Elongation of Homogeneous Armor

[lwd]

I did a quick review of his documentation yesterday and he did make a number of statements about the nose shape being a significant source of discrepancies from his formula. He didn't seem nearly as worried about up scaling.

[Thorsten Wahl]

It has often emerged that official range tables and documents like GKdos100 incorporated extrapolated, estimated, or computed data (as opposed to validated empirical data).
B

report 166 Lilienthalgesellschaft processes at shelling of armor plate Berlin May 1943
Lecture B. Hoyer "Calculation of heavy ships armor"
process of creation of pentration curves
experiment -shelling of armor plate
graphical comparison of single points of pentration with calculation formula

"The decision on the final shape of the curves is based on experiment."
"Questionable data are proven by additional shelling."

Graphs for foreign shells were established by mathematical interpolation of known data.

[RobertsonN]

This approach (GKdos100) based on experimental data for the shell in question and interpolation seems sound. Although it will not produce exact results for all ranges and inclinations, like a formula does, the fact that derived values are bounded by experimentally obtained data means that major errors are improbable.
Scaling or extrapolation, especially over two orders of magnitude, is more prone to error. M79APCALC seems idealized: shells are considered to be "unbreakable and non-deforming". However, for oblique impact, both moments and shear forces were great, and there is a lot of research material on this in, for example, the RN archives for the early post-war period. It is also the case that a shell might have deformed elastically during penetration but still be recovered whole and undeformed afterwards. In addition, M79APCALC is based on an almost solid shot (a tracer but no burster), which would likely increase its penetrative capabilities. The Germans were not interested in solid shots (they might not disable a tank) and were much concerned about fuzes not working (probably because of shell deformation) in the similar sized 88 mm antitank shells.
The calculations which show the Iowas to be vulnerable at the top of the Class B belt were probably done with M79APCALC. Accordingly, while there was probably some vulnerability here, it was likely to have been a good deal less than that predicted by M79APCALC.

[RobertsonN]

A feature of the GKdos100 penetration curves that has always slightly surprised me is that they stop at an obliquity of 20 deg or slightly more (about 70 deg in US usage). From the current discussion, I surmise this was the highest obliquity for which the Germans obtained consistent results. The only counter information I know for this is in Brenneke which says that tests were carried out on Wh at 15, 30 and 60 deg obliquities.
Nathan Okun in his famous analyses of the Hood and Bismarck used Gkdos100, not M79APCALC. On rereading his Bismarck analysis, I was struck at the point where he says he extrapolated the GKdos100 curves up from about 20 deg obliquity to 10 deg. Thereby he obtained the claimed short range vulnerability zone at 15600 yards.
I believe that the future of inquiry into WWII battleships lies in the study of historic research into major calibre shells and armor. Quite a lot, especially on RN and German work, is already in the public domain on the Internet, placed there by enlightened individuals. Perhaps there are other untapped sources, especially American. Comparison of penetration values is especially difficult because there were so many different kinds of penetration. For example, the RN seemed to include simply making a hole in the plate, with complete rejection of the shell, as penetration. Perforation was the term they used for the shell more or less penetrating whole.
Work on 3 in solid shot, while undoubtedly highly relevant to tanks, does not seem the way forward. I do not believe there is any all-in-one formula for penetration of everything from bullets to 80 cm shells, of widely differing characteristics. That would be too good to be true.

[alecsandros]

I believe that the future of inquiry into WWII battleships lies in the study of historic research into major calibre shells and armor. Quite a lot, especially on RN and German work, is already in the public domain on the Internet, placed there by enlightened individuals...

A quote from another part and another time of the forum:

"The first of these is well understood, and the 'discussions' -- if that is the proper word -- therein would involve more elucidation than arguement.

The second, which essentially involves the detailed prediction of energy dissipation and conversion during high-energy (sometimes multiple) impacts, is much less-well understood and -- regardless of the quantity of discussion -- is likely to remain fairly opaque. This is largely because our understanding of most of these sorts of phenomona remains what might best be described as 'semi-empirical', i.e. based upon the quantification of experimental results. Unfortunately, because very few systematic experiments were conducted, certainly to modern standards, there has been little-to-no differentiation of variables and hense very little upon which to base an equation set, even if it were assumed that a closed-form equation set exists, which is unlikely.

There have, of course, been large numbers of systematic experiments with relatively small caliber projectiles of more recent design, and theory in these areas is relatively well established, though often difficult of access due to security restrictions. There never was, and there is now never likely to be, a large accumulation of measured data on large-caliber nearly solid projectiles impacting heavy plate arrays at what would now be called moderate-to-low velocities. It is possible, and perhaps most probable, that such impact sequences will be best studied via the application of high-speed finite analysis dynamic computer programs employing numerical integration, but these remain (as before) difficult of access, and are -- sadly -- also at their root largely semi-empirical in nature. What this means is that the variables in the equation sets in such programs have been 'tuned' in order to permit the program to produce results which in effect 'mimic' the results of testing. In the absence of a large test-derived empirical data set to begin with -- which is unlikely to accumulate in the case of large-caliber impacts, etc. -- then even the best of these are unlikely to provide more than approximations of reality.

It's sad but true that we are unlikely, at least within the forseeable future, to be able to reconstruct with much validity the post impact phenomena associated with early Twentieth Century naval combat. The theory to understand projectile/target interactions was not clearly developed while the technology was in use and, as the hardware of both ships and projectiles of this era has slipped into the past and is no longer available for study, accurate reconstruction of what 'might have happened' is difficult or impossible. Further, as the years slip away, it becomes increasingly clear that the 'motherlode' -- the "King Tut's Tomb"-- of contemporary data on these subjects, which many felt was just hidden away in some archive somewhere, never really existed in the first place.

Bill Jurens"
Unfortunately, I slowly began accepting Bill's perspective...

[RobertsonN]

Thanks for this wisdom. Looks like a basically first principles type approach is out of the question.
However, a more limited piecemeal approach might be instructive. The problem is to make comparisons between different country's ships using entirely historic data and formulas, to include all the armor tests done. For German ships one would need to start from the Gkdos100 curves. These include empirical data and implicitly contain the protective value the Germans found for their armor. Using this and a historic armor penetration formula used by one (preferably both) of the countries concerned, together with the ballistic data for the foreign gun, one could scale for mass, velocity and inclination angle to find the penetration of the foreign gun. Comparisons could be made using different historic formulas. This approach would probably be more reliable for the various European 15 in guns as they were nearest to the German 15 in gun.
For the RN, I don't know of an equivalent for Gkdos100 but the period of immunity tables used by the RN could be used, with the proviso that the RN had discovered by 1946 latest that their deck penetration figures were optimistic. Here the value of the British vertical armor as found empirically by the British is automatically included. Of course, questions related to head shape, structural integrity, yaw, etc. would not be included, but neither are they apparently in other approaches.
Such an approach would be less ambitious than that attempted for at least 30 years now, but it would include all the historic empirical data, with the protective value of the armor included as actually found by the country in question. The scope for national bias, in selecting the starting off point or the values of particular constants, would seem less.

[lwd]

Thanks for this wisdom. Looks like a basically first principles type approach is out of the question.....

I suspect that at some point in the not too distant future it may become possible. There are tremendous strides being made in both the theory and the computer codes to model such interactions. A problem of course is that much of the work is classified and access to the codes is rather limited. I wouldn't be surprised however to hear say 10 or 20 years from now some one with access to the programs using the data points we have as references develops some very accurate tables. I wouldn't be surprised if they didn't either though.

[alecsandros]

The problem is to make comparisons between different country's ships using entirely historic data and formulas, to include all the armor tests done. [....]

Such an approach would be less ambitious than that attempted for at least 30 years now, but it would include all the historic empirical data, with the protective value of the armor included as actually found by the country in question. The scope for national bias, in selecting the starting off point or the values of particular constants, would seem less.

Such programs already exist. Bill Jurens developed one, Nathan Okun another. There are others, also, usualy confined to USN's specialists.

The problem is that the outputs of the programs can not be verified in reality. They can only be fine-tuned so that they produce *expected* results, in accordance with the tests that *had been done*.

The *tested* interaction between large caliber shells and variuos types of face-hardened or homogenous armor plates varies alot, and definitive full-scale tests can not be performed anymore.

Small-scale tests are not optimal for estimating large-shell impacts, as the smaller shells behave differently than the larger ones, both in pre and post-penetration trajectories and expected probabilities.

Thus, what can be done (and is already done) is to take the empirical data and "guess-match" it to the computer algorithms. The margin of uncertainty is large, probably between +/- 5-15%, and thus it hardly provides a meaningfull result.

[An example: the Japanese 460mm gun wasn't tested against US, RN, KGM or any other WW2 navy plate armor except that of IJN.
The shells had a softer AP cap than most contemporaries, and the armor plates deployed by the IJN also had "softer" faces, ranging mostly from 480 to 520 on the Brinell scale, if I remember. The only empirical tests of 460mm shells, if they were done, were done against this type of armor. The question: how would the same shell behave against a high-hardness armor plate, such as German KC n/A or US class A, given the softer cap ?

Yes, elaborate calculus can be done, but in the end the calculus can not be proved, because we simply lack the necessary hardware to test it.]

[delcyros]

SCALING caused by to low %elongation as evidenced in GKdos-100 curves comparing 20.3cm and 38cm L4.4 APC for 0.5cal thick Wh plates is not -as previously believed- a constant factor depending on diameter and %elongation difference.
We stumbled around this problem recently trying to verify Nathan Okuns SCALING formula for adjustments in plate Quality compared to very ductile US STS using the same GKdos-100 curves he used to establish this phenomen.
The GKdos-100 show a positive scaling at low obliquity but it's appearently highly dependent on obliquity and becomes an inverse factor at high obliquity, making SCALING preferable if You expect large calibre hits at high obliquity, f.e. deck hits.

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