Implementing Mathematical Modelling with Calculus of Variations to Design a Disaster Tent

Abstract

This manuscript shares results from a mathematical modelling project developed by a mathematics educator and a high school student to solve a real-life problem; durable disaster tents. The authors worked together to first design a tent, CaTent, by implementing biomimicry with design thinking. Through the process of mathematical modelling, the authors mathematise the problem with catenary which can be obtained by solving a calculus of variations problem. Then, reaching the equation for catenary curve modelling the poles of CaTent, the length of a pole is obtained, approximately 7.2834 meters. The total length of three poles necessary for a CaTent would be 21.8503 meters approximately, while the total amount of poles needed for a common disaster tent would be approximately 40.32 meters.

Keywords

• Mathematical modelling
• calculus of variations
• catenary
• design thinking
• biomimicry

References

1. Aslan-Tutak, F. (2020). Matematik eğitiminde disiplinlerarası etkinlikler ve STEM eğitimi. In Y. Dede, M. F. Doğan, & F. Aslan-Tutak (Eds.), Matematik eğitiminde etkinlikler ve uygulamaları (pp. 97-124). Pegem Publishing.
2. American Scientist. (2018, February 2). The perfect dome. American Scientist. https://www.americanscientist.org/article/the-perfect-dome
3. Biomimicry Institute. (2019, April 19). What is biomimicry? Biomimicry Institute. https://biomimicry.org/what-is-biomimicry/
4. Cornell University. (2023, February 16). Hanging cables and spider threads. Cornell University. https://arxiv.org/abs/2302.09054
5. Chen, D. A., Klotz, L. E., & Ross, B. E. (2016). Mathematically characterizing natural systems for adaptable, biomimetic design. Procedia Engineering, 145, 497-503.
6. Girgin, D. (2021). A sustainable learning approach: Design thinking in teacher education. International Journal of Curriculum and Instruction, 13(1), 359–382.
7. Gohnert, M., & Bradley, R. (2022). Membrane stress equations for a catenary dome with a variation in wall thickness. Engineering Structures, 253, 113793. https://doi.org/10.1016/j.engstruct.2021.113793
8. Hass, J., Heil, C., & Weir, M. D. (2000). Thomas' calculus: Early transcendentals (11th ed.). Pearson.

9. Karataş Aydın, F. İ., & Aslan-Tutak, F. (2023). Eğitim uygulamalarında tasarım odaklı düşünmeye yönelik çerçeve. In D. Girgin & Z. Toker (Eds.), Eğitimde tasarım odaklı düşünme yaklaşımı ve uygulama örnekleri (pp. 69-106). Nobel.
10. Sanne, F., Risheim, I., & Impelluso, T. J. (2019). Inspiring engineering in the K12: Biomimicry as a bridge between math and biology. ASME International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineers, Salt Lake City, Utah, USA.
11. Schaap, S., Vos, P., & Goedhart, M. (2011). Students overcoming blockages while building a mathematical model: Exploring a framework. In G. Kaiser, W. Blum, R. B. Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling: International perspectives on the teaching and learning of mathematical modelling, vol. 1 (pp. 137–146). Springer.
12. Scheer, A., Noweski, C., & Meinel, C. (2012). Transforming constructivist learning into action: Design thinking in education. Design and Technology Education: An International Journal, 17(3), 8-19.
13. Sol, M., Giménez, J., & Rosich, N. (2011). Project modelling routes in 12–16-year-old pupils. In G. Kaiser, W. Blum, R. B. Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling: The 14th ICMTA study (pp. 231–240). Springer.
14. Stanford University. (2024). d.school. Stanford University. https://dschool.stanford.edu/about