Geometric Concept of a Smooth Staircase: Sinus Stairs

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.