So I'm going to not set it at Force 6, as that might have effectively killed everyone. I will choose F3 instead. Anyway, the idea is to take all the air in the spell's area of effect and condense it into a very small area, where it will be under very high pressure. Then Jovan releases the spell, and the overpressurized air explodes outward, a lot like a thermobaric bomb (but with no fireball, just the shockwave).
If it's ok with you, pbangarth, I'd like to request a Logic + Physics roll in place of a Logic + Demolitions roll in this case , since I'm creating a physical (not chemical) explosion. Maybe boosting the rating 1 for every two or three hits, as it's a knowledge and not an active skill roll? For F3, I found a default damage value of 10 (rounded up from 9.89)P.
Anyway, here are the relevant rolls: Magic 4 + Power focus 4 + Spellcasting 3 = 11d6 =
. He is condensing it into a sphere of radius 0.1 meters.
. So Jovan takes 1S.
In case anyone cares about or is able to check my math, I've included it here (I'm actually not an expert in this at all, which is why it took me so long to update this). The basic idea was to find the pressure exerted by the spell to condense the air, convert that pressure into the energy released when it explodes, convert that to kg of TNT (for which we have a Rating value in Arsenal), and then use that to find the DV.
radius r = Force meters
volume V = 4/3*pi*r^3
standard temp and pressure: T = 273.15 degrees K, p = 100 kPa (14.504 psi)
Using Boyle's law, which states that p_a*V_a = p_c*V_c (where a = atmospheric and c=compressed),
p_c = p_a*V_a/V_c = n*R*T_c*V_c
However, the temperature would not change from the compression, because the atoms themselves have not absorbed any extra energy. So T_a = T_c.
Under these conditions, neglecting heat transfer, the compressed pressure would thus be 2.1599 x 10^7 kPa.
Taking into consideration heat transfer, if we assume adiabatic compression (no heat is transferred out of the system of air shaped by the spell),
then we use the heat capacity ratio / adiabatic index for air as an exponent, i.e. P*V^gamma = constant. The adiabatic index for air is 1.401.
Using this method, P_a*V_a^gamma = 100 kPa * 904.8^1.401 m^3 = 1.387 * 10^9.
After compression, then, P_c*V_c = P*0.004189^1.401 m^3 = 1.387 * 10^9, so P = 2.975 * 10^12 kg/m s^2 = 2.975 * 10^9 kPa. About 1/182 of the pressure
inside a nuclear bomb, and 7.8 times the pressure inside the Earth's core.
Using the Brode equation (
that I looked up here) as a rough approximation, the energy of the explosion is thus
E = (P_c - P_a)*V_c/(gamma - 1) = (2.975*10^9 kPa - 100 kPa)*0.004189 m^3 / (1.401-1) = 3.108 * 10^10 Joules = 31.08 GJ.
One ton of TNT = 4.184 GJ.
So if we assume adiabatic compression and expansion, then a F6 Shape Air spell condensing a sphere of air to a 0.1 radius sphere and then releasing it
would be energetically equivalent to 7.42 tons of TNT.
If we are more generous (or, like pbangarth, are a clever GM looking for ways to keep players from creating ridiculously powerful weapons out of creative applications of magic to physics) and assume that the resident mana screws with heat transfer by absorbing extra heat, and use the more conservative
2.1599 * 10^7 kPa, then using the Brode equation again, E = 2.256 * 10^8 Joules = 0.2256 GJ. This then converts to 0.053919 tons of TNT, or 48.914 kg of TNT.
This would convert to a damage value of approximately 27, using the demolition rules with TNT.
Let's reduce the force for this, as I really don't want to destroy the entire parking lot with us inside. Let's try Force 4.
That reduces the volume of shaped air to 268.08 m^3. Let's maintain the 0.1 m radius, so V_c remains at 0.004189 m^3.
So now the conservative compressed pressure is 100 kPa * 268.08 m^3 / 0.004189 m^3 = 6.3996e6 kPa. The Brode equation gives
E = (6.3996*10^6 kPa - 100 kPa)*0.004189 m^3/(1.401-1) = 0.06685 GJ, or 14.49 kg of TNT.
That would convert to a damage value of 3.806*4 = 15.22 = 15.
With F3, that affects a volume of 113.097 m^3, so the conservative compressed pressure becomes 2.6999 * 10^6 kPa. Then
E = 0.0282 GJ = 6.114 kg of TNT. Converts to 9.89 (9 or 10) damage.