Before modern weaponry like missiles and guns, other weapons and mechanisms were used to wreak havoc on a battlefield. One such weapon was the trebuchet, and specifically this experiment involves counterweight trebuchets. Simply put, the counterweight trebuchet uses any matter of weight to provide the force needed to fling projectiles at enemy ranks or castles. It was thought when using trebuchets, the greater the mass of the counterweight that was used, the farther and more destructive force the projectile would then have. This brings up the topic of investigation of the experiment, if the counterweight of a trebuchet is continually increased, does the distance of the projectile increase at a constant rate or does the projectile eventually reach a limit.
History is a subject that I have always had mixed feelings about, because some parts of history are somewhat bland with not much going on in terms of action, while others have rapid improvement of technology and weapons that are used in major battle. I personally love any part of history involving any type of turmoil that includes plagues, wars, or just a simple battle, because in times of great loss, human kind get creative in all sorts of ways. This creativity in the art of warfare has always intrigued me, therefore when deciding the experiment for this internal assessment, I tried thinking of technology that included physics and eventually found myself face to face with the trebuchet. The idea came to me when remembering a demonstration of a real trebuchet, and I decided to use this experiment to begin to understand the physics behind the trebuchet.
A trebuchet is a type of catapult, which is a common type of siege engine, which incorporates the use of a swinging arm to “throw” a projectile. The first trebuchet appeared in Ancient China during the 4th century BC, which used manpower to swing the arm. However, the more efficient counterweight trebuchet appeared around the Mediterranean in the 12th century and later spread to China in the 13th century. Counterweight trebuchets use gravity as its driving force, specifically; they use potential energy, which is stored by slowly raising the counterweight attached by a hinged connection to the shorter end of the beam. Once the counterweight is in place, the trebuchet can be loosed and the force causes rotational acceleration of the beam around the axle of the trebuchet. Newton’s Third Law is an important force of the trebuchet because the action of the falling counterweight sends an equal reaction of the arm beginning to spin forward. The sling, which holds the projectile, starts rotating with the beam and since the sling has to swing farther due to it being placed on the longer end of the arm, must move faster thereby transferring the increased speed to the projectile being carried. As the arm swings forward, the projectile is eventually thrown at the optimum angle based off of its placement on the arm and soars through the air, while the arm can continue to swing forward at full speed. This means that none of the power is lost from stopping slightly earlier, which is a common issue with other siege weapons such as catapults. While the trebuchet slowly faded away from the battlefield after the introduction of gunpowder, the trebuchet is still a revolutionary piece of machinery that terrorized every enemy that they faced.
If the mass of the counterweight of a trebuchet is increased at a constant rate, then the distance that the projectile is thrown will increase until a point because the weight that is added will only be a small fraction of the total weight thereby adding little to no extra distance.
The program that will be used for the experiment is “Interactive Physics” which allows for a virtual trebuchet to be created and programmed. By using a virtual model of a trebuchet, many factors such as wind resistance and pressure differences could be negated, thereby giving more accurate results. A preexisting trebuchet model is used for the base of the experiment and several aspects of the program are slightly altered to best fit the experiment. First, new dampers are programmed onto the different joints of the trebuchet to eliminate extra rotational forces that break the constraints put onto the program. Using different constraints on when the trebuchet can release the projectile and give it a maximum distance also altered the optimal angle of release. In addition, to make the data gathered more accurate, constraints were added to stop the projectile once it reached the x-axis, which was being used to simulate the ground. These constraints stopped the projectile in order for an individual to measure the distance accurately. Once all of the programming and added constraints were completed, the experiment could begin by hitting the run button on the program after setting the specific mass of the counterweight. Each data point was then recorded onto Microsoft Excel for the eventual data table and graph creation.
Picture of Trebuchet: Top
Equations to Support:
A trebuchet is a device that converts potential energy to kinetic energy:
From basic physics we know that the range of a projectile with initial velocity v and angle α is:
Thus, the maximum theoretical range of a trebuchet is given by:
From the data provided by the experiment, two different graphs could be produced with a linear equation and a polynomial equation each with its respective correlation coefficient. While at the beginning of the data collection process, the line of best fit appeared to be linear, but as more data points were acquired the data clearly showed that this was not the case. For the amount of data points acquired in the experiment, the higher correlation coefficient of the polynomial equation of 0.99969 allows for extrapolation of data points not calculated much more reliably then the linear model with a correlation coefficient of 0.97685. The equations above correspond to real life trebuchets, and while we can calculate some of the variables like velocity with the information known from the program, the angle of release and the height of the trebuchet were not calculated within the program. However, these equations would be of use if the experiment were trying to calculate either the velocity or the angle of release if additional programming was added to the simulation in “Interactive Physics.”
It is evident that the polynomial model fits the data of the experiment the best, as seen by the higher correlation coefficient. The model would allow for extrapolation of more data points, but more recorded data points would always be more beneficial for an experiment.
However, every experiment has areas where errors could occur and this experiment was no exception. As stated before, more data points would help to further strengthen the equations calculated and more clearly identify the potential limit that the trebuchet could reach. In addition, the trebuchet simulation that was programmed had an upper limit of 185 kg for the counterweight because the constraints that helped gather the data would start to fail due to the high rotational forces that incredibly heavy counterweights would exert upon the program. This could be remedied by running more extensive tests on the simulation to make sure that the program could function at higher weights. Further testing the program could perhaps bring the beginning weight down from 20 kg because the simulation wouldn’t function for any weight below 20 kg. If the trebuchet were also programmed to identify the different lengths and materials that the trebuchet was constructed out of, it would allow for more complex calculations to determine other factors such as optimal angle of release.
If these errors were to be fixed in a future experiment, it would be interesting to calculate whether or not different designs of trebuchets could greatly affect the results of the distance of the projectile. Overall, I was surprised by the results of the experiment and I am glad that the experiment gave me an excuse to learn more about physics and history in an engaging way.
Danielsson, Mats. “What Is the Physics Behind a Counterweight Trebuchet?” COMSOL Multiphysics©, 11 Oct. 2017, www.comsol.com/blogs/what-is-the-physics-behind-a-counterweight-trebuchet/.
“Trebuchet.” Medieval Squires, Mar. 2018, www.medieval-life-and-times.info/medieval-weapons/trebuchet.htm.
“Trebuchet Physics.” Real World Physics Problems, www.real-world-physics-problems.com/trebuchet-physics.html.
1. www.medieval-life-and-times.info/medieval-weapons/trebuchet.htm This website assisted in the background information of trebuchet and how they are built.
2. www.real-world-physics-problems.com/trebuchet-physics.html This website explains the physics behind a trebuchet with some helpful diagrams and explanation.
3. www.comsol.com/blogs/what-is-the-physics-behind-a-counterweight-trebuchet/ More explanation behind the physics with some animations to assist.
4. https://classes.engineering.wustl.edu/2009/fall/ese251/presentations/(AAM_13)Trebuchet.pdf A presentation of sorts that goes into detail behind more information about the trebuchet.
5. https://hackaday.com/2019/05/20/make-physics-fun-with-a-trebuchet/ Has an interesting video and different experiment involving trebuchets with a more technological approach.