Armour Piercing Projectile Penetration Calculator

Historical Background

Armour piercing projectile penetration has been a critical concern in military technology, particularly in tank warfare and naval battles. Since the 19th century, methods to estimate projectile penetration have evolved. Two prominent models include the Krupp formula, developed by the German arms manufacturer Krupp, and the DeMarre formula, often used by French military engineers.

Calculation Formula

Krupp Formula: \[ Penetration_{Krupp} = 100 \times \frac{V \times \sqrt{M}}{2400 \times \sqrt{\frac{C}{100}}} \] Where:

• \( V \) is the velocity in m/s
• \( M \) is the mass in kg
• \( C \) is the caliber in mm

DeMarre Formula: \[ Penetration{DeMarre} = P{ref} \times \left(\frac{V}{V{ref}}\right)^{1.4283} \times \left(\frac{C}{C{ref}}\right)^{1.0714} \times \left(\frac{M}{C^3}\right)^{0.7143} / \left(\frac{M{ref}}{C{ref}^3}\right)^{0.7143} \] Where:

• \( P{ref} \), \( C{ref} \), \( M{ref} \), and \( V{ref} \) are reference values for penetration, caliber, mass, and velocity.

Example Calculation

For a projectile with a caliber of 100 mm, mass of 10 kg, and velocity of 800 m/s, using the Krupp formula, we calculate: \[ Penetration = 100 \times \frac{800 \times \sqrt{10}}{2400 \times \sqrt{\frac{100}{100}}} = 333 \text{ mm} \]

Importance and Usage Scenarios

This calculator is vital for military strategists and engineers designing armored vehicles and ammunition. It helps estimate whether a given projectile will penetrate an armored target, aiding in both offensive and defensive planning. It is widely used in tank warfare analysis and naval gun design.

Common FAQs

1. What is the Krupp formula used for?

   • The Krupp formula estimates the penetration of armor-piercing projectiles based on velocity, mass, and caliber.

2. How does the DeMarre formula differ?

   • The DeMarre formula is more complex, factoring in reference values for velocity and caliber to estimate penetration, and is widely used in artillery analysis.

3. Can these formulas be used for modern ammunition?

   • While these formulas provide historical estimates, modern armaments may require more advanced modeling due to the use of composite and reactive armor.