danhaas wrote:
Thank you, you've pointed most of the physics. But you forgot that arrows have a metal tip, which can increase its average density a lot. One other thing is that objects of same form and density, but differente sizes, DO have different terminal velocities. Both cross-sectional friction and skin friction are proportional to the area of the body, and the weight depends on the volume of the body. That's why wind can lift sand but not rocks. There are a lot of parameters around, and they can certainly be tweaked so the arrow and the dwagon have the same terminal velocity.
And let's not forget that this is Erfworld, for christ's sake, the physics doesn't have to be the same.
Of course not, I was just pointing out some physics errors. By the way, the metal tip is not actually denser than the wood, or else it would tend to make the arrows flight sag a bit. An archer can compensate for this somewhat, but modern arrow heads are usually made so that centimeter for centimeter they have the same linear density as the shaft, which means they also have the same skin drag for their mass as the rest of the arrow. But the arrow head is not very large and contributes more to pressure drag.
Also I did not mean to imply that an arrow shot to maximum range was falling at terminal velocity. Far from it. An arrow fired for distance at 45 degrees has half its energy moving horizontal and half vertical. The vertical portion reverses direction as the arrow rises and falls, while the horizontal portion just decreases slowly from the point of launch. Terminal velocity in free fall occurs when the horizontal portion drops to zero (unless it was fired straight down, of course). An arrow will usually hit something long before this happens, even if only the ground.
