WTC 7: A short computation

Kenneth L. Kuttler

Professor of Mathematics

Brigham Young University

Provo, Utah 84602

Introduction

I provide a short computation, focused on World Trade Center building 7. Based on very favorable assumptions for achieving a fast fall, including ignoring resistance due to intact steel columns, I could only get the building to fall in about 8.3 seconds, whereas the observed roof-fall time is approximately 6.5 seconds. The problem is the large number of floors and conservation of momentum in a collision. Some of the “official” explanations about progressive collapse are evocative but they do not explain the difficulty in the rapid fall of the building along with what is evidently taking place when the video of the falling building is observed.

A short computation

Building 7 was 576 feet (176 m) tall. The speed of a ball bearing falling from the top of this building to the ground is therefore the solution to the equation

1 v2 = gh = 32 × 576

2

which yields v = 192. Thus the time to fall to the ground would be

576

= 6 seconds.

( 1922 )

It was observed that the building collapsed in just 6.5 seconds.1 Could this possibly happen as a result of pancaking floors collapsing from the top down? We show here that if the collisions are inelastic, such a scenario is impossible.

Assume there is not support for any floor when it is hit by the collapsing floors from above. Thus it is like the floor is just floating in the air when it is hit but it is stationary.

To make things general, let h denote the spacing between floors and let there be n > 2 of these

floors.

Let vk be the velocity of the conglomeration of k of the floors just before it hits the (k+1)st floor and let vk +1 denote the velocity of the larger conglomeration of floors immediately after the collision. Then by conservation of momentum