To determine the steel plate size needed for a 10-meter diameter submarine pressure hull, we need to consider how the hull will be constructed — usually from curved steel sections welded together.
1. Key assumptions
Diameter (D) = 10 m
Circumference = π × D = π × 10 ≈ 31.416 m
Typical large submarine hulls are made by rolling steel plates into cylindrical segments (often ⅓ to ½ of the circumference per segment).
We must account for bending allowance (plate deformation during rolling, which slightly lengthens the flat size).
2. Rolling into a full cylinder from one plate?
If hypothetically bending one flat plate into a complete cylinder (welding along one longitudinal seam), the flat plate width before bending = circumference + stretching/compensation for neutral axis shift.
In practice, for thick plates (submarines use high-strength steel, maybe 30–50 mm thick for a 10m diameter deep-diving sub), the neutral axis during rolling is roughly at mid-thickness.
So:
Flat blank length (for cylinder) ≈ mean circumference
Mean diameter = outer diameter − plate thickness
But since we usually specify the inner diameter as 10 m? Or outer diameter? Let’s clarify:
If 10 m is outer diameter (OD):
Outer circumference = π × OD
Plate thickness = t (assume 0.04 m = 40 mm for estimation)
Mean diameter = OD − t = 10 − 0.04 = 9.96 m
Mean circumference = π × 9.96 ≈ 31.289 m
The flat plate must be rolled so that its mid-plane forms this mean circumference. So the developed width of the plate = mean circumference.
But large submarines are rarely made from one plate wrapped fully around—instead, they make several curved sections (strakes).
Example: 3 strakes each covering 120° of circumference.
For one 120° segment:
So each plate’s width (before bending) ≈ 10.43 m (after rolling it will match hull curvature).
3. Plate length along submarine axis
This is independent of diameter—depends on how long each cylindrical section is. Typical ring-like section length might be 4–6 meters (limited by rolling mill capacity).
So each curved plate might be:
But wait — in manufacturing, we roll plate along its length to form a cylinder, so:
If we want a complete cylinder section 4 m long:
We take a flat plate of length = submarine section length = 4 m (this becomes cylinder axis length after rolling).
Plate’s width = mean circumference = ~31.29 m — but rolling a 31 m wide plate is impractical, so instead we divide into 3 segments:
Better: Each segment’s flat size:
Width in flat state = arc length for 120° = ~10.43 m
Length in flat state = axial length of section = L (say 4 m).
So plate size ≈ 10.43 m × 4 m before rolling into a curved panel.
4. Bending allowance consideration
For thick plate rolling to a radius R (mean radius ≈ 4.98 m), the difference between outer surface and inner surface length = π × t over 180° bend, but here we bend gently over full circumference in segments.
Since we roll to match the mean circumference, we cut the flat plate to mean circumference arc length—no significant additional allowance if rolling with symmetrical three-roller bending; but in practice, a small trimming allowance is left.
5. Practical answer
For a 10 m outer diameter submarine:
Plate thickness: ~30–50 mm high-strength steel (exact value from pressure depth calculation).
Typical curved hull strake size (for 1/3 of circumference):
Flat dimensions before rolling ≈ 10.45 m (width) × (section length, e.g., 4 m).
Total plates: Many such plates welded circumferentially and longitudinally to form the hull.
So the plate size = about 10.5 m × 4 m (for each strake) if building in 4 m long ring sections.
If making a complete cylinder in one rolling (possible for smaller diameters but not 10 m), you’d need a plate 31.3 m wide × submarine section length, which is beyond most mills’ capacity — hence segmentation is necessary.
Final concise answer:
For a 10 m diameter submarine, assuming building in 4 m long ring sections from 3 curved strakes per ring, each steel plate before rolling is roughly 10.5 m wide × 4 m long, with thickness 30–50 mm.
