>>508311997>>508311704>>508311566>>508311405Projectile Mass (Mp): 13,607.76 kg
Projectile Diameter (dp): 0.762 m
Nose Shape Factor (Np): 1.14
Concrete Compressive Strength (fc'): 34,473,800 Pa (equivalent to 5,000 psi)
Impact Velocity (V_imp): 730 m/s
Intermediate Constant Calculation (C):
The constant C for the NDRC formula is calculated as:
C = 3.8 * 10^-5 * Np * (Mp / (dp * sqrt(fc')))
1. Calculate the square root of concrete strength:
sqrt(fc') = sqrt(34,473,800 Pa) approx 5871.4385 Pa^0.5
2. Calculate the term (Mp / (dp * sqrt(fc'))):
(13,607.76 kg) / (0.762 m * 5871.4385 Pa^0.5) approx 3.0429 kg/(m * Pa^0.5)
3. Calculate the constant C:
C = 3.8 * 10^-5 * 1.14 * 3.0429 approx 0.00013192
Step-by-Step Calculation for Penetration Depth (x):
The formulas used are:
Impact Function (G): G = C * (V_imp / dp)^1.8
Penetration Depth (x): x = dp * (G + 1) (used when G > 1)
1. Calculate the ratio (V_imp / dp):
(730 m/s) / (0.762 m) approx 957.9921 s^-1
2. Calculate (V_imp / dp)^1.8:
(957.9921)^1.8 approx 344,484.0
3. Calculate the Impact Function (G):
G = 0.00013192 * 344,484.0 approx 45.44
4. Calculate the Penetration Depth (x):
Since G approx 45.44 (which is greater than 1), we use the formula x = dp * (G + 1):
x = 0.762 m * (45.44 + 1)
x = 0.762 m * 46.44 approx 35.38 meters
Final Result:
The calculated penetration depth for an impact velocity of 730 m/s is approximately 35.38 meters.
This is being very generous. I used the highest impact velocity I could find (basically Mach 2). This also assumes 5000psi concrete. Higher strength materials such as granite and, well... Stronger concrete would dramatically decrease penetration.