Bows and crossbows - revised

[Ashtagon]

Hmm, let's try working out the ceiling height rule mathematically...

Base assumption is that a proper stance for an adult human has the arrow loosed from a height of 5 feet, and that we want the maximum arrow height at the mid-point to be 10 feet. Extending a straight line means we are 'aiming' at a point 15 feet above the target (and allowing gravity to compensate to pull the arrow back down to him him).

A little bit of maths tells me that gravity will take 0.966 seconds to pull an object down 15 feet. That's our flight time. (distance fallen = time squared x 0.5 x gravity).

http://www.atarn.org/islamic/akarpow..._bow_tests.htm tells me that arrow velocities range from 150-350 feet per second (45-100 m/s). If we take the mid-point of that (250 fps), and multiply it by our flight time, we get 240 feet as the distance an arrow should be able to travel per 10 feet of ceiling height.

It's probably reasonable to reduce this to 200 feet, both because it's less brainwork in the middle of the game to use a round number, and because you want to be able to aim at the enemy's body, and not just at his feet.

So... looks like a revision to that ceiling height rule is in order.

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Edit: Let's assume we want to hit at his chest and not his feet. The mid-point is again 10 feet above ground, and extending the line to the target, we are pointing at a space 15 feet above ground, and we want to allow gravity to drop the arrow 5 feet (back to chest-height). This takes gravity 0.788 seconds. With the above-mentioned arrow velocity, that's almost exactly 200 feet travelled.

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So, overall...

Hand-thrown ranged weapons require a ceiling height of 10 feet per 100 feet of distance to the target.

Projectile/launched muscle-powered weapons (bows, crossbows, and slings) require a ceiling height of 10 feet per 200 feet of distance to the target.

Just for completeness...

Gunpowder weapons (and low-velocity modern mortars and grenade launchers) require a ceiling height of 10 feet per 1000 feet of distance to the target.

General-use modern firearms launch ammunition fast enough that gravity is unlikely to impose any meaningful ceiling-space requirement over any playable range.