How high can you throw something up in the air?

[Mok]

Two scenarios:

First - Sheer cliff facing the party, going up 50'. Party gets the idea for the Fighter to pick up the halfling and toss it up 50' to the top of the cliff, then the halfling could tie up the rope and lower it down.

Second - Party has defeated an NPC and has tied the NPC up in rope. The party starts arguing over whether they should kill the NPC. Eventually one character gets fed up with the argument, picks up the tied up NPC and tosses the NPC into the air. The NPC comes crashing down taking falling damage and killing the NPC.

Now, in both instances, the rules being used here are based around the fact that you can throw weapons out to five range increments. Improvised weapons have a range of 10', so you can throw something up to 50' with some vague hope of accuracy.

Further, in both scenarios, the thrower has enough strength that the object being thrown was a light load. The thrower was also large size so that the objects being thrown were two size categories smaller, brining it in line with stone hurling with giants.

So by RAW these things are legit, at least as far as you can cram them into RAW, but if you want to make it more realistic, then what was raised at the table was the issue of throwing horizontally versus throwing straight up.

The rules seem to be making the assumption that people are tossing weapons horizontally. Throwing things straight up isn't really be assumed.

Physics was beyond everyone at the table, and after googling this kind of question on physics web pages, I found stuff beyond my ken.

So I guess, beyond just general commentary of the whole situation, is there some rough ratio of how high one can expect to throw something strait up, versus horizontally? Do you just halve the distance?

[StabbittyDoom]

Disclaimer: Physics? In DnD? Heretic!
Disclaimer 2: I didn't account for air resistance, which would likely heavily reduce these values in the extreme cases (like a 50str colossal dragon). Also, this assumes you REALLY put your all into it, possibly straining yourself.

Since the "lift off ground" weight is a good indication of the maximum amount of force you can apply, you should use that.
F = ma. Lift off ground is your force. Divide this by the weight of the thing being thrown itself divided by gravity (w/32 for short) to get the acceleration. Presuming that you could only put about 0.25s of acceleration into the throw you would have something like:

velocity = (lift off ground * 32 / weight of object) * 1/4 (for time) = lift off ground * 8 / weight of object

If their character could lift it as a light load then their lift off ground was probably 6x the weight of the object.

velocity = 6 * 8 = 48 ft/s

This would be the initial velocity. After 1 second this would be reduced to 16. Then another 0.5s to 0. 1.5s in the air at an average of 24 ft/s is roughly 36 ft (so 35 in game terms).

For a "plug and chug" calcuation:
distance = vt - 1/2at^2
where t = velocity / 32; and v = velocity.
so distance = 48 * 1.5 - 1/2 * 2.25 * 32 = 72 - 36 = 36 feet

So final process is:
(l is lift off ground, w is weight of of object)
v = l * 8 / w
t = v / 32
d = vt - 16t^2

for a "object is equal to lift off ground" scenario you get this:
v = 8;
t = 1/4;
d = 2 - 1 = 1 foot (or in other words, no)

50str collosal dragon throws a 50lb halfling (the example I said you shouldn't use):
v = 208,800 * 8 / 50 = 33408; (past escape velocity)
t = 1044 (a little over 17 minutes! Just to go UP, again for down!)
d = 34877952 - 17438976 = 17438976 (or about 3302 miles)
Good thing falling damage is capped, 174389d6 anyone? (btw, the cap makes sense in light of physics. Thank you terminal velocity.)

Final Note: These are the ABSOLUTE maximums (except in the extreme high result cases). A character who doesn't wish to pull a muscle probably gets half the velocity. Air resistance will probably cut most distances down to about 2/3 (a complete guess, btw). If you get too far away, gravity starts to go down and increase the distance you travel (hence my reference to "escape velocity").

[Mok]

Wow! That's awesome and hilarious!

It isn't surprising, but I guess it really is hard to establish a ratio due to all of the variables. I think I might try and decipher what you did and then plug in all of the numbers so that I can get a breakdown of distance in relation to the encumbrance table.

[StabbittyDoom]

<post monster ate original post, oh well>

The equations I gave simplify to: d = (l / w)^2

It really isn't worth it to do all this math. Just say that you can only throw the willing or the helpless, that they have to be smaller than you, and that they only go up strength-mod squares. It's close enough, but doesn't require too much math or head-hurting. Players will understand that stronger = farther, and that's probably good enough.
If someone REALLY wants to throw something equal/larger, decrease their strength MOD by 10 if its equal size, and another 10 per size above. Fuzzy math says that's pretty close.
Halfling gets some mercy as that dragon can only throw it 100 feet now, rather than 3300 miles.

Spoiler:

I am one of those weirdos with a BS in math

Spoiler:

explosive runes

[Themetricsystem]

StabbittyDoom wrote:

** spoiler omitted **
** spoiler omitted **

Curiosity might have killed the cat... only so long as it didn't have evasion.

[Mok]

Thanks, that does sound more feasible.

In terms of fuzzy math, how does that break down in terms of encumbrance load?

Would it be something like this?

Light is Strength Mod in squares
Medium is Strength Mod in squares by half rounded down
Heavy is none or at most a single square

[StabbittyDoom]

Themetricsystem wrote:

StabbittyDoom wrote:

** spoiler omitted **
** spoiler omitted **

Curiosity might have killed the cat... only so long as it didn't have evasion.

The one who reads gets no saving throw. The cat has lost one life. Eight to go.

Quote:

In terms of fuzzy math, how does that break down in terms of encumbrance load?

Would it be something like this?

Light is Strength Mod in squares
Medium is Strength Mod in squares by half rounded down
Heavy is none or at most a single square

The size of the object has just as much to do with how far you'll be able to throw it as the weight (thanks to leverage and air resistance).

The "strength mod" squares approximation assumes about 50 pounds, and x4 weight per size for heavier things. If you double the weight (without increasing strength) it'll quarter the distance. Since load and strength mod are both calculated directly from strength score, load is already indirectly included. I'm pretty sure that's about as much fuzzy math you'll need.

[BobSlaughter]

As an old model rocketry fan, there was an old rule-of-thumb that was something like "For a rocket that reaches altitude X straight up, if fired on a 45deg angle, it will reach 1/2 X altitude but land 2X downrange." It's a basic rule called Tartaglia's Law.

Using this, then if you can throw something 100 feet horizontally, you can throw it 50 feet straight up, as a rough approximation.