Davis Loen
Nate Wisler
Alex Bruce
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Introduction
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Background:
Invented in China in 300 BC,
and used as a medieval siege weapon in 500 AD primarily by the French, the
trebuchet was used to project numerous of damaging projectiles over city walls.
These projectiles are quite creative, and have been recorded as being: feces,
dead bodies of humans and animals in degrading condition, fire, stones, sharp
wooden poles, burning tar, and fire (Trebuchet). Disease was effectively spread
this way. The masses of these projectiles commonly ranged from 110-220 pounds.
These projectiles were capable of going from 1000 feet. This was achieved by
using a counterweight to swing an arm up to 60 feet in length. Trebuchets were
disassembled until they reached the siege location, where they were erected
rapidly, with the help of many men (Castles and Knights). This easy
construction is one of the most important aspects of the design. The quicker it
can be constructed, the sooner damage can be inflicted upon the enemy. The use
of trebuchets is not limited to the Middle Ages, in the Current Civil war in
Syria, explosives are being hurled using trebuchets (Aikens).
Trebuchets function by using
a free swinging arm with a counterweight on one end, and a sling on the other.
Factors that affect the distance of the projectile launched are the weight of
the counterweight, the projectile, the length of the arm, the length of the
sling, and the angle that the projectile is released. To load the trebuchet,
the arm is tilted back, putting the counterweight in the highest position. This
maximizes the potential energy stored in the counterweight. This counterweight
is released when fired, which converts the potential energy stored in the
counterweight into kinetic energy to throw the arm forward. As the arm rotates
forward, the sling is rotated around the tip of the arm, where it disconnects,
launching the projecting at a 45 degree angle to maximize distance. The
potential energy stored in the counterweight is converted to kinetic energy in
the arm, sling and projectile.
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Problem Statement:
How does a trebuchets counterweight affect the distance that its
projectile is launched?
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We believe that a graph of our results (with the counterweight
mass as the independent variable and distance of the launch as the dependent
variable) will be essentially linear. As the counterweight becomes heavier and
heavier in comparison to the weight of the projectile, the distance travelled
will increase in parallel. We will attempt to achieve the greatest possible
projectile range while retaining the structural integrity of the trebuchet. The
range of the trebuchet is defined as the horizontal distance that the
projectile travels before hitting the level ground. The counterweight mass is
measurable on a scale and will be tracked in kilograms.
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Diagram
|
Counterweight |
Trial 1 |
Trial 2 |
Trial 3 |
Trial 4 |
Trial 5 |
Average |
|
3.63 kg |
4.57 m |
4.88 m |
5.49 m |
7.92 m |
9.14 m |
6.40 m |
|
4.76 kg |
4.57 m |
10.97 m |
7.92 m |
7.32 m |
5.79 m |
7.31 m |
|
5.90 kg |
12.50 m |
12.19 m |
15.85 m |
8.84 m |
8.53 m |
11.58 m |
|
7.03 kg |
5.49 m |
6.40 m |
6.71 m |
7.32 m |
7.92 m |
6.77 m |
|
8.16 kg |
13.41 m |
11.28 m |
8.84 m |
16.46 m |
19.81 m |
13.96 m |
|
9.30 kg |
15.54 m |
18.59 m |
20.73 m |
13.11 m |
19.20 m |
17.43 m |
|
10.43 kg |
16.15 m |
25.91 m |
25.91 m |
25.30 m |
26.52 m |
23.96 m |
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The results of our
experiment demonstrate the way the mass of a trebuchet counterweight affects
the launch distance of its projectile. Our study must conclude that increasing
the mass of a counterweight results in a similarly linear increase in launch
distance. Our hypothesis predicted that the results of our experiment would
appear as a linear function of distance (in meters) with reference to
counterweight mass (in kilograms). The given data would seem to directly
support our hypothesis. However, our results may be considered unreliable.
Taking into account systematic and human-based errors and uncertainties, the
validity of the model is devalued. For example, the average launch distance of
the trebuchet at a counterweight mass of 7.03 kg was a measly 6.77 meters. This
is completely inconsistent with the rest of the data and can only be explained
by a failure within the structure of the trebuchet and the angle of sling
release. That result equates the distance at 3.63 kg to that at 7.03 kg, which
is inconsistent with the physics behind the launch distance of a trebuchet.
Errors such as this suggest that the conclusion and hypothesis behind the
experiment may be questionable.
With the exception of the outlier in the middle of the data points, the
conclusion seems supported by the raw data. The launch distances increased
quite proportionally, as demonstrated by the 2:1 differences between the launch
distances at 3.63 kg (with an average 6.40 m launch) and 10.43 kg (with an
average 23.96 m launch). These data points support the possibility of the
function being linear as the hypothesis predicted. Additionally, the 5
individual launches at every single counterweight value result in a reasonable
amount of consistency in our average launch distance values. The data supports
the hypothesis and a conclusion that the function is linear.
However, this is not to say that the model is without flaws or opportunity for
improvement. There were definitely weaknesses in the design and method of our
investigation. First and foremost, the sling of the trebuchet (along with the
pin upon which the sling rests before the launch) had to be adjusted in the
middle of the experiment purely for the sake of making the trebuchet
functional. While well-designed and sturdily constructed, the trebuchet was
still flawed in that it was student-built and there are many considerations
that must be made with reference to the error included in that process.
Fortunately, the launch-by-launch data at a given counterweight mass turned out
to be very consistent throughout the experiment. Unfortunately, the adjustments
that were necessary during the testing of the trebuchet damages the reliability
and truth behind our raw data points. These kinds of alterations and
considerations may have been the driving factors behind the trebuchet’s failure
at specific weight intervals (namely 7.03 kg). The lab itself could have been
performed better in a number of ways, mainly via better initial construction of
elements such as the sling; this would allow for minimal adjustment during
experimentation. Additionally, one must consider the results that would be
acquired at counterweight masses above 10.43 kg, which was the maximum weight
tested. The downward acceleration of the counterweight must cap out at some
point (i.e. -9.81 m/s/s), which has a large influence on launch distance and
would likely have caused the function to plateau after a certain amount of
weight. This is something that might have improved the experiment by widening
the scope and allowing analysis of a different element within the physics of a
trebuchet. Overall, the trebuchet carried many failures, and as a result the
experiment did as well. This happens to be the nature of hand-built trebuchets,
and is to be partially expected when conducting the experiment. Despite these
inherent failures, the error within our specific iteration of such an
experiment might completely invalidate the model and this consideration is up
to the judgment of an external reader. Our hypothesis was supported by the data
and a conclusion was reached, but the legitimacy of the experiment is at
question.
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Works Cited:
Aikins, Matthieu. "How War in Syria
Turned These Ordinary Engineers Into Deadly Weapons Inventors." Wired.com.
Conde Nast Digital, 16 July 2013. Web. 04 Dec. 2015.
"Castles & Knights." Trebuchet. N.p., n.d. Web. 03 Dec. 2015.
"Trebuchet." Trebuchet.
N.p., n.d. Web. 03 Dec.
2015.
Related Websites:
https://www.wired.com/2013/07/diy-arms-syria/
Shows modern application of ancient Trebuchet
technology
https://www.q-files.com/history/castles-knights/trebuchet/
Explains traditional battle tactics of the trebuchet
http://www.ancientfortresses.org/trebuchet.htm
Explains the origin of the Trebuchet and its early
stages of developed
http://www.redstoneprojects.com/trebuchetstore/trebuchet_history.html
Explains the mechanics of the trebuchet
http://www.lordsandladies.org/trebuchet.htm
Outlines the projectiles frequently used by
trebuchets