Trashcano: Developing a quantitative teaching tool to understand ballistics accelerated by explosive volcanic eruptions

Abstract

Accurate predictions of volcanological phenomena, such as the trajectory of blocks accelerated by volcanic explosions, require quantitative skills training. Large outdoor experiments can be useful to convey concepts of volcanic processes to students in an exciting way. Beyond the fun aspects, these experiments provide an opportunity to engage with the physics of projectile flight and help promote mathematical learning within the Earth Sciences. We present a quantitative framework required to interpret ballistic trajectories and the outdoor experiment known commonly as "trashcano", taking a step-by-step approach to the physics of this problem, and deriving a range of mathematical solutions involving different levels of complexity. Our solutions are consistent with the predictions from established computer programs for volcanic ballistic trajectory modelling, but we additionally provide a nested set of simplified solutions, useful for a range of teaching scenarios as well as downloadable simulated datasets for use where the full experiment may not be possible.

Teaching about volcanoes

“…maps, rock samples/thin sections, physical experiments, and demonstrations; Figure 2) are consistent with what has been described in the wider geoscience education literature and volcanology specifically [e.g. Harpp et al 2005;Kastens et al 2009;Mogk and Goodwin 2012;Wadsworth et al 2018]. The prevalence of storytelling may stem from the narrative aspect of geologic and eruptive histories and of human connections to volcanoes and the Earth system.…”

Determination of permeability using a classic Darcy water column

“…In Earth sciences in particular, students often arrive at undergraduate levels without experience of data analysis, dimensional analysis, or experimental methods 11 . While this is not ne c e ssa rily a problem because the geosciences have a range of learning outcomes, not all of which demand strong quantitative skills, it is possible that weaknesses in data-based work such as shown here could hold students back 12 . We propose that this exercise could be a useful addition to many existing engineering, Earth sciences and geography curricula at the early undergraduate level or as part of high school (secondary education) physics or geography courses, and that this is an engaging example of how instructors can lead students from problem statement, through hypothesis testing, and to theoretical and empirical results at extremely low-cost.…”

Analog field-scale acoustic study of volcanic eruption directivity using a tiltable liquid nitrogen-charged water cannon

“…We developed an experimental apparatus (Fig. 1) to produce directed explosions consistent with a prior field experimental eruption approach (Wadsworth et al 2018). The setup included a 209-L steel barrel (diameter 572 mm and height 851 mm) partially filled to ~ 1/3 capacity with water at approximately ambient temperature.…”

“…The bottle rupture process may introduce unconstrained energy directivity effects. In addition, while we attempted to control the capacity of liquid nitrogen (N 2 ) into each bottle, prior experiments (e.g., Wadsworth et al 2018 and other unpublished experiments including a subset of our team) showed that larger volumes of N 2 increased the explosion yield. We estimate errors in N 2 bottle fill and water barrel fill to be within 5%, while the barrel inclination is known to within a couple of degrees.…”