Explosion Speed Calculations

The timeframe in which an explosion, which was caused by an explosive, expands a certain distance can be used in order to figure out a timeframe used to calculate the speed of a character.

In which cases can it be used?

In order to use this method to determine a timeframe the explosion has to be caused by a explosive, in other words by a reactive substance that contains a great amount of potential energy that can produce an explosion if released suddenly, usually accompanied by the production of light, heat, sound, and pressure.

That means that explosions caused through things like supernatural powers, lasers, lightning etc. can not be calculated using this method.

In order to get a result one will require a way to figure out the weight of the explosive used, determine or make a reasonable guess on the type of explosive used and figure out how far the fireball or blast wave of the explosion expanded in the timeframe.

Step 1: Making a guess on the type of explosive

The typical types of explosives one would see in media are C4 and TNT (Trinitrotoluene).

C4 is a type of plastic explosive, which can be freely formed like clay, usually comes in cuboid shaped packages and requires a detonator to explode.

If C4 isn't stated or something very similar to it is described or shown it usually is best to assume TNT is used.

Step 2: Determining weight of the explosive used

The weight/mass we determine through the following methods will be our "charge weight".

Method 1: Volume and density

If the explosive (bomb, or similar) is visible this method can be used. For it one first has to scale the volume of the explosive.

In order to then figure out the mass one has to multiply the density of the explosive with the volume.

Usual density of TNT is 1.654 g/cm³

Usual density of C4 is 1.72658 g/cm³

One should be careful to use the correct dimensions.

Method 2: Typical sizes and density

Explosives might appear in characteristic sizes.

A package C4 for example typically is 2 inches by 1.5 inches and 11 inches long, weighing 1.25 lb (0.57 kg).

If only the typical volume, but not the typical weight is known one can figure out the weight using the density, like in method 1.

Method 3: Relation to fireball radius

This is the least secure method and should only be used if the other two aren't possible.

The relation between fireball size and weight is:

D = 8.5 x W^0.341 

Where W is the weight of the explosive in pounds and D is the diameter of the fireball in feet.

If this method is used the type of explosive should be assumed to be TNT.

Step 3: Scaling radius of explosion

Next we want to figure out the radius the explosion extended to during our timeframe. Note that the timeframe starts at the point the explosion starts and not sooner.

In order to do so we just use the usual scaling methods.

One should pay attention that we are strictly speaking scaling how far the shockwave expanded, not the fireball. So if possible the extension of the shockwave should be estimated. Since that often is not feasible for short distances it is assumed that the fireball extents with the shockwave, if we talk about fireballs at larger expansion distances this can not be assumed anymore.

The result of the scaling of the radius is our "range".

Step 4: Figuring out the timeframe

For finally getting the timeframe we will use this calculator.

For the "Explosive Type" we will choose the one we guessed in Step 1.

For the "Charge Weight (kg)" value we will use the weight/mass estimated in Step 2. Keep in mind to convert it to kilogram before use.

One thing that might be necessary here is to convert "free-air data" to "surface data". The calculator calculates the explosions in terms of an explosion at the surface, which means a hemispherical explosion which at one side is restricted by the ground. Because of that if an explosion happens in the air or generally expands in all directions without being restricted at one side, the weight of the explosive has the be halved in order to account for that.

For the "Range (m)" value we will use the explosion radius determined in Step 3. Keep in mind to convert it to meter before use.

Then we click "Calculate Blast Parameters" and get a list of calculated values.

The only value interesting for us is "Time of Arrival (ms)". That value is the timeframe we wanted to determine. Using that one can calculate the speed of things that happened in the time the explosion expanded to the used range. Take heed that the value is in milliseconds (ms) and has to be converted to seconds before in speed in m/s can be calculated.

1 ms = 0.001 s

Additional Note: The "Shock Front Velocity (m/s)" value can be useful for certain cases as well, but keep in mind that it is the velocity of the shockwave exactly at the given range. It quickly drops with distance from the origin of the explosive so that constant speed of the shockwave based on that value shouldn't be assumed.