On the Origins of Scaling

Discussions about the history of the ship, technical details, etc.

Moderator: Bill Jurens

RobertsonN
Member
Posts: 171
Joined: Wed Jan 05, 2011 9:47 am

On the Origins of Scaling

Post by RobertsonN » Fri May 17, 2019 9:11 pm

Summary

Scaling is the feature of armor penetration curves which show a reduced critical velocity with increase in calibre for given T/D (plate thickness/shell calibre) ratio. Scaling is a feature of the penetration curves given in Gkdos100. Nathan Okun attributed this scaling to a reduced ability of Wh plates to resist shells of increasing calibre due to their lower value of elongation compared with some contemporary types of armor. Herein, I attribute this scaling, at least in part, to an inherently better capability of larger calibre shells to resist breakage and thus to require less of an increase in striking velocity to penetrate compared with a perfect unbreakable and undeformable shell.
The breakage mechanisms of shells at angle attack were described by Gercke in the USNMTE (1945). This mechanism demonstrates an inherent scaling in favour of large calibre shells although Gercke does not mention this. Furthermore, the axial breakage mechanisms occurring in and near normal attack, including shock-induced shatter and secondary inertia-based shatter, also turn out to demonstrate scaling to the favour of large calibre shells.

Neil Robertson
Last edited by RobertsonN on Fri May 17, 2019 11:04 pm, edited 2 times in total.

RobertsonN
Member
Posts: 171
Joined: Wed Jan 05, 2011 9:47 am

Post by RobertsonN » Fri May 17, 2019 9:55 pm

Angle Attack: Breakage Mechanisms and Scaling

On p. 93 of the USNMTE Gercke wrote:

'Because of the stresses caused by the transverse forces the projectile must be given a hardness gradient from the nose to the base in order to withstand them. In order to limit the value of M1 [the moment of force causing the initial turn away from the normal], the length of the projectile must be short, 4.7D being the maximum.'

'(a) In order to reduce the axial shock on the shell a penetrative cap is fitted and the hardness of the head of the shell is held below a certain limit in order that the projectile may penetrate whole. The figure was fixed at 57R^C for 7.5 and 8.8 cm. They held the opinion that the critical velocity did not increase with head hardness, but that the shell was more likely to break up and instead of a v^h [critical velocity for intact penetration] a v^g [critical velocity fpr broken penetration] would be obtained. If the hardness is too low the G^D value will increase [on p. 74 there appears v = G^D where v = v^h where D stands for Durchschlag, meaning perforation]. Gercke remarked that by increasing the hardness they could have lowered the critical velocity but the shell would have broken up and given a v^g but the Heereswaffenamt would not accept this and insisted on the shell being fit to burst behind the plate.'

'(b) The motion caused by M2 [M2: the moment of force causing the later turn to the normal] stresses the shell much less if the centre of gravity is near the point. This points to the advantages of short heads and especially the hemispherical head for angle attack.'

To reduce the chances of breakage and thus limit the velocity required to penetrate the Germans kept to relatively short and therefore light shells, and they avoided abrupt changes in hardness on the surface of the shell. They were also aware of the advantages of shells with hemispherical heads.

The above is for smaller calibre army shells but the general points made also apply to larger calibre navy shells. There was a trade-off between having a very hard head for normal attack and a gradual exterior hardness profile from point to base for angle attack. Consider a graph of exterior hardness against distance along the shell from point to base. Compare curves for, say, 8.8 and 38 cm shells. The range of hardness is similar for the two but the hardness range is expanded by a factor of 38/8.8 = 4.3 for the 38 cm shell. The hardness profile for the 38 cm has a significantly more gradual fall-off than the 8.8 cm. This means that on attacking plates of the same T/D the larger shell shows a lesser tendency to break in the mid-body region and can according penetrate whole at lower velocities than the 8.8 cm. Also the 38 cm shell can accommodate some increase in head hardness for normal attack while still being better than the 8.8 cm at angle attack. This is exactly scaling.

Neil Robertson
Last edited by RobertsonN on Fri May 17, 2019 10:29 pm, edited 1 time in total.

RobertsonN
Member
Posts: 171
Joined: Wed Jan 05, 2011 9:47 am

Re: On the Origins of Scaling

Post by RobertsonN » Fri May 17, 2019 10:20 pm

Normal Attack and Scaling

At normal attack it is axial forces causing compressive failure that endanger the shell including shock-induced shatter and inertia-induced shatter sometimes called secondary shatter as it occurs later than shock-induced shatter provided that it has not happened. With shock, shock waves caused by the impact move back into the shell and are reflected back when they reach the boundary of the shell or a region of abrupt change in material properties within the shell. When they arrive back at the impact point the sudden increase in stress induces the shell to shatter. When it is appreciated that the velocity of shock waves in a metal are a given value then it is seen that as shell calibre increases, so does its length and the time for the shock waves to arrive back at the front of the shell. This means that for larger calibres there is more time for the armor plate to break first and thus release the build-up of stress in the shell so that then the shell does not break. Accordingly, this process again shows a scaling that favours penetration of a given T/D ratio by larger calibre shells at a lower critical velocity than for smaller shells.

In the case of secondary shatter, the head of the shell is crushed between the armour plate and the inertia of that part of the shell the point can 'feel', which is determined by the speed of sound in steel. The speed of sound in steel is a given value. Larger calibre shells are longer so it takes longer for a given fraction of a larger shell to make its presence felt at the nose. This means the nose becomes progressively less stressed for a given time after impact with increasing calibre. A longer span of time is required before the stress at the point of the shell becomes high enough for shatter to occur. Again, this means that breakage of the armour plate is more likely to happen before the shell shatters so that then the stress on the shell is released allowing it to penetrate whole. This is another example of scaling.

Neil Robertson

User avatar
Alberto Virtuani
Senior Member
Posts: 3321
Joined: Mon Jul 08, 2013 8:22 am
Location: Milan (Italy)

Re: On the Origins of Scaling

Post by Alberto Virtuani » Tue May 21, 2019 10:05 am

Hi Neil,
thanks for this very detailed explanation of "scaling" benefits vs shattering of a shell.
I beg your pardon in advance if I ask a possibly stupid question, not having studied in detail the armor penetration theories.

I have read that a smaller caliber shell needs less energy to penetrate the same armor plate than a larger caliber shell (oversimplifying, the larger shell needs to destroy a larger part of the plate to fully penetrate while the energy is proportional to the mass and to the square of the velocity).

In case this is true, how does this combine with the shattering effect ?
I mean, which is the trade-off of the two effects (a smaller shell with equal energy penetrates more easily a plate than a larger one vs the same smaller caliber is more prone to shatter) ?
Do you have any example for typical WWII battleship shells ? Are there any tables showing the shatter velocity for typical WWII (capped and decapped shells) ?


Bye, Alberto
"It takes three years to build a ship; it takes three centuries to build a tradition" (Adm.A.B.Cunningham)

"There's always a danger running in the enemy at close range" (Adm.W.F.Wake-Walker)

RobertsonN
Member
Posts: 171
Joined: Wed Jan 05, 2011 9:47 am

Re: On the Origins of Scaling

Post by RobertsonN » Tue May 21, 2019 6:24 pm

Could you give a reference for that opinion you have read?

I have never come across anything suggesting that bigger plugs were in general thrown out of thick KC plates by large calibre shells than was the case for smaller shells against thinner armor. IIRC in US tests of 14 in APC against ultrathick Japanese NVNC plates (about 25 in thick) larger plugs than usual were thrown out. This probably indicates inferior quality of these unusually thick plates. Plugs were not in general destroyed by the impacting shell. Failure of the armor occurred through a shear failure around the surface the plug. Technically, this phenomenon is termed adiabatic shear banding.

The following examples from Gkdos100 make clear that as calibre increases the shell does better against the armor. In Hipper v. Suffolk the inner limit of Hipper against the British 8 in was given as 18700 m. The Hipper had a mildly sloped 80 mm Wh (0.4D) belt plus a thin sloped deck (30 mm, 0.15D). In Bismarck v. Royal Sovereign the inner limit of Bismarck against the British 15 in shell was given as 21000 m. The Bismarck had a 320 mm KC (0.84D) belt plus a 110 mm (0.29D) sloped deck. The Bismarck had, relatively speaking, about twice the thickness of protection against the 15 in shell as the Hipper had against 8 in shells. But the Hipper actually had a better inner limit against the shells it needed to face than Bismarck. [Admittedly, at 20 deg off the beam Bismarck's inner limit came down to 10000 m while Hipper's came down only a little to 17300 m.] No doubt the greater effect of air resistance on slowing down the smaller shell and altering its descent angle play a role in this example (countering this were the higher muzzle velocity of the 8 in gun (the Germans assumed 840 m/s compared with 745 m/s for the 15 in ( and the 2300 m lesser range of the inner limit in Hipper)).

It is clear from this example that either bigger shells are clearly superior to smaller ones or that thick armor is much inferior to thin armor. Almost certainly both these factors come into play.

Neil Robertson
Last edited by RobertsonN on Tue May 21, 2019 8:13 pm, edited 2 times in total.

Byron Angel
Senior Member
Posts: 977
Joined: Sun Mar 06, 2011 1:06 am

Re: On the Origins of Scaling

Post by Byron Angel » Tue May 21, 2019 6:51 pm

Hi Neil,
If I recall my reading correctly (with respect to face-hardened plate at any rate) there is an 'ideal' thickness where the intrinsic degree of resistance per unit of thickness is at a maximum (call this a figure of merit). The 'ideal' thickness varies slightly by manufacturer, manufacturing process and year/period of manufacture, but the degree of resistance per unit of thickness in all cases more or less slowly decreases as plate thickness increases.

Your comments welcome.

B

User avatar
Alberto Virtuani
Senior Member
Posts: 3321
Joined: Mon Jul 08, 2013 8:22 am
Location: Milan (Italy)

Re: On the Origins of Scaling

Post by Alberto Virtuani » Tue May 21, 2019 7:55 pm

Hi Neil,
you wrote: "Could you give a reference for that opinion you have read?"
Unfortunately not, I remember I have read it on a forum, possibly on this same forum (or on the former Hood website forum)...

Just to be 100% clear, my question was not about a 15" vs 8" comparison.
It was more a 16" slow shell (let's say a 1000kg with initial velocity 750 m/s) vs a 15" fast shell (e.g. a 800kg and 850m/sec) against the same armor plate.
As you said, the 15" is surely more prone to shatter due to its size and speed (I wonder what is the shattering speed for such a capped 15" shell). However, such a slow 16" has slightly less kinetic energy than "our" fast 15" and thus it should be in worse situation from penetration of a thick armor viewpoint, due to the fact that, being larger, it has to penetrate a bigger surface of the plate (490mm2 more plate at 90°impact angle), probably consuming more energy to do so.

This was the "trade-off" I was speaking about.


Bye, Alberto
"It takes three years to build a ship; it takes three centuries to build a tradition" (Adm.A.B.Cunningham)

"There's always a danger running in the enemy at close range" (Adm.W.F.Wake-Walker)

RobertsonN
Member
Posts: 171
Joined: Wed Jan 05, 2011 9:47 am

Re: On the Origins of Scaling

Post by RobertsonN » Tue May 21, 2019 8:27 pm

The scaling effect in going from 15 in to 16 in is likely to be distinctly less than the difference in impact velocity, although it depends a bit on what the range is as the 15 in will slow down more than the 16 in as range increases, reducing that 100 m/s difference. In this example the 15 in probably has a flatter trajectory till a long way down range, giving a more favorable impact angle on the side armor.

In scaling the thickness of the armor goes up to keep the T/D ratio the same. If OTOH the same thickness armor is assumed for both shells then, as you say, the 16 in must make a bigger hole, reducing its chances of penetrating,

Neil Robertson

RobertsonN
Member
Posts: 171
Joined: Wed Jan 05, 2011 9:47 am

Re: On the Origins of Scaling

Post by RobertsonN » Tue May 21, 2019 9:39 pm

It is often helpful in developing one's own ideas to talk to other people about them as here.

Looking at support for the ideas I am putting forward in Gkdos100: For the 38 cm APC sees against KC n/A that the curves are very close together at 90 deg obliquity (normal) are very close together (a difference of less than 10 m/s). The curves for the 20.3 cm APC are a little further apart at 90 deg (at least 10 m/s). As far as the critical velocities are concerned the curves for the 20.3 cm APC v. 180 mm KC n/A fall at perhaps 414 and 424 m/s. The curves for the 38 cm APC against 340 mm fall at perhaps 391 and 398 m/s. Looking for the 38 cm APC at the curves for 340 mm thick plates at 30 deg obliquity then the difference between the intact and broken curve is about 43 m/s. For the 20.3 cm APC the scaled plate thickness is 181.6 cm. Looking at the curves for the 180 mm thick plates then at 30 deg obliquity the difference between the intact and broken curves is slightly over 50 m/s.

The larger the difference between the broken and intact curves the more susceptible the shell is to damage. Raising the velocity reduces the time the breaking forces act on the shell so that there comes an increase, large or small, for which the shell penetrates barely intact (which is what the intact curves represent according to Hoyer). The differences between the curves for the 20.3 cm and 38 cm APC against scaled plates are modest but they are in the direction predicted on the basis of the ideas I gave above, which I believe are sound as far as they go. The danger, of course, is that there may be other factors which might act counter to the ones I have identified. As far as the around 25 m/s lower critical velocities for the 38 cm APC are concerned one can attribute this either to a lower resistance of thicker plates against bigger shells, to a better resistance to breakage of bigger shells, or to a combination of the two,

Neil Robertson

User avatar
Alberto Virtuani
Senior Member
Posts: 3321
Joined: Mon Jul 08, 2013 8:22 am
Location: Milan (Italy)

Re: On the Origins of Scaling

Post by Alberto Virtuani » Wed May 22, 2019 7:13 am

Hi Neil,
many thanks again for your answers (and further patience....).

Do you have any examples of shattering velocities for typical WWII shells?

Does any formula exists to estimate the shattering velocity for a certain shell against armor based on calibre, final speed, weight, angle of impact, etc, (including the "key" parameter of being the shell still capped or uncapped when hitting the plate, of course) ?


Bye, Alberto
"It takes three years to build a ship; it takes three centuries to build a tradition" (Adm.A.B.Cunningham)

"There's always a danger running in the enemy at close range" (Adm.W.F.Wake-Walker)

Thorsten Wahl
Senior Member
Posts: 707
Joined: Mon Apr 27, 2009 4:17 pm

Re: On the Origins of Scaling

Post by Thorsten Wahl » Wed May 22, 2019 8:38 am

hatched area from A954868 COMPARATIVE Effectiveness of armor defeating ammunition available at DTIC.mil

depending on head shape, hardness of projectile vs hardness of plate, size of the cavity for the explosive ... the area can differ, ther are kumulative effects and at different obliquity/speed combinations a once positive effect may be reversed.
a954868 COMPARATIVE Effectiveness of armor defeating ammunition.jpg
a954868 COMPARATIVE Effectiveness of armor defeating ammunition.jpg (85.41 KiB) Viewed 198 times
on this chart a special feature became visible as the abcissa used Cosinus(obliqity) for the obliquity. The penetrated lenght through the plate for a single speed becomes a almost straight line with a downward trend. This striking linearity can be explained as a lenghtenend path of the projectile trough the plate by turning of the projectile during the first stages of the impact.

In this case the "turning effect" of projectile appears in the order of 15 degrees to explain the seemingly "reduced penetrated total thickness for higher obliquities a single velocity" in flight direction.
Last edited by Thorsten Wahl on Wed May 22, 2019 10:20 am, edited 3 times in total.
Meine Herren, es kann ein siebenjähriger, es kann ein dreißigjähriger Krieg werden – und wehe dem, der zuerst die Lunte in das Pulverfaß schleudert!

User avatar
Alberto Virtuani
Senior Member
Posts: 3321
Joined: Mon Jul 08, 2013 8:22 am
Location: Milan (Italy)

Re: On the Origins of Scaling

Post by Alberto Virtuani » Wed May 22, 2019 9:41 am

Hi Thorsten,
I can't read the legends in the picture. What is represented in "abscissa and ordinate" in the graph ?

What are the different curves representing ? (sorry for such "stupid" questions)


Bye, Alberto
"It takes three years to build a ship; it takes three centuries to build a tradition" (Adm.A.B.Cunningham)

"There's always a danger running in the enemy at close range" (Adm.W.F.Wake-Walker)

Thorsten Wahl
Senior Member
Posts: 707
Joined: Mon Apr 27, 2009 4:17 pm

Re: On the Origins of Scaling

Post by Thorsten Wahl » Wed May 22, 2019 10:20 am

Original is of low quality

its a comparison showing areas of superiority of armour piercing capped(APC) or armor piercing(AP) shot (90 mm) of the same type at different t/d vs obliqity for a certain quality of armor

above dashed line APC superior
below dashed line AP superior

Abcissa obliquity
above abcissa values 0, 20, 30 , 40 ,45, 50, 55, 60
below abcissa the corresponding 1/cos(obliquity) values 0°= 1, 60° = 2,0 etc

Ordinate t/d starting with 0.4 ending with 2.2

lowest speed is for 1800 fs

uncapped shells at the begining of ww2 typically shattered at about t/d = 0.5 at 30 degree obliquity when fired against homogenous armor(M79 is such a candidate)
later high quality experimental 7,5 cm Pzgr could survive impacts against t/d = 1.0 facehardened plates
Meine Herren, es kann ein siebenjähriger, es kann ein dreißigjähriger Krieg werden – und wehe dem, der zuerst die Lunte in das Pulverfaß schleudert!

User avatar
Alberto Virtuani
Senior Member
Posts: 3321
Joined: Mon Jul 08, 2013 8:22 am
Location: Milan (Italy)

Re: On the Origins of Scaling

Post by Alberto Virtuani » Wed May 22, 2019 4:54 pm

Hi Thorsten,
thanks a lot for the explanation.

Bye, Alberto
"It takes three years to build a ship; it takes three centuries to build a tradition" (Adm.A.B.Cunningham)

"There's always a danger running in the enemy at close range" (Adm.W.F.Wake-Walker)

Post Reply