Adding Brode's Method to the Explosion Yield Calculations Page

[Flashlight237]

I have made calcs using Brode's Method, which have been met with approval through various calc members, so I think it's a good idea to add it in. I'm pretty much the first Calc Group member to extensively use the method even. I think a case should be made for using Brode's Method.

See, all explosion formulae are approximations rather than anything absolute, which I don't think the wiki seems to really take into consideration. What would matter more is where the approximations are used. The current "air explosion" formula uses a formula used specifically for nuclear explosions, which I'm pretty sure is deprecated thanks to NUKEMAP, while the ground explosion formula, which works well enough as a ground explosion formula and is used in UN documentation, assumes that all explosions are hemispheres consisting of air. Fiction has plenty of ways to tell you how wrong that logic is.

Is this a hemisphere?:

Is this a hemisphere?:

Are these hemispheres?:

If explosions can appear as oblong ellipsoids, plus signs, or even Pac Man ghosts (bear in mind Minecraft explosions are programmed in the form of rays in a cube, not spheres) then there's a good chance that our current explosion methods are flawed.

Brode's Method, however, works around these flaws. Brode's Method takes volume, a universal concept among all shapes, and gas composition (blimps have helium) into account AND has applications for both air and ground explosions. Brode's Method works like this.:

E=((P2-P1)*V)/(γ-1) Where:

• E is the explosion energy in joules
• P1 is starting or ambient pressure
• P2 is the burst pressure
• V is the volume of the gas
• γ is the heat capacity ratio of the gas in question (1.4 for air)

And comes with a provision for ground-level explosions:

"When the explosion occurs at ground level, the calculated value of the energy is conventionally multiplied by 2 to take into consideration ground effects, like the reflection of the shock wave"

-The Italian Association of Chemical Engineering, 2013

However, I feel that there is work to be done in this regard. Two sources put pressure in bars: https://onlinelibrary.wiley.com/doi/pdf/10.1002/9780470925287.app2
https://www.aidic.it/cet/13/32/023.pdf (This one shows overpressure in relation to both burst pressure and distance at least, but doesn't seem to show how it's calculated).

Whereas the guy who originally proposed the method to the wiki used pascals: https://vsbattles.com/threads/brodes-method.150036/

Which admittedly had thrown me off and pretty much means I have to go back and fix every calculation I've done that uses the method. I think the forum member who originally proposed Brode's Method used Study.com as a reference. Fortunately, one of the two sources provided the original source of the formula, which is here: https://pubs.aip.org/aip/pfl/article-abstract/2/2/217/858419/Blast-Wave-from-a-Spherical-Charge (DOI:10.1063/1.1705911)

Problem is the article is paywalled, and who the hell would pay $40 for an article they're only gonna use for a forum thread?

But yeah, once we work out how to work Brode's Method in as a third explosion yield calculation method, we should be good in regards to calculating explosions regardless of shape and composition.

 

[KLOL506]

Pretty sure this was tried already and DontTalkDT rejected it here.

 

[KLOL506]

@DontTalkDT

 

[KLOL506]

Also, regarding the pressures used, I found these two comments.

 

[DontTalkDT]

Are you intending to use the formula for explosions like you posted or for pressurized vessels?
Because for explosions like you posted it kinda doesn't work, as you need the pressure of the gas before the explosion happens (that's P2) contrary to the overpressure of the shockwave. (which is what our usual explosion formulas use)

Like, fairly sure Bodes method is in fact just an approximate calculation of the work necessary to compress an ideal gas. (and if that doesn't happen in a container it's an overestimation)
In that context I'm fairly sure the volume would also not be the volume of the shockwave or fireball (i.e. the explosion parts you see), but the volume of the explosive.

 

[Flashlight237]

Are you intending to use the formula for explosions like you posted or for pressurized vessels?

The former, but I'm willing to accept the latter too.

Because for explosions like you posted it kinda doesn't work, as you need the pressure of the gas before the explosion happens (that's P2) contrary to the overpressure of the shockwave. (which is what our usual explosion formulas use)

Like, fairly sure Bodes method is in fact just an approximate calculation of the work necessary to compress an ideal gas. (and if that doesn't happen in a container it's an overestimation)
In that context I'm fairly sure the volume would also not be the volume of the shockwave or fireball (i.e. the explosion parts you see), but the volume of the explosive.

See, when writing this, I had acknowledged half-way through, I literally had to Google "burst pressure vs overpressure" just to figure out what the heck went up and I was left with more questions than answers. And yet, using what we got with both the current formulae and Brode's method, that's where things got a little tricky. See, under the formula used for nuclear explosions, I got this for a 100-meter-radius explosion.:

(0.1/0.28)³/1000=4.555393586*10^-5 megatons of TNT

Which equates to 45.554 tons or 190.598 gigajoules. Not dividing by two because I'm treating this explosion like a nuclear explosion and not the usual brand of incendiary explosions we go for.

Yet with the UN formula, we get something like this.:

100^3*((27136*1.37895+8649)^(1/2)/13568-93/13568)^2=80.3684356986 tons of TNT

Which is 336.262 gigajoules.

Yet under Brode's Method assuming the burst pressure is just 20 psi over 1 atm, this is what I got.:

100^3*π*4/3/2=2094295.102 m³

Which results in this:

(239220.146-101325)*2094295.102/(1.4-1)=7.220172961*10^11 joules

With one of the sources saying it's the weakest formula out of four used. It's less which one's an overestimation and more the formulae we either have or find hardly bore consistent results.

 

[DontTalkDT]

See, when writing this, I had acknowledged half-way through, I literally had to Google "burst pressure vs overpressure" just to figure out what the heck went up and I was left with more questions than answers. And yet, using what we got with both the current formulae and Brode's method, that's where things got a little tricky. See, under the formula used for nuclear explosions, I got this for a 100-meter-radius explosion.:

(0.1/0.28)³/1000=4.555393586*10^-5 megatons of TNT

Which equates to 45.554 tons or 190.598 gigajoules. Not dividing by two because I'm treating this explosion like a nuclear explosion and not the usual brand of incendiary explosions we go for.

Yet with the UN formula, we get something like this.:

100^3*((27136*1.37895+8649)^(1/2)/13568-93/13568)^2=80.3684356986 tons of TNT

Which is 336.262 gigajoules.

Yet under Brode's Method assuming the burst pressure is just 20 psi over 1 atm, this is what I got.:

100^3*π*4/3/2=2094295.102 m³

Which results in this:

(239220.146-101325)*2094295.102/(1.4-1)=7.220172961*10^11 joules

With one of the sources saying it's the weakest formula out of four used. It's less which one's an overestimation and more the formulae we either have or find hardly bore consistent results.

The problem with that is that I think you are not using Brode's formula right. (I have to admit that I'm not 100% sure how the formula happens. I always end up with a mole factor too much when trying to derive it. But from the explanations in the documents it looks like it to me)
The pressure you are looking for is not 20 psi (which isn't the burst pressure) and the volume you are looking for isn't 100^3*π*4/3/2.

The volume you are looking for would be the volume of the bomb (before it detonates) and the pressure you are looking for is the pressure that is building up in the bomb before the shockwave starts. Which is a simplified assumption, because obviously explosion and expansion starts at the same time and stuff.

Like, a good case to use it, in my understanding, would be the explosion of a pressure cooker. Like, say you take a pot like that, fill water into it, and put it on the stove to boil. At some point the pressure in the pot becomes too large and the pot explodes.
That would probably be well calculated using Brode's law. In that case, the volume isn't the volume occupied by the resulting shockwave. It's the volume inside the pot. And the pressure isn't the overpressure of the shockwave, but the burst pressure of the pot (i.e. how much pressure the pot can hold before being destroyed i.e. the pressure inside the pot right before the explosion).
So, regular pressure cookers can withstand at least 1 bar more than regular pressure, likely more. And its volume may be 8 liter or so. So P2 - P1 = 2 bar - 1 bar = 100000 pascal.
8 liter = 0.008 m^3.
E=(100000*0.008)/(1.4-1) = 2000 J

Doing the same for, say, a bijuu dama would be hard.
The volume you would want to look at is probably the volume of this ball, rather than of the explosion:

​

But how exactly you would figure out what the pressure inside that chakra ball is I have no idea.

 

[Antvasima]

Thank you for helping out, DontTalk.

 

[IdiosyncraticLawyer]

@Flashlight237

 

[IdiosyncraticLawyer]

@Flashlight237 @Antvasima This thread appears to be rejected, so we should close it unless Flashlight is interested in making any new arguments.

 

[Flashlight237]

Nah, I accepted it at this point.

 

[IdiosyncraticLawyer]

Nah, I accepted it at this point.

Okay, I'll have this closed.

 

[Antvasima]

I have closed this thread.