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Geometric Concept of a Smooth Staircase: Sinus Stairs

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Abstract

Reflections on the characteristics and use of staircases lead to the question: how they could be designed to achieve a more comfortable walking. The fundamental rules for stairs go back to Vitruv, Alberti, Palladio, and Blondel. Especially, Blondel’s formula gives the rule to consider the human step length for the stairs’ design. Friedrich Mielke played a significant role in the development of scalalogy, the science of stairs in the late twentieth century. On this background, the artist Werner Bäumler—Laurin developed in the 1990s the idea to create a staircase similar to a smooth hill. The result was the design of a sinus staircase following the sinus curve in its inclination starting from the horizontal plane with a slight rise and again the transition to the horizontal plane when arriving on the higher level. Laurin’s drawings and models to describe his idea will be presented as well as a graphical method to design sinus stairs for architectural situations. The sinus stairs offer, with continuously changing step height and step depth according to the sine curve, smooth movements, as if walking onto a natural hill. We built with our students a sinus staircase as a walk-in project in order to test the thesis, which had been confirmed by the built project.

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References

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Acknowledgments

Special thanks to Werner Bäumler—Laurin for sharing his idea of the Sinus Stairs with us, to provide his drawings, writings, and photos as well as to come to the Imagine Maths 7 conference with his models. The figures are reproduced with courtesy of Werner Bäumler.

Thanks to Prof. Joachim Wienbreyer, University of Applied Sciences, Friedrich-Mielke-Institute, Regensburg, to provide us insight in the Friedrich-Mielke-Institute with details of the research. And last but not least many thanks to my engaged and motivated students: Benedikt Blumenröder, Yuliana Brehmer, Moritz Brucker, Marian Buchheiser, Sabrina Funk, Jana Gretz, Jonas Heuser, Sarah Lutgen, Emmanuel Niyodusenga, Ernst-Markus Rauska, Anna Specchio, Angelika Walz, and Philipp Weber.

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Correspondence to Cornelie Leopold .

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Leopold, C. (2020). Geometric Concept of a Smooth Staircase: Sinus Stairs. In: Emmer, M., Abate, M. (eds) Imagine Math 7. Springer, Cham. https://doi.org/10.1007/978-3-030-42653-8_10

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