User blog:ThePerpetual/Hero's Path: Various Basic Spell Calculations

(Disclaimer): This blog is still a work in progress. I will finish it at a later time.

It's occurred to me that just the basic spells in Hero's Path are probably some fairly impressive stuff, what with how some of them go and all

They're generally supposed to be comparable to one another, but I'm fairly certain we'll have at least one major Outlier? We'll cross those bridges when we get there. Oh, and obviously I'm not exactly doing every category of spell, since that would be kinda, uh... redundant, probably? Ah well.

As for general areas of effect for offensive spells? As I'd envisioned it,


 * "A meter or two" (Tier 1)
 * "Several meters" (Tier 2)
 * "Dozens of meters" (Tier 3)
 * "Hundreds of meters" (Tier 4)
 * "Thousands of meters" (Tier 5)
 * "Several kilometers" (Tier 6)

And the range in each case is the next category up (save for Tier 1, which like Tier 2 is dozens of meters.) Need some space to use gigantic area of effect attacks, after all.

As for Tier 6, the Ultima branch of offense magic, I'd just the range up one to dozens of kilometers I suppose? (shrug) Seems like the logical progression of that.

Essentially, being able to toss around Fifth or Sixth Order Offensive Magic makes you a terrifying tactical nuke in the verse, and beings with that kind of firepower are feared within the verse for their ability to lay waste to the world around them.

Fire
Fire is pretty simple, it's just some basic fireball-type stuff

The only statements I recall making regarding the actual intensity of the fire would be that Great Fire (Tier 3) is as hot as lava (~950 Celsius on average seems safe), and that Supra Fire (Tier 5) approaches the temperature of the surface of the Sun (~5600 Celsius: since it's "approaches", I'll use the slightly lower 5000 Celsius as a low-ball)


 * Flame's Mass: .3 kg/m^3
 * Heat Capacity of Oxygen: 919 J/kg*K
 * Standard Temp. of Flame: 1200 C

Which makes the first statement kinda pointless? Ah well

Tier 1


 * Volume of Sphere with Radius (1.5): 14.14 m^3
 * Mass of Flame: (X * 0.3) = 4.24 kg
 * Potency: (# kg * 919 * (1200 - 23)) =

Tier 2


 * Volume of Sphere with Radius (5): 523.6 m^3
 * Mass of Flame: (X * 0.3) = 157.08 kg
 * Potency: (# kg * 919 * (1200 - 23)) =

Tier 3


 * Volume of Sphere with Radius (24): 57905.84 m^3
 * Mass of Flame: (X * 0.3) = 17371.75 kg
 * Potency: (# kg * 919 * (1200 - 23)) =

Tier 4


 * Volume of Sphere with Radius (200): 3.35e+7 m^3
 * Mass of Flame: (X * 0.3) = 1.005e+7 kg
 * Potency: (# kg * 919 * (1200 - 23)) =

Tier 5


 * Volume of Sphere with Radius (2000): 3.35e+10 m^3
 * Mass of Flame: (X * 0.3) = 1.005e+10 kg
 * Potency: (# kg * 919 * (5000 - 23)) =

Tier 6


 * Volume of Sphere with Radius (5000): 5.24e+11 m^3
 * Mass of Flame: (X * 0.3) = 1.572e+11 kg
 * Potency: (# kg * 919 * (5000 - 23)) =

Ice
Ice spells tend towards pretty "spikes" and such, so something akin to a cone shape with a height of double the radius, and 20% hollowness, is about right here I think. All ice spells freeze water to a depth sufficient to support the weight of multiple squadrons of people: ten people, with a weight of about one ton total (counting gear and the like), would likely need ice of a thickness of 17.5 centimeters, or 0.175 meters.

Anywho, let's get this on the road


 * Freezing Air into Ice: 566055.24 Joules/m^3
 * Freezing Water into Ice: 418000000 Joules/m^3

Tier 1


 * Volume of Cone with Radius (1.5), Double That Height, and 20% Hollowness: 5.656 m^3
 * Volume of Ice Sheet with Radius (1.5) and 0.175 m Thickness: 1.24 m^3
 * Potency: (566055.24 * X) + (418000000 * Y) = 521521608.4 Joules, or 0.1246 Tons of TNT. Small Building level.

Tier 2


 * Volume of Cone with Radius (5), Double That Height, and 20% Hollowness: 209.44 m^3
 * Volume of Ice Sheet with Radius (5) and 0.175 m Thickness: 13.74 m^3
 * Potency: (566055.24 * X) + (418000000 * Y) = 5.86187e+9 Joules, or 1.401 Tons of TNT. Building level+.

Tier 3


 * Volume of Cone with Radius (24), Double That Height, and 20% Hollowness: 23162.336 m^3
 * Volume of Ice Sheet with Radius (24) and 0.175 m Thickness: 316.67 m^3
 * Potency: (566055.24 * X) + (418000000 * Y) = 1.45479e+11 Joules, or 34.77 Tons of TNT. City Block level.

Tier 4


 * Volume of Cone with Radius (200), Double That Height, and 20% Hollowness: 1.344e+7 m^3
 * Volume of Ice Sheet with Radius (200) and 0.175 m Thickness: 21991.15 m^3
 * Potency: (566055.24 * X) + (418000000 * Y) = 1.68001e+14 Joules, or 40.153 Kilotons of TNT. Town level.

Tier 5


 * Volume of Cone with Radius (2000), Double That Height, and 20% Hollowness: 1.344e+10 m^3
 * Volume of Ice Sheet with Radius (2000) and 0.175 m Thickness: 2199115 m^3
 * Potency: (566055.24 * X) + (418000000 * Y) = 8.52701e+15 Joules, or 2.038 Megatons of TNT. Small City level.

Tier 6


 * Volume of Cone with Radius (5000), Double That Height, and 20% Hollowness: 2.096e+11 m^3
 * Volume of Ice Sheet with Radius (5000) and 0.175 m Thickness: 1.37e+7 m^3
 * Potency: (566055.24 * X) + (418000000 * Y) = 1.24372e+17 Joules, or 29.726 Megatons of TNT. City level.

Big, tall ice is quite stronk

Lightning
Tier 1

Tier 2

Tier 3

Tier 4

Tier 5

Tier 6

Earth
Tier 1

Tier 2

Tier 3

Tier 4

Tier 5

Tier 6

Holy
While holy attacks don't behave like true light, when not suppressed they have a tendency to shine "like the Sun". I didn't exactly establish exact parameters for from how far away is the big problem, but I can probably assume that it shines like the Sun (apparent magnitude: -26.8) from past the edge of its area of effect, in each case. About double the edge of the area of effect seems about right.

Tier 1


 * Distance to App. Lum. -26.8: (((1 + 2)/2) * 2) = 3 meters
 * Potency: 1.4945e-4 Gigawatts, or 149450 Joules per second. Wall level.

Tier 2


 * Distance to App. Lum. -26.8: (5 * 2) = 10 meters
 * Potency: 1.6606e-3 Gigawatts, or 1660600 Joules per second. Wall level.

Tier 3


 * Distance to App. Lum. -26.8: ((12 * 2) * 2) = 48 meters
 * Potency: 0.03826 Gigawatts, or 38260000 Joules per second, or ~0.0091 Tons of TNT. Small Building level.

Tier 4


 * Distance to App. Lum. -26.8: ((100 * 2) * 2) = 400 meters
 * Potency: 2.657 Gigawatts, or 2.657e+9 Joules per second, or 0.635 Tons of TNT. Building level.

Tier 5


 * Distance to App. Lum. -26.8: ((1000 * 2) * 2) = 4000 meters
 * Potency: 265.7 Gigawatts, or 2.657e+11 Joules per second, or 63.5 Tons of TNT. City Block level+.

Tier 6


 * Distance to App. Lum. -26.8: (5000 * 2) = 10000 meters
 * Potency: 1660.6 Gigawatts, or 1.6606e+12 Joules per second, or 396.89 Tons of TNT. Multi-City Block level.

Well, then. Holy doesn't do well with calcs, it would seem.

Zie
And of course, there is the non-elemental spell, Zie. Unlike it's more mundane kin, Zie as a non-elemental spell dissolves matter it destroys into its mere component animating pieces, rather than simply damaging and destroying matter in the more mundane way that other elemental attacks do- while I'm pretty certain that E = mc^2 doesn't apply here, I believe atomization does: being capable of reducing living flesh at minimum to such component pieces within a spherical area of effect is probably potent.


 * Atomization of Human Body: 72416.33 Joules/cubic centimeter

Without further ado,

Tier 1


 * Volume of Sphere (with radius 150 in cm): 1.41e+7 cm^3
 * Potency: 1.02107e+12 Joules, or 244.04 Tons of TNT. Multi-City Block level.

Tier 2


 * Volume of Sphere (with radius 500 in cm): 5.24e+8 cm^3
 * Potency: 3.7946e+13 Joules, or 9.069 Kilotons of TNT. Town level.

Tier 3


 * Volume of Sphere (with radius 2400 in cm): 5.79e+10 cm^3
 * Potency: 4.19291e+15 Joules, or 1.002 Megatons of TNT. Small City level.

Tier 4


 * Volume of Sphere (with radius 20000 in cm): 3.35e+13 cm^3
 * Potency: 2.42595e+18 Joules, or 579.82 Megatons of TNT. Mountain level+.

Tier 5


 * Volume of Sphere (with radius 200000 in cm): 3.35e+16 cm^3
 * Potency: 2.42595e+21 Joules, or 579.82 Gigatons of TNT. Large Island level+.

Tier 6


 * Volume of Sphere (with radius 500000 in cm): 5.24e+17 cm^3
 * Potency: 3.79462e+22 Joules, or 9.069 Teratons of TNT. Country level.

Yeah, that's about what I had thought.

For what it's worth? Vaporization wouldn't yield much lower than this: titanium's value of 49079.7 J/cc, for example, would essentially just reduce these results to two-thirds their current value.

That said, with Zie being harder to learn/taking more mana to cast, it's easy to justify this result being separate from the rest.