Wednesday, January 04, 2006

6 Degrees Deflection? (PC)

Numb3rs is is a very good show, and it is gratifying that they portray math and science in such an enlightened manner.
However, the writers are not perfect in their use of math.
The first thing a physicist (a personal bias here since that is what I am) will do, even before doing a lengthy calculation, is a back of the envelope calculation. They do this to make sure their numb3rs make sense.
Charlie should have done this in episode 1x4 Structural Corruption.

After his experiment with the plumb bob he says that the building deflects 6 degrees.

Lets think about this for a second... does this numb3r make sense?

Back of the envelope time:

---- Start Fermi Problem ---

A side note about back of the envelope... approximations are fine.
For instance, pi = 3 (like in the bible) works just fine.

6 degrees ~ 1/10 radian.
Deflection at the top of the building is h*angle.

Therefore, with a 6 degree deflection the building will deflect approximately 1/10 th of its height.

If the Cole building was 100 feet (10 stories, a figure far too low) the top will have deflected 10 feet.
The building looks to be around 50 stories, or about 500 feet tall, so this corresponds to a deflection at the top of about 50 feet!

---- End Fermi Problem ----

This is a huge numb3r!

Poor Charlie would be puking while trying to hang the plumb bob, because of course this would not be a static deflection.

I did some quick calculations for the heck of it, taking into account rigidity of steel, some order of magnitude values for Young's modulus for steel (http://scienceworld.wolfram.com/physics/YoungsModulus.html)
with some adjustments for structure, and calculated a 30 mph wind on a 500 foot tall 100 foot wide building and obtained a deflection of about 0.2 degree at most.
This would give a deflection of around 2 feet for a 500 foot building.
This is pretty close to what was calculated for a building such as the world trade center.


Ahh, the power of numb3rs.

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