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(OT) Request for an answer to a difficult mathematical question
- Thread starter Edena_of_Neith
- Start date
der_kluge
Adventurer
I'm not sure how much matter was used in the A-bomb dropped on Hiroshima or Nagasaki(sp) but it wasn't a lot. There's a LOT (as exemplified in the equations above) of energy in matter. I mean, c - the speed of light is a huge number (despite the arguments about it's exact value), and when you multiply that by the amount of matter, and then square it, you're talking about a huge chunk of energy.
If you, in fact, put a person in an A-bomb, the amount of energy would easily destroy the planet.
If you, in fact, put a person in an A-bomb, the amount of energy would easily destroy the planet.
die_kluge said:
Actually, atomic and thermonuclear bombs don't even convert all of their matter-fuel into energy. They aren't terribly efficient, and convert only a small percentage of the matter into energy. If you are working at bomb-level efficiency, you can put a human-sized mass into a bomb, and not destroy the planet.
Mind you, this begs the question - would you want to perform magic in this fashion? Cannibalize your own body for the energy?
This would likely be a monumentally bad idea. This isn't energy "stored" in the human body that we are talking about. That energy is the human body. You cannot start ripping off bits of it willy-nilly to do magic and expect everything to be okay.
Zappo said:
The Eldren techno-mages in my game had a spell called Ground Zero which had the effect of a small nuclear explosion centred on the caster (but he's protected from it), it costs him 1d4 hp worth of mass.
Doomstar the 500th level Eldren Wizard used it to kill 40,000 Mabden warriors with one spell, AIR.
fuindordm
Adventurer
Spell Energy
All, right, you got me started...
A large human (100kg), if converted to energy with 100% efficiency, produces 100 kg x (3e+8m/s)^2 Joules of energy by E=mc^2. This comes out to 9x10^18 J. That's a safe upper limit.
A human weighing 100kg burns about 2500 food calories per day; this is about 10,000,000 Joules of energy. So basing spells off the chemical energy in your body ought to be able to produce effects requiring several thousand Joules, after which you'd feel like eating a nice meal. Want to diet? Cast more spells!
For comparison, the Sun radiates 3.9x10^26 J/sec.
In 1997 the US consumed 99.2 x 10^18 J of energy (including fossil fuels and electricity)
In 1999 New York consumed 4.518 x 10^18 J.
The energy content of a spell is easiest to calculate if its effect is purely mechanical:
Mage Hand can lift 5 lbs (2.27 kg) up to 30 ft (9.14 m), which costs 200 J.
Feather Fall at 1st level can make 300 lbs (136 kg) fall at a constant rate for 1 round, covering 60 feet (18.3m). This costs 136kg*9.8m/s^2*18.3m = 24,400 J per round, and scales proportionally with the mass.
Levitate at 3rd level can make 300 lbs rise at 20 feet (6.1m) per round for up to 30 minutes (300 rounds). This is equivalent to traveling 60 ft/round for 100 rounds, so requires 100 times as much energy as feather fall: 2,400,400 J. This seems to be barely within the human capacity.
Fly is a bit weird because the maximum load is a function of the caster's strength and size, not the spell. For an average human at maximum load, the spell lasts as long as levitate but the PC can travel straight up only 50% faster--so overall Fly only provides 50% more energy to fight gravity than Levitate. For a human with Str 12, their own weight + max load is probably about 300 lbs--but Levitate can boost the mass by 100 lbs per level, while Fly is stuck, so at the same caster level levitate has already caught up to Fly. The kinetic energy provided by Fly is high, but insignificant compared to the amount of gravity that can be countered: 22,800 J at max load or 25,600 J with a light load (150 lbs). Of course, Fly includes the control feature and the auto-feather fall, and one could potentially expend a lot of energy executing manoeuvers. If one spent the entire duration of the spell accelerating up to max speed in one round, then decelerating to zero in the next, they could burn a maximum of 12,500,000 J over 50 minutes--so the control factor does give us another factor of 10 or so.
Finally, Telekinesis: the sustained force is 25 lbs/level x 20 feet/round x 1 round/level, or 500 foot-pounds x level^2. At 10th level, we get 50,000 foot-pounds which is equivalent to only 67,800 Joules! This spell is unique in explicitly gives you the energy expended, so we can't squeeze out a hidden capacity through "control factors".
It does give you fine manipulation, however, and can be used as a combat spell in a pinch. A 250-lb. object with this much energy is traveling at a speed of about 23 meters per second. This is the speed it would have after free-falling for 2.4 seconds, by which time it would have covered a distance of 90 feet--so the 10d6 damage given by the spell is actually about right for the given energy (assuming that falling damage is realistic).
It seems like a good rule of thumb is that the mechanical energy provided by a spell is about 100 times greater per spell level, but at higher levels this capacity gets cut way down for greater control. If the amount of food energy seems unreasonable to you compared to these effects, remember that we couldn't normally generate such large amounts in 6 seconds through muscle action--but we could, for example, spend 15 minutes winching down a catapult that could impart this much energy to a 250-lb boulder. Machinery lets us convert food energy to impressive amounts of mechanical energy by the magic of work: expending a little force over large distances is just as good as expening a huge force over short distances. If magic runs off our body energy, then it needs to do something similar.
Maybe wizards create ethereal constructs that "wind up" (like a spring) while they sleep and store their body energy in a quickly retrievable form?
--Ben (an astrophysicist)
All, right, you got me started...
A large human (100kg), if converted to energy with 100% efficiency, produces 100 kg x (3e+8m/s)^2 Joules of energy by E=mc^2. This comes out to 9x10^18 J. That's a safe upper limit.
A human weighing 100kg burns about 2500 food calories per day; this is about 10,000,000 Joules of energy. So basing spells off the chemical energy in your body ought to be able to produce effects requiring several thousand Joules, after which you'd feel like eating a nice meal. Want to diet? Cast more spells!
For comparison, the Sun radiates 3.9x10^26 J/sec.
In 1997 the US consumed 99.2 x 10^18 J of energy (including fossil fuels and electricity)
In 1999 New York consumed 4.518 x 10^18 J.
The energy content of a spell is easiest to calculate if its effect is purely mechanical:
Mage Hand can lift 5 lbs (2.27 kg) up to 30 ft (9.14 m), which costs 200 J.
Feather Fall at 1st level can make 300 lbs (136 kg) fall at a constant rate for 1 round, covering 60 feet (18.3m). This costs 136kg*9.8m/s^2*18.3m = 24,400 J per round, and scales proportionally with the mass.
Levitate at 3rd level can make 300 lbs rise at 20 feet (6.1m) per round for up to 30 minutes (300 rounds). This is equivalent to traveling 60 ft/round for 100 rounds, so requires 100 times as much energy as feather fall: 2,400,400 J. This seems to be barely within the human capacity.
Fly is a bit weird because the maximum load is a function of the caster's strength and size, not the spell. For an average human at maximum load, the spell lasts as long as levitate but the PC can travel straight up only 50% faster--so overall Fly only provides 50% more energy to fight gravity than Levitate. For a human with Str 12, their own weight + max load is probably about 300 lbs--but Levitate can boost the mass by 100 lbs per level, while Fly is stuck, so at the same caster level levitate has already caught up to Fly. The kinetic energy provided by Fly is high, but insignificant compared to the amount of gravity that can be countered: 22,800 J at max load or 25,600 J with a light load (150 lbs). Of course, Fly includes the control feature and the auto-feather fall, and one could potentially expend a lot of energy executing manoeuvers. If one spent the entire duration of the spell accelerating up to max speed in one round, then decelerating to zero in the next, they could burn a maximum of 12,500,000 J over 50 minutes--so the control factor does give us another factor of 10 or so.
Finally, Telekinesis: the sustained force is 25 lbs/level x 20 feet/round x 1 round/level, or 500 foot-pounds x level^2. At 10th level, we get 50,000 foot-pounds which is equivalent to only 67,800 Joules! This spell is unique in explicitly gives you the energy expended, so we can't squeeze out a hidden capacity through "control factors".
It does give you fine manipulation, however, and can be used as a combat spell in a pinch. A 250-lb. object with this much energy is traveling at a speed of about 23 meters per second. This is the speed it would have after free-falling for 2.4 seconds, by which time it would have covered a distance of 90 feet--so the 10d6 damage given by the spell is actually about right for the given energy (assuming that falling damage is realistic).
It seems like a good rule of thumb is that the mechanical energy provided by a spell is about 100 times greater per spell level, but at higher levels this capacity gets cut way down for greater control. If the amount of food energy seems unreasonable to you compared to these effects, remember that we couldn't normally generate such large amounts in 6 seconds through muscle action--but we could, for example, spend 15 minutes winching down a catapult that could impart this much energy to a 250-lb boulder. Machinery lets us convert food energy to impressive amounts of mechanical energy by the magic of work: expending a little force over large distances is just as good as expening a huge force over short distances. If magic runs off our body energy, then it needs to do something similar.
Maybe wizards create ethereal constructs that "wind up" (like a spring) while they sleep and store their body energy in a quickly retrievable form?
--Ben (an astrophysicist)
Xeriar
First Post
Nice post, Fui Levitate is a 2nd level spell, though.
A pound of fat holds 3,500 kilocalories, or at 4.2 joules to the calories, 14.7 million joules (I erred above, oh well).
This puts most third level spells in range of a pound of fat, and a REALLY good sized meal... But the Telekinesis spell throws things out of whack, for sure...
Levitate is a 2nd level spell, though.A pound of fat holds 3,500 kilocalories, or at 4.2 joules to the calories, 14.7 million joules (I erred above, oh well).
This puts most third level spells in range of a pound of fat, and a REALLY good sized meal... But the Telekinesis spell throws things out of whack, for sure...
Anabstercorian
First Post
I think we can safely say that YES, if you're converting matter directly to energy using magic, then you can burn your spare matter all frickin' day and still have enough extra mass to take a crap. Average human has a little under half a pound of poop inside his intestines. What's the joule content of that?
Sorry to nit pick, but you cannot use Einstein's theory of relativity (E=mc^2) to calculate the energy in a human body. Einstein's theory calculated how much energy an object would have if you accelerated it to the speed of light, whereupon all the matter disintigrated into dissociated particles of energy.
This is an important point. The energy in a pound of peanuts is theoretically infinite, but what you can practially extract from them is a whole other story, and it depends on what process you use. If you burn it in an oven, you will get one quantity of energy as heat. If you eat the peanuts you will get a a different quantity of energy in caloric value. If somehow you can accelerate them to the sped of light, you could probably blow up planet Earth.
I side with Xeriar, in that the energy you can get from the human body would be 3,500 kcal per pound of fat, 1556 kcal per pound of muscle, and probably next to nothing for bone. In other words, a wizard's body slowly wastes away as he casts spells, much like he is starving to death.
This is a phenominally cool concept, and it makes high level spells a truly life-threatening prospect. A wizard could spend months gaining enough weight to become obese enough to survive the casting of a 9th level spell, which would leave him emaciated, possibly turning his skeleton to mush in the process.
This is an important point. The energy in a pound of peanuts is theoretically infinite, but what you can practially extract from them is a whole other story, and it depends on what process you use. If you burn it in an oven, you will get one quantity of energy as heat. If you eat the peanuts you will get a a different quantity of energy in caloric value. If somehow you can accelerate them to the sped of light, you could probably blow up planet Earth.
I side with Xeriar, in that the energy you can get from the human body would be 3,500 kcal per pound of fat, 1556 kcal per pound of muscle, and probably next to nothing for bone. In other words, a wizard's body slowly wastes away as he casts spells, much like he is starving to death.
This is a phenominally cool concept, and it makes high level spells a truly life-threatening prospect. A wizard could spend months gaining enough weight to become obese enough to survive the casting of a 9th level spell, which would leave him emaciated, possibly turning his skeleton to mush in the process.
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