How long to swing across a chasm?

A high elf and a mountain dwarf stand on the edge of a 150' chasm. They are without modification to their racial speeds, so the elf moves at 30' and the dwarf moves at 25'.

Two ropes are anchored above the chasm, fixed in such a way as to allow a medium creature to swing from one side of the chasm to the other.

They grab the ropes and swing, arriving safely on the other side.

How long, by the rules, does it take them to get there?

Is it speed determined?

If it is speed determined, then the elf gets there in 5 rounds and the dwarf gets there in 6. I suppose if Dash is applicable, they get there in half that time.

But that doesn't make much sense, because speed is a characteristic describing how fast something moves, moving under its own power, or as a result of its own power.

Is it physics determined?

If it's physics it's pretty iffy. Magic is so much more reliable! But on earth it would be the square root of the length of the pendulum in meters (thanks Dale M.), so in this case we wouldn't know because the length of the rope isn't given, but it would be the same length of time for both the dwarf and the elf.

If we go by your logic, as long as they like because if, after stepping off they decide not to use any movement then they hover in place. From this we can conclude that they are not using their movement to move; they are in fact falling.

If we ignore a lot of real world effects like friction, the elasticity of the rope, the fact that the rope is not massless and that the characters are not point masses among other things the period (i.e. the time it takes to go from here, over to the other side and back) of a pendulum on Earth is twice the square root of the length (in m) of the pendulum. So to go across and not come back equal to the square root of the length (in m) of the pendulum.

Assuming 6 second rounds, a rope up to 36m (about 120 feet) long takes 1 round to get across, up to 144m (about 470 feet) takes 2 rounds.

Now, there are all sorts of complications you could add in like running and jumping so that the pendulum swing is bigger than the chasm and so crossing the chasm itself takes less time, or more real world physics because the pendulum is not constrained to a single plane it is a Foucault pendulum and you can solve those differential equations if you want. However, for the rather granular nature of D&D mechanics if you just say that a rope up to 120 feet gets you across in 1 round and one up to 470 feet takes 2 I think you will be close enough.

• Well, that's a good point. Also, if it was movement-based, they'd be able to use dash I think to move faster.
– Jack
Mar 5 '16 at 2:47
• A single pendulum swing is half the period of the pendulum, i.e. once the square root of the length. Also: Hurray for earth physics making things easier! Mar 5 '16 at 8:39
• Although a counter-argument to your point in the first para is that when a character jumps, they can't decide to hover in place, and jump is in part affected by the speed attribute.
– Jack
Mar 5 '16 at 12:42
• A helpful way to think of the swinging rope is as a vehicle with its own fixed movement, rather than as having anything to do with a character's personal movement. Mar 9 '16 at 4:08