I don't know about height, i'm guessing probably for cannons any way.

I have read that they do get better, more precise, after each shot IF they are shooting at the same still target. Kind of makes sense.

That's why they won't be too hot against fast moving loose ranked troops.

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All my actions are dedicated to the memory of my great Lord Frederick I who one day knighted a poor woodsman and man-at-arms. Ich der Salut der mutig Barbarossa