Close Explosion Durability Cross-Section Problem

[ElajRuengies]

Ok so, in accordance with the Inverse Square Law, durability from tanking an explosion is gonna be-

• [cross-section of the character * the intensity of the explosion in AP/m2]

-with various area formulas for whatever shape the attack is- usually a sphere or hemisphere, meaning the intensity is-

• Sphere: (Yield / (Radius^2 * 4 * Pi))
• Hemisphere: (Yield / (Radius^2 * 2 * Pi))

This equation naturally assumes that every part of the character's surface is about the same distance away from the explosion, which works once you're like, 1.5 or more meters away, assuming the thing tanking is human-sized (a fair assumption). However, problems occur when explosions are really close- let's say a 1 ton spherical blast occurs 20cm away from Character A's face;

• Intensity: 1000 / (0.2^2 * 2 * Pi) = 1989.436789 kg / m2
• Durability: 1989.436789 * 0.68 = 1352.817016 kg

Somehow, Character A withstood 1.35 tons of TNT from a 1 ton explosion.
This is because the cross-sectional area of the character is larger than the cross sectional area of the blast when it hit Character A's face, and ignored how the explosion's area would get bigger, but also decrease in intensity, the more of Character A it reaches. To illustrate (note- the drawing is a guesstimate)-


So, what do I do in this situation?
(This is not a hypothetical problem btw- I brought this up because I have to calculate an explosion happening right in front of a character's face)

 

[Arceus0x]

the link links me to a "Zoinks! you've taken a wrong turn!" page with creepy animal portraits looking at my arrow

 

[ElajRuengies]

the link links me to a "Zoinks! you've taken a wrong turn!" page with creepy animal portraits looking at my arrow

Fixed

 

[Armorchompy]

We usually scale point-blank explosions to durability directly

 

[ElajRuengies]

We usually scale point-blank explosions to durability directly

I thought that only applied if the explosion happened literally inside the person, or if it occurred within their closed hands, or they are hugging a bomb which is smaller than their body

1. The explosion happens inside the character's body
2. The explosion is fully covered by the character in some form (Like their hands or body covering the bomb or source of the explosion)
3. The character is face-hugging/bear-hugging the bomb/explosion source or standing/sitting/crouching right on top of it or directly adjacent to it and the bomb/explosion source happens to be smaller than them

...Ah, I see-
But even a point blank explosion that's on the character's skin would only hit them with half the yield, since the other have would just blast the air in the opposite direction of the character

 

[Chariot190]

Then just half it if you wanna get really caught up on details.

 

[ZillertheBucko]

not a calc guy, but I actually thought of this issue before and it doesn't make sense that a character would 100% scale to an explosion if they're not taking all of the explosion's energy. Swallowing an explosion or completely containing one with your hands or a technique would make sense, but if you're standing away from a massive explosion then, it could end up being that the character only took like 2% of the actual force of it? again, not a calc guy, but this seems like a thing where calcs should specifically use the volume of the explosion that actually made contact with the character
because I'm fairly certain that if a few minor pieces of a house survive a nuke, the remaining pieces of the house wouldn't be tier 7 durability

 

[Arceus0x]

not a calc guy, but I actually thought of this issue before and it doesn't make sense that a character would 100% scale to an explosion if they're not taking all of the explosion's energy. Swallowing an explosion or completely containing one with your hands or a technique would make sense, but if you're standing away from a massive explosion then, it could end up being that the character only took like 2% of the actual force of it? again, not a calc guy, but this seems like a thing where calcs should specifically use the volume of the explosion that actually made contact with the character
because I'm fairly certain that if a few minor pieces of a house survive a nuke, the remaining pieces of the house wouldn't be tier 7 durability

yeah...that's like the basics of this

https://vsbattles.com/threads/how-does-square-law-work.135535/

 

[CuteAnimeNekoGirl99]

iirc correctly if the character is about 20 cm away from the bomb you can scale dura fully

 

[ZillertheBucko]

that shouldn't be allowed for obvious reasons

 

[ElajRuengies]

iirc correctly if the character is about 20 cm away from the bomb you can scale dura fully

That's because the sphere's area is around 0.68 m2 at 23.26... cm away, and body's cross section is 0.68 m2, even though at least half, if not much more of the explosion isn't actually hitting the character.

Anywho I figured out something that works as I solution- I just used the surface area of the face for my specific calc since that's what's at the radius's length to the epicenter, and the rest of the body's gonna be hit with exponentially less energy as it's further away, so it can be ignored.

 

[KLOL506]

The formula starts to go haywire even with the 0.68 m^2 surface area if you get closer than 23 cm, it was never designed to calculate yields tanked that close. Bigger the dude, bigger the surface area, so you can see the problem that arises with this.

In your scans the bomb itself is way smaller than the character itself and it happens right in his face, so might as well scale to the full yield at that point. Assuming it got closer, because using your px scaling and using average human head, it's not close enough to qualify.

Anyway, @DontTalkDT and @DMUA can explain more.

 

[KLOL506]

not a calc guy, but I actually thought of this issue before and it doesn't make sense that a character would 100% scale to an explosion if they're not taking all of the explosion's energy. Swallowing an explosion or completely containing one with your hands or a technique would make sense, but if you're standing away from a massive explosion then, it could end up being that the character only took like 2% of the actual force of it? again, not a calc guy, but this seems like a thing where calcs should specifically use the volume of the explosion that actually made contact with the character
because I'm fairly certain that if a few minor pieces of a house survive a nuke, the remaining pieces of the house wouldn't be tier 7 durability

Again, nukes obviously won't allow you to get near the epicenter because in general they're just so much bigger than you, the actual uranium core wouldn't even be close to 20 cm range becasue of the shelling alone, preventing you from scaling to the full yield to begin with.

And the inverse-square law doesn't work with volume, it works with area affected and distance from the boom.

 

[ZillertheBucko]

Again, nukes obviously won't allow you to get near the epicenter because in general they're just so much bigger than you, the actual uranium core wouldn't even be close to 20 cm range becasue of the shelling alone, preventing you from scaling to the full yield to begin with.

And the inverse-square law doesn't work with volume, it works with area affected and distance from the boom.

not a calc guy still so I can't say much about this

 

[DontTalkDT]

I believe for point-blank explosions we usually scale to the full yield.

Otherwise, this can of course be accounted for with more math. It's a lot of work, though.

 

[ElajRuengies]

The formula starts to go haywire even with the 0.68 m^2 surface area if you get closer than 23 cm, it was never designed to calculate yields tanked that close. Bigger the dude, bigger the surface area, so you can see the problem that arises with this.

In your scans the bomb itself is way smaller than the character itself and it happens right in his face, so might as well scale to the full yield at that point. Assuming it got closer, because using your px scaling and using average human head, it's not close enough to qualify.

Anyway, @DontTalkDT and @DMUA can explain more.

The problem with that is
1. Scaling to the full yield results in a definite outlier for the character's durability (48.4 Megajoule explosion to a character that gets staggered by 1.5 Megajoule hits) and
2. Even if it literally exploded on top of his face, half of the explosion would go into a hemispherical blast expanding in the opposite direction of said face, meaning a bomb detonating on someone only scales their durability to half its yield. And the epicenter of this explosion was still tens of centimeters away from Suchan, meaning the energy taken would be much less than half.

I believe for point-blank explosions we usually scale to the full yield.

Otherwise, this can of course be accounted for with more math. It's a lot of work, though.

If I have to bust out Pythagoras and human head height zones in order to create a gradient of energy intensities that the different parts of the character's body will feel as the explosion gets bigger and encapsulates more of him while decreasing in intensity, I will.

 

[KLOL506]

The problem with that is
1. Scaling to the full yield results in a definite outlier for the character's durability (48.4 Megajoule explosion to a character that gets staggered by 1.5 Megajoule hits)

Outliers are outliers, it really has no meaning on a calc's mathematical formula.

2. Even if it literally exploded on top of his face, half of the explosion would go into a hemispherical blast expanding in the opposite direction of said face, meaning a bomb detonating on someone only scales their durability to half its yield. And the epicenter of this explosion was still tens of centimeters away from Suchan, meaning the energy taken would be much less than half.

Like I said, your pixel-scaling doesn't put the explosive's epicenter to be anywhere close to the 23 cm required to pull the whole "scales to the full yield" solution assuming average cross-sectional area of 0.68 m^2 getting hit. I got 0.33 m from the face assuming average head size, so the whole "opposite direction" argument here falls flat.

 

[ElajRuengies]

Outliers are outliers, it really has no meaning on a calc's mathematical formula.

Fair enough

Like I said, your pixel-scaling doesn't put the explosive's epicenter to be anywhere close to the 23 cm required to pull the whole "scales to the full yield" solution assuming average cross-sectional area of 0.68 m^2 getting hit. I got 0.33 m from the face assuming average head size, so the whole "opposite direction" argument here falls flat.

...I'm sorry what?

Oh, you were under the impression I had objections to him scaling to the full yield because I thought he was close enough for the formula jumble that I brought up in the first post to happen- yeah, I know that he's far enough away that he's not gonna scale to a higher yield than the original explosion; the half-yield durability for point-blank explosions was in response to-

In your scans the bomb itself is way smaller than the character itself and it happens right in his face, so might as well scale to the full yield at that point. Assuming it got closer, because using your px scaling and using average human head, it's not close enough to qualify.

The problem I'm having is that using cross-sectional area at 33cm away, meaning a sphere area of 1.36847776 square meters, is that this would imply that all of his cross-section is roughly 33cm away from the epicenter of the explosion, even though it isn't. Most of his body is much further away because height adds to distance, and would feel the blast at a significantly lower intensity than (48.4/1.37) 35.3 Megajoules per m2. To do the math-

• The radius of 33cm measures from the epicenter to the middle of his head
• Humans in art are typically 8 heads tall, meaning the distance from the middle of his head to his feet would be- and using the height of a Korean dude in his 20s, (174.6 - (174.6/2/8)) = 163.6875cm
• His body's roughly perpendicular to the direction of the blast at his head, meaning the distance from the epicenter to the bottom of his feet will be the diagonal of a right triangle, with the small leg being the distance to his head of 33 cm, and the big leg being the distance from the middle of his head to the bottom of his feet, or about 163.7cm
• 33^2 * 163.6875^2 = 27882.59766, sqrt(27882.59766) = 166.9808302 cm
• The distance from the epicenter of the explosion to the bottom of his feet is ~166.98 cm, meaning the intensity of the blast there will be-
• 48.4 Megajoules / (4 * 1.6698 * Pi) = 2.306593378 Megajoules per m2
• Intensity at face / Intensity at feet = difference
• 35.3 / 2.3 = 15.34782609

There is over a 15 times drop off in intensity across the character's cross-section, with the face being subjected to over 35 Megajoules per m2, while the feet are hit with about 2.3 Megajoules per m2, so multiplying the character's cross-section by the intensity of the explosion right at the face is a massive highball.

(And I can't just use the mean of the two values either, since the intensity doesn't decrease linearly, it decreases exponentially with the square of the radius. I vaguely remember a way to get an exponential mean or something from geometry but I don't know what it's called...)

 

[KLOL506]

Fair enough

...I'm sorry what?

Oh, you were under the impression I had objections to him scaling to the full yield because I thought he was close enough for the formula jumble that I brought up in the first post to happen- yeah, I know that he's far enough away that he's not gonna scale to a higher yield than the original explosion;

Aye, that was the impression I was under until I did the distance between the bomb and the head myself.

the half-yield durability for point-blank explosions was in response to-

The problem I'm having is that using cross-sectional area at 33cm away, meaning a sphere area of 1.36847776 square meters, is that this would imply that all of his cross-section is roughly 33cm away from the epicenter of the explosion, even though it isn't. Most of his body is much further away because height adds to distance, and would feel the blast at a significantly lower intensity than (48.4/1.37) 35.3 Megajoules per m2. To do the math-

• The radius of 33cm measures from the epicenter to the middle of his head
• Humans in art are typically 8 heads tall, meaning the distance from the middle of his head to his feet would be- and using the height of a Korean dude in his 20s, (174.6 - (174.6/2/8)) = 163.6875cm
• His body's roughly perpendicular to the direction of the blast at his head, meaning the distance from the epicenter to the bottom of his feet will be the diagonal of a right triangle, with the small leg being the distance to his head of 33 cm, and the big leg being the distance from the middle of his head to the bottom of his feet, or about 163.7cm
• 33^2 * 163.6875^2 = 27882.59766, sqrt(27882.59766) = 166.9808302 cm
• The distance from the epicenter of the explosion to the bottom of his feet is ~166.98 cm, meaning the intensity of the blast there will be-
• 48.4 Megajoules / (4 * 1.6698 * Pi) = 2.306593378 Megajoules per m2
• Intensity at face / Intensity at feet = difference
• 35.3 / 2.3 = 15.34782609

There is over a 15 times drop off in intensity across the character's cross-section, with the face being subjected to over 35 Megajoules per m2, while the feet are hit with about 2.3 Megajoules per m2, so multiplying the character's cross-section by the intensity of the explosion right at the face is a massive highball.

(And I can't just use the mean of the two values either, since the intensity doesn't decrease linearly, it decreases exponentially with the square of the radius)

I don't think that would necessarily matter in the long run, since in fiction we consider all parts of the body to be equal to each other in terms of dura.

 

[ElajRuengies]

Aye, that was the impression I was under until I did the distance between the bomb and the head myself.


I don't think that would necessarily matter in the long run, since in fiction we consider all parts of the body to be equal to each other in terms of dura.

True, the rest of his body should be about as durable as his face, but his face's area isn't 0.68 square meters, it's like 0.063 square meters (the surface area of one's skin for men is about 18,000 cm2, and the face makes up about 3.5% of that), so his face is only taking (35.3 MJ/m2 * 0.063), 2.224 Megajoules, which is way less than the total explosion.

 

[ElajRuengies]

@KLOL506 Random side note but I'd like to thank you for getting me to use Paint.net- gosh it makes things easier