How to calculate fire feats.
Step 1: Finding the temperature of the fire[]
First, you need to find the temperature of the fire. The temperature of the fire can be estimated by its colour. You can refer to this table.
- Red
- Just visible: 525°C
- Dull: 700°C
- Cherry, dull: 800°C
- Cherry, full: 900°C
- Cherry, clear: 1000°C
- Orange
- Deep: 1100°C
- Clear: 1200°C
- White
- Whitish: 1300°C
- Bright: 1400°C
- Dazzling: 1500°C
- Blue: 1649°C
Step 2: Finding the density of the fire[]
Fire, like air, obeys the ideal gas law, meaning that it's density depends on its temperature. For that, you can use this calculator to figure it out.
For pressure, input 1.103 Bar for sea level. Specific gas constant of air is 287.05 J*kg*kelvin. Then input the temperature of the fire and you'll get the density of the fire.
For example, a 900°C fire would have a density of around 0.3 kg/m^3.
Step 3: Finding the mass of the fire[]
Next, you need to find the mass of the fire. This step is extremely simple. You just have to find the radius of the fire either by pixel scaling, angular scaling or other methods, and find the volume depending on what shape the fire is. Usually the fire would be the shape of a sphere or a cylinder, and the formulae are 4/3πr3 and πr2h respectively.
Then you simply have to multiply the volume by the density of the fire in order to find the mass of the fire.
Step 4: Finding the yield of the fire[]
Then, you can just calculate it like a normal temperature-changing calculation, using the equation E=m*c*ΔT.
- E is the energy, which is the result you are trying to find
- m is the mass, which have found in the third step
- c is specific heat capacity, which is 919 j/kg for air
- ΔT is change in temperature, which is the temperature of the fire you found in step 1 deducted by the original temperature. Usually you can assume this to be 16°C, the average global temperature.
Alternative Method[]
An alternative method would be to calculate the energy released by the fire. Fire releases 418 000 Joules of energy per 32 grams of oxygen, or 13 062.5 J/g of oxygen.
In this case, first you have to figure out the temperature of the fire just like the first method, as well as the volume of the fire.
However, you have to multiply the volume by 20.95%, since that's the percentage of oxygen in the air.
Then you can use the same calculator in Step 2 to find the density of oxygen at the temperature of your fire. However, this time, the partial pressure of oxygen is 0.230527 Bar since it is 20.9% of air; and the specific gas constant is 259.8 J*kg*kelvin.
For example, oxygen for a 900°C fire would have a density of around 0.08 kg/m^3.
Then, you multiply the volume by the density to find the mass of the oxygen for the fire.
After that, you multiply the mass of the oxygen (in grams) by 13 062.5 to find the energy released by the fire.
Durability From Tanking A Fire[]
We can use this calculator to find the conduction heat loss rate. Although the result is in Watts, this is good estimate of a character's durability from tanking a fire.
The average human body surface area is 1.73 m^2.
The average thickness of the human skin is 3 mm.
Human skin has a thermal conductivity of around 0.209 W/m°C.
Normal skin temperature is about 33°C.
Plugging in all these numbers as well as the temperature of the fire, you can find the durability required to survive a fire.
For example, a human surviving a 900°C fire would result in around 104 493.73 Watts, or Wall level durability.
Note: If the character tanked the fire for less than a second, you have to multiply the result by the amount of time he was covered by the fire. However, if the character tanked the fire for more than a second, there is no need to multiply the result by the time.
Maximum internal energy intake[]
If an object is heated it usually doesn´t get hotter than the source of the heat. If the object is as hot as the heat source the energy itself emits to its surroundings should be equal to the energy it is infused with. That means there is a maximum amount of thermal energy an object can take in through a certain source of heat.
Therefore, if the value you calculated is higher than the maximum internal energy intake, you should just use the maximum internal energy intake as the durability of the character.
In order to calculate this energy you need to find out how much energy will be necessary to heat the object to this temperature, from the point that it has no internal energy. For this you can just use the formula E=m*c*ΔT. In this case, c would be equal to 3470.
For example, assuming a 900°C fire (which is 1173.15 K) and an ideal body weight of 62 kg, the maximum internal energy intake would be:
3470*62*1173.15 = 252 391 491 Joules, Small Building level