Pentration formulas (I think)

[Borys]

Ahoj!
I think P3D likes stuff like this:
http://www.bobhenneman.info/forum/viewtopic.php?t=505&postdays=0&postorder=asc&start=0
Q: What is the formula for calculating the effective thickness of inclined armor? That is, how do you find the equivalent thickness in vertical armor of, for example, a 15in plate inclined 20 degrees?


   

A: Maybe Bill Jurens can speak on this with authority. I did this simulation on a CAD program. The actual idea is a right triangle with the 90 degree angle on the outside hull and the hypotenuse being the path the shell travels. A 20 deg tilt on 15 inch armor equals 15/Cos (20) = 16 inches. Doesn't seem like much but if the shell is hitting at an angle of 20 degrees, then it sees 15/cos(40) = 19.5 inches in the path of travel. A shell hitting vertical armor at a 20 degree angle only "sees" 16 inches of armor. If you read Mr. Juren's article on armor and guns, you will get an appreciation of what constitutes good armoring.

A: There are no really reliable closed-form solutions to allow for obliquity effects, as a great deal depends upon differences in the quality and geometry of the armor and the attacking projectile. Some projectiles are nominalized for best penetration at 0 degrees obliquity, i.e. normal impact, whereas others are nominalized to perform best when striking at an angle.

As a rough rule of thumb, one might use the formula V1 = 1/[ ((L^2) +2000) / cos L ] to estimate the penetration velocity relative to that required at zero degrees obliquity, i.e. normal impact. The formula is designed so that the normal impact velocity, Vo, is always 2000 f/s. Thus, for an angle of obliquity of 20 degrees, ( L^2) +2000 = 2400 and cos L is 0.93969. 2400/0.9397 = 2554, and the velocity ratio, V1, is therefore equal to 2554/2000 =1.277. Therefore, if the projectile just penetrated at 1700 f/s at normal obliquity, the penetration velocity at 20 degrees would be equal to roughly 1700 x 1.277 =2170 f/s.

If you work this out, the multipliers become roughly:

0 deg = 1
5 deg = 1.016
10 deg = 1.066
15 deg = 1.152
20 deg = 1.277
25 deg = 1.448
30 deg = 1.674
35 deg = 1.969
40 deg = 2.350
45 deg = 2.846
50 deg = 3.500
55 deg = 4.380
60 deg = 5.600
70 deg = 10.088
80 deg = 24.190

These figures are certainly not gospel, but are probably good enough for 'back of the envelope' calculations and first-cut approximations. Getting closer would require a good deal of rather specific information about the exact geometry and chemistry of the plate that was being attacked, the exact geometry and chemistry of the projectile attacking that plate, and probably some test results to use in calibration. There are many other formulas that give similar, but not necessarily more accurate, results. This formula does not discriminate between face-hardened and homogeneous plate; in practical terms differences are likely to be relatively small. One has to start somewhere...

[P3D]

Penetration roughly scales as V to the 1.4th power for homogenous plates. Effective thickness for an inclined plate should be multiplied by 1/cos(alpha)^2.8.

However, the NaAB program I am using for the calculations shows a smaller inclination effects.