Following the crashes of two Comet 1s in early 1954 due to metal fatigue, all future Comets (and the few surviving Comet 1s that were rebuilt rather than scrapped, all of them in military service) were redesigned to mitigate fatigue stresses; among other changes, the passenger windows were changed from round-cornered squares to circles. However, the windows in the roof of the forward cabin for the aircraft’s ADF antennae, which are of almost identical construction to the passenger windows except for being filled with opaque fiberglass (in which the ADF antennae were embedded) rather than transparent panes, and which are considered to be one of the two possible locations (the other being one of the passenger windows) for the rivet hole that gave birth to the fatal crack in one of the crashed Comets (no wreckage was ever recovered from the second crash beyond that floating on the surface, as the depth of the water would have made salvage operations cost-prohibitive at the time), retained their original rounded-square shape. Admittedly, the Comet’s subsequent service history seems to have vindicated this judgment (no Comet would ever again break apart in the air from fatigue damage, despite still having squarish ADF windows), but de Havilland didn’t know that at the time, and they thought it prudent to roundify the passenger windows, so why didn’t they do the same for the ADF windows?
1 Answer
It wasn't the square-ish windows (they still had round corners, just not as rounded as modern square windows). They knew square windows were less than ideal stress wise and built the frame structure to take the expected loads. They just screwed up the calcs and didn't quite make them heavy enough.
The problem was stress concentrations at the rivet holes in the areas of the corners were higher than calculated. They could have just beefed up the structure with more rivets and doublers. The switch to round was to alleviate the stress problems without the weight penalty of reinforcing the structure.
The holes in the roof were already sufficiently beefy, or perhaps they added a reinforcement. You will see square holes in pressure hulls on various airplanes for component pass-through all the time, where a square hole is desirable for some reason. If you make the frame heavy enough, it's not an issue. It's just that a round hole is a bit lighter than a square one so most of the time a round hole is preferred.
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1$\begingroup$ Its worth noting that the Comets series of accidents triggered a massive investigation into the field of metal fatigue, resulting in significant additional research done into the matter - it wasnt simply a case of "they screwed up", it was more of a case of "the accidents exposed a deficit in knowledge" which was subsequently filled in to the benefit of the entire aviation industry (test results and research papers were shared with the aviation community). $\endgroup$– MooCommented Jul 5, 2019 at 5:14