All objects in D&D hit a terminal velocity of 25.399 m/s - the standard falling speed is 500 feet per six seconds.This is regardless of shape or size - all objects end up falling at that speed due to the physics of the game, regardless of how far they fall (blame it on magic, I suppose).
From there, it isn’t too hard to calculate the emerge - you can use the density of Platinum to calculate mass and then it is a simple matter of KE = (1/2)mv^2.
Except there is where you get to a real problem - at impact, you’ll have to model the how that kinetic energy is transferred, taking into account light, heat, etc. You simply cannot do that with this fact pattern - you would need to know what type of ground is being hit and dozens of other factors.
So, even though we do, in fact, have velocity due to the game’s rules, you still do not have quite enough to get any further than the kinetic energy—at least not with perfect accuracy.
For fun though, let’s calculate the kinetic energy. 75,000 square feet a side gives us a cube with sides of 273.861 feet, or a cube with volume of 20,539,595.906 cubic feet.
That gives us a cubic centimetre volume of 581,616,586,344.438.Platinum’s density is 21.45 grams per cubic centimetre, giving our cube a mass of 12,475,675,777.088 kg.
Plug that into our handy KE formula and you get 4,024,086,616,217.8 J
Seems like an unmanageably big number, right? It is, but not really than big - the low terminal velocity as compared with real world physics and the fact the exponential factor of velocity is so important to kinetic energy keeps things relatively manageable.
In terms of energy, that is just a smidge less than a 1 kiloton nuclear weapon - 0.962 kt to be exact. That is 1/15th of the atomic bomb dropped on Hiroshima for reference.And, it should be noted, an atomic bomb is a lot more efficient in its energy usage than a pure impact would be, so you’d get an even lower destructive yield than might otherwise be accepted.
Okay, but still, let’s go further - we still need to calculate damage, and dynamite is still our best bet. A stick of dynamite in D&D weighs 1 pound.Dynamite is also fairly efficient, but we are still using it for reference because it is what we have in units we already are working with.
Our platinum cube has the force of .962 kilotons of dynamite; 962 tons - 1,924,000 sticks of our 1 pound dynamite.
Dynamite deals 3d6 damage for the first stick increasing by 1d6 damage for each subsequent stick. We will ignore the cap on damage since this is not operating on explosive logic. That gives us 1,924,002d6 damage.
Average roll on a d6 is 3.5, so the average damage would be 6,734,007.
Again, that’s very rough math and uses some false equivalencies and hand waiving away some of the more complex physics.
This is correct on earth; it is not in D&D - if you look at the first six seconds of falling speed and use the formula for calculating acceleration given distance fallen and time (S = S0 + V0t + (1/2)at^2), you get a gravitational acceleration of -8.467 ms^2 on the D&D planes.
All objects in D&D hit a terminal velocity of 25.399 m/s - the standard falling speed is 500 feet per six seconds. This is regardless of shape or size - all objects end up falling at that speed due to the physics of the game, regardless of how far they fall (blame it on magic, I suppose).
From there, it isn’t too hard to calculate the emerge - you can use the density of Platinum to calculate mass and then it is a simple matter of KE = (1/2)mv^2.
Except there is where you get to a real problem - at impact, you’ll have to model the how that kinetic energy is transferred, taking into account light, heat, etc. You simply cannot do that with this fact pattern - you would need to know what type of ground is being hit and dozens of other factors.
So, even though we do, in fact, have velocity due to the game’s rules, you still do not have quite enough to get any further than the kinetic energy—at least not with perfect accuracy.
For fun though, let’s calculate the kinetic energy. 75,000 square feet a side gives us a cube with sides of 273.861 feet, or a cube with volume of 20,539,595.906 cubic feet.
That gives us a cubic centimetre volume of 581,616,586,344.438. Platinum’s density is 21.45 grams per cubic centimetre, giving our cube a mass of 12,475,675,777.088 kg.
Plug that into our handy KE formula and you get 4,024,086,616,217.8 J
Seems like an unmanageably big number, right? It is, but not really than big - the low terminal velocity as compared with real world physics and the fact the exponential factor of velocity is so important to kinetic energy keeps things relatively manageable.
In terms of energy, that is just a smidge less than a 1 kiloton nuclear weapon - 0.962 kt to be exact. That is 1/15th of the atomic bomb dropped on Hiroshima for reference. And, it should be noted, an atomic bomb is a lot more efficient in its energy usage than a pure impact would be, so you’d get an even lower destructive yield than might otherwise be accepted.
Okay, but still, let’s go further - we still need to calculate damage, and dynamite is still our best bet. A stick of dynamite in D&D weighs 1 pound. Dynamite is also fairly efficient, but we are still using it for reference because it is what we have in units we already are working with.
Our platinum cube has the force of .962 kilotons of dynamite; 962 tons - 1,924,000 sticks of our 1 pound dynamite.
Dynamite deals 3d6 damage for the first stick increasing by 1d6 damage for each subsequent stick. We will ignore the cap on damage since this is not operating on explosive logic. That gives us 1,924,002d6 damage.
Average roll on a d6 is 3.5, so the average damage would be 6,734,007.
Again, that’s very rough math and uses some false equivalencies and hand waiving away some of the more complex physics.
This is correct on earth; it is not in D&D - if you look at the first six seconds of falling speed and use the formula for calculating acceleration given distance fallen and time (S = S0 + V0t + (1/2)at^2), you get a gravitational acceleration of -8.467 ms^2 on the D&D planes.
Bro ima sit here in the corner and be dumb
PM me TOMATO let the games begin
Thomas the train
Our Friend Bob
That is my oh so glorious nickname according to drummer
https://www.dndbeyond.com/forums/off-topic/adohands-kitchen/173323-barbarian-wars
Join our ranks