By Nathan Okun
Updated 07 September 1999
Underwater travel of projectiles is based on the fuze delay time and the stability of the projectile (that is, its ability to keep going nose-first, rather than tumble due to the much more powerful drag effects under water).
Fuze delay varies somewhat from projectile to projectile and some projectiles may be blind (dud) on the surface of the water, but go off due to the much higher shock of hitting a steel plate. The post-WWI Japanese ex-BB TOSA trials seem to indicate the last, as the projectile fuze delay (they were using the British-spec 0.025-second nominal delay), even if abnormal, was not anywhere near long enough to give the explosion within the ship if the fuze had been activated on entering the water. So it probably activated on hitting the TOSA's lower hull, as it got a classic "textbook" delay effect. Very few projectiles except for the Japanese super-long-delay Type 88 and improved, even longer delay, Type 91 will go very far under water if their fuzes work anywhere near specification.1
As to stability, long, pointed windscreens, which are good for minimum drag in air, are poison under water as they add considerable surface area to the sideways forces on the nose and they also move the forces much farther from the center of gravity, giving them added leverage. Both of these effects means that a long, pointed projectile will very rarely be able to continue nose-first for any distance underwater. The resultant tumbling effect will slow it down almost immediately, so it will not go far horizontally before sinking downward.
A very blunt or near-flat nose eliminates most of the sideways area that the drag forces of the water can act on and also shortens the distance to the center of gravity, making rotation more difficult. This is why many air-dropped torpedoes have flat noses (with beveled or rounded edges to reduce drag somewhat). The Japanese took this to the extreme in their Type 88 and later Type 91 AP shell designs with their break-away windscreens and "cap head" noses. These designs resulted in a flat face with an area of 50% of the maximum projectile cross-sectional area after any impact at all, including water impact. German post-1930-designed WWII AP projectiles used aluminum windscreens that also snapped off on water impact, resulting in the very flat, sombrero-shaped forward face of their AP caps acting exactly like the flat nose of a Japanese Type 91 AP projectile--although only German AP projectiles with dud fuzes would travel very far under water.2 USA WWII AP projectiles used steel windscreens, but they also had large triangular pop-out plugs in their upper end and many small circular pop-out plugs ringing the lower nose just above where they jointed the AP cap edge. These were to allow water to ram through to make the internal dye bag color the splash of a miss--each ship having its own color (Japanese Type 91 projectiles did the same, but did not need any cutouts in their windscreens, which were break-away, as mentioned above). This might have made USA projectiles tend to be able to move farther under water, too, but, as with the German AP projectiles, their fuze delays would stop most from going very far after hitting the water.
Thus, except for the Japanese projectiles, underwater hits were a very iffy thing from enemy gun projectiles, even under optimum angles of fall and striking velocity and hit distance from the near side of the target. Underwater hits happened several times during WWII, but I know of no underwater hit that penetrated through any ship's side anti-torpedo system into the ships "vitals," other than the single hit on forward main magazine of the USS BOISE by a Japanese 8" Type 91 AP projectile, which was designed to do this on purpose--and even these projectiles hardly ever got an underwater hit!
Putting a lot of design effort into stopping such rare hits does not seem to be "cost-effective" unless it is REALLY CHEAP to do!
1) In other words, a normal AP fuze would explode the shells very shortly after they struck the water.
2) Nathan's point about dud German shells being able to travel some distance underwater should be noted as a reasonable explanation as to how an unexploded shell from the KM Bismarck wound up in the lower hull of the HMS Prince of Wales. In addition, the theory about an underwater hit penetrating into the magazines of the Hood and causing her demise should now be assigned a lower probability.