Considerations for Calculations of Heavy Armor for Ships

B. Hoyer, Berlin

Introduction

The following document is one of 18 reports that were presented at a 1943 symposium
on armor and projectile development that was held in Berlin. The papers that accompanied the
presentation were subsequently published in a secret issue of the journal Bericht 166 der
Lilienthal-Gesellschaft, with the British obtaining a copy in the immediate post-WWII period.
Bericht 166 was placed in the British Ministry of Supply files under the reference GDC 10/611
from TPA 3/T.I.B.. We are currently seeking the remainder of these documents because they
provide a far greater degree of insight into ongoing German R&D in the field of armor and
projectile developments than has been the case in many documents we have reviewed. Any
help you can provide in securing this report would help further numerous research efforts in
countless ways.

The Document translated below is entitled:

Heavy Armor Plates for Warships (Die Berechnung Schwerer Schiffspanzer). Hoyer, B. (1943).
OBERKOMMANDO DER KRIEGSMARINE BERLIN (GERMANY): Berlin. Germany.

We are very thankful to Ulrich Rudofsky for translating this document, which he did with
his usual competence and clarity. The document’s literal title is bit deceptive because it relates
far more too designing methods for calculating armor penetration than it does with the actual
layout of naval armor systems. We invite the interested reader to take note of the following
elements within the text that may be of interest:

1. The Germans were acutely aware of the immune zone concept and how to manipulate it to
good effect. In fact, most of the article is devoted to means of calculating the inner and outer IZ,
both with regards to shells that barely fail to penetrate, and those that penetrate intact. The
effects of ejected plugs and discs are seen as much less important than the effects caused by
the penetration of intact shells.

2. Mention is made several times the past and ongoing R & D on various pre-war armor
schemes and shell experiments, and this correlates well with what was presented in ADM
213/951. To date, every primary source document we have studied on German between-war
naval R&D reveals very active programs, and reference is made to experiments that could
further our understanding on a number of subjects.

3. A brief review is made to various foreign armoring schemes, including the “All or Nothing”
system. Apparently, the author found this system “primitive” but not without some advantages. A
similar review is made of projectile development, although here the many material and technical
variables involved militate against any absolute views being presented.

4. It is noted that a series of experiments were done at various obliquities to improve the
performance of German shells at incidence of impact greater that 30 degrees. This research
stands in very stark contrast to claims that no such testing was done by the “reactionary and
conservative” German naval R&D community. Indeed, an entire section of the paper deals with
these obliquity effects, although we need more details of the experiments that were conducted –
which may be found in other papers in this series.

5. Mention is twice made of decapping principles. In one case, we see this reference applied to
an initial layer of non-cemented armor that is useful in facilitating a shell’s subsequent
destruction via contact with an inner layer of tempered armor. This correlates very well with
experiments mentioned in ADM 213/951, and indicates that the Germans and Italians were very
much on the same track with regard to decapping in the early 1930s. In another reference, it is
noted that the external layer’s decapping ability will result in a loss of shell mass, although this
is dismissed from the rather quick and dirty formulaic approach that is taken toward deriving IZ
charts.

6. With regards to the outer armor layer used aboard German heavy ships, the author notes
post-penetration shell velocity effects very prominently in at least one section of the report.
Once again, this correlates very well with sections of ADM 213/951. Equal attention is given to
the energy required to defeat the external layer, and this invites us to examine the energy
dynamics that the Germans were considering in much greater depth. The velocity issue may
relate to fuzing concerns, but this is not explicitly stated. But the energy loss issue is a critical
factor to consider in a shell’s subsequent performance against the inner layer of the system.

7. Nothing is done with regard to working yaw and trajectory changes into the algorithms that
are used to develop the penetration curves. This is in marked contrast to some of the material
presented in ADM 213/951, which dwells on these subjects. The author notes that some may
take exception with his dismissal of decapping effects, etc., in his calculations, but he maintains
that the advantages in practical applications outweigh these nuances – at least based on his
body of literature.

8. The feedback at the end is interesting. The two competing means of addressing penetration
are presented as a detailed examination of the theoretical underpinnings of shell/armor
penetration dynamics and the use empirical formulae that are largely based on actual testing.
Each has certain advantages, and it is clear that this conference must have been a lively affair
between the theoretical and practical application devotees. In this respect, Hoyer is very much
in the practical camp – and perhaps at the extreme end of that group.

There are many other tidbits one will glean from this document, so let us now cut to the
chase.

George H. Elder.

2
 [Considerations for] Calculations of Heavy Armor for Ships

B. Hoyer, Berlin

In the course of the past few days, a great many formulas were presented to you in
several lectures that claimed to solve the problems of armor penetration on purely theoretical
grounds, and even by the employing exacting principles of physics. However, a closer look at
this will reveal that all these formulas somehow always contain a hidden empirical factor that
was derived from some sort of ballistic experiment. Furthermore, one notices that these
formulas are imbued with certain limitations by their creators. For example, we are asked to
accept that the projectile has no armor piercing cap and that its entire manufacture conforms
exactly to the projectile’s idealized type, from which a certain empirical factor was spun off.
Moreover, only homogeneous material is always and explicitly assumed for armor plate
[calculations]. But the terrible enemy does concern himself with these limitations, and even we
ourselves use homogeneous and hardened armor materials side by side, as well as projectiles
of most diverse types. In order to apply the presented formulas to practical problems, new tests
are indispensable to determine other empirical factors, and experimentation, again, will have the
final word.

Therefore, for problems of armor penetration, the Navy has always given preference to
testing, namely, tests on the actual original [materials or ships]. You are probably asking
yourself why the subject of this cont ribution is, “The calculation of heavy armor for ships”, and I
must admit that this title is not quite correct. The inherent meaning is much more closely related
to formulating a computational method that will take the earlier experimental data obtained at
the firing ranges, etc., and applying these results to the problems of today. Firing data that were
collected in many years of work at the firing ranges are systematically analyzed in order to apply
these results in the present task.

What sort of task this encompasses has already been briefly mentioned in the
introduction by Captain Meusemann. This primarily involves a problem of two ships engaged in
a battle, and the determination of the most advantageous distance, i.e., the most advantageous
range in which one’s own ship is relatively well protected, but at which there is an expectation
that a decisive hit could be scored on the enemy. In other words, the tactical foundation for the
conduct [behavior] of the ships in battle is to be established. However, the reverse case can
occur when tactical considerations take precedence over the implications indicated by actual
technical data. The underlying question most often concerns how much weight is available for
armor in a ship of a certain weight, after subtraction of the weights taken up by the propulsion
equipment (i.e., speed) and the artillery, in particular the turrets, in order to determine the
optimal distribution of the horizontal and vertical armor. I will get to the basic concepts of
“Horizontal and Vertical Armor” later, as well as the various parameters of armor design options.

The previously mentioned range in which one’s own ship is not in danger, is the so-
called zone of protection that is formed by the so-called zones of penetration, and these are
determined by the upper and lower penetration zone (Fig. 1: Zones of Penetration).

3
 Upper penetration zone.............distance =...
Lower penetration zone.............distance =...

Figure 1. Zones of penetration.

The sketch shows the cross-section of the main frame of a heavily armored ship. As a
typical armor arrangement, the usual distribution of German ships with vertical protection and a
[supporting] armored deck scarp [slope] was chosen. The two arrows indicate the preferred
aims of fire within the upper and lower zones of penetration. These two concepts can be best
understood in the following way. The opponent that fires at the ship with a heavy flat trajectory
gun at very close range would relatively easily penetrate the lateral protection, i.e., the heavy
vertical plate in the sketch, since he has at his disposal a very high terminal velocity and a very
advantageous impact angle. By increasing the distance, however, the terminal velocity
decreases and the angle of fall increases, i.e., the prerequisites for a penetration become less
likely, until, finally, no penetration will occur after crossing a certain limiting distance. The
distance from 0 to the limiting borderline distance is called the “lower penetration zone”. By
increasing the distance of the gun to the target even farther, nothing else occurs for a time. The
side-protection is hit with even more disadvantageous angles and, therefore, becomes
impenetrable. Hits upon the horizontal protection are still ineffective since the angle of fall and,
therefore, the angle of impact are still too small. By further increases in distance, the moment
approaches when the horizontal protection is penetrated as a result of the steadily increasing
magnitude of the impact angle. One can derive the upper penetration zone from this distance to
the maximal distance of the gun’s absolute range.

4
 Before I discuss the actual method of computation, I have to make several comments
about the various factors that have an influence on armor penetration (Fig. 2). Simply stated
[these are the variables]: the velocity at the target [impact velocity], the true [real] angle of
impact, the characteristics of the armor, and the characteristic of the shell. Although the mention
and consideration of these 4 factors may seem simply self-evident, I must, however, point out
that only the impact velocity on the target [Vz] and the impact angle need to be taken into
consideration in all armor penetration formulas. The actual characteristics of the armor material
are still considered in only a very few advanced formulas; while the quality of the shell and its
construction no longer appears in any formula. You will see in my subsequent demonstrations
how particularly important the consideration of these factors is.

Now let us discuss a few individual facts about each of these factors. The final velocity
of the projectile, i.e., the Vz (striking velocity at the target), at a given distance is ascertained
from the firing table. Naturally, the assumption is that this pertains to one’s own gun and one’s
own ammunition for which a firing table is available. Calculating the chances of the opponent
achieving penetration against our own ship is obviously a more difficult problem. At best, the
opposing gun’s Vo [muzzle velocity], shell weight, and shell’s approximate external
measurements are know from the foreign press or from reports by an informer. By assuming a
certain “i-value” [I believe this is a trajectory function defined by, amongst other variables, air
resistance (a function the shell’s cross-sectional area), initial velocity, shell mass, and shell
form. GHE] for the shell’s external ballistics, a firing table can be computed. In this manner, our
Navy has made graphic firing tables produced by the Friederich Krupp A.G. Company for
almost all foreign heavy naval guns.

= angle of fall of the projectile

= relative position angle of ship
K = angle of heel or roll
= angle of inclination of the armor belt
Schußtafel = firing table
Lage = relative position

Figure 2. Factors that affect armor penetration

5
 In addition to the velocity, the shell’s angle of fall on the target, i.e., the angle between
the projectile’s trajectory and the water’s surface, can by simultaneously derived. However, this
angle is only of interest to us in cases of direct hits against the horizontal protection. In all other
situations, the armor somehow lies angled in space [in one plane or another relative to the shell]
and thus the true impact angle of the projectile on the target must be obtained by considering all
other factors that influence the impact angle. These other influences are the ship’s relative
position angle (bearing), the ship’s angle of heel, and the angle of inclination of the armor itself.
The position angle is defined as the angle that is formed by the directional line of fire and the
opponent’s course (Fig. 3). It should be noted that sailors have a special set of designations for
these angles of position. He does not give this in terms of the position angle itself, but as its
deviation from 90º. The left ship A in the sketch has a position angle of 90º relative to the line of
fire and, therefore, its position is 0 degrees [1 dez = 10º] . The ship on the right, B in the sketch,
has a position angle of 60º, so its course is, therefore, “30º toward” [90º]. In other words, it [A] is
approaching [closing on] the opponent [B] on a course of 3 dez = 30º. A commonly occurring
error must be pointed out. Ships that are on a parallel course with each other do not always
have a position of 0 degrees. It is possible that ship A is approaching at as many degrees as
ship B is paying off. This is demonstrated in the lower part of the sketch.

Figure 3. Relative angle of position

The third influence on impact angle is the heel angle that is caused by the ship’s lateral
list. We leave it open whether the ship has a permanent list due to flooding or has a brief list
due to the ship’s inherent rolling motion.

The inclination angle of the ship’s armor is determined by the arrangement of the armor
plating. Most of the time, this angle concerns the armor belt’s outward inclination relative to the
water’s surface which is done in order to decrease the lower zone of penetration.

6
 All four angular influences must now be graphically or mathematically summarized in
order to determine the shell’s true angle of impact. This is calculated by using spherical
trigonometry formulas or with the aid of a nomogram. For practical applications, all firing tables
that contain penetration curves have such nomograms attached. Obviously, it is not certain that
such angular data will ever occur in a real battle. The purpose is to simply give the ship’s
artillery officer an opportunity to determine the proper orientation angle for his own ship relative
to an opponent’s before a battle commences.

Several more words are in order about the third factor, the armor properties. It was
already pointed out in the preceding lectures that there are a great number of armor application
possibilities between the strength grades of 50 kg/square millimeter and 200 kg/square
millimeter. It may calm you down, if I assure you that only a strength grade of 70 to 90
kg/square millimeters will be applicable to ship armor. Obviously, this applies only to
homogeneous materials, but we can also happily make this assumption, based on reliable
evidence, for the application of homogeneous material used by foreign countries. The
homogenous armor plate is used everywhere where one has to count on flat [point blank]
trajectory hits by heavy caliber shells, and an especially ductile [tough] behavior must be an
absolute requirement. In particular, homogenous armor is applicable in places where armor
plating is an aspect of the ship’s structural load-bearing integrity, especially the armored deck.
Earlier lectures have already demonstrated to you in great detail that armor quality is not
exclusively determined by tensile strength. I would like to point out to you that, in addition to
tensile strength, data for yield-point, elongation, compression [contraction], and notch strength,
there are no definitive and predictive measurements for the quality of the material’s behavior
under fire. Rather, each and every armor material has a specific ballistic behavior that very
often is not in absolute concordance with the technical material-testing data. I will discuss later,
in detail, the various options in the arrangement of a ship’s homogeneous armor plating. As a
reminder, I am showing you here Figure 4 of a 120 mm thick homogeneous plate, quality type
Wh, that was fired upon with a 33 cm armor-piercing shell at 30º. Except for the deep
indentation and imprint of the projectile’s cap on the plate, a further progressive reaction cannot
be observed.

Figure. 4. Firing tests on an 120 mm homogeneous plate

7
 In addition to this homogeneous material, the so-called KC material plays a major role in
the armoring of heavy ships (Fig. 5).

Figures. 5a and 5b. Firing test on KC plates

This KC material has been produced by carburization and face-hardening the outer
surface up to approximately 1/3 of the plate’s thickness, which adds considerably to its shell-
fragmenting properties. The tensile strength of the plate’s backside, similarly to homogenous
armor plates, amounts to 70 to 90 kg/square millimeter. An attempt to mathematically express
the behavior of such types of KC material by using data from materials testing is,
understandably, even more complicated than for homogeneous material. The scaling
[splintering] of the tempered layer on the front surface, shown in Fig. 5, provides a
demonstration of the random events that such a plate must absorb. However, it must be pointed
out that such splinter formations are merely cosmetic blemishes that do not affect the nominal
penetration limit of the plate. By contrast, of greater importance are the plate’s hardness
gradient, i.e., the type and mode by which the tempering layer diminishes with the thickness of
the plate, and if and to what extent there are stress fissures between the hardened and the
homogenous layers. The notorious lid formation that often occurs at the plate’s backside (Fig. 5
u = unten = below) has practically no influence on the penetration limit of such plates. One can
state that approximately half of all KC plates have the tendency for lid formation. It remains
uncertain which plates are prone to form plugs and which tend to form lids. The problem of plug

8
or lid formation has been the subject matter in many conferences and discussions, but it has
never been adequately resolved. If one disregards the fact that such lids could easily contribute
to destruction of a secondary nature, then this problem is not very pressing, since, as was
mentioned at the outset, the limit of penetration is not affected by lid formation.

Now, a few words about armor plate arrangement (Fig. 6). The simplest form that one
can imagine is a four-cornered box (left sketch: King George). This very primitive, but really not
so crude, arrangement is used almost exclusively by the Americans, and also the English, in
their most modern ships. Practically the same principle is demonstrated in the sketch on the
right, with the exception that the side armor protection is inclined inward to produce less
favorable impact angles as well as to add structural advantages to the ship. But it needs to be
pointed out immediately that this type of arrangement is rather unpopular among shipbuilders.

The third important feature (Fig. 7) is the side protection which has a slope [scarp]. This
arrangement is also frequently used in German ships because the scarp provides additional
protection when the vertical side protection is penetrated by retarding [slowing/deflecting]
projectiles and plate debris from damaging vital areas and by limiting flooding. Generally, the
scarp is made from homogeneous material that has the same thickness as the armored deck. I
will not discuss further armor layout options here since their mention would drag us into lengthy
considerations of shipbuilding and tactical subjects. I will just mention here the utilization of an
outer [external, preliminary] skin of armor plating for the purpose of de-capping the projectile in
order to induce disintegration of the unprotected projectile upon its contact with the tempered
main armor plate.

9
 Fig. 7. Armor-plate arrangement Fig. 8. Penetration curves

Curves = Plattenstärke = plate thickness.

X axis = Winkel = angle.
Y axis = Vz = striking velocity at the target.

In conclusion, let me say a few words about the characteristics of projectiles. The
projectile must be capable of penetrating hostile armor protection far enough and intact, so that
it can detonate in the ship’s interior. The explosive charge must be sufficient enough not only for
the disintegration of the shell itself and the destruction caused by its large shrapnel pieces, but,
in case of a hit on ammunition chambers, and shell storage areas, etc., it must be able to
contribute to the detonation of the ammunition stores. For this reason, a rather standard
projectile type has evolved for the 15 cm to 40.6 cm armor-piercing shell. The projectile has a
relatively short casing with a massive head and very thick walls. The charge is only slightly more
than 2% of the shell’s total weight. The shell-head radius measures 1.3 decimeters [13 cm]. In
tests, this rounding-off proved to be effective for shooting angles of between 60 and 45 degrees.
In principle, the sharp point is useful for vertical shelling and the blunt tip for oblique shelling. In
order to understand the magnitude of the shell tip form’s influence on penetration, the following
serves as an example. In vertical shelling, a 38 cm armor-piercing shell weighing approximately
800 kg does not have any greater effect than a 30.5 cm shell with a weight of 400 kg, because
the 38 cm shell has a head radius of only 1.3 decimeters while the 30.5 cm shell has a head
radius of 2 decimeters. The 30.5 cm armor-piercing shell is mentioned only in order to explain
the influence of an extremely slim tip. Otherwise, this is an obsolete shell as shown by it s
peculiar cap shape (Firth cap). Presently, the usual design consists of a broad cap with a
“saddle-seated nose”. However, the cap’s form has much less influence on penetration
efficiency than does the relative mass and type of hardening employed. The projectile’s shell
and cap have a tough core and a tempering of approximately 200 kg/square millimeters tensile
strength at the tip, i.e., on their surface. Tests have shown that the depth of tempering over the
entire circumference of the cap has a major influence on penetration efficiency. The purpose of
the cap in these projectiles is not only to protect the shell tip, as has been mentioned once in a
previous lecture, but, by virtue of its mass and hardness, the cap should also act like a
sledgehammer on the cemented and tempered plate and thus prepare the entrance for the rest
of the projectile. In addition, the tempered edge of the cap may aid in embedding the projectile
during an oblique shot and may even induce it to right itself.

The ballistic hood, presently made of Silumin [silicone-aluminum alloy], serves only an
external ballistic function [in flight] and is of no technical consequence in the actual penetration.
The goal of all recent experimental work for replacing Silumin with a substitute material, such as
sheet metal and pressure-molded materials [plastics], has been to overcome the deviating
[aerodynamic] pressures that occur at extremely level [flat] trajectories.

10
 It is self-evident that in addition to structural data, the quality of the material itself and
the quality of the tempering procedure are of decisive importance. This is even more important
for naval purposes, where there is an absolute requirement for a penetration that holds the shell
intact. Since conversions [necessitated by shortages] from the proven Cr-Ni-Mo steel to Mo-
free steel or even simply Cr steel, the difficulties in tempering such projectiles have grown
considerably. Despite the reduction in scarce materials, the penetrating power of the projectiles
was maintained according to previous standards. Fluctuations in the quality of shells used at the
frontline are reduced by appropriate ballistic acceptance tests. Whether similar quality control
could be expected from the opponent’s corner cannot be stated with certainty. However, from
investigations of French shells, it is apparent that considerable discrepancies in quality control
do occur.

Herewith, the various influences on armor piercing are sufficiently illuminated.

Obviously, a purely computational formulation incorporating the two latter parameters, i.e.,
influences of the kind of armor plate arrangement and the type and quality of shell, is simply not
possible. As mentioned at the outset, the Navy has instituted experimental procedures in its
place that will provide the missing empirical values by the actual firing of well-characterized
shells at well-characterized plates. This does not necessarily mean that for a specific armor-
plate combination, a corresponding full-scale model will be built and then fired upon. Rather,
data are compiled from [multiple] shots on individual plates from different angles, and finally,
representative graphs are prepared. It has been proven effective to summarize these firing data
in the format shown in Figure 8. [see above]

(The impact angle is used as the abscissa, the terminal velocity as ordinate, and the plate
thickness as the parameter). Such sets of curves are established by defining the penetration
limit for destroyed (Vg = “g” = gesprengt [?] = exploded or “g” may be “Grenze = limit or critical
or absolute limit) and intact (Vh = “h” = heil = intact, hale or sound) projectiles and by
supplementing the individual points by a compensating [extrapolating] calculation. I had
mentioned at the start that the Navy is interested mostly in the cases that show an intact
penetration [by the projectile]. Despite this fact, the sets of curves take into account the values
for disintegrated [shattered] projectiles, since these data will be required for subsequent
calculations, and because in individual cases (e.g., hits against the barbette) even a shattered
shell at the limit of its effectiveness may be of interest [due to the damage it can cause]. For a
better understanding, I have to explain to you the concepts of Vg and Vh. The value Vg is the
penetration limit for a destroyed projectile and it represents the velocity at which the energy of
the projectile is just about consumed during the penetration [attempt] of the target plate, i.e.,
when the projectile becomes stuck intact within the plate or when it breaks apart and an
approximately equivalent weight portion of shattered armor plate is deposited in front and
behind the plate.

Vh, i.e., the zone in which the projectile remains intact [hale, sound], is defined as the lowest
speed at which the plate is penetrated and the projectile is still barely intact. Therefore, the
difference between Vg and Vh is also a measure of the projectile’s durability and quality.

The previously mentioned normalization [compensation, equalization,?] of the single

firing data points was done according to a penetration formula devised by the Krupp firm. With
the aid of this normalization computation it is possible to use an individual graph with relatively
few firing data points. However, the supposition is that rather similar projectiles are used.
Obviously, after such a mathematical normalization [extrapolation] of the curves, values in
certain questionable places on the curve need to be verified by actual firing tests. The finalized
characteristics of the curves, as they are used for future computations, is thus settled, here
again, by experimentation.

Years of work have produced such sheets of penetration graphs for both types of armor
plates [homogeneous and face-hardened], as well as for all armor-piercing shells used by the
Navy. Furthermore, these curves have been established by mathematical interpolation for
foreign calibers and other projectile weights, so that there are penetration curves for practically
all available naval shells of German and foreign origin. The entire material has been
incorporated into a so-called Atlas of Penetration by the Krupp firm. This penetration atlas forms
the basis of all computations.

11
 Please, allow me to say a few words about the mathematical procedures. The question
about which plate thickness is penetrated by a given projectile at a given distance can be
readily answered by referring to the penetration curves. The impact angle and the terminal
velocity can be derived from the distance; therefore, the parameter for plate thickness
penetration can be obtained from the curves, possibly by interpolation. The reciprocal question,
namely, at what distance a given plate thickness will be pierced by a certain shell, can’t be
derived by this method, since from each curve for a defined plate thickness a multitude of
possibilities arises from taking into account the various combinations of terminal velocities and
impact angles. Only one of these combinations is possible to examine by use of the firing table.
In order to find this combination and, thus, obtain the limiting [critical] distance, a graphic
method must be applied (Fig. 9).

Starting with the firing table graphics, i.e., by entering the terminal speed (Ve) at a given
distance (E) in the curve, one obtains an intersect for the necessary velocity (Vnot) for
penetration from which the velocity limit is read off on the abscissa. The curve for the necessary
velocity (Vnot) is best obtained by determining several points using arbitrarily assumed
distances derived from the firing table and the penetration curve. When these points are
connected, a necessary velocity (Vnot) curve is obtained. The position [lay] of the Vnot -curve
will always vary depending on whether the determination being made involves the upper or
lower penetration zones (Figs. 9 and 10). Additional difficulties often are encountered in
establishing the lower penetration zone because the side protection occasionally consists of a
combination [composite] of armor plates. The penetration calculation of such armor plate
combinations, however, can be solved very readily, and in practice the energy requirement is a
sufficiently accurate factor. The necessary penetration energy is equal to the sum of individual
plates thickness in the combination and their relative angular positions and the necessary
energy for the marginal [critical] limit of the shot [Note: This is a greatly simplified approach].
This type of calculation makes the assumption that the energy consumed by the plate at the
marginal limit of the shot is equal to that energy which is consumed by a penetration of a plate,
with an arbitrary surplus being included in the calculation. The correctness of this assumption
has been verified by experiments. For this purpose, tracers were attached to the shells during
night-firing and the penetration was analyzed by photometric recordings from behind the plate.
The residual velocity was determined from the time-of-flight points, and the consumed energy
was then calculated retrospectively.

Fig. 9. Graphic determination of the limiting Fig. 10. Graphic determination of the limiting
[critical] distance [range]. (Upper penetration zone) [critical] distance [range]. (Lower penetration zone)

Ve = Terminal velocity
Vnot = Necessary velocity
E = Distance in hectometers
Eg = Limiting [critical] distance.

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 Furthermore, such a type of calculation could raise an objection, because during the
penetration of an armor-plate combination, the projectile’s cap may have been already knocked
off by the encounter with the initial [preliminary] plate and, therefore, the projectile may have at
least another weight and perhaps even a change in behavior [e.g., trajectory and yaw]. It should
be mentioned that the influence of this weight loss by de-capping is entered into the calculation
twice with opposing signs, and, thus, this error cancels out. The other possibility, that the
absence of the cap has an influence on the durability of the shell, only has some bearing,
especially when de-capping occurs while piercing an initial plate that is homogeneous, and then
encountering a hard-tempered plate. However, this case is extremely rare (pre-armor principle).
Generally, the shell has to pierce a tempered armor (belt) and then the non-tempered (scarp).
Comparative analyses between the results of calculations of energy input and experimental
firing against real targets also proved that this simple input is sufficient for practical purposes
[Note: This is a very fast and dirty way of doing these calculations].

Upper penetration zone (40.6 cm armor-piercing shell, weight = 1,030 kg)

E 1 2 VI VII Vnot Armor plate arrangement

hm Grad Grad Grad m/s m/s m/s

250 22 22 22 198 > Vo -
300 29 29 29 158 585 604
350 37 37 37 120 415 432
330 34 34 34 130 468 486

Lower penetration zone (40.6 cm armor-piercing shell, weight 1,030 kg)

150 10 68 40 365 378 581

200 15,5 62,5 45,5 390 315 501
250 22 58 52 420 265 497
300 29 51 59 480 232 533

E hm = distance [range] in hectometers

Grad = omega angle of fall of the projectile in degrees
1 Grad = alpha 1 angle in degrees
2 Grad = alpha 2 angle in degrees
VI m/s = velocity I meters per second
VII m/s = velocity II meters per second
Vnot m/s = velocity necessary meters/second
Lage = position

Fig. 11 Determination of limiting [critical] distance [range] (Example)

13
Fig. 12 Graphic determination of the limiting Fig. 13 Graphic determination of the limiting
distance (both penetration zones) distance (optimal triangular scarp
configuration)

Geschoß:…….Shell: 40.6 cm armor piercing shell, L/ 4.4, weight: 1030 kg

Obere Zone = upper zone
Untere Zone = lower zone
Schutzzone = zone of protection
dez = 10º
Vg = velocity at which the projectile fractures on impact

In conclusion, let us examine a brief example (Figs. 11 and 12). For a battleship with
inclined side-armor made of 300 mm KC, a scarp of 150 mm Wh and an horizontal protection
consisting of an upper deck and an armored deck of 50 + 150 mm Wh, the zone of protection is
to be calculated for relative bearings of 0 degrees, 20º, and 30º. The necessary computations
for the upper and lower penetration zones are shown in Fig. 11 and the ancillary curves for the
determination of the penetration zones are shown on Graph 12. At a position of 0 degrees, the
resulting zone of protection is in the distance range of = 260 hm to distance = 334 hm. It is
clearly seen how great an influence the angular position has. At 20º, the zone of protection is
increased almost two-fold (in terms of distance), and at a position of 30º, no penetration at all
can occur at the lower zone of penetration.

Furthermore, this kind of graphic presentation is not only a good method to determine
the limiting distances for a given combination of armor, but it gives a good overvi ew of the
general aspects regarding the effectiveness of an armor protection scheme. Please, allow me to
give you another brief example. A basic analysis of the formation of the scarp triangle is shown
in graph, Fig. 13, i.e., the optimal relationships of thickness between the armor belt and the
scarp.

The Vnot [velocity necessary for penetration] for a combination of 300 mm KC + 150
mm Wh lies lower than the Vg [velocity when shell breaks up without penetration] at a passable
battle distance. Therefore, the combination [of plates] is still penetrated above 300 hm. A re-
enforcement of the scarp by just 60 mm, however, tips the scale of the curve into the region of
shorter distances so decisively upward that the Vnot curve for the combination of 300 KC + 210
Wh lies already above the Vg curve at all distances. In other words, a scarp triangle that

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consists of 300 mm KC and 210 mm Wh (below 80 degrees against the horizontal plane) is
secure against any hit by a 40.6 cm armor-piercing projectile weighing 1030 kg.

Unfortunately, my time is up and I cannot give you further examples. Suffice it to say to
you that these methods have been able to answer all questions that have arisen from practical
experience.

Nevertheless, even the Navy tried, at least in their certain subsections, to replace
empiricism with scientifically exact calculations. Various attempts were made, but during the war
such scientific work had to be dropped completely because of shortages in personnel and time.
However, this is justifiable, because the necessary documents [manuals] for answering any
really practical questions are already at hand. Naturally, the intention to resume these scientific
labors later is self-evident, probably after the war is over and when sufficient personnel are
again available. It is hoped that even the numerous materials alluded to here, which are based
on many years of comprehensive efforts and experimentation, will provide valuable assistance
to the future scientific endeavors. The Navy will naturally be glad to provide these documents to
other offices which are engaged in similar research.

Discussion

Gercke: In support of the “empirical” penetration formulas that have been communicated in
several lectures and whose deficiencies various speakers have pointed out, the following
comment is made. Their great utility lies in the fact that they facilitate the establishment of
penetration curves for a certain caliber’s test results and allow the additional extrapolation for
the incorporation of other calibers and certain controls; namely, the more [data], the larger the
scope of validity. Formulas that have a high degree of validity can be established, as in the case
of the penetration tests by the Navy, when only one shell type and only few plate types are dealt
with. Therefore, it was possible to summarize, in a single penetration formula, the entirety of
armor firing tests that used 15 to 40.6 cm armor-piercing shells against homogenous as well as
KC plates. Therefore, the complete data for the individual calibers could be combined in graphs
as a single unified system, which now permits the incorporation and extrapolation of test results
as characteristics for the development of penetration curves of other calibers for subsequent
ballistic calculations, and, thus, provides a saving in firing tests. With regard to the question of
the calculations for armor penetration, basically two methods need to be differentiated. One
way, starting with a simple physical concept of the penetration process, is to develop a
computational procedure as Burkhadt has proposed; the aim of his end-result could state
[penetration characteristics]: given a shell drawing and the material specifications of the shell
and plate [it impacts]. Then, the calculation may perhaps investigate the marginal [critical] limit
of the penetration velocity for various impact conditions as well as the influence of related
variables, e.g., projectile shape. The alternate way of calculating armor penetration would start
with the establishment of empirical formulas; if developing of relevant empirical expressions can
be accomplished from purely mathematical interpolation formulas in which the physical behavior
of the controlling parameters, such as material specifications or the projectile’s shape, appear to
be very carefully considered. Then, the final goal cannot result in obtaining a generally
applicable penetration formula, but at best a set of formulas, each of which is valid only for a
certain shell and plate type.

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