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Computer Science, Mathematics and Environmental Science

Medieval Machines and Marshmallows

A Suprising New Summer Course

The summer program at AUP offers a set of immersive classes intended to give students a different perspective on Paris and all that the University has to offer. Perhaps none of the 2018 offerings had a more eye-catching title than ‘Medieval Machines and Marshmallows.’ The brainchild of Professor Claudio Piani, the course debuted on our summer offering for the first time this year. We couldn’t resist getting the inside story on how it came to be.

The playful concept was initially inspired, rather unexpectedly, by a tragic piece of news. In 2002, a visitor to the Middlemoor Water Park in the UK was fatally catapulted by a life-size trebuchet, missing the safety net by several meters. On reading about the accident, Professor Piani’s reflections moved from mortality to the basics of ballistics, energy, statistical likelihood and Newtonian physics. He wondered if and how the accident could have been prevented with the right foundational understanding of those principles. From those initial musings, Professor Piani sought to design a course that would enable students to put these fundamental principles into action, asking each participant to build a catapult and a trebuchet capable of flinging a marshmallow across the science laboratory.

I comfort myself in the thought that, should any of my students come across the chance of being hurled through the air for over a distance of 100 meters, they will decline politely and opt for the merry-go-round.

Prof. Claudio Piani

What can you learn by hurling marshmallows at your fellow students across a science laboratory? Well, as it turns out, quite a lot.

History of classic physics and engineering

The class begins by examining the common-sense approach of the ancient world to the physical environment. We consider the laws of dynamics according to Aristotle and see that they make perfect sense as long as you do not look too closely or too carefully. And looking too closely and too carefully is what Galileo and Kepler did, albeit in different realms, leading to a simple formulation of the law of inertia that governs the universe, or most of it at least. This leads us to Newtonian dynamics and the concept of acceleration, force and energy in all its various manifestations.

Mathematical models

In this class, you derive and solve the equations that describe the trajectory of a flying projectile, namely a marshmallow, under the effects of the Earth’s gravitational field and, possibly, air friction. You do this using a freely available and intuitive plotting software to visualize potential solutions and identify new ones. Indeed, calculus is not a prerequisite for this class, though some familiarity with Cartesian coordinates is helpful. You will find that “using mathematical solutions” is to “finding mathematical solutions” as “driving a car” is to “building a car”.

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Building medieval siege engines in the laboratory

This is the central activity of this course. The lab sessions are based on the step-by-step construction of a simple catapult and, subsequently, of a more complex trebuchet. The transformation of potential elastic energy to kinetic energy is examined in a real (well, to the degree that lab and marshmallows as applied to “siege weapons” constitutes “real”) setting. Also predictive strategies, based on the understanding of basic physics principles and the underlying mathematical models, are developed and tested. Students understand how error and uncertainty are transmitted along the mechanisms to the projectile’s target. Crucially they learn to predict not only the estimated point of impact but the probability of missing as well.

Professor Piani notes that “I comfort myself in the thought that, should any of my students come across the chance of being hurled through the air for over a distance of 100 meters, they will decline politely and opt for the merry-go-round.”

Find out more about Summer at AUP or read up on the COMPUTER SCIENCE, MATHEMATICS, AND ENVIRONMENTAL SCIENCE Department.