Ethan Putnam

An Investigation in the Digital World: Trebuchet and Counterweights

Introduction .:.Top

The trebuchet had been at the pinnacle of siege technology in the Middle Ages. Using a counterweight as the key source of power, the machine transfers gravitational energy into kinetic energy. The trebuchets were constructed for a particular siege/battle and the projectiles were created from the surrounding area. There was not a standard for the Middle Age trebuchet or its ammunition, hence the siege engineers had to constantly adjust counterweight and projectile mass to complete their given objective.

As an avid student of history, this greatly inspired my investigation. I recreated a watered-down version of the Middle Age siege engineer’s dilemma with a simulation in Interactive Physics. I wanted to investigate how the change in mass of the projectile would affect the range. It was my belief that if the projectile weight is increased, the result would be a shorter range due to the greater mass having a greater downward force (F=mg). Google Sheets will be used to create visuals with a regression line that best fits the data collected.

Procedure & Design .:.Top

Materials:

A Mouse & Keyboard Procedure:

One week prior to the experiment, I researched how to create and manipulate a trebuchet in the Interactive Physics program. The trebuchet program was launched on the computer and the units were adjusted for the experiment. The trebuchet was superimposed on am an x-y grid. Then, a value input box was created for the mass of the projectile. The program was set to run until the projectile first contacted the x value determined to be the “ground” in accordance with the positioning of the trebuchet. The range from the projectile’s contact with the ground from the trebuchet was digitally measured. The data was recorded and the process was repeated.

Variables:

 Independent Variables Dependent Variables Controlled Variables The mass of the projectile The distance (range) from the trebuchet The angle of release The mass of the counterweight Length of the arm Fulcrum point

Data Analysis .:.Top

Raw Data Excel | Text.| Above  is the recorded raw data with the projectile mass decreasing by .5 kg and the resulting range in meters. Graph 1’s exponential regression line was y=262e^0.423x and the correlation coefficient was .988. This appears to be the best fit my data well which would lead one to suspect that the projectile range is proportional to the mass. However, there are noticeable outliers after 4 kg. The model clearly reflects that there is a relationship between projectile mass and range from the trebuchet with lighter projectiles having greater range than heavy projectiles. It should be noted that the exponential regression line does not reach 0 m (range).

Linearized Data displays the same mass values with the range adjusted for linear regression with the equation . Graph 2 shows the data in the Linearized Data. The linear regression line was y=0.0381x+8.49E^-03 and the correlation coefficient was .96. Interestingly, the weight values after 6 kg are seen to vary from the linear tendency of weights 1-7 kg. The data is shown to not be an exponential equation as suspected, hence the points being farther away from the linear regression line. Out of the two graphs, the exponential regression was the best fit as reflected in the higher correlation coefficient.

Linearized Data: Graph 1: Exponential Regression Graph 2: Linear Regression

Conclusion .:.Top

It is clear that the exponential model best fits my data, as evident in the higher correlation coefficient. I am of the belief that extrapolation of lower masses should be considered due to the visualized consistency of my lower mass values.

The changes in the construction and arrangement of the trebuchet. The arm length or height of the device could be examined. Additionally, the length of the fulcrum point could be adjusted closer to or from the counterweight end to change the amount of force on the projectile. I assume that a  fulcrum point closer to the projectile end would result in a smaller range than a position equidistant from both ends.

This experiment would become stronger and more accurate with the addition of more trials. As a result of time, the number of trials performed is less than extensive; therefore, the conclusion from this particular experiment is limited and my confidence is not high. I performed the experiment in a simulation which removes many of the environmental possibilities for error, however the projectile’s first contact with the ground needed to be estimated as the projectile would bounce at higher masses. I had to replay the simulation to the point of the first contact to retrieve the data. The introduction of the human element in an otherwise near perfect machine could explain the differences between the data points after 6 kg on the graphs. Despite this one error, the experimentation method removes many other sources of error.

In conclusion, I am surprised by the benefits of simulations as a means to conduct research. Not until this experiment had I used completed an investigation in the digital world. The simulation proved to be especially superior in mitigating errors that would have come about in a real-world test such as environment and consistency issues. I was surprised by the efficiency of the simulation and look forward to the future development of more complex simulations.

https://www.youtube.com/watch?v=nVfCKaOoCZs- This video helped outline the basic physics understanding of the trebuchet in order for the creation of the computer model. Additionally, key variables were identified that would indeed effect the distance the projectile traveled.

https://www.youtube.com/watch?v=cp1kjPh_jXA- This video aided in the design and creation of the computer model of the trebuchet within the program, Interactive Physics.

https://en.wikipedia.org/wiki/Range_of_a_projectile-This is a Wikipedia entry. It has a really good section on Ideal Projectile Motion: Flat ground.

https://www.sciencebuddies.org/science-fair-projects/project-ideas/ApMech_p013/mechanical-engineering/effect-of-trebuchet-arm-length-or-counterweight-mass-on-projectile-distance- This website gave a brief history on the development of trebuchets and introduces the importance of the counter weight in regard to the distance the projectile is thrown. The various calculation attempting determine the distance of the projectile are especially useful.

https://www.real-world-physics-problems.com/trebuchet-physics.htmlhttps://www.real-world-physics-problems.com/trebuchet-physics.html -This website explained the function of the key parts of the trebuchet and spoke on the importance of the angle in which the projectile is release in regard to distance. Furthermore, the assumptions identified aided in the creation of the computer simulation.

https://en.wiktionary.org/wiki/trebuchet https://en.wiktionary.org/wiki/trebuchet%20-This is a Wikipedia entry on the trebuchet. The picture of a real trebuchet aids in the understanding of the history and practical use.

Bibliography .:.Top

FARRELL, SCOTT. “Arms and Men: The Trebuchet.” HistoryNet, 23 June 2016, www.historynet.com/weaponry-the-trebuchet.htm.

Johnson, Tegan. “Effect of Mass on the Regulation of Ice.” The Effect of Temperature on Magnet Strength, 2018, tuhsphysics.ttsd.k12.or.us/Research/IB18/TJohnson/index.htm.

Science Buddies Staff. "Effect of Trebuchet Arm Length or Counterweight Mass on Projectile Distance." Science Buddies, 17 Nov. 2017, https://www.sciencebuddies.org/science-fair-projects/project-ideas/ApMech_p013/mechanical-engineering/effect-of-trebuchet-arm-length-or-counterweight-mass-on-projectile-distance. Accessed 25 Jan. 2019.