horizontal rather than vertical use, buckled and

folded along the horizontal chords (see figure 3.3). With not enough spaghetti to even build the

original design, much less strengthen the rectangular sides, a brand-new design had to be created.

To avoid going over-budget with the spaghetti, a simpler design based on the initial idea

of a small, triangular base and a simple tower built on top of it was created. To alleviate the

bending problem with long spaghetti that required multiple trusses that had plagued the last

design, this design switched from four 10 cm layers to eight 5 cm layers. Each layer side was

designed with struts that would essentially create an isosceles triangle within each side. The idea

of shrinking layers to both save spaghetti and create a stronger base reemerged, with the base at

bottom starting as an equilateral triangle with 7cm sides, shrinking until the top had just 5cm

sides (see figure 4.1). Again, blueprints were drawn to scale to act as a guide for both

calculations and cutting spaghetti to precisely the correct length (see figure 4.2). This eventually

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ran into the same problem the last design with shrinking layers encountered; if the layers

remained similar, it would be impossible to stack them on top of one another directly.

Figure 4.1. Miniature diagram of fourth

design.

Figure 4.2. To-scale drawings of each layer

side in fourth design.

To allow for the layers to shrink while still touching the layer below, every other layer

was rotated 180 degrees. Thus, while per layer the tower was virtually identical to the last

design, from above the design would resemble a 6-pointed star rather than a triangle. After

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concerns about the overhanging triangles that resulted, vertical pillars were added to connect the

vertices of the alternating layers; to achieve this, the initial idea of shrinking layers was dropped

and each layer was identical: an equilateral triangle with a 6 cm base, 5 cm high, and an isosceles

triangle made from struts within each side (see figure 5.1). An initial test of just one layer

showed that while the trusses bore the weight of a textbook, the wall pillars snapped (see figure

5.2). To solve this, the wall pillars were double-reinforced. While this design held a lot of

promise, it was abandoned after the first layer of the design was rebuilt with double-thickness

sides and one side of the base of the next layer was accidentally snapped (see figure 5.3 and 5.4)

because it was too fiddly trying to match up layers with a five cm gap between each and to make

sure the overhanging triangles were equal on each side.

Figure 5.2. Overhead and side view

diagrams of fifth design.

Figure 5.2. Remains of test of fifth design

after pillars snapped under weight of

textbook.

This led to the final design, a combination of the previous two. It was a simple,

equilateral-triangle-base tower with 6cm sides and each layer 5cm tall, with a total of eight layers

to reach the required 40cm. The pillars were also double thick on every other layer to preserve

strength while saving a bit of spaghetti. The struts were more inspired by the third design,

featuring the X trusses were had initially thought up as well as a central, vertical strut to make up

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for the lack of contact in the middle of each horizontal chord and prevent those from bending

(see figures 6.1 and 6.2).

Figure 5.3. Side view of second building of

fifth design.

Figure 5.4. Overhead view of second

building of fifth design, with the part of the

base of second layer that snapped visible.

Figure 6.2. Close-up on one layer of final

design.

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Figure 6.1. Completed tower using final, sixth design.

ANALYSIS

The final tower did not manage to support the full 2.6 kg, instead supporting only 2kg.

The main problem was that the top of the tower was not level; it was impossible to balance a

clipboard on the top. Though the tower could sustain the weight of the two, 1 kg weight stacked

on top of each other, the additional force placed on top of this unevenness caused the tower not

to bend but, just to tilt. Because of this, during official testing the tower toppled over and was

still completely undamaged as the fall sent the weights flying and thus there was no force besides

that of gravity on the relatively light tower itself. However, when the 2.6 kg textbook was placed

onto the tower, the textbook toppled over before the tower did; the uneven surface meant the

textbook tilted onto the lower side of the tower, placing more weight on that side. That caused

the tower itself to bend on the other side to compensate and eventually snap at the third layer

from the bottom.

Because the tower broke relatively cleanly throughout the layer, with breakage in both

the pillars and the struts, that demonstrates that there were not any major points of weakness in

the structure. Theoretically, the tower design worked well. Where the tower failed was in the

practical construction. During construction, the spaghetti pieces were cut to precise lengths

beforehand, and then assembled and bound with hot glue. However, the hot glue itself added a

level of thickness unaccounted for in the design, and pieces likely would not have been glued at

precise 90 degree angles as a glob of hot glue prevents precise alignment with the piece below.

Both of these factors would have varied the actual vertical height of the tower from the

theoretical, and that vertical height would have varied on each side of the tower itself, creating

the unlevel surface that eventually meant the failure of the tower.

To improve upon the tower, modification of the construction process would be necessary.

Pieces of spaghetti should be cut as they were needed, so as to account for minor fluctuations in

height immediately. For example, if the joint already has a large blob of hot glue, the next piece

should be cut slightly shorter to account for the spaghetti piece sitting not directly on top of the

other pieces, but on the hot glue instead. In addition, after each layer, a clipboard or some other

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flat object should be placed on the tower to ensure it is level; if it is not, the layer after can be

modified to account for that.

CONCLUSIONS

As a whole, this study effectively taught lessons about engineering design and

construction.

Through the process of testing designs, patterns about what designs were stable emerged,

like the importance of triangles and many joints for force to be distributed. In addition, it showed

how weaknesses could be accounted for in multiple ways; each with distinct advantages. The

bendiness of the spaghetti could be alleviated by cutting it shorter, which had the added benefit

of increasing the number of contact points, or doubling up on spaghetti in key segments, which

helped increase overall strength. Other lessons were learned through trial by fire, like the

importance of keeping records so the same error of design isn’t made again.

The construction itself showed that while having a clear blueprint and design is vital, it is

equally important to not get bogged down in perfection; it is more important to make what exists

work than strive towards an impossible theoretical design. In addition, it demonstrates how

things that may not even be thought of in the design affect the end product; the hot glue adding a

thickness had not even been considered and had to somehow be accounted for or just accepted as

part of the process.

The end tower was a physical culmination of all the failed attempts and lessons learned

thereof, drawing on both the structures and the building techniques of the previous designs to be,

even though it did not completely succeed.

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REFERENCES

“Truss.” NEXT.cc, http://www.next.cc/journey/discovery/truss. Accessed 21 Sept. 2017.

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