I agree with what your saying about the wieght issue, and that there is some sort of curve to it. It would make sense for 88mm round made out of steel (its the lighter one) to have less performance than an 88mm round made out of tungsten (heavier), if their velocities are the same.
Heres an example of a balance between velocity and wieght (the reason for wieght and not caliber is its implied that the larger caliber, the greater the wieght).
These are the 100m penetration values for the Panther, Tiger, and Tiger 2
Panther:
____Range_100m
Angle
0_______176(mm)__________925 m/sec APCBC
30______134
60______62
Tiger:
____Range_100m
Angle
0_______154(mm)__________773 m/sec APCBC
30______120
60______61
Tiger 2:
____Range_100m
Angle
0_______228(mm)__________1018 m/sec APCBC
30______173
60______77
You can see that the Panther beats out the Tiger by having a greater velocity (the diameter might have helped in this case too), even though the round itself is lighter (which I would guess is that its able to put more kinetic energy into a point, through the combined effort of its mass, velocity, and diameter, than that of the Tigers 88mm). But now take a look at the Tiger 2, it has a heavier round and an even greater velocity, so even though the round itself is broader, it puts more kinetic energy onto the target.
One of the issues as rounds get broader is there is more surface area for the round to penetrate. This is one of the problems with tungsten APFSDS rounds, they like to mushroom up during penetration, decreasing their performance because as they penetrate, they constantly have to penetrate more and more surface area.
So all that means that essentially Im agreeing with you in that there is a balance between mass, velocity, length, and diameter when calculating penetration.
Now onto the Modern rounds. Now you said that "This is just one more reason why reducing caliber is not necessarily better, and indeed, may prove counter productive if the shot becomes too long."
Now this is true if both rounds stay the same length, and keep the same velocity, because one round is going to have more mass and a smaller diameter (smaller point of pressure) is not going to make up for it.
But, and this is a big but
, that is why designers lengthen rounds. By lengthening the round, your increasing the mass while keeping a smaller diameter. So now you have the mass of a larger caliber round, the diameter of a smaller caliber round, as well as a greater velocity than both (more momentum, greater aerodynamics). This is why modern APFSDS rounds are the way they are, its a win-win situation.
Before I move on though, I'll explain why more length to erode is better. As a penetrator erodes, it loses mass and kinetic energy. So by having more length to erode, it keeps its mass and kinetic energy longer, meaning it can penetrate for a longer time before stopping. About the time it takes for the penetrator to enter the crew compartent, I believe that the whole penetrator doesnt need to be completely inside before devastating effects occur. As soon as the penetrator starts to enter the compartment, it sprays molten spall into the inside of the compartment. Unlike WW2, where AP rounds would "bounce" around on the inside of a tank once it penetrated, modern APFSDS rounds have the possibility of shooting straight through an armored vehicle. If you read the part about the "silver bullet" in my last post, youll see what I mean. So all effects come from spall, and the pentrator hitting anything on its straight line through the target. So now it has to hit personall exactly or go straight through ammunition and the like.
Now you said that "Lengthening the penetrator while decreasing caliber is only advantageous
to a point, beyond that it becomes counter productive." Now your right to a certain extent. As we've discussed before, everything is a balance. So yes, once you get so small and long, things start to get weak and have a tendency to bend or break. So designers try to find a balance between length and diameter. At the same time, theyre looking for new alloys, new materials.
I would like to point out though that designers dont just make the diameter smaller to make the point of pressure smaller (thats why penetrators have pencil shaped points, and thats also why DU's adaibatic failure/shear is so beneficial), but they do it mostly to decrease weight to keep velocity. An Ideal situation would be to have a decent diamter, but countinually increase the length of the penetrator while maintaining velocity.
So once you reach an optimum l/d ratio, or even an optimum diameter, the only way to go is to lengthen, so now your increasing mass. To counter-act the loss of velocity incured (since were at an optimum, we cant make the diameter any smaller), designers have to boost the performance of other factors. By lightening the Sabot petals, you increase the initial velocity. By designing better propellents, you can increase the velocity even more. The US did both of those last aspects with their M829A2 round. The M829A2 is marginally heavier than the M829A1, and with the lighter Sabot and better propellent, it has a greater velocity, meaning better overall performance.
So yes, you can only get smaller and longer before you have to keep a certain diameter then legthen (thearby increasing mass) and increase the performance and quality of other factors.
P.S. I didnt mean to question you with that 5:1 ratio thing, I just really didnt know, Sorry.