How far does a character fall in a single round? If my
griffon-riding character falls off his mount 300 feet up, how
long do other characters have to catch him?
This ends up being both a rules and a physics question. The
short answer is, “In a single round, you fall far enough to hit
the ground in the vast majority circumstances that come up in
the game.”
Here’s the long answer: A falling character accelerates at a
rate of 32 feet per second per second. What that means is that
every second, a character’s “falling speed” increases by 32 feet.
The distance he falls in that second is equal to the average of
his falling speeds at the beginning of that second and at the end
of that second. Thus, during the first second he falls 16 feet (the
average of 0 feet and 32 feet, which are his speeds at the start
and end of that second). During the next second he falls 48 feet
(the average of 32 feet and 64 feet). He falls 80 feet during the
third second, 112 feet the fourth second, 144 feet the fifth
second, and 176 feet the sixth second. That’s a grand total of
576 feet fallen in the first round alone, hence the short answer
given above—the number of falls occurring in any campaign
longer than this is probably pretty small. For ease of play, you
could simply use 500 feet as a nice round number—it’s easier
to remember.
Of course, the character falls even farther the next round,
although acceleration soon ends due to the resistance of air on
the falling body (this is what’s called terminal velocity). If the
Sage remembers his high-school physics, terminal velocity for
a human body is roughly 120 mph (equivalent to a speed of
1,200 feet per round, or 200 feet per second); thus, the
character’s falling speed hits its maximum in the first second of
the second round. It’s safe to say that after 2 rounds the
character will have fallen nearly 2,000 feet, and will fall
another 1,200 feet per round thereafter.
In the example you give, other characters would clearly
have no more than a round to react, and it’s possible they’d
have even less time. Remember that despite the sequential
nature of D&D combat actions, things are happening very
quickly—virtually simultaneously, in many cases. As a DM,
I’d probably allow every character a chance to react to a long
fall (such as the one you describe), as long as their action
occurs before 1 full round has passed from the start of the fall.
(As a side note, that’s why feather fall allows its caster to cast
it even when it isn’t her turn—otherwise, adjudicating its
timing would be a nightmare.) The difference between “you
watch the character fall all the way to the ground before you
can react” and “the character starts to fall, what do you do?” is
really just up to the DM’s sense of fun and fair play. Off the top
of my head, I’d say that anything up to 50 or 60 feet is clearly
too fast to react to (barring a readied action, of course), and
anything that approaches 250 feet or more should probably
allow characters some chance to react, but that’s purely a
personal opinion.
Whatever decision you make, try to make the same
decision every time, so that players know what to expect. If this
situation comes up a lot in your game, it’s probably worth
creating a house rule so you don’t have to try to remember
what you did last time. (If your campaign routinely features
300-foot falls, your characters might want to invest in some
rings of feather falling!)
Now, if you start altering certain assumptions—such as the
force of gravity, or the density of air that’s resisting the falling
character, or even the mass of the falling character—these
calculations become less useful. Yet, unless your numbers are
much different than the standard values, you can still use these
as benchmarks.
