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## Tuesday, August 2, 2016

### Flat Earth Follies: buildings would crumble due to walls not parallel!

The first problem with the idea that walls for big buildings would 'crumble' if the Earth was round is that, whatever the actual angle between the walls, gravity would be pulling STRAIGHT DOWN so long as the walls are plumb.  Now, no wall is PERFECTLY plumb anyway and what I intend to show is that the angle is SO SLIGHT in practice between the walls that even this point is irrelevant.

So just how out of parallel would plumb walls be in a really big building.

The Willis Tower is 195 feet wide at the widest point and 1,729 feet tall.  Technically the walls aren't that tall but we will just assume they are.

Let's figure out how parallel those walls would be on a round Earth.

So what we need to know is, given two lines from the center of the Earth out through the surface which are 195 feet apart, what distance are they at when they are 1729 feet further out.

Our good friend the Right Triangle comes into play here.  We just need to figure out the angle the lines make at 195 feet apart from one Earth radius away, and then extend that same angle out an additional 1,729 feet.

We will use this Angle calculator to help us - select 13 decimal places option.

First we calculate the angle:

g = 195 feet
r = 20890566 feet

gives us an angle of α = 0.0005348192579° - a VERY TINY ANGLE.  This is a clue.

Now we just need figure out what g would be at the top, when we add 1729 to r = 20892295

r = 20892295 feet
α = 0.0005348192579°

Which gives us g of 195.016 feet.  So it's a MERE 0.016 feet wider at the top over 1729 feet.  That is WELL BELOW the margin of error for measuring how plumb a wall of that size is.

TWO TENTHS OF AN INCH from bottom to top.  A surveyor couldn't even detect that - you would need specialized equipment to get a reading that accurate over half a kilometer.

So this is an absurd concern.  No contractor would be expected or required to factor in something so slight into a building design.

The Earth is BIG should be your take-away from this.