The Azn, I also think your drawing is inaccurate. When looking at it, the catapults higher up shoot a farther horizontal distance - which I believe is your point. But what that drawing shows is not the advantage of height, but rather that the catapults higher up have more power than those down below, which is not the topic here. All catapults, regardless of their height, throw their loads (assuming the loads are the same) the same distance, and from there it's gravity against inertia. In your drawing, your catapults far up shoot a farther horiontal distance than those down below before the inertia vs gravity thing starts (that would certainly take the load forward some more, but more downwards).
It's hard to explain this without a picture, and
mine isn't accurate either, but it shows the difference between what it should be and what you drew. The diagram on the left shows three same-power catapults shooting the same loads, and on the right is what your diagram says. Because I know I won't be accurate I did not draw the trajectories all the way, but even so you can see that it's not first and foremost a question of height, but rather a question of the proportion of height against the distance in front of the catapult that is still your own castle. Certainly the overall distance the highest catapult shots is greater than the lower catapults. But the lower catapults have less Minas Tirith to shoot over too.
Secondly, the advantage in height does not mean the catapult has power to shoot farther. It does not come in with the horizontal distance the catapult projects it's load. It comes after, when the load is already losing height. In this matter I think
Mumriken has the better illustration of the trajectories. They are all, regardless of height, the same parabola, but the more room they have the farther they can go - but you know that after a certain point a parabola changes vertically more than horizontally.
And lastly, I want to say again this point that is unrelated to diagrams but also important. Minas Tirith probably did not have catapults at its higher levels,
especially that jut of rock in the Citadel.