O'Neill Cylinders

[Langy]

Nope. That _is_ the meaning of the term now, even if the meaning isn't proper given the origin of the word. Happens all the time.

Agreed.

This gives us the condition
R^3 + 2 * L R^2 - L^2 R - L^3 / 3 > 0

If you plug this equation into Wolfram Alpha, you can get solutions for R and L given the other number. Examples:

R = 20:
L < 33

L = 50:
R > 30

In other words, if lwcamp did his math right, your O'Neil cylinder isn't going to be stable if it's got a radius of 20 kilometers and a length of 50 kilometers.