Highlights
- Hyrule's gravity is approximately three times higher than Earth's, according to a fan's mathematical analysis of Link's fall speed and position data.
- The user used a parabolic curve to analyze the data points, revealing Link's acceleration due to gravity in Hyrule as 28.2 m/s^2.
- The user also conducted pendulum experiments to confirm the gravity measurement and measured Link's height using a unit of distance in Hyrule, suggesting it matches an average human height.
A talented Tears of the Kingdom fan (mathematician?) discovered that the gravity in Hyrule may be three times higher than our standard Earth gravity, and provided detailed mathematical insights for those interested in learning how this discovery was made.
First, JukedHimOuttaSocks had Link stand on a platform that could disappear after a short time and recorded the speed at which Link could fall. Then, over the course of a 60-meter fall, they recorded Link's Z-coordinates (the position of a given object in 3D space) for every meter of these 60 meters and carefully analyzed the data.
What they noticed was that Link's fall followed a specific pattern (captured in the Reddit post using a parabolic curve with a quadratic term). In simple terms, the data points look like a smooth curve when plotted on a graph. By analyzing this graph, the user was able to figure out how fast Link was accelerating downward due to gravity during his fall, and the result turned out to be approximately 28.2 meters per second squared (m/s^2).
The normal acceleration due to gravity on Earth is about 9.81 meters per second squared (m/s^2), and that makes the calculated 'Hyrulic' gravity three times the average. The user also claims to have conducted a separate set of pendulum experiments (measuring the time it takes to complete a full swing, and calculating the expected value of gravitational acceleration based on the measured length and period of each pendulum). The result of these experiments was the same, 28.2 meters per second squared (m/s^2).
The user also considers the hypothesis that the unit of distance in Hyrule may not actually be meters. Therefore, they placed a 4 unit long beam next to Link to make sure, and it turned out to be double his height plus 0.5 units. From this, they can deduce that Link's height is 1.75 units. If the units are meters, this would mean that Link's height is about 5 feet 9 inches, which seems feasible for someone of our average human height.
The user's meticulous and impressive work has been praised by real physics teachers, reflecting the high quality of their efforts. It is also safe to assume that there are still many secrets to be discovered in Tears of the Kingdom's Hyrule, just waiting for eager explorers to uncover them.