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The Physics of the Goblet Dance

Photos by LHT & Cherlyn Wagner

By Rosalyn Acosta, published on May 2, 2024

I am a multi-disciplinary dancer based in San Francisco. I first performed the goblet dance in 2005. Since then, my approach has evolved and I continue to push the boundaries of this dance. It’s important for me to explore the ethereal qualities that arise when tapping into the form, construction, feeling, and truth of this unique dance while at the same time not being restricted by the perceived physical limitations of dancing on top of the goblets. 

My relationship with the goblets is constantly evolving. As an inquisitive being, I have always been intrigued by the physics behind this dance. I recently received insight into the fascinating properties of glass from Wendy Gu, Assistant Professor of Mechanical Engineering at Stanford University, and Shayna Leib, a multimedia and world-renowned glass artist. 

Rosalyn: How is it possible that I can dance on goblets without them breaking? 

Professor Wu: We think of glass as a delicate material – and it is! But, a lot depends on how the weight of the dancers is applied to the goblets. The class of materials that glass belongs to – ceramics – is weak in tension (pulling) or bending, but quite strong in compression (pushing). Glass is about ~150 times stronger in compression than in tension. Because the dancers are pushing down on the goblets, the force is mostly applied in compression so the goblets do not break. The domed shape of the goblet also leads to compressive rather than tensile forces. 

Because the dancers are pushing down on the goblets, the force is mostly applied in compression so the goblets do not break.

Lastly, the speed that the force applied to the goblet matters. Stomping on the goblet will cause it to shatter, but slowly shifting weight to the goblet will not. This can be observed in ceramic dinner plates as well, which can be piled high with food or other plates without breaking but may shatter if dropped or hit on the edge of a hard surface. This is because ceramics cannot absorb the energy from a high-speed impact quickly, so the energy instead goes into forming cracks.

Rosalyn: I am not stationary and dance around with the goblets by sliding them across the floor while standing on them (I only dance on wood surfaces). How does the friction of the goblets moving on the wood floor, plus my weight, not cause them to break? 

Friction is a force that opposes the direction of motion. If we look at the glass goblet and wooden floor under a microscope, they will look rough. It’s the rubbing of these microscopically rough surfaces that leads to the resistance force that is friction.

Professor Wu: Friction is lower if the surfaces are smoother, and is proportional to the force that pushes the surfaces together (the weight of the dancer). Smooth glass sliding on polished or waxed wood would result in a lower frictional force than two rough surfaces (e.g. tennis shoes on pavement). 

Over time, some of the rough protrusions on the surfaces will break off, which will make the surfaces rougher. Cracks are more likely to start at rough surfaces on the wine goblet which could cause it to break. Yet, friction is necessary! Without friction, a small lateral force on the goblet would cause it to shoot across the floor, which would make dancing difficult. 

Rosalyn:  Is there a way to assess the maximum weight that a goblet can hold?

Professor Wu: The maximum weight can be estimated by using the strength and dimensions of the glass. The strength of a material describes how much load per area can be sustained before the material permanently warps or breaks. On Wikipedia, the strength of glass is reported to be

1 GPa in compression (the weight pushes on the glass, rather than pulls on the glass). GPa is a unit of pressure or force per cross-sectional area (1 GPa is equivalent to 109 N per m2). We will use the cross-sectional area of the goblet stem, which we will assume to be the location where the goblet breaks. Using 1 cm as the diameter of the stem results in a force of 78.5×103 N that can be sustained by one goblet. This is equivalent to 17,648 lb (4.448 N is equal to 1 lb), or more than 100 people who each weigh 150 lbs!

In reality, much less weight can be sustained, because this calculation assumes a “perfect” goblet. A real goblet will have flaws (chips, scratches) that will weaken the glass. In addition, the forces will not be perfect in compression (e.g. the dancer’s weight shifts left or right during the dance, such that a bending force is applied to the stem). Yet, this analysis shows that it may be surprising and visually arresting that Rosalyn and her partner can dance on wine goblets, but the goblets can safely sustain their weight.

Rosalyn: How do you determine when the glasses are worn out and need to be replaced (explaining stress points, cracks, etc in more technical detail)?

Professor Wu:  Brittle ceramics such as glass are extremely sensitive to flaws such as chips, scratches, or other imperfections. This is because cracks tend to start at these features. When a crack forms in a brittle ceramic, any additional force (adding more weight) causes the crack to grow until the structure shatters. Goblets should be visually inspected to be flaw-free before the start of dancing!

Rosalyn: And lastly, as an artist working with glass in a much different manner than me, can you explain what it’s like manipulating this material when glass blowing?

Glass is a temperamental, mysterious substance.

Shayna: Anyone who winds up successfully working with it has to do two things: understand it deeply and predict what it’s going to do, as well as be able to really control it by working within its constraints. It will accept a hard touch or a soft touch, and I’ve seen both styles in my peers.

In order to master a material, you really have to understand it deeply and there’s a lot to understand about glass. There’s the knowledge-based aspects of it, like understanding how to heat and cool it, working with color and the effect of coefficients of expansion. I tend to categorize casting, fusing, and slumping as the knowledge-based glass art forms. There is more of a recipe to accomplish something using those techniques.  But there are also the practice-based art forms like glassblowing, lampworking, and neon. These tend to rely on practiced intuition, and your success in these more difficult methods comes down to honing a deeper understanding of how glass behaves.  Particularly with blowing, you’re using your whole body, and gravity plays out on a much larger scale than it does with lampworking or neon. The quicker you can hone your understanding and intuition, the more successful you are with glass. You have to know when to heat it, how to get certain parts hot while others remain more cool, and how to move with gravity, letting it do some of the heavy lifting for you.

When you begin working with glass, you’re constantly fighting gravity. It’s one continuous struggle. But as you progress, you come to understand how to let it work FOR you. For example, in elongating a neck of a vessel and thinning out certain walls. There are so many nuances, from the flip of a wrist, to how you touch it with tools. Beginners always wind up using a heavy touch: smashing it, pushing too hard, trying to get the glass to submit. 

But if you watch a master, they are usually working in such a way that they make everything flow in controlled chaos. It looks like they’re one second away from disaster, but they know what they’re doing with every micro-movement.

Rosalyn: We often take glass for granted and view it as a commonplace material in our daily lives. We rarely think about the intricacies of how this substance exists in its many forms and touches so many aspects or our lives from water glasses, windows, tables, smartphones, computer screens, and so many other items. Thank you so much, Wendy and Shayna, for sharing your wisdom and personal experiences in working with this fascinating material.