Yeah but the Yumi was a short bow on the bottom, long bow up top. Sort of a hybrid even if, overall, it was one of the largest types of bow ever made.
The other points, about being on horseback giving no benefits to penetration or damage, are very true. This has been tested and retested, and the dangerousness of a mounted archer is provably NOT in it's damage or penetration, rather in their mobility and their area-of-threat since they can move fast and see far from their elevated perch. A moving or stationary horse adds no measurable damage or penetration.
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Parabolic arcs, once set up for one object, could easilly be set up for everything else, if done correctly. The acceleration of any object towards the ground is a constant, being measured as "1 G" (9.8 meters per second per second, acceleration). This does not change depending upon velocity or even distance from the earth.
A spacecraft in orbit falls at ~9.7 m/s
2. However it moves forward so fast that the earth is curving away at the same rate, so the craft never hits ground, even tho it is being acted upon by nearly the same amount of gravity and constantly falling. If the craft begins moving faster, the ground will curve away faster than they are falling, and the craft can be said to be moving outward from it's frame of reference. In reality however, it's trajectory is still curving toward the Earth at the same rate, it is merely moving laterally faster than the earth curves.
A bullet fired from a gun will hit the ground at the same time as one dropped from the same height. The bullet's lateral motion does not affect it's downward rate of descent in any way. Additionally, the bullet is not traveling fast enough for the curvature of the earth to allow it to be considered to be in orbit, so the bullet will indeed hit ground at nearly the same time as the bullet which was dropped. Arrows are similar, although their aerodynamic properties mean it falls somewhat slower when moving laterally.
Gravity affects everything equally, and outside of special cases (such as friction or magnetics) everything will always fall down at the same exact rate while in the same gravitational environment.
I sincerely hope that this is being taken into account. Right now there is no "gravity" in the game. Everything just "looks down" and "hits ground", generally not even passing through the areas in-between. At least this was the way it worked last time I saw any real science done on it, and since Magma Pistons still work I would imagine that is still the case.
If, instead, every object gained downward acceleration every tick that it was unsupported, "parabolic minecart paths" and "falling arrows" and "realistic catapults" would fall into place naturally and without even having to think about it. The only complexity introduced in those two later situations would be getting the AI to understand it has to aim farther up the farther away the target is... which can be calculated relatively simply by a binomial equation.
It seems Toady has already thought of this:
Assuming gravity works like real world gravity and you can invent a time unit (obviously not linked to the dwarf mode calendar, which moves too fast for this), then a choice has been made. It wouldn't make any fewer dragons fit in the tile though. I think for the purposes of the minecarts it turned out to be 2m x 2m x 3m with 10 clicks / second, but it isn't that important or far-ranging in effect.
So here's to hoping he's made it generalized enough to be applied to any kind of object.