Here's the short answer to the multiple thin decks vs. the single thick one.

The issue is local stiffness, in this case the only area that matters is that at the point of impact of the shell (or immediately surrounding it).

Penetration by a shell is very similar to a hardness test. The area hit with the penetrator is small, but there is a given amount of support around it due to whatever is holding it. In the case of armor plate, there is framing behind the plate which supports it and adds stiffness. Since this framing is assumed to be distant relative to the impact zone of the shell it is ignored for immune zone calculations.

Since the framing is ignored, we can cut to the heart of the matter. The only way to locally increase the stiffness of the plate without considering the framing behind it is to thicken it (or add shape to it - but this is not feasible when the plate is rolled and surface hardened ("cemented")).

When a shell strikes armor it must first penetrate the surface, and then deform (or splinter) the rest of the plate out of the way. The stiffness of the plate is critical in determining whether or not the shell will penetrate.

If we were looking at this as a structural analysis, the many thin plates
with the spacing would be considerably stiffer in a structural calculation
like bending (*exponentially* stiffer as the thickness of the steel's value
to the moment of inertia a given distance perpendicular to the axis of
loading of the structure is cubed in standard calculations ("h^{3}" below),
and then the distance between the thinner plates factors in *again* (as the
distance from the neutral bending axis to the extreme fiber "c") in the
calculation for stress) - the formula for moment of inertia (I) of a rectangular
section is b*h^{3}/12 - the formula for stress in bending is M*c/I where:
M=the bending moment (length * force) c=distance from the neutral bending
axis to the extreme fiber I=the moment of inertia of the section Therefore,
the total effect of this distance is multiplied to the 4th power, and the
thinner plates happily add up their strength (and then some).

This is all well and good, but we're not talking about structural design,
here we are talking about local impacts. What this means now is that the
"h^{3}" in the moment of inertia calculation comes back to haunt us. The
many thinner plates are considered *separately* in this calculation. (This
one's a bear and I really don't want to write it out here)

Because its effect is *exponential* in nature, there is not a linear correlation
between the *local* stiffness of the single thicker plate vs. the many thinner
plates. Now the many plates, because they are too distant relative to each
other, can't help each other out. The single thicker plate is *exponentially*
stiffer than the many thinner plates because it's "h" value is *locally*
higher.

The effect of raising "h" to the 3rd power is so pronounced that it
even over comes the loss in velocity and tip effectiveness caused by penetrating
the individual plates *in sequence*.

Now, I know you must think I'm nuts for calling this the short version, but it is. The long version takes two years of calculus and differential equations, and roughly three years of statics, dynamics, strength of materials, physics and metallurgy.

To provide a rule of thumb: The single thicker plate is more effective
at resisting penetration by a shell because it is *locally* stiffer than
the many thin plates, and penetration by a shell is a *local* phenomenon.

- 5 February 1999
- Updated.