User:ThePerpetual/Sandbox4

Hero's Path Calcs: The Reduxening
Some time ago, I ran some calculations for Hero's Path: however, several have been rendered outdated with the shifts to the canon that have since occurred. That, and I simply disagree with some of my old results. It seemed fitting to compile them all in a new Blog, so...

Oh, one thing to note just in general, before I start: among the many shifts that have occurred for the verse is my own conception of it from "a video game in progress" to simply focusing on the setting and story-line for the verse proper. With that said, "loading screen time" isn't really an acceptable timeframe for the various travel speed feats, so I'm cutting back to "a reasonably short off-screen time period". One minute (60 seconds) should serve those purposes well enough.

Well, without further ado...

Lightning-Speed Cannonballs
This one is relatively simple: Captain Darte Jones's flying ship Skyweave uses a Magitek galvanizer to fire leaden cannonballs at the speed of lightning towards his targets without incinerating them due to the immense launch force/friction. This, of course, would carry a lot of energy with the shot:

Mass: Given this was a 6 inch diameter shot, I can use 0.1405*d^3, where d is the diameter in inches, to get it's weight in pounds (0.1405 * 6^3 = 30.348 lbs.)

Then multiple by 0.45 to get 13.657 kilograms...

Then, plug it in to 0.5mv^2 for

Potency: (0.5 * 13.657 * 440000^2 = 1.32200e+12 Joules, or 315.966 Tons of TNT. Multi-City Block level.

Zain and Magus both can deflect these via a swing "at the last second": I don't consider that to be 4 inches, but rather when the projectile comes into reach (i.e. when it reaches the tip of the blade.) Deflection of a blow is generally done with the blade's center of mass, which Zain as a trained fighter would know, and for something oncoming like that would need to be a wide and forceful arc, I'd think (120 degrees.) Which means that probably half of that swing is completed by the time the cannonball goes from the tip of the blade distant to its center of mass.

A longer longsword's blade is ~1.1 meters, so half of that: 0.55 meters: is how far our lightning-speed cannonball cannonball when one-sixth (sixty degrees) of a circle with a radius of (0.55 meters + Zain's arm + the extra grip/crossguard between Zain's hand and the blade).

Zain's Height: 1.82 meters * | 7/15 = ~0.85 meters

And with the crossguard being a bit broader than usual, plus there usually being a bit of space between the hand and the crossguard, using a little bit over an inch (3 cm, or 0.03 meters) seems acceptable.

Radius: 0.55 + 0.85 + 0.03 = 1.43 meters.

This is the "radius" of a complete circular swing about Zain, so we need to find one-third of the circumference (60 degrees) from here-

2(1.43 m)(π) = Circumference = 8.980 m

C/6 = 1.497 m

So, 1.497 m in the time it takes the lightning-speed projectile to travel 0.55-

Speed: (1.497/0.55) = 2.722 times faster than lightning (440000 m/s) = 1197680 m/sec, or Mach 3491.78.

Zain vs Tessera
Zain yeets Tessera to Earth at speeds enough to match/exceed a nearby lightning bolt, after awakening the Verethragna Form over the course of their Act I battle.

Potency: 45.3 kg (Tessera's Mass) * 0.5 * (440000 m/s)^2 = 4.38504e+12 Joules, or 1.048 Kilotons of TNT minimum.

Force = Mass * Acceleration is a thing here that applies to Lifting Strength, so that's probably a hella strong Lifting Feat

Storm Cloud distance being 460 meters would make the time frame for something moving 440000 m/s to reach the bottom (460/440000) = 0.001045 seconds. Acceleration = Δv / Δt, or (440000 m/sec)/(0.001045 sec), or 421052631.579 m/s^2.

There's our A. M is just Tessera's mass of 45.3 kg, so then we'd get 19073684210.5 Newtons of Force. I'm told that 9.81 Newtons is equal to lifting one kilogram, so /9.81 and the final result is

Lifting Strength: 1944310317.08 kg of effective Lift, or 1.94 times baseline Class M.

After the Storm
Tessera did disperse the storm over the volcano that Dragonwood Village was situated upon, albeit kinda slowly That's got to be worth something, right?

Seeing as the Worldwood Shrine (the top of the summit) was intended to be one of the tallest mountains in Colorado, using the minimum height of one of the Colorada "fourteeners" seems to fit in this case (and a 45 degree slope assumption, since that too is a lowball as you'll see.)

This gives us 4269 meters to work with, for our base height. DMUA said at one point that Storm Clouds are usually assumed to be ~460 meters high, so this being imagined within that ballpark/created by Tessera herself means that all 4269 of that cuts into our height: (8000 - 4269 =) 3731 meters. And the radius of our cylinder would just be the 4269 of before, since that's the width of the mountain, so...

2.13613e+11 m^3, * 1.003 = 2.14254e+11 kg.

Since the storm was dispersed enough within "a few minutes" of dialogue, wrapping up the Arc, etc.: enough to not be raining over Dragonwood (about halfway down the mountain, I'd think) anymore after Tessera waved her hand and some air ripples carried Zain's power with the Malkuth up into the air to poke holes in the Banemist: I think that a few minutes is a serviceable Mid-End timeframe. Two as a High-End, and four as a Low-End... And, dispersal distance of (4269/2) = 2134.5 meters in all cases.

Low-end: 2134.5 meters / 240 meters = 8.89 m/s

Mid-end: 2134.5 meters / 180 seconds = 11.86 m/s

High-end: 2134.5 meters / 120 seconds = 17.79 m/s

Plug that in to a nifty KE Calculator, and...

Potency:
 * Low-End: 8.46647e+12 Joules, or 2.024 Kilotons of TNT.
 * Mid-End: 1.9107e+13 Joules, or 3.601 Kilotons of TNT.
 * High-End: 3.3904e+13 Joules, or 8.103 Kilotons of TNT.

Houston We Have Inbound
The crew fly first from Colorado to Houston, this marking the end of Act I. Using our previous Colorado-to-Houston distance of 1329.44 kilometers, and our new timeframe of 1 minute, this is a pretty simple feat:

Travel Speed: 1329440 meters / 60 sec = 22157.33 m/s, or Mach 64.60.

High Hypersonic+.

Throwing A Purple Person
Towards the end of the Unseen Village section of the first area Zain encounters, a massive giant, once a sentinel at rest in front of a cave entrance, is petrified into violet Yesod-infused crystal. Zain's response, of course, is to simply pick the sitting statue up, and toss it aside.

But how heavy was it?

Well, for starters, we need to find the mass of the average human, as well as their height. Last I checked, these values were 70 kg and 1.74 meters, about: simple enough.

However, this particular giant belonged to the race of Mountain Giants, which tend to measure roughly 25 feet (7.62 meters) tall. That would make our giant (7.62/1.74 =) 4.38 times taller than the average dude. Assuming roughly average build... that makes him

70 x (4.38)^3 = 5881.94 kg.

But... all of this still assumes the guy is made of meat. Currently, he is made of violet crystal- the closest thing I can think of is amethyst, which has a density of 2.66 g/cubic centimeter (2660 kg/cubic meter.) Compare that to the human body density of 985 kg/cubic meter, and...

5881.94 kg x (2660/985) = 15884.22 kg

So, Class 25 on it's own, but since he'd picked it up and chucked it, F = M*A can be useful here.

I had figured Zain kinda just tossed the crystallized giant off to the side, about thirty feet or so, so... I guess I could use t = √(2y/g) to determine the timeframe, with y being Zain's height of 1.82 meters and g being just, you know, the rate of gravity.

√(2[1.82]/[9.8]) = 0.609 seconds

30 feet = 9.144 meters, and 9.144 meters/0.609 seconds = 15.015 meters/second.

(15.015 m/sec)/(0.0609 sec) = 24.655 m/s/s.

(15884.22 * 24.655) / 9.81 = 39921.04 kg effective lift. Or, ~1.6 times baseline Class 50, almost four-fifths of Class 100. Okay, okay...

Act II
Round two, let's go.

Metenros Makes Mountains
So, the idea is that Metenros, an ancient and powerful drow lord, drags a chain of mountains up from the earth... but I'd never really given very much thought as to how large a mountain chain would actually be, but a lot of what I'm seeing online seems to indicate that the number's not usually seven... beyond that, there's the land that lies in between the mountains to account for. On top of even that, there were a myriad of tunnels in the mountains that Metenros used to hide in (the reason he'd done this to begin with), so...

I'm just going to take a mountain chain in the Alps, and use that as my reference.

Volume of Mountains: 8377600000 cubic meters each, about, or

(8377600000 x 7 =) 58643200000 cubic meters

The density of granite is 2.75 g/cub. cm, or 2750 kg/cub. m, so the mass here is 1.6127e+14 kg

And the speed? Well, if they move to their full height in approximately 4 seconds, it's as simple as

2000 meters/4 seconds = 500 meters/second.

Plug this all in to the kinetic energy calculator...

Kinetic Energy: 2.0159e+19 Joules, or 4.82 Gigatons of TNT

Not bad, not bad. But...

Grand Mountain Slam
Metenros's second mountain feat, in which he creates an two halves of a mountain and, having trapped Zain in his created web, slams each half together without further ado. How much kinetic energy might this be?

Fortunately, we can reuse the parameters of the mountains from before, so

Height: 2000 meters

Radius: 2000 meters

Volume: 8377600000 cubic meters

Mass: 2.3038e+13 kg

Since each half started about one diameter apart from the other, each moved approximately half its diameter (its radius) in about half a second, or so, so

(2000/0.5 =) 4000.0 m/s

Kinetic Energy: 1.8430e+20 Joules, or 44.05 Gigatons of TNT. Not bad, not bad...

Breaking Out
Zain manages to not only break free from Metenros's web while in this predicament, he also cracks apart and lifts the whole top half of the mountain up, tossing it towards Metenros to distract him from his next attack.

Just a quick lifting strength thing-

Top "Half" of the mountain is actually a lot less than half of its mass, since it has halved height and radius (1000 meters each)

This comes out to be 1/8th the total mass, or (2.3038e+13/8 =) 2.8798e+12 kg. Lower-end Class T.

Around The World
More Traveling Feats

Areas all over the world begin to open up around now, which means the previous timeframe can be plugged into the distance of half of the world's circumference (40075000 m/2 = 20037500 meters).

Low-End: 20037500 m/ 30 sec = 667916.7 m/s, or Mach 1947.28.

Mid-End: 20037500 m/ 25 sec = 801500.0 m/s, or Mach 2336.73.

High-End: 20037500 m/ 20 sec = 1001875.0 m/s, or Mach 2920.92.

To The Moon
The surface of the moon is a place that can be traveled to during Ruin's siege upon Earth... distance to the moon is 382500 km on average.

382500000 meters / 30 seconds = 12750000 m/s, or 0.0425 C

382500000 meters / 25 seconds = 15300000 m/s, or 0.051 C

382500000 meters / 20 seconds = 19125000 m/s, or 0.0638 C

Simple, simple.

...That's No Moon-!
Later on, Tessera pierces through a massive space station/mech thing of sorts, called the Starfall. Large enough to "cast a shadow across all of India", and piloted by Ruin at its core, Tessera's beam not only pierced its outer shell and blasted through Ruin to the other side, it also blew up the Starfall itself. Notably, no debris from the station itself rained upon Earth, having been scattered into motes of dust and the occasional small chunk of debris:

So, vaporization, or at least... half, if not more of it, was. (Edit: I'll assume all, below, since it'll not make a very big difference, but you'll see on that one.) I'll assume a metal presumably similar to iron.

EDIT (04/02/19): Scrapping some previous versions of the calculation, from before, and redoing this using my almighty powers to draw out roughly what I had imagined in 3D Paint.

The red is the Starfall, being pushed towards Earth: the green. That gold is used for the Ki Thunder in this instance, which traveled the marked distance in a single "shot", or frame (0.33 seconds). After the nova emanating from the point of contact dissipates enough to be transparent (a couple of seconds), the whole thing can be seen to have expanded from the point of contact, a cloud of tiny metal pieces floating away from the core, where Ruin exploded.

Earth's Diameter: 12742000 meters

Starfall: 12742000 * (23/115) = 2548400 meters, divided by 2 = 1274200 meters in radius. Or, for the volume of the sphere, 8.6656e+18 cubic meters.

Assuming 80% hollowness inside of the ship (which effectively divides the volume, and thus mass, by 5), and using iron's density of 7860 kg/cubic meter, the mass of the Starfall is 1.3622e+22 kg.

Specific Heat of Iron: 460 J/kg*K Room Temperature (assuming most of the steel was kept regulated, as the inside of it was relatively Earth-like while Zain's crew was infiltrating it.): ~23 degrees Celsius Boiling Point of Iron: 2861 degrees Celsius 2861-23 = 2838 degree Delta Latent Heat of Fusion (Iron): 247112.54 Latent Heat of Vaporization (Iron): 6213627

(1.3622e+22 kg) * (460 J/kg*K) * (2838 K) + (1.3622e+22 kg) * (247112.54) + (1.3622e+22 kg) * (6213627) = 1.0579e+29 Joules. Or, 25.28 Exatons of TNT. Multi-Continent level+ on its own, but...

There's also the Kinetic Energy from the Starfall being pushed to each side, (3.61/2) = 1.805 pixels in each direction.

First, each pixel is equal to

12742000 meters/115 px = 110800 meters/px

With this taking ~2 seconds, the speed of dispersal will equal 55400 meters/second.

Plugging this into our mass of 1.3622e+22 kg, we get 2.0904e+31 Joules, or ~5.00 Zettatons.

Adding these together yields a final value of 2.1009e+31 Joules, or 5.02 Zettatons. Small Planet level.

"Lightning Moves Faster Than Lightning"
EDIT (04/02/19): Using the above shot in place of the old values, now. That distance, being single-frame, is still almost definitely quite fast.

...and Ruin dodges these nigh-point blank in the ensuing person-to-person fight...

110800 meters/px * 334.77 px = 37092516 meters,

/ (1/30 seconds) for the timeframe = 1112775480 meters/second.

Or, 3.71 times the speed of light. Basically just a laser, really.

Maintaining Equilibrium
The Genesis Egg: Tiphareth obtained by Zain during the fourth Act is revealed to not only be the true form of the Sun, which is in fact it's physical manifestation as a guardian of humanity, but the force responsible for maintaining the orbit and Manifestation of the Celestial Warspheres on the solar system's outer edge, which serves as its last line of defense against the growing Qlippoth incursion that Ruin's forces were fleeing. Most of these Warspheres are each roughly identical to the Starfall, the Starfall having been one such sphere re-purposed for use against Earth's defense forces by Ruin's magitek engineers- however, there exists one of roughly comparable size to the Earth itself, having been modeled after it as a sort of sanctuary for life...

Inverse Square Law Time, I guess?!

The formula is E= 4*U*((Er/Br)^2), where Finding the GBE in and of itself might be a pain...
 * U = the body's GBE,
 * Er = the explosion's radius,
 * Br = the body's radius,
 * And E = energy total.

U = 3G(M^2)/5R, where So, 3(6.674e-11)((1.7114718e+24)^2) / 5(6371000) = U = 1.84107e+31 Joules. Plugging this in...
 * G = the gravitational constant (6.674e-11)
 * M = the mass (in this case, 2.16642e+20 cub. meters [Volume of sphere with 80% hollowness] * 7900 kg/cub. meter = 1.7114718e+24 kg)
 * R = the radius (6371000 meters)

The explosion radius would have to be well beyond the distance between the Sun and Pluto (30 AU), since they reside at the far edge of the Kuiper belt, towards the edge of the "inner" Solar System. I'll use it's outer edge (50 AU) as my distance

1 AU = ~1.496e+11 meters, *50 =

7.48e+12 meters

And now,

4(1.84107e+31)((7.48e+12/6371000)^2) = F (Final energy),

F = 1.015122e+44 Joules, or 1.015 Foe. Large Star level.

...which, well, is weak on its own, but it's important to remember that there's a lot of these things. At least three for every Earth-to-Sun distance of space (0.333 AU each) around the perimeter of the Kuiper Belt... though, probably a good bit more. Something like the distance between the Earth and Venus when they're aligned in their orbits (~40 million kilometers, or ~0.267 AU) should be a fine low-ish end.

Even assuming only one of every five Warspheres are of sufficient size to support life, that's 1 of these per 1.335 AU of the perimeter...

Perimeter of Circle with Radius of 50 AU: 314.16 AU

314.16 / 1.335 = 235.32 planet-sized Warspheres, rounded down to 235-

1.015 x 235 = 238.525 Foe. Pretty low Solar System level, but Solar System level nonetheless.

Space Flight
Since this, too, becomes a destination that can be reached within the story given our old timeframe... well, yeah. I'll stick with the average of 50 AU to keep things simple-

7.48e+12 meters / 30 seconds = 249333333333 m/s, or 831.69 C

7.48e+12 meters / 25 seconds = 299200000000 m/s, or 998.02 C

7.48e+12 meters / 20 seconds = 374000000000 m/s, or 1247.53 C

Constellation Forms
The Celestials, such as Odin, are constellations in the sky in their truest state. Being components of their "body", the stars that make up these celestials (and the energy binding them to their shape) can be shifted, twisted, etc. by the Celestials in question... so, more Inverse Square Law time.

I couldn't find a whole awful lot about how far apart the stars in various constellations are... but these constellations seem comparable to our own real-world Orion, whose stars vary between being 243 and 1360 light years away from us. It doesn't account for the horizontal distance between them, I suppose, but it makes for a nice enough lowball:

1360 - 243 = 1117 light years in diameter (558.5 light year "blast" radius)

U = 5.693e+41 Joules

Er = 5.284e+18 meters (558.5 LY)

Br = 659700000 meters

E = 4U(Er/Br)^2

4(5.693e+41)((5.284e+18/659700000)^2) = E

E = 1.4609e+62 Joules, or 1.4609 ExaFoe.

Granted, the actual main cast probably don't scale to this at this point in the story- at best, they get some small portion of it...

Act V
And finally, the top-tier stuff.

Final Showdown: The Great Sloan Wall
The Great Sloan Wall is where Zain initially reawakens from the Daathe into the Malkuth (material reality), whereupon he recieves some directions back to Earth from the spirits of the elves who once made their home there: though, following a ride there within the spacecraft he managed to salvage (with Magus's help), he can fly there and back freely (along with the rest of the party, once they recieve their final power-up) within our standard timeframe...

Distance between Milky Way and Great Sloan Wall: ~1 billion light years

Timeframe: 30/25/20 seconds

Casual Intergalactic Flight (Low-End): 1.0519e+15 C, or 1.0519 quadrillion times light speed

Casual Intergalactic Flight (Mid-End): 1.2623e+15 C, or 1.2623 quadrillion times light speed

Casual Intergalactic Flight (High-End): 1.5779e+15 C, or 1.5779 quadrillion times light speed

Naux Avatar's Morphegael Blazing
Naux Omega, in a bid to turn the tables on the protagonists as they put him to the proverbial ropes, intentionally misses an attacking Magus with a Morphegael Blazing so as to aim it directly towards a distant Earth; a beat, and Tessera, figuring out what is going on, activates her one-time-use "Return to Earth" gadget Magus crafted in case of an emergency prior to the showdown and parries the attack. Thus, Naux fails to peel open the world and reach Yggdrasil's root, though he did begin to better control the matchup by virtue of moving the fight back to Earth...

If a "beat" is to be taken to be around two, three seconds, then this is another workable speed feat, since the whole party can dodge this without too much trouble at close range

1000000000 light years / 3 seconds = 1.0519e+16 C, or 10.519 quadrillion times light speed.

That's, uhh, about it I suppose. The rest of the stuff in the verse isn't exactly quantifiable in terms of calculations or would be redundant. So,

Final Yield
Act I

Lightning Speed Cannonballs
 * Low-End: 188.79 Tons of TNT
 * Mid-End: 251.95 Tons of TNT
 * High-End: 335.93 Tons of TNT

Deflecting a Cannonball: Mach 4107.29

Zain vs Tessera: 1.038 Kilotons of TNT

AFter the Storm
 * Low-End: 2.024 Kilotons of TNT.
 * Mid-End: 3.601 Kilotons of TNT.
 * High-End: 8.103 Kilotons of TNT.

Flying to Houston
 * Low-End: Mach 129.20
 * Mid-End: Mach 155.04
 * High-End: Mach 193.80

Lifting A Purple Person: Class 25+

Act II

Metenros Makes Mountains: 4.82 Gigatons of TNT

Grand Mountain Slam: 44.05 Gigatons of TNT

Breaking Out: Class T

Around the World
 * Low-End: Mach 1947.28.
 * Mid-End: Mach 2336.73.
 * High-End: Mach 2920.92.

Act III

To The Moon
 * Low-End: 0.0425 C
 * Mid-End: 0.051 C
 * High-End: 0.0638 C

...That's No Moon-!: 5.02 Zettatons of TNT.

"Lightning Faster Than Lightning": 3.71 C

Act IV

Maintaining Equilibrium: 238.525 Foe

Space Flight
 * Low-End: 831.69 C
 * Mid-End: 998.02 C
 * High-End: 1247.53 C

Constellation Forms: 1.4609 ExaFoe

Act V

Final Showdown: The Great Sloan Wall
 * Low-End: 1.0519e+15 C
 * Mid-End: 1.2623e+15 C
 * High-End: 1.5779e+15 C

Naux Avatar's Morphegael Blazing: 1.0519e+16 C