Marketing and SEO experts would suggest creating website content that would interest the greatest possible audience, give it a click-bait title, and cram it full of keywords. And if I did that, you would be about to read an article on dry eye hacks right now. But doing all that would contribute nothing to the world’s knowledge base, and would simply regurgitate what has already been written about hundreds of thousands of times. So instead, I am going to write about something completely novel that has never been discussed before on the internet, a topic residing at the intersection of optics and architecture. And sitting at this intersection is the Calgary Saddledome, more specifically the hypothetical question of “If the Calgary Saddledome was made of glass, what prescription would it have?”. For the few dozen people who have read this far, I hope you enjoy the rest.

Top down view showing the Saddledome as being almost perfectly circular

Imagine if the iconic Calgary Saddledome, a staple of the city's skyline, was made entirely of glass. Now, take that thought a step further and ponder what the prescription of such a colossal lens would be. It's a whimsical idea that combines architecture with optics, and it invites us to view the world through quite literally a different lens.

Firstly, let's consider the Saddledome as it stands—a vast structure with a unique, curved design that has housed countless events since its opening in 1983. Contrary to popular opinion, the building is almost a perfect circle when viewed from the sky. This circular structure has a diameter of approximately 130m, with the iconic roof having a center point located 14m below the higher point of the edge ring and 6m above the lower point of the edge ring, therefore giving the appearance of a saddle. The proper term for this shape is a hyperbolic paraboloid and can be modelled by the mathematical formula Z=(Y^2/b^2)-(X^2/a^2). A hyperbolic paraboloid is also the shape of a Pringle’s potatoes chip and interestingly enough, the shape of glasses lenses used correct for certain types of astigmatism.

Various 65mm glass lens blanks with their clay models laying in front of them, The clay models help show the surface curvatures easier. On the left is a convex lens, the middle an astigmatic lens, and the right a concave lens.

Now lets consider the lenses in a pair of glasses. Every lens in every pair of glasses starts as a lens blank which is a round, thin piece of glass or plastic with a surface that is concave, convex or both based on the desired prescription. The size of the lens blank can vary, but most are around 65mm in diameter. A lens blank with very little prescription will feel almost completely flat in your hand, with similar dimensions to a drink coaster. A lens blank with a higher prescription may feel thicker in the middle or thicker on the edges based on if the prescription is for nearsighted or farsighted correction. An astigmatism lens would be a combination of these with the lens blank having edges that are thicker in certain areas and thinner in others. Once a person chooses a pair of frames, the eye opening on the frames is traced and a lens matching this size is then cut out of the lens blank and inserted into the chosen pair of frames.

So now that we have some background, we can approach the question of “If the Calgary Saddledome was made of glass, what prescription would it have?” from two different angles, each giving us two very different answers:

If the made-of-glass Saddledome itself was the lens blank (therefore being much, much bigger than the typical 65mm in diameter lens blank) and we were to cut a small circle out of the roof and pop that into a pair of glasses, what prescription would it have?
If the made-of-glass saddledome was shrunk down from its 130m diameter to 65mm diameter, and inserted into a pair of glasses, what prescription would it have?

A pair of glasses with the lens from question 1 in the right lens and the lens from question 2 in the left lens. The right (far) lens is essentially flat, while the left (close) lens is definitely saddle shaped. Note: both lens were modeled to the actual parameters discussed in this article and are not simple approximations.

For question no. 1, if we were to extract a small, 65mm diameter lens blank from its roof, the resulting piece would paradoxically have an almost negligible prescription. This is because the curvature of such a small segment taken from the massive dome would be very minimal, equivalent to taking a 0.1mm diameter round patch off of the surface of a soccer ball. That microscopic patch would for all intents and purposes appear to be flat. For those wondering, the actual prescription in this scenario would be +0.002-0.005x180 (the last number, the axis, is arbitrary but lets use 180 as that’s the most common axis). This prescription is very small, approx. 100x smaller than the smallest prescription an Optometrist could ever find during an eye exam.

Now, let's entertain question no. 2, an even more fantastical scenario: shrinking the entire Saddledome down to a mere 65mm in diameter. In this case, the prescription of the lens blank would be approximately +5.00-9.25*180. This describes a very high astigmatism lens, one that would exhibit very obvious concave and convex meridians. This prescription is pretty dramatic, especially the -9.25 diopters of astigmatism, although I would wager their are people with a prescription similar to this walking around although extremely rare.

The concept of a glass Saddledome is, of course, purely hypothetical, but it serves as an interesting exercise in cross-disciplinary thinking. It also highlights the inverse relationship between the magnitude of a curve and the resulting power of a lens. The large curves found in the world of architecture would all create extremely weak lens since the power of a lens is calculated by taking the inverse of the radius of the circle that created it. Therefore the Las Vegas Sphere would create a very, very weak lens while a small glass marble would create a very strong lens.

If you made this far, thanks for reading.