Quote of the Day
Many people want to leave a better world for their children. I'm trying to leave better children for my world.
— Carlos Slim
I have received a number of questions recently on how the curvature of the Earth affects building construction. In general, the effects of the Earth's curvature are ignorable because most man-made construction is on too small of a scale to notice the effects of the Earth's curvature. One well documented exception is the Verrazano-Narrows bridge, whose design took into account that the bridge towers are 1 5/8 inch farther apart at the top than at the bottom. In this post, I will show how to compute this value.
The calculations here are straightforward. My intent is to show that there are some structures that must take the Earth's curvature into account. There are two other examples that I know of: Stanford Linear Accelerator (Source), and Fermilab's neutrino communication experiments (Source). For more examples, see this comment.
Figure 2 shows how to compute the 1 5/8 inch of additional separation based on the drawing in Figure 1.
The Earth's curvature will only have significant effects on massive structures that are sensitive to small errors. With the Verrazano-Narrows bridge, we are talking about a structure with a size on the order of a 1000 feet and the effect of the Earth's curvature is ~1 inch.