About modern MBT design philosophy, angled armor and modern ammunition

Lert: Three of the best MBT's currently in service everyone here would agree are the M1 Abrams, Challenger 2 and the Leopard 2. It's the design choices on these tanks that this thread wants to address.   First the Abrams:     If you note the front armor, both hull and turret, you'll see that they are flat slabs of armor under a minimal angle.   Now the Leopard 2:   This is the 2A5, but the 2A6 and 2A7+ have the same armor layout.   You will note that the both the front hull and turret armor of this tank are sharply sloped. What do the germans know that the americans don't? Or, vice versa, what do the americans know that the germans don't?   Then there is this, the Challenger 2, considered by many to be the best protected, most heavily armored of the three:     It has a flat, relatively unangled hull front with a relatively highly angled turret face.   So, what gives? We have:   - The american design with flat, slab everything - The german design with sharp angled everything - The british design with flat hull and angled turret   But wait, it gets even more interesting:     This picture of an older generation Leopard 2, from the 2A4 block in this case, shows a very flat, unangled, slab turret face. Yet the 2A5 and upwards have the sharp angles. What gives? Aren't those shot traps?   ... Well, not really. The sharp angled wedge shape on the turret front of the Leopard 2A5 and upwards is actually a wedge-shape add-on piece of spaced armor. This picture of a Leopard 2A5 turret under construction shows the near side of the turret before the addition of the spaced add-on part, still showing the flat turret face of the 2A4. Here and here are two pictures of those wedges of shaped armor. My understanding is that they serve to deform penetrators before they reach the actual turret armor, which is still flat and unangled, like in Abrams.   Wiki backs me up in this:   "The A5 introduced a wedge-shaped, spaced add-on armour to the turret front and the frontal area of the sides. These spaced armour modules defeat a hollow charge prior to reaching the base armour, and causes kinetic-energy penetrators to change direction, eroding them in the process; it does not form a shot-trap since it doesn't deflect the penetrators outwards to hit the hull or turret ring."   The way this is phrased and from viewing the pictures of the armor addons, this leads me to believe that kinetic penetrators are meant to penetrate the wedge armor, being deflected inwards because of normalization and losing a lot of their penetrating potential before hitting the actual turret face armor, as per my crappy MSPaint drawing:     However, this is just wild guessing on my part; I claim no particular understanding or knowledge.   So, all this new information changes my earlier list to:   - The american design with flat, slab everything - The german design with sharp angled hull and flat turret face - The british design with flat hull and angled turret face   So, my questions are:   - Why the radical difference in design? What's the philosophy behind them? - The german designers chose to add the wedge shaped spaced armor pieces to the Leopard 2 when the flat design of earlier Leo's as well as Abrams was 15+ years proven. So why the change in philosophy? - What does sloping do to modern ammunition? - Why is Leopard 2 so sexy? Mmmmmmmm ....   Note: Modern ammunitions interact with armor and slope differently from the ammunition of the time period that WoT encompasses. Don't bring your WoT theorems into this discussion, this is about modern composite armor, modern high density and chemical ammunition and modern design philosophies.   As a thank you for reading, have a video which celebrates two of these three amazing machines along with some classic rock: