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I recently began browsing the 5e PHB when I noticed that there was no distance per round when falling under the Falling category. Is there a set fall speed and if so, what is it?

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up vote 15 down vote accepted

The rules have no explicit guidance on falling kinematics. Mostly.

Free-falling motion isn't tackled in the rules. Back to that in a moment.

Feather Fall allows one to fall at 60 ft. per round (6 sec.), or at a speed of 10 fps without suffering damage. Free-fall, which is injurious, should be faster than that. A little high-school physics will tell us that a body falling freely (assuming g=32 ft/s2) for 10 ft. will attain a final speed of ~25 fps. So this all makes sense: 10fps=no damage, 25fps=1d6 damage.

Distance fallen:

To me this means it's not inherently unreasonable to use the simple classical physics in this situation: assuming acceleration due to gravity similar to that experienced at sea level on Earth and ignoring air resistance at low speeds:

starting from rest: \$ d_{\text{1 round}} = 576\text{ ft} \$

starting from rest: \$ d_{n\text{ rounds}} = 576 \times n^2\text{ ft} \$

Falling speed: your average velocity during the fall would be \$\sqrt{16d}\$, in feet per second. (Your final velocity is twice that.)

For those who really want a refresher on simple kinematics, assuming uniform acceleration and starting velocities of zero:

  • \$ \text{distance traveled} = \frac{1}{2} \times \text{acceleration} \times \text{time}^2 \$
  • \$ \text{final velocity} = \sqrt{2 \times \text{acceleration} \times \text{distance traveled}} \$
  • \$ \text{average velocity} = \dfrac{\text{final velocity}}{2} \$
  • \$ \text{time of fall} = \sqrt{\dfrac{2 \times \text{distance traveled}}{\text{acceleration due to gravity}}} \$

In bad (non-SI) units the acceleration due to gravity is approximately 32 feet per second2.

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As a side note, the terminal velocity of a falling human is around 176 fps (120 mph). You don't accelerate forever, which is why falling damage tops out at 20d6. (D&D is really not interested in working out the airspeed velocity of an African swallow carrying far too much coconut, which is why it goes for the quick calculation of 1d6 damage per ten feet.) – Paul Marshall Feb 20 at 3:06
4… Mike Mearls agrees, but in nice rounded numbers. – J. A. Streich Feb 20 at 3:10
Wikopedia has a good article on terminal velocity – Brian Jun 3 at 14:40

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