Look up to someone on a balcony. You only see their head and maybe their upper torso. They see your entire body however, and it’s harder to find cover from something above.
Projectiles have potential energy when shot from uphill to downhill, they’re going to go further than if they were shot on flat ground. You also need more energy to fight gravity and reach an elevated target.
You can’t pour boiling oil upward. At least not as easily as you would downward. Gravity assist.
And it’s tiring to run uphill and you don’t want to be tired when you’re going to have to fight for your life in melee.
It’s more tiring to swing a sword upward than downward due to gravity. Again you don’t want to be tired and be easier to kill.
If yotur downhill the easiest target is your head so you’re going to suffer more grievous wounds on average.
It’s not always best (especially with modern weaponry), but more often than not, it is.
A few things:
Gravity: Walking up a hill is draining. Now imagine fighting your way up a hill.
Sight lines: You can see farther, so it’s harder to be surprised by the enemy when you have the high ground. And if you can see them (but they can’t see you), that means you can shoot at them, and they can’t shoot at you.
Weapons go farther: Whether it’s spears, arrows, rocks or bullets, a high vantage point increases the distance your weapon can be effective.
Combat, to a large degree, is all about energy. Biological energy (sustenance, speed and movement), chemical energy (firepower, smoke screens etc.), and so on. High ground gives you free extra energy due to gravity, and takes energy away from your opponent. In essence, it’s easier to drop a brick on someone’s head from above than it is to throw that same brick back up.
There are a few reasons. One is that a high ground means hiding spots. If you take a hilltop, you can hide part of your army behind the hill. Armies don’t fight like one mass against the other, they are often split up, based on the tactics of the army leader. Knowing what your enemy does below you while being able to hide some of your tactics, is a huge advantage.
Also you should not imagine a high ground as a little grassy bump. A real-world natural high ground (what the tactics book did mean by high ground) also comes with natural obstacles. It’s kind of a package deal. So if you manage to take a hilltop, it comes with some loose rocks and tricky soil that you can carefully climb in advance but your enemy must deal with it while charging against you. It’s kind of difficult to efficiently fight while climbing and balancing, meanwhile your opponent has a stable stand and only needs to poke at you.
The advantage against projectiles is again a thing that becomes a real thing with hills. Obviously a few meters of slight, grassy elevation did not matter, but a higher, steeper ground did. With low energy projectiles the little gravity effect did count but the edge of a hill also serves as a natural cover.
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