Davis Loen

≠≠≠Nate Wisler

Alex Bruce

Justin Nguyen

Table of Contents

 

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Background

Problem Statement

Hypothesis

Results

Conclusion and Evaluation

Works Cited

 

 

 

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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Hypothesis:

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

TrebuchetFull.jpg

Side Brace.jpg

Arm.jpg

 

IMG_2154.JPG

 

 

Results:

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

 

 

 Link to Data Text File

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Conclusion and Evaluation:

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 trebuchetís 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