Well yeah, but if it's of diameter, the area of the shell has to increase geometrically, because of er...geometrics.
Crap, I realize my last post was missing the key word "mass" in that sentence.
Yes, if you take a cylinder of metal and increase its diameter its mass will increase. However in this case it really is irrelevent and depending on the taper of the new shell, it may weigh more or less. It is about the design of the gun and cartridge. As noted above, the German equivalent to the 76mm that the Shermans used, was a 75mm gun and they had far better 75s for penetrating armour.
Also note that widening the shell will similarily decrease its penetration power (all else being equal) the main advantage of the larger guns (say, 75mm over 47mm) was it allowed for higher velocities, not just due to mass, but also larger propellant charges. But eventually the benefit declines as the barrell needs to be longer and the forces on the gun are ever greater to achieve that velocity. It seems that, at that time, the sweet spot for tanks was the 75mm range.
What say1988 says is correct. The diameter of a round is only one factor in calculating its mass, and mass is only one factor in determining its total energy, which is only one factor in determining its penetrative power.
Using the Germans' collection of 75s as a reference again:
The older KwK 37 L/24 of early,
short-barrelled PzKpfw IV fired a projectile (armor piercing - AP) that weighed
6.8kg at 385 meters/second.
The KwK 40 L/48 of the later,
long-barrelled PzKpfw IV fired a projectile that weighed
6.8kg as well, but a longer gun barrel and more powerful propellant charge meant that same mass was moving
at 740 m/s. Additionally, it had a more advanced round (armor piercing, composite rigid in US parlance, or APCR) that weighed only
4.1kg, but that traveled at
990 m/s.
The KwK 42 L/70 of the
Panther fired an AP round that weighed
7.2kg that moved at at
925 m/s and a
4.75 kg APCR round that moved at
1120 m/s.
The upshot of all this is that, despite being of similar dimensions, the three guns (and five rounds) had differing levels of performance.
Armor penetration at 500m:
- KwK 37 L/24 - 38mm
- KwK 40 L/48 - 96mm
- >>APCR - 108mm
- KwK 42 L/70 - 124mm
- >>APCR - 174mm
Additionally, different materials and designs improved or impeded a round's and, therefore, a guns performance. Intuitively, one would expect the hardest, sharpest round to be the most effective, but harder shells tended to shatter upon impact. Sharper shells were indeed more effective against vertical armor plate, but as sloped armor became the norm, it was found that they would ricochet more easily off the front of tanks like the Panther or the T-34. Blunter shells, on the other hand, would dig their corners into sloped armor and thus be less likely to bounce off.
And this speaks only to kinetic energy rounds. High Explosive (HE) rounds for use against soft targets and High Explosive Anti-Tank (HEAT) rounds again vary from gun to gun even with the same barrel diamenter. For instance, while the 76mm Sherman was markedly more effective versus armor, the lower velocity of the M3 gun on the 75mm Shermans, with its smaller propellant charge, allowed it to be packed 1.5 LB of explosives into its projectile to the 0.9 LB of the M1 76mm gun despite the extra 1mm of diameter of the larger round. This was a major factor in the US Army refusing to deploy 76mm Shermans despite the troops clamoring for a gun that could stand them in better stead against the Tiger or the Panther.
