Blast Radius Calculator

Explosive Yield (\( W \)):

Scenario:

1. What is the Blast Radius Calculator?

Definition: This calculator computes the blast radius (\( D \)) of an explosion using the Hopkinson-Cranz scaling law, based on the explosive yield (\( W \)) in TNT equivalent and the scenario (fragmenting munitions, bare explosives, or restricted access).

Purpose: It is used in safety analysis, military planning, and engineering to estimate the safe distance from an explosion to protect people and structures.

2. How Does the Calculator Work?

The calculator uses the following Hopkinson-Cranz scaling equations:

For fragmenting munitions (public access): \( D = 634 W^{1/6} \)
For bare explosives: \( D = 130 W^{1/3} \)
For restricted access (no public): \( D = 444 W^{1/6} \)

Where:

\( W \): Explosive yield (g, kg, t, oz, lb, st, US ton, long ton of TNT);
\( D \): Blast radius (cm, m, km, in, ft, yd, mi).

Steps:

Enter the explosive yield (\( W \)) with its unit.
Select the scenario (fragmenting munitions with public access, bare explosives, or restricted access).
Convert the yield to base units (kg of TNT).
Calculate the blast radius using the appropriate formula based on the scenario.
Convert the result to the selected output unit and display \( D \), formatted in scientific notation if the absolute value is less than 0.001, otherwise with 4 decimal places.

3. Importance of Blast Radius Calculation

Calculating the blast radius is crucial for:

Safety Planning: Determining safe evacuation distances around explosive materials.
Engineering: Designing structures to withstand blast effects.
Military Applications: Assessing the impact of explosives in combat scenarios.

4. Using the Calculator

Example 1 (Fragmenting Munitions, Public Access): Calculate the blast radius for 1 tonne of TNT:

Explosive Yield: \( W = 1 \, \text{t} = 1000 \, \text{kg TNT} \);
Scenario: Fragmenting Munitions (Public Access);
Blast Radius: \( D = 634 \times (1000)^{1/6} \approx 634 \times 3.981 \approx 2524 \, \text{m} \);
Result (in meters): \( D = 2524.0000 \, \text{m} \);
Result (in centimeters): \( D = 252400.0000 \, \text{cm} \).

Example 2 (Bare Explosives): Calculate the blast radius for 1 lb of TNT:

Explosive Yield: \( W = 1 \, \text{lb} = 0.453592 \, \text{kg TNT} \);
Scenario: Bare Explosives;
Blast Radius: \( D = 130 \times (0.453592)^{1/3} \approx 130 \times 0.768 \approx 99.84 \, \text{m} \);
Result (in feet): \( D = 99.84 \times 3.28084 \approx 327.6 \, \text{ft} \).

5. Frequently Asked Questions (FAQ)

Q: What is the Hopkinson-Cranz scaling law?
A: It is an empirical method to estimate the blast radius of an explosion based on the explosive yield, using different scaling factors for various scenarios.

Q: Why are there different formulas for different scenarios?
A: The scenarios account for different blast effects: fragmenting munitions produce shrapnel, requiring a larger safety distance; bare explosives focus on the shock wave; restricted access reduces the safety margin.

Q: Does this calculator account for environmental factors?
A: No, this calculator uses simplified empirical formulas and assumes ideal conditions (e.g., no terrain effects, air density variations, or wind). Real-world blast radii may vary.