Marked for Death: A Rational Naruto Quest

[ProperAttorney]

...Are we sure about this, and are we also sure that two storage seals (basically what Tunneler's Friend are) interacting with the same air at the same time won't cause a sealing failure?

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Not until we test it. Also not sure that they'll actually interact with the air at the same time. I can't upload discord images here so I'll ping you there

 

[faflec]

Not until we test it. Also not sure that they'll actually interact with the air at the same time. I can't upload discord images here so I'll ping you there

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If we haven't tested the basic failure modes we probably shouldn't be showing off to Shikamaru until we have. For that matter, we shouldn't be talking to him until we have the components completed.

 

[ProperAttorney]

If we haven't tested the basic failure modes we probably shouldn't be showing off to Shikamaru until we have. For that matter, we shouldn't be talking to him until we have the components completed.

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We are reading that plan very differently. I didn't see that as showing off to Shikamaru. We're asking for his analysis on the research tree, if it's even worth pursuing, possible unintended consequences, etc. You know, what Shikaku told us we should have done with Skywalkers before releasing them.

 

[Insert]

We are currently considering researching a series of seals to allow us to destroy sections of Rock at distance (Suborbital strikes).

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Would a phrasing change like this be a good idea? Maybe even something more overt?

 

[faflec]

We are reading that plan very differently. I didn't see that as showing off to Shikamaru. We're asking for his analysis on the research tree, if it's even worth pursuing, possible unintended consequences, etc. You know, what Shikaku told us we should have done with Skywalkers before releasing them.

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• Meet with Shikamaru to discuss Rock Strategies, high OPSEC.
  • We are currently researching a series of seals to allow us to destroy sections of Rock at distance (Suborbital strikes).
  • Shikaku once told us to come up with countermeasures before releasing WMDs.
  • We have preliminary ideas for protecting Leaf from this type of attack (Skyslicer nets, 5SB shields).
  • Could he provide his analysis regarding topics of concern?
    • Do not mention Kei's request to spare some Tama.

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Please note the emphasis, my understanding of the plan is that we're asking him for assistance in devising countermeasures before using the WMDs, not before assembling them.

Side note: @Insert

• Skyslicers won't stop the rocks falling unless my understanding of them is off, and the WMD will still have sufficient speed to cause catastrophic damage.
• 5SB shields aren't going to defend us unless we have a literal dome over Konoha and extending deep underground to avoid earthquake-esque aftershocks. You don't need perfect accuracy with a sufficiently-fast moving large object.

 

[Veedrac]

Our best measuring stick for storing a gas is Implosion Seals. With a radius of 1-20 m, an Implosion Seal is capable of storing (V = (4/3)πr^3) between 4.2 m^3 and 33510 m^3 of atmosphere pressure air. We'll use 33510 m^3 as our absolute maximum and aim to be well below it.

Okay, so now we have our maximum volume to store. We are currently operating under the premise that we are staying within the troposphere, so we'll use 12 km as our maximum operating height. By dividing 33510 m^3 by 12000 m, we get 2.8 m^2. So long as no one seal has an absorption area of 2.8 m^2 when dropped from <=12 km, they won't exceed our observed maximum air storage of 33510 m^3.

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We calculated that maximum area of our seal can be 2.8 m^2, the current size of the bottom of our projectile. Since this is the absolute maximum, let's split it into 4, just to be on the safe side. This means that each seal will cover an area of 0.7 m^2.

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I didn't note it before, but since it's the QM-incited topic of conversation, this math isn't quite right. You have to account for air moving to refill the prior volume, which happens at about the same rate, the speed of sound, thus you have to consider the volume absorbed over time, not over distance. 30,000 m³ / 300 m³/s ~ 100s. A drop from 12km in a vacuum will take 50s. This means that the 0.7m² seals would only by a factor of 2 off the tippity top upper bound, rather than being a factor 4 off. On the other side, air density high in the sky is much lower, which is where most of the time will be spent, and this could easily halve or third these quantities.

IMO this doesn't really change anything, these are tiny margins and we could easily lose a factor 10 or 100 instead, but, you know, there's some math.

 

[faflec]

Would a phrasing change like this be a good idea? Maybe even something more overt?

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This would be fine, though Shikamaru/Shikaku have already considered the idea of dropping large objects from height and may or may not be confused at how our additions make the threat any more dangerous than their current model.

 

[Veedrac]

300 METs

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The metabolic equivalent of task (MET) is the objective measure of the ratio of the rate at which a person expends energy, relative to the mass of that person, while performing some specific physical activity compared to a reference, set by convention at 3.5 mL of oxygen per kilogram per minute, which is roughly equivalent to the energy expended when sitting quietly.

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3.5 mL/kg/MET × 100 kg × 300 MET / 20% ~ 0.5m³. FWIW.

 

[faflec]

3.5 mL/kg/MET × 100 kg × 300 MET / 20% ~ 0.5m³. FWIW.

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Okay, so now we have our maximum volume to store. We are currently operating under the premise that we are staying within the troposphere, so we'll use 12 km as our maximum operating height. By dividing 33510 m^3 by 12000 m, we get 2.8 m^2. So long as no one seal has an absorption area of 2.8 m^2 when dropped from <=12 km, they won't exceed our observed maximum air storage of 33510 m^3.

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So at a conservative estimate (dropping an object of 1 square meter cross-section) 12000 meters...24000 seals.

...Did I do that math wrong?

 

[Insert]

So at a conservative estimate (dropping an object of 1 square meter cross-section) 12000 meters...24000 seals.

...Did I do that math wrong?

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I'm reading that as needing 1 seal per 2.8 m^2 of surface area on the projectile. So an object with a 1m^2 cross-section would need about 0.35 seals, mathematically speaking.

 

[faflec]

I'm reading that as needing 1 seal per 2.8 m^2 of surface area on the projectile. So an object with a 1m^2 cross-section would need about 0.35 seals, mathematically speaking.

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I don't see how you're getting this at all. 12000 m height * 1 m^2 cross section = 12000 cubic meters of atmosphere the object must travel through straight down (I'm ignoring sides here). Each seal has 0.5 cubic meters capacity according to Veedrac, so 12000 m^3 / 0.5 m^3 per seal = 24000 seals.

 

[Insert]

I'm now confused by the specifics here, but we have the power of Sealing Research on our side.
A better seal to drop the rock is just a higher TN, in whatever flavour we can figure out how to make work.

 

[faflec]

I'm now confused by the specifics here, but we have the power of Sealing Research on our side.
A better seal to drop the rock is just a higher TN, in whatever flavour we can figure out how to make work.

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I personally just want to make sure we have confirmation that this system works (complete the seal, preliminary testing to compare speeds/accuracy) before taking it to Shikamaru.

 

[Insert]

I personally just want to make sure we have confirmation that this system works (complete the seal, preliminary testing to compare speeds/accuracy) before taking it to Shikamaru.

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That's fair. We're mainly asking about precautions for such a technology existing and possibly being used against us and whether this tech should be pursued, but maybe that should be more clear in the wording.
Come to think of it, it also parallels EM nukes in deployment, so we might get some insight into that issue as a bonus.

 

[ProperAttorney]

So at a conservative estimate (dropping an object of 1 square meter cross-section) 12000 meters...24000 seals.

...Did I do that math wrong?

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Like I said earlier, Tunneler's Friends are not a good measurement for the maximum capacity of stored air. We have two seals, Implosion Seals and Tunneler's Friends. We want the capacity and throughput of Implosion Seals with the massively reduced area of a Tunneler's Friend, as well as the TF's continuous nature. We're not literally putting 24000 Tunneler's Friends on the payload. We found the volume of air that an implosion seal can store (33510 m^3), we estimated a maximum operating height (12000 m), which gives us the area that a single seal can manage in order to seal the same amount of air as an implosion seal (2.8 m^2).

You can't tell me that a seal cannot store 33510 m^3 of air, when we have had seals that store 33510 m^3 of air since the ~20th chapter in the story.

 

[faflec]

That's fair. We're mainly asking about precautions for such a technology existing and possibly being used against us and whether this tech should be pursued, but maybe that should be more clear in the wording.
Come to think of it, it also parallels EM nukes in deployment, so we might get some insight into that issue as a bonus.

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My main question in that regard is how much the seals matter in terms of...well, damage. Is an Air Tunneler system dropping a large object that much more powerful than just dropping the object from the same height?

 

[Veedrac]

My main question in that regard is how much the seals matter in terms of...well, damage. Is an Air Tunneler system dropping a large object that much more powerful than just dropping the object from the same height?

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It is unlikely. It doesn't affect velocity much, per my prior arguments, and even unreasonably optimistic assumptions like going from 330 m/s to 470 m/s would only result in a factor 2 improvement in energy. That's even less of an improvement than it sounds like since it's a kinetic weapon rather than an explosive; putting twice the energy in a bullet doesn't make the bullet twice as deadly. You might as well just drop more rocks.

 

[faflec]

Like I said earlier, Tunneler's Friends are not a good measurement for the maximum capacity of stored air. We have two seals, Implosion Seals and Tunneler's Friends. We want the capacity and throughput of Implosion Seals with the massively reduced area of a Tunneler's Friend, as well as the TF's continuous nature. We're not literally putting 24000 Tunneler's Friends on the payload. We found the volume of air that an implosion seal can store (33510 m^3), we estimated a maximum operating height (12000 m), which gives us the area that a single seal can manage in order to seal the same amount of air as an implosion seal (2.8 m^2).

You can't tell me that a seal cannot store 33510 m^3 of air, when we have had seals that store 33510 m^3 of air since the ~20th chapter in the story.

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Sealing Project: Air Tunneling.

• Hazou knows that air slows him when he sprints.
• Idea: Tunneler's Friend that stores faster, so air doesn't slow a falling object.

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We are basing the Air Tunneler seal off of the Tunneler's Friend seal. A finished Air Tunneler seal is going to be functionally identical to the Tunneler's Friend seal save for the storage speed, including in capacity. Increasing the capacity to that of the implosion seal would be another more complicated series of projects (Implosion seal -> larger Air Tunneler) since you need to reconcile two different branches of the storage seal tree and the TN for that is going to be...a lot harder IMO.

Fake edit: @eaglejarl @Velorien Assuming the implosion seal volume stored is true (and I'm pretty sure it is) Kagome's implosion seals can store up to 41049.75 kg worth of air. Which is...uhh...not according to the maximum mass limits of 100kg /1 cubic meter that standard storage scrolls have.

 

[Veedrac]

We are basing the Air Tunneler seal off of the Tunneler's Friend seal. A finished Air Tunneler seal is going to be functionally identical to the Tunneler's Friend seal save for the storage speed, including in capacity. Increasing the capacity to that of the implosion seal would be another more complicated series of projects (Implosion seal -> larger Air Tunneler) since you need to reconcile two different branches of the storage seal tree and the TN for that is going to be...a lot harder IMO.

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Sounds like we're approaching from the wrong direction, and we should instead just try to make an implosion seal variant that seals continuously until full.

41049.75 kg

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Please people, round.

 

[faflec]

Fake edit: @eaglejarl @Velorien Assuming the implosion seal volume stored is true (and I'm pretty sure it is) Kagome's implosion seals can store up to 41049.75 kg worth of air. Which is...uhh...not according to the maximum mass limits of 100kg /1 cubic meter that standard storage scrolls have.

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Assuming a cubic centimeter's worth of volume once the implosion seal is destroyed, we get a density of 4.1E10 kg/m^3 at the moment of air release. Which...uhh...I'm not a physicist. But that sounds really really dense.

 

[Veedrac]

Assuming a cubic centimeter's worth of volume once the implosion seal is destroyed, we get a density of 4.1E10 kg/m^3 at the moment of air release. Which...uhh...I'm not a physicist. But that sounds really really dense.

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IIRC the QMs based it off of Radvic's analysis:

Radvic's Analysis of Implosion Seal Demonstrated Damages and Methods for Achieving Said Damage

Abstract​

This post address the problem of implosion seals. Specifically that the mechanism implosion seals work off of are hilariously more powerful than they are described as being in the story. The damage implosion seals cause is due to the way they force things into the same space, creating explosions of energy. This post attempts to determine "how much space would a 20 meter radius implosion seal need to unstore it's contents into in order to achieve the damage stated in the chapter we saw it used." For reference, the (so far as I know) sole passage describing the damage caused by an implosion seal is here:

I find that reducing the volume of a 20 meter radius sphere to a 18.7 meter radius sphere is enough to cause the damage stated in story.

Introduction​

In real life, there are very few cases where something like this happens, because compressing gas much is prohibitively energy expensive. The pressures increase astronomically as the radius of the sphere the air takes up decreases. The closest real life example available is things like compressed air accidents. But even these rarely reach the sorts of pressures implosion seals may reach trivially. For example, the video shows a nearly lethal explosion at ~100 psi, or ~7 atm. Implosion seals as currently stated get pressures up to 64,000 atm. Clearly, implosion seals deal with things outside the realm of real life experiences. This means we will need to look at several models to determine what exactly they do.

Intuitively, it is easiest to just say they work as an ideal gas, according to the kinetic theory of gases, and so then we just need to determine what happens during the adiabatic expansion of the gas, look at the blast wave created by such a thing.

Aside from traditional gas and pressure concerns, there may be problems with putting too much air into a single place and forming exotic matter like black holes or white dwarfs. As humans lack the energy and containment to reach the kinds of pressures which implosion seals will need to do the damage described, it is not immediately obvious if these things will or will not form. Thus, after using more traditional gas methods to determine the energy, we will look at the resulting conclusions on the amount of pressure that it creates, and if that will do something with nuclear physics.

Methods​

This section examines the amount of damage which releasing a bunch of gas of a certain pressure would do. We use two models to translate from the damage description to a determination of how much space the seal unstored its contents into. First, we will examine blast overpressure and how it would damage the forest in the only canon description we have for the damage of the seal. Next, we will use an explosive damage calculator to find the equivalent amount of TNT which would produce this amount of blast overpressure. Finally, we will determine how much work must be done on a system at constant temperature to add the amount of energy the seal must give off.

Forest Damage Analysis​

First, we compare to the damage a nuclear weapon does to a forest as in table 5.149 in this book on nuclear weapon damage descriptions, specifically, that severe forest damage is caused by winds of 130-140 mph. According to this source a 5 psi overpressure blast difference should be sufficient to cause sustained 150 mph winds. So, to have knocked down all the trees in a "perhaps thirty meters across" section, there must be a 5 psi blast overpressure out to 15 meters from where the implosion seal was set off.

Note: I had initially intended to examine the cratering described in the chapter to determine the blast strength, but in real life, most nuclear cratering is caused by vaporization (Chapter VI), which, presumably, implosion seals aren't doing (unless the QMs actually intend for a single implosion seal to be equivalent to a nuclear weapon).

Damage Conversion to TNT​

Now that we know we need a 5 psi overpressure blast, we can use this explosives impact calculator to calculate how much equivalent explosives of TNT we would need for the a 5 psi overpressure blast (or Reflected Pressure, as they term it). 5 psi is 35 kPA, which guess and check determines is about 4 kg of TNT. So, to do the damage described in the chapter, we need a blast equivalent to 4 kg of TNT from a single 20 meter radius implosion seal.

TNT Conversion to Sphere Reduction​

Now, we need to determine how much energy adding air of a constant volume to a system is equivalent to. Implosion seals have been stated to release air at the same temperature they took the air in, but at a smaller volume. For the purpose of this calculation, we will only examine the energy the seal adds in the storage. This is justified by claiming that the seal is broken in a very low pressure environment, so the energy up to the first atmosphere is irrelevant to the explosion. We can calculate the energy added by the implosion seal's volume changing act by calculating the work required to do the compression. This work will be released by the burst implosion seal as energy when the seal breaks. We can calculate the work done on a system of constant temperature via the isothermal compression and expansion equation:

W = nRT ln(Vf/Vi)

Where n is the number of moles of gas (in mol)
R is the ideal gas constant (8.314 4598 J mol-1​ K-1​)​
T is the temperature (in K)
Vf is the final volume (in m^2)
Vi is the initial volume (in m^2)
and W is the work done (in J)

Solving for Vf we find

Vf = Vi e^(W/(nRT))

Then, plugging our numbers (T = 293 K, Vi = 20^3 * 4 / 3 * pi m^3 = 33500 m^2, n = 33500 mol, W = - 4 kg of TNT = - 1.6 e7 J (via this conversion) we get

Vf = 27500 m^3

or, a sphere of radius 18.7 meters.

Esoteric Effects Check​

This sort of seal will not result in pressures greater than 5 atm, so is within the bounds of modern air compressors and thus will not cause any esoteric effects on its own.

Conclusion​

So, to cause damage to the trees as described in Chapter 12 Part 2, or approximately 4 kg of TNT, implosion seals absorbing air from a 20 meter radius sphere should release their air in a 18.7 meter radius. This would not increase the air pressure of the area they release things in by more than a 2 atm, so would avoid any esoteric effects (like accidental fusion) at this level. Note that this would also be sufficient to kill anyone present in this area, but likely not to create the described crater.

Comments and Critiques
​

Anyone reading this can help by checking my numbers and logic, or making slightly different assumptions (e.g. trees destroyed to a larger radius etc). I've tried to explain what's happening and source all the places I used to find this out, so, in theory, anyone could check it and comment reasonably on it.

With that said, there are three fairly obvious issues which can be raised against the above model. Ultimately, I think each of them has an answer (which is why I used the above model). The problems and solutions are as follows:

First, it turns out that cratering is mostly caused by vaporization (Chapter VI). So, to achieve the damage a crater would imply, we probably actually need to vaporize something, which I don't think is what an implosion seal is intended to do. This is why I went with "dozens of trees were knocked down"a crater was made of 15 meter radius and 1 meter depth." The difference in damage based on "made a huge crater" and "made a berm of trees" is large, I would estimate 2 or 4 orders of magnitude. If @eaglejarl @Velorien @OliWhail wants to use the crater depth and width as the decider of how strong implosion seals are going to be instead of tree destroyed values, I would estimate that by determining the magnitude of bomb which creates such a crater at optimal cratering depth, and then perform the "TNT Conversion to Sphere Reduction" to determine how much the sphere's volume must be reduced. A fairly easy way to explain the difference in damage the crater implies from the knocked down trees is to say that the local chakra voles had a nest in the area which collapsed.

Second, the assumption of "we can ignore the first atmosphere unsealed" by implosion seals is quite suspect. If we assume that the background is at 1 atm, suddenly the implosion seal gains a fair amount of power, since it's creating a large area of 2 atm (aka 300+ mph winds). This would sustantially increase the damage caused by an implosion seal, making a more accurate description of the damage it does to a forest "hundreds of trees were knocked down" rather than "dozens of trees were knocked down."

Third, it is unclear how sustained the blast from an implosion seal would be. This significantly changes the required pressures to knock down trees, and thus the amount of psi the blast must have. If the pressure wave is unsustained for instance, then it likely needs to be substantially larger, since trees won't fall over if exposed to 140 mhp winds for only 0.03 seconds. 4 kg of TNT doesn't knock over trees like this because it only gives out a shockwave, instead of a sustained flow. I'm assuming that since the implosion seal actually adds air to the situation the airflow is more sustained.

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which on a scan says that compression is from a 20m-radius sphere to an 18.7m-radius sphere. Note that yes, this is incongruent with the idea that implosion seals destroy themselves from the onrushing air, that's just what happens when QMs put ideas in the story before math gets done upon them. (This is also a contributing factor to why SINs are so much stronger than normal implosion seals. Even a SIN-1 should be much stronger than a normal implosion seal.)

 

[eaglejarl]

which on a scan says that compression is from a 20m-radius sphere to an 18.7m-radius sphere. Note that yes, this is incongruent with the idea that implosion seals destroy themselves from the onrushing air, that's just what happens when QMs put ideas in the story before math gets done upon them.

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The seal is destroyed by the inrushing air. Its contents are then released and reappear in a volume around the (now-destroyed) seal. That volume is a sphere of 18.7m radius, interrupted by the ground so perhaps only a hemisphere etc.

(This is also a contributing factor to why SINs are so much stronger than normal implosion seals. Even a SIN-1 should be much stronger than a normal implosion seal.)

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A SIN-1 is an implosion seal. It's in the name: Stacked Implosion-seal Nuke. Making a SIN-1 simply means setting off an implosion seal in such a way that it is protected from the inrushing air. You then have a filled seal which, when destroyed, releases its contents.

 

[Random Word]

Assuming a cubic centimeter's worth of volume once the implosion seal is destroyed, we get a density of 4.1E10 kg/m^3 at the moment of air release. Which...uhh...I'm not a physicist. But that sounds really really dense.

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Surely you're joking, Mr. Faflec! While nowhere near as dense as the core, that's an order of magnitude denser than the surface of a neutron star. Talk about an 'esoteric effects check'! At sea level that's 33 500 cubic metres of air compressed into a cubic centimetre... oh, and that is indeed the volume of a sphere of radius 20 m. Wow. To compress it all into a cubic centimetre if destroyed... well, let's see. pV = nRT, molar mass of air is 28.97 g/mol and we have 41 049.75 kg of air, so 1 416 974.46 mol. Assume 25 degrees C. So pressure is 3.5E15 Pa, and a volume of 1 cubic centimetre (Oh! so both sides of the equation are equal to energy, neat), so 3.5E9 joules (3.5 GJ). Well, that was surprisingly tame! So just a little less than a tonne of TNT. A big boom, but less than 1/20 000th of a nuclear bomb.

Oh, ninja'd - so the destruction doesn't compress the air to a cubic centimetre. That makes more sense.

 

[Orisha91]

I really want a plan where Hazou demonstrates what he can think up in front of Shika and Asuma instead of just informing them about what we're doing. The looks on their faces when they see the true power of explosions...

 

[Veedrac]

The seal is destroyed by the inrushing air. Its contents are then released and reappear in a volume around the (now-destroyed) seal. That volume is a sphere of 18.7m radius, interrupted by the ground so perhaps only a hemisphere etc.

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Radvic's calculations assume that the air is released into a vacuum. He mentioned the difference in this part,

Second, the assumption of "we can ignore the first atmosphere unsealed" by implosion seals is quite suspect. If we assume that the background is at 1 atm, suddenly the implosion seal gains a fair amount of power, since it's creating a large area of 2 atm (aka 300+ mph winds). This would sustantially increase the damage caused by an implosion seal, making a more accurate description of the damage it does to a forest "hundreds of trees were knocked down" rather than "dozens of trees were knocked down."

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This larger effect should be akin to SIN1.

Fixing this discrepancy would require a different method. I don't think it would be that hard to do, actually, like they could take only a fraction of the atmosphere, rated down to the wanted effects.