Can the Heat Radiation Formula Enhance Magical Fireballs in Tabletop Gaming?

[gibberingmouther]

How much radiant energy is released by a regular TNT explosion? Is radiant heat just emitted from the fireball? Once again, this is for my tabletop game.

I found a formula that calculates the temperature of gas in the shockwave front from the overpressure. Would that include radiant energy? The heat of the fireball is mostly just kinetic energy of gas particles, right?

 

[member 656954]

Hi gibberingmouther,

It's not quite what you're asking for, but have you checked out the https://nuclearsecrecy.com/nukemap/ calculator?

It includes a 'Thermal radiation radius' that you can set for various levels of burns, and shows the radius at which this would likely occur. Closer to the detonation, thermal radiation is the least of your problems, and further out the radiant energy would not produce that level of burns. I dropped an atomic bomb in my novel 'Guardian' and this, with some research on how bombs explode and various YouTube video examples, gave me a good feel for the effects the protagonist encounters.

Cheers,
Tghu

 

[jrmichler]

I have run across the number of 2000 BTU per pound of high explosive several times. That would be total energy released, I don't know how much of that would be radiant heat. Since the explosion consists of the material (solid TNT) suddenly converting to gas with energy release of 2000 BTU/lb, you could estimate the temperature of the fireball. Maybe somebody else here could estimate radiant heat from fireball temperature.

Partial data point: My dad once poured a pound of black powder on the ground and set it off. He said it was a good thing that he was ten feet away, or he would have been seriously burned.

 

[member 656954]

Lees' Loss Prevention in the Process Industries (Fourth Edition) might help with your deliberations:

"9.24.2 Decay Relations for Specific Hazards
Decay relations can be obtained from the simpler hazard models for fire, explosion, and toxic release, as described by Poblete, Lees, and Simpson (1984) and Lees, Poblete, and Simpson (1986).

The intensity of heat radiation from a fireball is:

$F= \frac E {4πr2}$

where E is the heat radiated (kW), F is the heat radiated on the target (kW/m2), and r is the distance (m) from the center of the fireball to the target."

A kg of TNT produces 4.612 MJ which methinks should be 4612 kW, and you can refer to https://www.nist.gov/el/fire-research-division-73300/firegov-fire-service/fire-dynamics to determine the radiant heat effect based on the size of your explosion and distance away. Noting of course, that ambient conditions - smoke, fog, trees, etc. - will mitigate the energy transfer.

 

[essenmein]

Lees' Loss Prevention in the Process Industries (Fourth Edition) might help with your deliberations:

"9.24.2 Decay Relations for Specific Hazards
Decay relations can be obtained from the simpler hazard models for fire, explosion, and toxic release, as described by Poblete, Lees, and Simpson (1984) and Lees, Poblete, and Simpson (1986).

The intensity of heat radiation from a fireball is:

$F= \frac E {4πr2}$

where E is the heat radiated (kW), F is the heat radiated on the target (kW/m2), and r is the distance (m) from the center of the fireball to the target."

A kg of TNT produces 4.612 MJ which methinks should be 4612 kW, and you can refer to https://www.nist.gov/el/fire-research-division-73300/firegov-fire-service/fire-dynamics to determine the radiant heat effect based on the size of your explosion and distance away. Noting of course, that ambient conditions - smoke, fog, trees, etc. - will mitigate the energy transfer.

The equation just takes the total quantity E and divides it by the surface area of a sphere, so the quantity could be anything, energy, power, weight etc. Then TNT, like any chemical potential source, produces fixed energy per volume or weight, not power, the power would be determined by how quickly that energy is released, and i bet that all the energy in TNT is released a whole lot faster than 1 second so the instantaneous power would be very high, which is why its so destructive, it puts a lot of energy in something very quickly. So energy in TNT is ~4.2kJ/g, but if that were released in 1e-3 second then the power is 1000x this value.

Then a lot of the energy in an explosion is in the pressure wave, not radiated heat, I've done some reading on nuclear explosions and in some ways that's conceptually easier to think about, at time = 0 some mass is turned into energy, mostly in the form of light (gamma, xray etc), which then gets adsorbed in the immediate air which is super heated and then rapidly expands and rises (classic double flash, shock wave mushroom cloud), so hilariously in space they are just a blink of bright light with little of the physically destructive force we see in an atmosphere (or solid for that matter), I can't remember the exact proportions of heat energy/pressure energy/radiation but seem to remember the thermal output in the form of IR was surprisingly lowish, like 10-20%.

 

[gibberingmouther]

Thank you Tghu, jrmichler, and essenmein! This is all potentially useful information, especially the heat radiation formula.

I finished the first draft for my game manual. After that I have made some changes and the biggest one is for the magic section. The heat radiation formula could be useful for standard magical fireballs in particular.