How Far Do Character Fall Per Round?

[Deskepticon]

So you've just been thrown out of an aeroplane at 12,000 ft and your enemy forgot to give you a parachute. "Drats! Not again," you think, as you wonder how long you have before you eat dirt.

Hey folks. So I decided to throw together a little chart showing how far a character falls each round. I won't bore you with the math, but I used average figures for things like fluid density, drag coefficient, etc. I'm assuming the character doesn't want to fall faster, so I factored in an average person spreading their arms and turning horizontal, providing as much surface area as possible. I then rounded to the nearest even number to get nice, clean integers.

Terminal velocity is hit around the 15 second mark, or during the third round. After that the character stops accelerating and falls at a constant velocity.

Round .... Distance
1 (6 sec) ... 164 yards (82")
2 (12 sec) ... 486 yards (243")
3 (18 sec) ... 840 yards (420")
+1 (+6 sec) ... +360 yards (+180")

So you got tossed from a Cessna at 12,000 ft (4000 yards). Keep calm. You've got 11 rounds to figure this out, because on the twelfth round your dust.

Hope you enjoyed this folks. Maybe it will prove useful, maybe not. Either way, I had fun putting it together.

Cheers!

[Deskepticon]

If you're interested in freefall distances, the formula is:

d = 1/2gt²

Where "g" is gravitational acceleration (9.8 m/s² at sea level) and "t" is time.

(Edit- don't forget to convert from meters to yards. Just multiply by 1.09
or
replace "9.8" with 10.7. Either works.)

For the first 30 seconds of freefall, the numbers are:

Round ..... Distance
1 (6 sec) ... 192 yards (96")
2 (12 sec) ... 772 yards (386")
3 (18 sec) ... 1736 yards (868")
4 (24 sec) ... 3086 yards (1543")
5 (30 sec) ... 4822 yards (2411")

[SeeleyOne]

I have wondered about this before but did not want to do the math.

I wonder how much a difference it makes if you were going up before you lost power or if you were already in a dive.

[Deskepticon]

I have wondered about this before but did not want to do the math.

Yeah, the math can be a little daunting. There is a lot of variation, such as if you are in a low- or high-pressure zone, how big a character is (both in terms of mass and surface area), how strong the winds are, etc. I kept it simple and ignored a lot of that stuff, because, heck, it's just a game.

I wonder how much a difference it makes if you were going up before you lost power or if you were already in a dive.

If you were going up, such as climbing in a jet, you'd subtract the distance gained from gravitational acceleration from your initial velocity until you stop gaining altitude. Then you'd start from 0 velocity, just as if you've been dropped. Any lateral motion doesn't really factor in much (at least not enough for a tabletop game).
__________

If you were already in dive and lost power, you would add your initial velocity to the distance from gravitational acceleration. So if you were flying at about 500 mph (244 yards/sec), you'd simply add that to the distance-per-round for a falling jet.

You can probably use the chart above (the first one, not the freefall one), but it won't be very accurate. That chart is based on a falling human, and a jet falling nose-down is going to have a much higher terminal velocity, since it's more aerodynamic. In other words, the distance it falls each round would be higher than for a human, and it will continue to accelerate longer as well.

But just for the sake of the example, 500 mph (244 yards/sec) is 1464 yards per round. That would be added to 164 yards in the first round of falling, for a total distance of 1628 yards (814"). In the second round you'd add the initial velocity of 1464 to 486, and so on.

[Deskepticon]

If you were going up, such as climbing in a jet, you'd subtract the distance gained from gravitational acceleration from your initial velocity until you stop gaining altitude. Then you'd start from 0 velocity, just as if you've been dropped. Any lateral motion doesn't really factor in much (at least not enough for a tabletop game).

I realized this might be a bit more complicated than I made it sound. Whether or not anyone actually wants to inject this much verisimilitude into their game is up to them, but the way this would work is as follows (using the chart for a human just as an example):

Assuming a jet is climbing at a 45° angle at 500 mph (1464 yards per round), that means they are gaining altitude at a rate of 732 yards per round (and moving laterally 732 yards).

If they lost power, they would subtract 164 yards in the first round, meaning they only gain 568 yards of altitude. In the second round, they'd subtract 486, gaining only 82 yards of altitude. In the third round their vertical velocity hits 0, and they begin falling.*

If the jet was at 4000 yards (12,000 ft) when it lost power, it begins the third round at 4650 yards (568+82).
___
* Note that this assumes the pilot holds the craft at a 45° angle the entire time. For game purposes, it would probably be better to have the pilot make a manuevering roll to "level out" the craft, turning whatever velocity they have into lateral motion and attempting to glide their way to a less harsh landing.

For what it's worth, I didn't have aircrafts in mind when I made this thread.

[SeeleyOne]

Yeah, I was thinking about the adding/subtracting as that is how you do it with the velocity of cars.

This topic just reminded me of an old gaming memory. Long ago when I was new to GURPS we were playing in a fantasy campaign. I was a mage and my brother was an ogre. That gaming group had some oddities in that some players felt that they were the only players at the table. We were at a dungeon that had a huge spiral staircase that went down many miles. For some reason the party went down the stairs ahead of me and the ogre. After a while, we got bored. We went to a nearby farm, stole a cow, and then took the cow to the dungeon. I lit the cow on fire and the ogre pushed it into the center of the stairs, which was a pit of many miles. After going down the stairs all the way, the party (without us two) found a portal at the bottom. A demonic dragon came out. Just as the fight was about to start, the cow hit the dragon at terminal velocity. Dead demon. Two players screwing around due to boredom took out a boss with a cow thanks to gravity.

[lunchmoney]

...twelfth round your dust.

Was loving this until I hit this part. Thought you were better than that

[Deskepticon]

Nope.