From'The Loss of the HMS Hood: A Re-Examination" by William Jurens:
http://www.warship.org/no21987.htm
"Speculations concerning Prinz Eugen's shells usually revolve around the idea that although her projectiles would have had little or no chance of penetrating Hood's belt armor at the specified range and obliquity, due to their "plunging" trajectory, they might have set off the after magazines after penetrating Hood's relatively thinly armored decks. In support of this, one article purporting to reproduce a diagram of the relative trajectories of Bismarck's and Prinz Eugen's guns has been drawn so as to give an angle of fall exceeding 35 degrees.78 A quick examination of the range tables, however, shows that such an angle is highly exaggerated, to say the least. In reality, due largely to the higher initial velocity of Prinz Eugen's guns, at the range at which Hood was engaged the angles of fall of both Bismarck's and Prinz Eugen's guns were remarkably similar. Over the ranges of interest, the angle of fall of Prinz Eugen's projectiles was only about 13°-19°, an angle which cannot in any meaningful sense be construed as "plunging fire." Further, the striking velocity of Prinz Eugen's shells could not have exceeded about 460 meters per second. Even assuming that the shells could have found a spot to hit the deck directly, at the calculated angle of fall the official German armor penetration curves for this gun, though not reproduced here, allow them a penetration of only about 40-60mm of homogeneous armor at best. In fact, as was the case of the 380mm gun, the curves for these conditions are effectively "off the graph," strongly implying almost no possibility of intact penetration at all. Even at the closest possible range, belt armor penetration at the calculated obliquity of 47° would have only been about 100mm for an intact projectile and 103mm for a broken one, both of which are well under the thickness of even Hood's uppermost and thinnest belt.
Although a hit from Prinz Eugen could possibly have caused the fire in Hood's after superstructure, it would have been almost impossible for such a hit to have penetrated to the after magazines.79 Prinz Eugen may have been able to hurt the Hood, but she would almost certainly be unable to kill her."