The Math of Falling

[Klytus]

I having a physics brain-fart and need some help. I know the rate at which an object falls is 9.8m/sec^2 (or 32.2 ft/sec^2 in English) I am just having a hard time remembering how it works. If I do not have this right, please set me straight.

 

I drop an object, and for one second, it will move at a rate of 32.2 feet/second. On the second second, it is now going 64.4 feet.second. On the third second, it is doing 96.6 feet/second.

 

Is this right? Or am I way off?

 

And at which speed does one hit terminal velocity?

 

All I'm trying to do is figure out (roughly) "If I drop someone from this height, how long do the heroes have to save them?"

[Barton]

Terminal V for humans is about 90mph or so. Someone may have an exact number, if so please post it.

For falling I just use the Hero 5th ed. rules, simple and close enough for me to reality.

[keithcurtis]

Actually IIRC, the Hero rules are correct on velocity, but off on distance. Using 10m/s^2, you will be travelling at 10m/s at the end of one second. What the charts fail to remember is that that is the end velocity. You are starting from zero so the whole distance fallen is 5m, not 10m. IOW, you fall 2.5 hexes, not 5. This mistake is perpetuated throughout the chart.

 

The actual chart should read (for distance fallen and rounding):

1s = 2"

2s = 10"

3s = 22"

4s = 39"

and so on...

 

The actual formula for distance fallen is:

 

(5 x seconds x seconds)/2

 

 

 

Hexes per second of velocity should be:

 

5 x seconds of fall.

 

 

actually, the "5" above should be "4.8767998432", but 5 will do for a game chart. This is working from 32 f/s/s.

 

My advice? Ignore reality and use the chart. It's faster, more intuitive and no one ever listens to me anyway.

 

Keith "Newton" Curtis

[Supreme]

Originally posted by Barton

Terminal V for humans is about 90mph or so. Someone may have an exact number, if so please post it.

For falling I just use the Hero 5th ed. rules, simple and close enough for me to reality.

I don't know exact numbers, but terminal velocity is actually a product of air resistance. In a vacuum, an object with continue to accelerate towards the gravitational body until it hits that body. I'd heard that terminal velocity for a normal human who wasn't trying to dive or brake (i.e. spreading their arms for more air resistance) was around 190 MPH, not 90. But I could be wrong.

[SirViss]

I remember it being around 300 km/h, and that's pretty close to 190 mph, so I would use that as a good start...

[CorpCommander]

When I was a physics major...

 

I heard it was 125mph. A quick search of the internet found this:

 

http://hypertextbook.com/facts/JianHuang.shtml

 

200kph or 56 meters per second or 124 mile per hour.

[JMHammer]

Keith is right, plus...

 

Klutus said:

All I'm trying to do is figure out (roughly) "If I drop someone from this height, how long do the heroes have to save them?"

 

Your basic distance formula:

S = 1/2 A T^2

S = Distance

A = Acceleration due to gravity

T = Time

 

Solving for T in order to answer your question, the formula is:

T = (2 S / A)^(1/2)

[Read: T equals the square root of (two times S divided by A)]

 

Example: Working in metric and using nice round numbers, A is 10 m/s/s. Let's say S is 180 m. 2 S = 360. 360 / 10 = 36. 36^(1/2) = 6. So, your heroes have 6 seconds to save the falling character.

 

How you'll handle this in-game is another story. If it were me, I'd say that if any character can get to the falling character's position at the beginning of the segment of the saving character's phase, or below that position, he may attempt to catch the falling character and use his strength (and unused movement as strength) to reduce / eliminate damage.

 

If you want more realism, a character's strength isn't going to do jack to prevent falling damage. All those "snatched inches from the ground" images from TV and the comics are as fantastical as the antigrav flying people and laser eyes - when I see it on the animated JL, it makes me wince. A careful catch from a fall reduces damage in the same way that falling onto a rubber sheet reduces damage: Velocity from FAST to zero occurs over a longer time (a good fraction of a second instead of instantly), i.e.less acceleration (or, as you might care to describe, deceleration) is applied to the impacting body. "It's not the fall that kills you, it's hitting the ground at the bottom," or, "It's not the fall that kills you, it's the huge acceleration that occurs near-instantaneously at the bottom."

 

See Good Source of Info for terminal velocity information.

 

John H

[Farkling]

The few times I have wanted realism in falling damage, I have rolled the damage as a move through and applied it to both targets. They can subtract their STR dice from the velocity before toting it up. (after all, STR allows compensation for the impact if we follow Champs logic)

[Tech]

This is another example of why I like the Hero Games rules. Where else are you going to have math discussed to prove or disprove rules? Still, I'd go with the book for falling, although I find the more realistic chart interesting. I'd like to see the more realistic chart fully written out to terminal velocity.