Indeed. Although Mr Honey's "three significant figures" calculation was a (very reasonable) bit of literary license. The OP's suggestion that they can now predict 1272 "cycles" against an actual of 1290 is somewhat fortuitous, given that the da/dN input figure is only known to slightly better than 1 significant figure. Also, this prediction relies on knowing the actual initial and the final crack lengths.
It's a bit more nuanced than that. The fundamental problem was that they created undetectable cracks at many of the rivet holes because of flawed manufacturing techniques.
It also appears that one of the coal bunkers was on fire throughout the last journey and they couldn't put it out. The heat weakened one of the internal bulkheads. John
Although you could argue that it was the third, as it sailed to France and then Ireland, before continuing on its way to New York. Three journeys, one voyage.
I take it your reference to da/dN is to the Paris equation and the exponent of 5 derived from testing data. This is derived from the many points obtained in testing (the slide titled "Modern Analysis ? Fatigue Crack Growth Plot"). A statistical analysis - presumably done at the time and not mentioned in the presentation - will give the confidence bands for the value of the slope ((which isn't the same thing as confidence bands for the regression), and so although the number 5 looks bald compared to say 5.002, it will be known to a confidence limit.
On your point about cracks, it doesn't really matter what the initial crack length was in itself, the critical thing is that it can grow, even from a tiny manufacturing defect, under stress. AIUI the critical stress intensity factor K1c for the material will give the crack length at which catastrophic failure will occur. Knowing that, Paris gives the number of stress cycles to reach that point.
When visiting the De Havilland Museum recently I had an interesting conversation with one of the volunteers, a retired employee and he said that the crucial problem with the Comet's construction was not the corners of the windows but the metal used to fabricate the fuselage being too thin. He knew the exact gauges which I can't remember now, but it was just one gauge too thin. Pressurised cabins of the same configuration but with thicker metal were subsequently used on many types with no fatigue problem at all.
ISTR a TV documentary on the development of the Comet. In it, a pilot who was flying an early one at a Farnborough(?) air show heard a large bang from the airframe, and guessed that a skin panel had been over-stressed and buckled, his speculation was that this was due to the skin thickness being insufficient.
Lovely museum, well worth a visit; been there many times in the past.
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