ExplosionModels

Class for computing the explosion and deflagration models.

class casex.explosion_models.ExplosionModels[source]

This class implements a model for the lethal area for an explosion, the lethal thermal area for explosion as well as deflagration, and the size of a deflagration fireball (which is also considered lethal).

The main sources for the models are [1], [2], [3], and a brief review of explosion and deflagration is given in Annex F [4].

The models are all based on TNT equivalent mass, since this is how the literature does it. This means that for any of the models it is necessary to convert the fuel amount to a given TNT mass which has the same energy density.

static TNT_equivalent_mass(type_of_fuel, fuel_quantity)[source]

Compute the equivalent mass of TNT for a number of fuels.

Compute the amount of TNT in kg equivalent in energy density to a given type of fuel. This value is used for the explosion and deflagration computations.

Available types of fuels are:

Fuel type

Energy density

Mass density

TNT

4.184 MJ/kg

–

Gasoline

46.4 MJ/L

0.75 kg/L

Diesel

45.6 MJ/L

0.83 kg/L

Jet A1

43 MJ/L

0.80 kg/L

AvGas

44.7 MJ/L

0.69 kg/L

Methanol

19 MJ/L

0.79 kg/L

LiFe batteries

1.8 MJ/kg

–

LiOn batteries

0.8 MJ/kg

–

Liquid hydrogen

142 MJ/kg

–

Liquid butane

27.8 MJ/kg

–

Note

The above values are drawn from a variety of sources of unconfirmed reliability. As such, these are the authors’ best guesses at appropriate values.

Parameters

  • type_of_fuel (enums.FuelType) – The type of fuel.

  • fuel_quantity (float) – [L] The amount of fuel.

Returns

TNT_mass – [kg] TNT equivalent mass.

Return type

float

static fireball_area(TNT_mass)[source]

Compute lethal area for fireball (deflagration).

Compute the size of a fireball for a given amount of propellant. The model is found in [2] page 62.

Note

See note for lethal_area_explosion.

Parameters

TNT_mass (float) – [kg] The equivalent TNT mass for the propellant.

Returns

area – [m^2] Size of area of fireball.

Return type

float

static lethal_area_explosion(TNT_mass, K=7.14)[source]

Compute lethal area for explosion.

Determines the lethal area for an explosion. The model used is

\[A_{explosion} = \pi D^2\]

where \(D\) [m] is the distance from the explosion, where it is no longer lethal. It is given as

\[D = K W^{1/3}\]

where \(K\) [m/kg \(^{1/3}\)] is a scaling factor for the acceptable risk and W [kg] is the TNT equivalent mass [1], [2], [3].

A recommended value for the scaling factor for 3.5 psi overpressure is 18 ft/lb \(^{1/3}\) (also called K18, for unprotected persons), which is equal to

\[K = 7.14~\mathrm{m/kg}^{1/3}\]

in SI units. For details on this value, see [1].

Note

The area given by the used model assumes a near-perfect combustion of the fuel, which typically requires a close to ideal mixing of fuel and oxidizer. As this normally do not happen during an aircraft crash, the model tends to be rather conservative in the estimate of the lethal area. For more detail on this, please consult Annex F [4].

Warning

The model for lethality caused by explosions has not been deeply investigated, and the model is provided as is, with references to it origin. Ultimate responsibility for determining the lethal area at an explosion rests with the user.

Parameters

  • TNT_mass (float) – [kg] Equivalent TNT mass to the explosive material. Use TNT_equivalent_mass to determine this value.

  • K (float, optional) – [kg/m^(1/3)] Scaling factor for acceptable risk (the default is 7.14).

Returns

area – [m^2] Size of the lethal area, which is in the form of a disc.

Return type

float

static lethal_area_thermal(TNT_mass, p_lethal)[source]

Compute lethal area for thermal radiation (deflagration).

Computes the lethal area for deflagration based on the thermal radiation. Model is taken from [2] page 61.

Note

See note for lethal_area_explosion.

Parameters

  • TNT_mass (float) – [kg] The equivalent TNT mass for the propellant.

  • p_lethal (float) – [-] A number between 0 and 1 indicating the target lethality.

Returns

area – [m^2] Size of lethal area.

Return type

float

1(1,2,3)

Department of Defense. DoD Ammunition and Explosives Safety Standards: General Explosives Safety Information and Requirements (DOD 6055.09-M, Volume 1). Technical Report, 2012.

2(1,2,3,4)

John A. Ball, Michael Knott, and David Burke. Crash Lethality Model - Report no. NAWCADPAX/TR-2012/196. Technical Report, Naval Air Warfare Center Aircraft Division, 2012.

3(1,2)

Meredith J. Harwick, John Hall, John W. Tatom, and Robert G. Baker. Approved Methods and Algorithms for DoD Risk-Based Explosives Siting. Technical Report, DDESB, jul 2009.

4(1,2)

JARUS. JARUS guidelines on SORA - Annex F - Theoretical Basis for Ground Risk Classification. Technical Report, 2022. JAR-WG6-QM.01.