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Viewing blog entries in category: Percy Jackson and the Olympians calcs

  • Tacocat
    The original blog is here.

    This operated under the premise of, you know, a round Earth. However, new information from Percy Jackson's Greek Gods seems to corroborate the idea of a flat--at least, relatively so--Earth, as was theorized in the ages of Ancient Greece.



    The above is official art from the Greek Gods book. Obviously this is a loose representation, but the text pretty much describes it exactly like this; sky above, Earth in the middle, Erebos/Tartarus below. We know this is possible because everything in the fiction is described as mortals basically seeing whatever they want or can comprehend, regardless of what's the truth, via the Mist. I mean, the Earth is still as massive and as large, it's just not ellipsoidal. Magic convinces the mortals otherwise. Same goes for the sky.

    Anyway, with this information, it's completely logical that Atlas, and thus the characters who took on his burden, supported the entire mass of the sky.

    Mass of the sky would be 5.3x10^18kg.

    Now Percy stood completely upright from a crouched, kneeling position in the times that Artemis threw Atlas straight at him. This had to be pretty damn fast--faster, at least, than the time-frame for free-fall of that distance. I'm just gonna say 1m, considering Percy's pretty damn tall for a 14-year-old (5'10" or 11" by then).

    PE=mgh
    PE=5.3x10^18*9.8*1
    PE=5.194e19J

    or about 12.4 gigatons.
  • Tacocat
    At the end of the third book in the PJO series, Nico sends these spartoi to the Underworld by opening a passage to it in the ground.

    The Underworld happens to be 2310 miles, or 3717585 meters, underground.

    Now, the return trip didn't necessarily have to happen so fast, but I'm concerned with how quickly the flames traversed that distance. The gap was wide enough to encompass four of these spartoi and twenty feet long. Seems to me that at least one of these guys had to be in free-fall, and the flames got there in time for Percy to say they'd been taken by the fire rather than having fallen into the gap.

    Gonna use average dude height, or 1.7 meters, for the free-fall formula.

    h=.5gt^2
    1.7=.5(9.8)t^2
    3.4=9.8t^2
    .347=t^2
    t=.59s

    3717585/.59=6300991.5m/s

    or about mach 18,532.
  • Tacocat
    In Piper's sole three chapters of HoH, Khione, Greek goddess of snow, attacks the group of demigods as they sail across the Mediterranean toward Epirus. Her presence alone is enough to cause freezing rain. Freezing rain occurs when the surface temperature is 0 Celsius or lower, yet either higher atmospheric temperatures or atmospheric pressures aren't suitable for snow.

    She also passively churns the sea and summons a storm cloud large enough that Piper can no longer see the sky, but meh :maybe

    Anyway, her effects extend all the way to the horizon going by the narrative.

    Piper is standing above deck on the Argo II, which is tall enough to fit the 12.8m Athena Parthenos statue in only the stables.

    Distance to horizon formula is d=3.57*sqrt(h).

    d=3.57*sqrt(12.8)
    d=12.77242km

    According to the chart in the linked Wikipedia page, our height would extend up to about 2.3 kilometers and our temperatures range from -2 to about 4 degrees C. I will use 4 uniformly.

    But as for the affected volume...

    vcylinder=pi*r^2*h
    v=pi(12772.42/2)^2*2300
    v=925793169852.33m^3

    Apparently, cruises in the Mediterranean can expect 86-88 degrees F at sea. That's around 30 degrees C.

    Density of air in 30 degree temperatures is about 1.1644 kg/m^3.

    925793169852.33*1.1644=1077993566976 kg

    So Khione basically dropped this mass of air from 30 degrees to 4 degrees or less, or a change in temperature of 26 degrees.

    Specific heat capacity for air between 40 degrees and -50 degrees is 1.005.

    Q=specific heat capacity*mass*change in temp
    Q=1005*1077993566976*26
    Q=28167971905082880J

    or about 6.7 megatons.

    Really, that figure should be negative, but that's just indicating that she sapped this energy rather than put it into the atmosphere.

    Anyway, Khione's doing this so passively that she hasn't even arrived in the Mediterranean yet. When she does, it starts snowing and hailing and Piper notes that the temperature drops so drastically so quickly that her "ears pop" and her body starts to freeze.

    Leo Valdez using his pyrokinesis was able to overpower a direct attack from Khione and make the surrounding area nice and toasty.
  • Tacocat


    Not really, but the feat does entail bubbles, so yeah :distracted

    That's 3717585m.

    In The Lightning Thief, Percy, Grover, and Annabeth travel to the Underworld to bargain with Hades. Things go sour and he attacks them, but Poseidon thought ahead and provided the trio with pearls, which expand into protective bubble vehicles, to get them home safely.

    A few moments sounds pretty short. 3-10 seconds :nod

    3 seconds

    3717585/3=1239195m/s

    or about mach 3645.

    5 seconds

    3717585/5=743517m/s

    or about mach 2187.

    10 seconds

    3717585/10=371758.5m/s

    or about mach 1093.

    So mach 1093-3645.
  • Tacocat
    The crack in the Dining Pavilion, of course :maybe

    In the third book, Percy goes on a quest to save Annabeth from Atlas. Artemis gets there first and is coerced into holding the sky, so some hunters of Artemis also go to rescue their patron. Bianca di Angelo, Nico's sister and a huntress, is chosen as a member of the quest and Nico asks Percy to protect her. But she dies, and when Percy returns to camp without her, Nico blames him.

    Also during the quest, Atlas sets a band of undead skeleton warriors birthed from the teeth of a dragon on poor old Percy. They hunt him cross country until they break into camp and interrupt Percy telling Nico that Bianca is dead. Nico is enraged because he thinks Percy is trying to kill him, so being the son of Hades he (awesomely) opens up a one-way track to hell.

    Well Percy says the fissure was 20 feet long, which is equivalent to 6.096m. The width spans all four warriors who arrange themselves in phalanx formation whenever they attack, so I'm going to say about 4 meters for the other width.

    Percy comes across a sign in Camp Jupiter that indicates Hades to be 2310 miles underground. That's 3717585m.

    The volume of an elliptical cylinder is pi*r1*r2*h.

    v=pi*(6.096/2)*2*3717585
    v=71196023.572m^3

    Dunno much about compressive strength, but Mike says for rock it's about 200 MPa.

    1 Pa=1 N/m^2

    71196023.572*200*1000000=14239204714400000 N*m

    1 J=1 N*m

    14239204714400000J

    or about 3.4 megatons.

    Eh.
  • Tacocat
    Not quite, but good enough for a feat.

    Originally, Piper, Jason, Leo, and Hedge were in Aeolus's very own Castle in the Sky. Then he tried to kill them, so Mellie rocketed them all the way from Pike's Peak to Walnut Creek, California, right next to Mt. Diablo. Gonna be using ballistic trajectory for this.

    http://www.distancefromto.net/

    Pike's Peak is 1,486,900m from Walnut Creek, Cali.

    Pike's Peak is also 4,302m in elevation.

    So 4302 meters plus a fourth of a mile is 4503.168m.

    http://www.convertalot.com/ballistic_trajectory_calculator.html

    Using a theta of 0, that's a little more than 49,000m/s

    or about mach 144.

    :distracted

    Not really gonna get into all that CoM business :maybe

    Using 45 degrees, that comes out to about mach 11 :tomasulk
  • Tacocat
    Alright, so I did a bunch of research and found an actual way to calculate this.

    First, the feat.

    Spoiler: The feat
    Just some background first to validate this.

    Apollo tells it like it is. He should know; that's his ride.

    Basically, mortals conceptualize the power these gods dick around with in ways they can understand. They still pack that energy, though.

    Anyway.



    Spoiler: The explanation
    So to explain a little bit before going into all the math gibberish, stars are measured in magnitudes as far as brightness is concerned.

    Percy actually seeing these stars get brighter, ignoring the conspicuous lolfiction FTL light, means he's observing an increase in apparent magnitude. These stars are ones that neither he nor Annabeth noticed before, and demigods study astrology and astronomy like their lives depend on it (they do in some cases). Ergo, these stars are either invisible or barely visible to the human eye. 6th and lower magnitude stars fit this bill. By the end of the feat, Percy describes these stars to be some of the brightest in the sky, at least for a little while.

    So Artemis pretty much increased these ~magnitude 6 stars to ~1st magnitude stars. Now, with different stars this is a bit harder to calculate, but with the same star, it's quite easy--simply take a circa magnitude 6 star and calculate its luminosity were it a magnitude 1 star, then subtract its true luminosity from the result.


    Spoiler: The calc
    According to this, the closest ~magnitude 6 star is Beta 61 Cygni, at a distance of 11.1 Ly. This is important, because constant distance is integral to this whole process.

    The star's luminosity is .085 that of the Sun.

    Sun's luminosity is 3.842e26 watts.

    3.842e26*.085=3.2657e25 J/s

    Keep that tucked in the back pocket.

    Now we have to calculate the luminosity were the apparent magnitude 1.

    To do this, we need to first find the Bolometric magnitude, which is pretty much a unit relative to luminosity in that it measures a star's total energy output. To do this, we first need to find the absolute magnitude.



    where M is the absolute magnitude, m is the apparent magnitude, and D is distance in parsecs. 11.1 Ly is equivalent to 3.4032027795 parsecs.

    M=1-5((log(3.4032027795)-1)=3.3405608636979465

    Now we have to find Bolometric magnitude.



    where Mbol is the bolometric magnitude, Mv is the absolute visual magnitude, and BC is the bolometric correction.



    Beta 61 Cygni is classified as a K6 star. So I'm using the average BC between a K5 and K7 star, which would be -0.755 (column V is for main sequence stars). Dunno if it works like that but fuck it :distracted

    Mbol=3.3405608636979465-0.755=2.5855608636979465



    Now, we also need the bolometric magnitude of the Sun.

    Lstar/3.842e26=10^((4.75-2.5855608636979465)/2.5)
    Lstar/3.842e26=7.34134535
    Lstar=2.82e27 J/s

    To get to change in luminosity imposed by Artemis, we take the original luminosity and subtract it from our result.

    2.82e27-3.2657e25=2.787343e27 J/s

    Now, according to Wikipedia, Orion has 88 notable stars. It'd be kinda stupid if Percy could immediately recognize the shape of a Huntress from 7 stars, especially considering how they're arranged in Orion.

    Anyway.

    2.787343e27*88=2.45286184e29 J/s

    or about 58.6 exatons per second.


    Final result:

    58.6 exatons per second.

    Well, this is still a really big low-end, taking into account this only considers the nearest magnitude 6 star. Also, Artemis does this extremely casually after nearly being beaten to death by Atlas and while in her cosmically nerfed form.

    Amidoinitrite? :distracted
  • Tacocat
    During Jason's fight with Enceladus, Ivlivs breaks and releases enough energy to blast that shit into the top of Mt. Diablo. The crater is 30 feet deep, but what about the diameter? Well, Leo implants a giant ax in Enceladus's breastplate and Enceladus falls headfirst from the edge of the pit and slides down the side. Therefore, the radius has to be at least as long as Enceladus is tall.

    vcone=pi*r^2*h
    v=pi*9.144^2*9.144
    v=2401.92m^3

    Sounds a lot like vaporization to me, considering the walls of the crater were fused and there was smoke everywhere. Gonna use the value for granite, which IIRC is 25700J/cc.

    2401.92*1000000*25700=61729344000000J

    or about 14.8 kilotons.

    Both Jason and Enceladus took this point blank. Also of note, Enceladus says he's easily the least of his brethren.
  • Tacocat
    In The Lightning Thief, Luke, resident douchebro of the series, gives Percy winged shoes gifted to him from Hermes to "help" on the first quest. Actually, Luke wants Percy to wear them so when they go to the underworld, Kronos can use the curse on the shoes to suck Percy into Tartarus and claim the Master Bolt which Percy is carrying. But Percy can't fly because Zeus is a prissy bitch, so he gives the shoes to Grover the satyr. When the time comes that Kronos does try to suck them into Tartarus, Grover's hooves slip out and Kronos gets a few empty sneakers, much to his chagrin.

    Annabeth's first line in HoH says she and Percy fell for nine days before reaching ground. Both of them describe Tartarus to be a vacuum, which I took literally, but Annabeth says wind rushes in her ears on the way down, so there's air resistance. That means I have to use maximum velocity for their fall.

    Now, calculating their maximum velocity would be tedious, but thankfully I can use recorded data for skydivers.

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

    Scroll down and you'll see several higher values than the first few, the latter of which are probably for higher altitude skydiving. Percy and Annabeth were huddled together quite intimately the entire way down. I'd think 200mph, or about 89m/s, would be safe to use.

    So nine days give or take at a velocity of 89m/s.

    89(60*60*24*9)=69,206,400m

    And, actually, the gravity in Tartarus is much greater than Earth's gravitational constant...

    Well, whatever :distracted

    So the mouth of Tartarus extends for roughly 70,000km. That might sound weird, but Tartarus actually leads to the abyss that is Chaos so I don't think it really cares how big the Earth is.

    Anyway.

    So in The Lightning Thief, Grover almost gets sucked into Tartarus due to Kronos's curse. When the titan sees the shoes are empty, he gets mad and tries to pull the demigods in. The entire conversation quite generously takes a minute (I timed myself reciting it with several...several second pauses).

    This means the shoes had to traverse the entire length of Tartarus in that minute for Kronos to see they were empty.

    69206400/60=1153440m/s

    or about mach 3392.5.

    That isn't to say that they could achieve these speeds while carrying Grover, but given that they're defective replicas of Hermes's sandals...
  • Tacocat
    Basically the same principal as Dio's.

    Spoiler: Time-frame
    During this scene, Kronos grills Ethan for information about Percy's Achilles Heel. He decides to freeze time around a Canadian in the corner to seem more imposing, and the stop lasts for as long as the conversation. Then, Luke, whose soul is still buried within his body, starts fighting Kronos's consciousness which causes the Titan lord to falter with the stop.

    I've run through the dialogue in these scene a few times. Seeing as they're talking pretty casually and Kronos tends to speak in a sharp drawl, continuous dialogue never took any less than 50 seconds. Tack on another 10 seconds for shit that happened during the scene, and we get a minute. Would be longer, but Luke had to fuck it up by fighting :ippy


    Spoiler: Strikes
    http://www.narutoforums.com/blog.php?b=20405

    So generic demigod weapons suped up by the Hephaestus cabin can fire at mach 159. Base Percy has sufficient reactions to combat gods who laugh at weapons far superior to this. Water boosted Percy can outspeed these gods. Water boosted Percy with the Achilles Curse is fast enough to blitz Hades, one of the three most powerful gods. And Kronos is able to push Percy to the limit with both of these boosts. Technically, TLO Percy and Kronos should be comparable to quadruple digit mach gods, but whatever.

    Anyway, casual mach 159 combat speed for Kronos.

    Now we have to get the number of strikes he can throw in a minute.

    Well, let's get his arm length.

    In order to ascend to his divine form, Kronos enter's Luke's body to sustain his consciousness. Luke is about 6'1", or 1.83m, tall.

    An average human arm will typically be about 3.5/8ths of the body's height.

    1.83(3.5/8)=.8m

    Assuming Kronos were to strike while alternating arms, I wouldn't really have to account for the distance he has to pull his arms back.

    (159*340)/.8=67,575 strikes per second.

    Sixty seconds makes that 4,054,500 strikes per minute. Er, I think.

    I'll take a thenth of that to account for Kronos slowing down, though PJO characters do have stupidly high stamina (I'm talking Percy fighting every single monster ever for a month straight).

    Anyway, 405,450 strikes.


    Spoiler: Striking strength
    http://www.narutoforums.com/blog.php?b=19942

    If you look in the comments, you'll see that Percy has durability in the hundreds of gigatons from catching the sky and stopping it in its tracks. This is Percy when he's thirteen years old with no Achilles Curse and no water in sight. Therefore, it'd easily apply to any god/Titan/Olympain bane (sans maybe Encelaedus and Alcyoneus). I'll use the PE value of 4.4 gigatons.

    For reasons explained in the comments, Percy will have gigaton level striking strength. Kronos while ascending casually smacks Percy's water-boosted w/ Curse of Achilles attacks aside.


    405450*4.4e9=1.8 petatons

    Right? :hmm
  • Tacocat
    This is a different kind of calculation. I found some interesting stuff concerning Kronos's time-stop over Manhattan :maybe

    Basically, Kronos is passively manipulating time around Manhattan to keep mortals out of the Olympian-scale war. There are magical boundaries surrounding Manhattan which prevent Kronos from slowing stuff in the city, subverts the fact that everyone in the war is operating in real-time. Also, dmigods have innate time-stop resistance, as explained by Silena.

    Anyway, I figure I can use the inverse-square law to measure how efficient Kronos's time-stop is.

    As a resident of New Jersey, I can tell you that we drive pretty fast on the highway. I tend to average 75-80 mph on my way to work. However, the speed limits tend to average around 65, so I'll use that.

    Percy says the cars are crawling at around 1 mph, which means they're going 65 times slower.

    Unfortunately, 50 miles isn't our radius because Annabeth shifted the scene. It's still a New Jersey highway, though.

    http://www.distancefromto.net/distance-from/United+States/to/Antarctica

    This tells me Hoboken, which is a fair estimation to use, is 3.97km from the Empire State Building.

    Now, intensity is directly proportional to power and inversely proportional to the radius of influence, noted in the following...

    I=P/(4pi*r^2)

    ...where I is intensity, and P, power, is over the surface area of a sphere with the radius of the affected region.

    Well if shit is 65 times slower 3.97km out, I suppose 65 would act as intensity?

    65=P/(4*pi*3970^2)
    P=65*(4*pi*3970^2)
    P=12873725190

    I think I'm understanding this right :hmm

    Anyway, what does this mean for the OBD? Well, standard starting distance is 20m, correct?

    I=12873725190/(4*pi*20^2)
    I=2,561,146

    If I'm understanding this correctly, opponents will be rendered 2.5 million times slower at standard starting distance under the influence of Kronos's passive time-hax in a nerfed form...
  • Tacocat
    Just something I remembered after seeing a kid and his dad playing with firecrackers across the street. Don't take this too seriously (unless you want to :maybe).

    The first installment in the PJO series, titled The Lightning Thief, quite obviously centers around the theft of a lightning bolt. More specifically, Zeus's Master Bolt. Cue Olympian-scale bitchfest. Chiron explains this to Percy in the following quote.

    http://www.si.edu/Content/consortia/Zimbelman_presentation.pdf

    Apparently, Chinese firecrackers yield 30J.

    The Tsar Bomba hydrogen bomb is, according to Wikipedia, 210PJ in yield.

    Well damn :maybe

    So 30 joules is to 210 quadrillion joules as 210 quadrillion joules is to the Master Bolt.

    Thus, the proportion would be...

    (210e15/30)210e15=1.47e33J

    or about 351 zettatons.

    :nod
  • Tacocat
    The Lost Hero opens with Jason, Piper, and Leo wrecking the Grand Canyon Skywalk in true demigod fashion. After driving off a few monsters, Annabeth and Butch arrive to bring them to Camp Half-Blood.

    Cue internal relationship monologue from Piper. However, this runs through her mind at the same time that the following conversation goes down.

    In that last paragraph, Piper didn't black out; she simply couldn't see temporarily. This couldn't have lasted a more than a few seconds, or she'd have freaked out.

    As for the entire conversation, it lasts for pretty much from their departure to their arrival at "a totally different place", which happens to be Camp Half-Blood. This couldn't have lasted more than a few minutes.

    I ran through this conversation with my friend without telling him what it was for to ensure that it would sound natural. It never took more than 2 minutes, so I'll use 3 minutes to account for Piper's loss of eyesight and to consider a low-end.

    Camp Half-Blood is in the Long Island sound.

    Using this site, I get the distance from the Grand Canyon to Long Island to be 3413.86km.

    3413860/(3*60)=18965m/s

    or about mach 56.

    Any god worth his beans is going to be faster than a pegasus. Percy as a 12-year-old with little training can combat Ares. At 13 he can face Atlas without dying horribly. At 14 he shits on Phobos. Most impressively, however, 15 years has him absolutely wrecking Hades and Hyperion and even combating Kronos. Then, at 16, Percy murders Polybotes, who fights with Poseidon. You probably know where I'm going with this :zaru
  • Tacocat
    In PJO, it is told that gods take human forms because their true forms would make mortals shit themselves.

    In the quote above, Hera reveals that the gods enter their true forms by converting themselves into pure energy.

    I tried to find the average mass for a Greek woman, but it really only took me to fat burning websites, so world average it is.

    Apparently, the world average is about 55.3383 kilograms. However, the gods decide to take human forms which are roughly 15 feet tall, according to Percy.

    So, using the above link's formula and healthy BMI of 18.5, I can get Hera's mass. That 1/703 factor seems to be constant, based on the second mass listed.

    15(12)=180in

    18.5*180*180*(1/703)=852.63lbs

    or about 386.75kg.

    The speed of light is roughly 299792458m/s.

    E=mc^2
    E=386.75*299792458^2
    E=34759356537646422227J

    or about 8.3 gigatons.
  • Tacocat


    Of course we can't really say how much mass the sky has, but we can get a value for how much energy is necessary to flatten the mountain.



    This is Mt. Tamalpais, upon which Atlas is eternally condemned to separate Ouranos and Gaia forever. That is, unless someone takes his place. Should he let go, the mountain and everything within 100 leagues, or 555.6 kilometers, will be flattened.

    I figured compressive strength was the most logical thing to use for this calc, based on the verbiage in the quote.

    Anyway, Mt. Tam is 747m in prominence.

    (747/115)668=4339m

    This obviously isn't the entire thing, but I had trouble finding clear pictures of the whole mass.

    Gonna calc this as a cone. Now, some of you might be kinda skeptical, but keep in mind that this is like the low-ball of all low-balls, considering everything within a 277.8km radius is also being flattened. That includes many, many Californian cities, as well as other mountains.

    vcone=(1/3)pi*r^2*h
    v=(1/3)pi*2169.55^2*747
    v=3682040377.3m^3

    Now, I don't know much about compressive strength, but I took a look at EM's Fantastic Four bit feats, part 6 and saw that he had compressive strength for rock at 200MPa.

    1Pa=1N/m^2

    3682040377.3 m^3*200000000 N/m^2= 736408075460000000 N*m

    1N*m=1Joule

    736408075460000000J

    This obviously only accounts for Mt. Tam, so I might be doing a bit or research to see what significant masses reside within a 277.8km of the thing to add to this value. In any case, this should be a lot higher.

    Edit:

    I'll put in a few more mountains which I found to be within the 277.8km radius.

    Apparently, this includes Mt. Diablo (eat your heart out, Jason :maybe).



    This is Mt. Diablo. The line I drew might seem kinda long, but it does account for the base as well as the peaks behind this tallest one.

    Mt. Diablo has a prominence of 949m.

    (949/104)1024=9344m

    (1/3)pi*4672^2*949=21692045095m^3

    21692045095(200000000)=4338409019031559578J

    At the other end of the Diablo Mountain Range rests Mt. Hamilton.



    (951/153)800=4972.55m


    (1/3)pi*2486.275^2*951=6156125446m^3

    6156125446(200000000)=1231225089200000000J


    If we add all of these values up, we get 6306042183691559578J

    or about 1.5 gigatons.

    Now that I think about it, I probably should have used elevation instead, seeing as flattening would bring everything to sea-level. Also, Atlas likely meant a 100 league radius which would boost this a lot. Oh well, small-island level it is:distracted

    Edit: Okay, well as of HoH we know that primordial gods are unequivocally the things they represent, so...

    SA of Earth is 510,072,000 km^2. The radius of our affected area is 277.8 km, so the area would be a bit more than 242445.6 km^2.

    http://hypertextbook.com/facts/1999/LouiseLiu.shtml

    Mass of the sky seems to be 5.3x10^18kg.

    (242445.6/510072000)5.3x10^18=2519177057356608.5kg

    PE=mgh
    PE=2519177057356608.5(9.8)749
    PE=18491263436408977711.7J

    or about 4.4 gigatons.

    If we take Atlas's instant statement to mean a second...

    KE=.5mv^2
    KE=(2519177057356608.5*749^2)/2
    KE=706630424177057362554.25J

    or about 169 gigatons.
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