The $2.3 billion technological marvel, the Las Vegas Sphere, opened Friday, 29 September 2023. It’s 112 meters (m) (366 ft) high and 157 m (516 ft) wide at its broadest point. It’s the largest spherical building in the world at 81,300 m2 (875,000 ft2). It includes seating for 18,600 people, and all seats have high-speed internet access. Haptic technology is incorporated into 10,000 of the venue’s seats.
This initial FAQ begins with a look at the magnitude of the Sphere and considers some of the mathematical tools used to produce massive immersive environments. Other FAQs in the series look at the wide range of advanced technologies needed to create the Sphere, including the 16K immersive display, infrasonics, haptics and 4D effects, spatial audio, and how the content is created.
The Sphere’s interior has a 15,000 m2 (160,000 ft2, 4 acre) 16K resolution wraparound LED screen with over 170 million pixels. It’s claimed to be the world’s largest and highest-resolution LED screen. The exterior has 54,000 m2 (580,000 ft2, 13 acres) of additional LED display space (Figure 1).
The Sphere features a spatial audio system using beamforming and wave field synthesis technologies. The sound system includes 1,600 speaker arrays installed behind the LED panels, along with 300 mobile modules with 167,000 speaker drivers controlled by a massive computer-controlled concert-grade audio system. With that many speakers, individual beams of sound can be directed to multiple locations in the venue simultaneously. The sound system also can deliver sound through the floorboards. In addition to haptics, 4D features (additional sensory inputs), including scent and wind, can be used.
The Sphere website lists two dozen mathematical elements that helped inform and guide the design process for the immersive audio, video, haptic, and 4D effects. The following are a few examples:
Wave field synthesis and Huygens-Fresnel
Wave field synthesis (WFS) is a key technology used to deliver an optimal audio experience to the entire audience in the Sphere. With a conventional loudspeaker system, even with surround sound, optimal sound quality is limited to specific groups of seats, the so-called sweet spot. WFS can deliver lifelike immersive sounds across the entire audience; every audience member gets a tremendous audio experience regardless of where they are sitting.
The Huygens-Fresnel Principle is a key. It describes how sound waves propagate and combine into new wave forms. WFS can be used to produce artificial wavefronts that are synthesized with many individually driven loudspeakers (Figure 2). In the Sphere there are 167,000 individually amplified loudspeaker drivers, controlled by a massive computer-controlled concert-grade audio system. With that many speakers, individual beams of sound can be directed to multiple locations in the venue simultaneously.
More sound math
The Helmholtz-Kirchhoff Integral helps keep the Sphere’s sound crystal clear. It was originally developed to study the scattering of acoustic waves in applications like sonar. It is now being applied in the Sphere to account for and control sound scattering that can otherwise cause a ‘mushy’ audio experience for some seats.
The Kirchhoff Integral Theorem describes a surface integral that can be used to calculate the solution of the homogeneous scalar wave equation at an arbitrary point in space. This theorem is important for the Sphere’s audio beamforming technology.
4D effects and infrasonics
The Navier-Stokes Equations can describe the conservation of mass and momentum balance for Newtonian fluids. They are used to model ocean currents, air flowing around an aircraft wing, blood flowing in a vein, and similar physical phenomena. In the Sphere, they control 4D effects like the distribution of fog to create atmospheric reimaging and immersive otherworldly effects.
The (two-way) Wave Equation is a second-order linear partial differential equation for describing waves or standing wave fields like sound. In the Sphere, a first-order one-way approximation of the wave equation that’s much easier to calculate is used to program and control the infrasonic haptics and audio systems. The system simulates 4D effects from smells to shifts in gravity.
Creating visual environments
The Sellmeier equation describes the relationship between refractive index and wavelength for a transparent medium and can be used to determine the dispersion of light. It’s used in the Sphere to control how light ‘filters’ through the venue and create visual simulations from the surfaces of alien worlds to the bottom of the ocean (Figure 3).
Summary
Numbers are an important aspect of the experience in the Sphere. It’s not just the massive number of speakers, the size and resolution of the LED display, and other physical dimensions; it’s also about the science and mathematics used to create the immersive experience.
References
Acoustic investigation of wave-field synthesized virtual sound sources using a 3D microphone array, Berlin Beamforming Conference
Patents that “shaped” the Sphere, Parola Analytics
Sphere, the science
The generalized Sellmeier equation for air, Nature
Wave Field Synthesis, Fraunhofer
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