Appendix I

Diving Depth and Pressure Hull Strength

The ability of U-boats to dive to extreme depths came as a surprise to the RN and considerably reduced the effectiveness of the asdic/depth charge system as a result of the longer ‘dead time’. In consequence, it is worth while giving some consideration to the realistic operational diving depth of German submarines.

There are three main ways in which the pressure hull of a submarine may fail as a result of sea pressure:¹

overall collapse, in which a whole compartment collapses because of instability associated with inadequate frames;

interframe buckling, in which the plating between frames buckles in a large number of nodes round the circumference; this is not normally caused by static pressure but could be excited by a depth charge explosion;

yielding of the plating between frames.

There is a degree of approximation in the calculation of all these modes and in their application to real submarine operation. A considerable factor of safety is then applied to the calculated collapse depth to allow for errors including:

depth excursions; a small loss of control can lead to disaster if the submarine is deep;

errors in building, eg failure to maintain circularity, defects in the steel or in welding;

errors in calculation, either in the theory or in the execution of the design.

This leads to three depths governing the operation of submarines: collapse depth (whose meaning is all too clear), operational depth (with a big factor of safety) and test depth (it was normal to test at least one of each class to a depth greater than the operational depth).

During the 1930s, British designers could only calculate the case of plating yield between frames; the frame size was based on experience and was, understandably, cautious (ie heavy).² German theoretical work on pressure loading of stiffened cylinders led to an accurate method of designing frames, so that they could use much lighter frames with confidence. British designers inspecting U-570 after she surrendered were amazed by the small frames.³ The weight saved in the lighter frames went into thicker plating, while the U-boats also gained from welding (probably worth another 50 feet of depth) and slightly stronger steel (yield strength of 22 tons/in²; cf British S-quality steel, 18.5 tons/in²). Initially, the Germans adopted a very cautious factor of safety, of about three. With experience and knowledge of the value of deep diving, this was relaxed.

British plating strength was calculated using the ‘boiler formula’, which was surprisingly accurate:

pressure (depth) = s.t/R (in consistent units)

This gives the plating collapse depth for the Type VIIC as 1,033 feet. Rössler, quoting von Sanden/Gunther, gives 820 feet.⁴ The official operational depth was 100 metres, consistent with a factor of safety of three. The figure for interframe buckling was similar to the plating collapse depth, while that for frame collapse was some 20 per cent greater. Rössler gives the greatest recorded depth as 876 feet, by U-331 (she was lucky). The Type VIIC-41 had thicker plating and a diving depth of 120 metres. Figures for the Type IX were similar.