possessives - "I know Bryan’s height" or "I know Bryan height"?

I know that the first is correct. Is the second correct too? Why?

And two more examples to make it clearer:

I know the tower height

vs

I know the tower's height

vs

I know height of the tower

Answer

English is flexble and allows many nouns to function as modifiers, but it has a subtle effect on meaning.

I know the tower height.

Here, I understand that height is a noun, and tower is an adjective answering the question height of what? or what kind of height?.

But this makes it seem like tower height as in "the height of a tower" is an important idea or concept on its own and that the listener/reader ought to be familiar with that or the reason for that - e.g. in this case, heights of towers seem to be something that you work with so much that you are shortening the words used to express it.

Usually you want to avoid this unless you are getting into the technical jargon of a profession or "shop talk".

Now, given the above, if you were to do this with a proper noun, you would be de-personalizing, as though the proper noun is just a thing, or a non-human object. And of course, since it's a modifier, you still need your article in front of it.

I know the Bryan height.

Here, it seems you are saying that Bryan is not a real person - I would guess it's some technical jargon, some aspect of a craft or profession - like "Pythagorean theorem" or similar.

Now:

I know the tower's height

I know the height of the tower

mean the same. X's Y can mean "Y physically belongs to X" or "Y that which is an attribute/quality belonging to X".