A Dangerous Skyscraper
The Walkie Talkie Building at 20 Fenchurch Street in London has quite a hot history. Back in 2013, multiple people who had parked their cars in front of the building came back to find that parts of their car had melted! Why is this the case?
There
ere is a portion on the front of the building that has a shape similar to a paraboloid (though it does not appear to be exactly a paraboloid). Because of this, when the sun was in a certain position, its rays were reflected off of that portion of the building's windows and directed to a focal point near the street level. This caused a tremendous amount of heat.
People walking past wouldn't get hurt because they would only be in the focal region for a fraction of a second, and we can withstand large temperatures for short times. But when a car was parked in this immense heat, it can melt! In fact, someone even used this heat to fry an egg to demonstrate the dangers of this building.
Luckily, the building’s design only caused this problem when the sun was at a particular angle relative to the front of the building. Because of this, the intense heat only occurred for about two hours per day; otherwise, the sun would be too high or too low. Also, this phenomenon could only happen over the course of two to three weeks in the year, as this was when the path of the sun crossed the front of the building.
So why aren't cars still being melted? After this problem was reported, the architects affixed permanent window shades outside of the windows to prevent the sun's rays from reflecting onto the street level.
Sample Problems
1. Are there other interesting reflective patterns that could exist if the front of the building was shaped differently? What if it was flat? What if it was part of an ellipsoid? What if it was part of a hyperboloid?