In S07E01 - Dragonstone, the gates of Dragonstone open inwards.
Why? Isn't it easier to ram down when it can be pushed open? The hinges are high enough to be inaccessible, and could easily be reinforced/hardened during wartime.
Answer
This is an interesting physics problem. Counter intuitively, it looks like opening inward is actually stronger!
From a strength perspective, it doesn't matter whether the doors open inward or outward. What matters is whether an attacker's actions cause tension or compression. If you have the typical doors you see in castles, a battering ram hit causes tension - the wooden beams pull against each other to resist the ram. If you bow the doors out a bit, you can see that they cause compression instead. Trying to ram the doors causes the doors to try to close more, compressing all of the timbers.
Different materials handle tension and compression in different ways. Concrete, for instance, is very good at compression loads but falls apart under tension loads. Accordingly, you'll always see concrete structures in compression. Look at a bridge, and you'll always see an arch to it, ensuring the whole bridge is in compression.
Wood, on the other hand, is much better at tension loads. Compression loading focuses all of the forces on one part of the door, while tension loading lets wood do what it is best at. If you rammed a door in compression, the wood would rapidly splinter, rather than bending to soak up the energy and momentum. (There's more to it, dealing with cross grain and along-the-grain forces, but that's another physics lesson)
So you definitely want a door structured so that battering rams cause tension. If you run the geometry, you see that it's really hard to have a door open outwards and exhibit tension under attack.
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