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Re: The right way and the wrong way.
Posted By: knivetsil, on host 208.0.9.194
Date: Wednesday, September 11, 2002, at 13:42:21
In Reply To: Re: The right way and the wrong way. posted by wintermute on Tuesday, September 10, 2002, at 05:29:53:

> > Yes, but tall towers are much, much more space-efficient than relatively low buildings. Let me remind you of the purpose of skyscrapers in the first place: to save space. Just think: if the WTC were a one-story building, it would take up 110 times as much land area as it did. Now granted, space doesn't matter as much when human safety is put into the equation, so I believe the pyramid-shaped design is very favorable, as far as stability goes. The pyramidal design, I think, would be able to withstand an airplane crash much better than a rectangular prism of the same base and height, since the ratio between the support below the hypothtical impact point and the mass above it will always be better. In other words, pyramidal buildings tend to be bottom-heavy, a much more favorable design than a rectangular prism of equal height and base. Furthermore, a pyramidal building would have 1/3 the volume of its rectangular counterpart. However, because of of its structural superiority, it could be built much taller than a rectanguler building, thus increasing its volume. If the twin towers were built three times as tall and in the shape of a pyramid, I actually believe that far fewer people would have died.
> >
> > kniv"too late"etsil
>
> Of course, it would need the ground floor to be about a mile on each side, which might not be very easy in the middle of New York. But can someone work out how much floor space you would have in there? Would you actually need any other buildings?
>
> winter"That would be HUGE"mute

Nono, the base would have the same area as that of the original. It would only be three times taller, since if it were of the same height and base, it would have 1/3 the volume, so building it 3 times higher would restore its volume to that of the original...

Okay, I think I am being kind of confusing. So, let me put it this way. The formula for the volume of a rectamgular prism is Base x Height. So, if one of the WTC towers were 1500 feet tall (I have no idea of their dimensions, I'm just guessing) and its base were 1600 square feet (or 400 feet on each side), it would have a volume of 2.4 million cubic feet. If each floor were 10 feet tall, then it would have 240,000 square feet of office space.

The formula for the volume of a rectangular pyramid is 1/3 x Base x Height. If one of the WTC towers were a rectangular pyramid with the same height and base, it would have one-third the volume of its rectangularly prismal counterpart. So if, again, the floors were 10 feet each, then it would have 80,000 square feet of office space.

However, if the base remains constant, then the volume of a pyramid will vary directly with the height. So, if the WTC towers had been rectangular pyramids rather than rectangular prisms, had the same base, were three times as tall, and the floors were spaced the same, then they would have had the same amount of office space (thus not compromising their commerciability), the same base (thus not increasing the cost for land), in a pyramid form (thus enhancing its durability), and three times as tall (thus enhancing its builder's ego). All in all, a favorable alternative to the rectangular prism.

kniv"all that mental math"etsil

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