Pyrotechnics | The Energy of Fireballs:
E = (π/6)D³p/(γ-1)
"Explosions" by Dr. Saxton (physicist) outlines one method to estimate the magnitude of certain weapons by quantifying the visible fireball they produce with:
E = (π/6)D³p/(γ-1) where E is energy in joules, D is fireball diameter in meters, P is pressure (101325Pa), and y = 1.4 for the diatomic mix of Earth's atmosphere[¹]. This approximates the energy content of the fireball itself but doesn’t account for any other effects in an explosion. The heat energy of the visible fireball isn't useful in explosive demolition or armour-penetration and is, therefore "waste energy" in regards to fulfilling these roles.
Heat energy:: is the initial total detonation energy of an explosive, much of which is converted into mechanical work in military explosives
Mechanical work: describes the more useful destructive energy that makes an explosive effective in demolitions or armour penetration. Mechanical energy is expressed in an explosion through shock waves & the kinetic energy of fragments or projectiles.
Fireball energy estimates: do not account for any mechanical work and represent a fraction of an explosives total energy.
Table A1 approximates fireball energy content in Joules (J) from E = (π/6)D³p/(γ-1) for fireballs between 1 meter and 40 meters in diameter. A tenfold increase in diameter corresponds to a thousand times increase in energy content.
A1: Fireball Energy
T"The determining factor in the conversion of the heat of explosion into mechanical work is the amount of product gases available for expansion. In the case of TNT, 10 moles of gas are produced for each mole of explosive. We can exploit this fact to make predictions about the actual explosive strength of other chemicals. This is known as the Berthelot approximation[...]
The relative explosive strength calculated in this manner is of limited use. What is really important is the actual strength which can only be measured by experiment. There are a variety of standard tests, most of which involve a direct measurement of the work performed. Here are some example measurements for RDX:
Ballistic mortar test: 140 %
Trauzl block test: 186 %
Sand crush test: 136 %
[...]all of which compare favourably with our Berthelot approximation." - Introduction to Naval Weapons Engineering: Chemical Explosives[²]
Blaster-artillery-weapon (BAW) systems are dial-a-yield for effect. Anti-personnel fire is generally provided through sustained barrages of lower-energy blasts, wherein each discharge yields a casualty radius of several meters but does not inflict significant damage to the surrounding environment. Full power bombardment is reserved for the destruction of heavy armour & fortified structures.
Larger 20m - 40m (65′ - 131′) fireballs
The proliferation of 20-meter through to 40-meter explosive fireballs denotes a capacity to harness multi-gigajoule scale energy-yields.
The estimated heat-energy-content of larger fireballs generated TIE fighter laser cannons & MTT blaster cannons peak at around 10 gigajoules.
This approximation is corroborated by estimates based on anti-materiel firepower in the destruction of metal walled structures & rock asteroids[¹].
As noted, the approximated energy-content of a visible fireball does not account for the energy of shock-waves, heated-shrapnel and destructive anti-materiel effects in solid material, nor does it consider any melting or vaporisation.
Smaller ≤10m fireballs
"The initial expansion of an explosion follows the power-law rule of the Sedov solution. This behaviour ends when the fireball is affected by the pressure of the ambient medium, such as the planetary atmosphere in the case of explosions on the ground. Ultimately the fireball slows and stops expanding at a point where its internal pressure matches the external pressure. A measurement of the volume of the fireball at this isobaric stage gives an estimate of its heat energy content.
The pressure of a gas is p=nkT, where n is the number of particles per unit volume, k is Boltzmann's constant, and T is the temperature. The internal energy per unit volume is u=p/(γ-1), where γ is the adiabatic index, a constant depending on the nature of the gas particles. For monatomic gas or plasma, γ=5/3; for the principally diatomic mix of the Earth's atmosphere, γ=1.4. The total heat content of a spherical fireball of radius r or diameter D is therefore E = (4π/3)r³p/(γ-1) = (π/6)D³p/(γ-1).
Assuming that the explosion expanded from a well-defined point, with negligible mixing with external material or energy sources, then the estimated fireball energy is a lower limit estimate of the yield of the weapon that created the explosion. The remainder of the energy may heat or transmute the non-gaseous debris, or may propagate away in other forms: sound and shock waves, emitted light, neutrinos (in the case of nuclear explosions), gravity waves (for very violent stellar events).
Note that there must be an ambient medium in order for the fireball's expansion to halt in a temporary condition of pressure equilibrium. Such a medium may be air, or perhaps the pressure of a background magnetic field (a complicated topic). In open space, the Sedov solution (with its inherent deceleration in expansion) proceeds until the excess heat of the fireball is entirely radiated away, or until some other external influence comes into play."
- Curtis Saxton, astrophysicist
STAR WARS Episode VII: The Force Awakens:(TIE fighter laser blast)
STAR WARS Battlefront II (MTT laser blast)
STAR WARS Episode II: Attack of the Clones (AT-TE cannon blast)
STAR WARS: Episode VI: Return of the Jedi (AT-ST laser blast)
STAR WARS Battlefront (AT-ST laser blast)
STAR WARS Technical Commentaries: Explosions (external link)
Introduction to Naval Weapons Engineering - Chemical Explosives (external link)