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Skyscraper Heights Analysis

-- Number of skyscrapers as a function of height --

by Egbert Gramsbergen
**Vertical axis: height in meters,
horizontal axis: number of buildings with at least this height**

Based on Marshall's Hot 500, july 1999.

The orange points are actual building data, the purple line is an approximation given by a simple exponential function
h(n) = h_{0} - h_{1}log(n)
with
h_{0} = 452m and h_{1} = 45m
(or, if you prefer half-values
h(n) = h_{0} - h_{2}·^{2}log(n)
with
h_{2} = 31m.

What about the missing part, say n > 800 (or h > 150m)? Mindless extrapolation of the purple line towards the right produces a total number of buildings in the world of approx. 22000, which is clearly rediculous. If we reduce the average slope by a factor 4, we end up in the region of 10^{9}, which should be about right.

For a similar graph for city skylines rather than individual buildings, see the World's Best Skylines - analysis.

What about the missing part, say n > 800 (or h > 150m)? Mindless extrapolation of the purple line towards the right produces a total number of buildings in the world of approx. 22000, which is clearly rediculous. If we reduce the average slope by a factor 4, we end up in the region of 10

For a similar graph for city skylines rather than individual buildings, see the World's Best Skylines - analysis.

created: 1999-07-23 last update: 2002-02-20 |