Plus, a properly designed and torqued flange joint should not allow any relative motion under any loading condition. There should be no angular displacement at that location.
Yes scr4. From your picture, the flange bolts are maybe 1.5 inch thick while the shaft is 4.5 inch thick. Also there is gap between bolts and the bolt circle diameter (and hence the torsion) is much larger than the shaft.
The bolts look at least 4 inches diameter to me, but that doesn’t really matter. Where exactly could this flanged joint deflect more than a fraction of a degree?? The shaft is welded to the flange (or cast as a single piece?). The two flanges are bolted together with 16 bolts on a very large bolt circle. Assuming those bolts are properly torqued, there is no play between those two flanges.
What gap are you talking about? Do you mean the gap between the bolt diameter and the diameter of the clearance holes on the flanges? This is irrelevant. The friction between the flanges insures there is no play between the flanges.
Scr4 - you maybe right and I maybe completely on the wrong track.
I am a Chemical Engineer (not a MechE) and my observation above is based on practical installations of piping and equipment in the field :
If a 300ft shaft is made rigid, it will be very difficult to align. Plus Thermal stresses, if any, will also cause deformation forces.
I have routinely seen flexible couplings on many rotating equipment designed to absorb vibrations and impacts.
In my experience fatigue is the predominant failure mode for such applications.
Anyways - if you believe the above is not the case, I’ll defer to your judgement.
OK so you are talking about a coupling specifically designed to flex. The link I posted above does not seem to show that type of coupling.
This cite says a tortionally flexible coupling like a Geislinger coupling is necessary for piston engines because of their uneven torque. Which would imply steam turbines (like those on nuclear powered ships) wouldn’t need them.
Yes, the shaft is composed of multiple sections bolted together. In fact all sections will not necessarily have exactly the same polar moment of inertia: the section that passes through the hull, the tailshaft, will often be bulkier and stiffer than the sections inside the hull, the sections of lineshaft. But basing the deflection on the lineshaft dimensions (which I assume were quoted) is probably close enough for purposes here.
However, there will not be relative movement at the flanged bolted connections between lineshaft sections and the tailshaft, not significant anyway with respect to the value calculated by assuming the shaft is one piece. Unlike a flanged connection in piping where, generally, relative torsional movement is countered just by the frictional force generated by tightening the bolts, the couplings on a ship’s propeller shaft have fitted bolts machined precisely to the flange holes.
Taking a step back, the static deflection of the shaft at full power is not a key design parameter itself. It’s just that the shear stress in the shaft has to be acceptable, and engineers must model the engine/shaft/propeller system to identify and avoid resonant torsional vibration. IOW that the prop is some degrees ‘behind’ the engines at full power is not itself a problem assuming only moderate shear stress in the shaft. The big problem would come if that angle oscillated resonantly, which was a big problem in some past high powered ships (among other modes of vibration). The calculation of that assumes the shaft is one piece of a given rigidity, it can’t include indeterminate torsional movement between sections of lineshaft at the
couplings. [edit re flexible couplings, these are used to avoid resonant torsional interaction between engine and gear, as well as allow some misalignment of engine and gear, usually in geared diesel ships, seldom in steam turbine surface ships, but something like them must be employed in nuclear sub plants where the engines/gears on a sound isloating ‘raft’ with relative movement, anyway lineshaft couplings would be ‘solid’, with fitted bolts]
I believe the calculations given are correct, so 15 deg in the Iowa case with all parameters nailed down, and doubt the inputs for the CVN are wrong enough for it to be way higher.
Agree that 15 degree will be the case for a rigid shaft.
I am equally convinced that one and half turns at full torque is reasonable when accounting for the numerous “joints” on the shaft, the 300 ft length of the shaft and the desire to avoid shock / vibrations.
I think the OP’s question remains unsolved until someone with real marine shaft design experience can chime in.
I wouldn’t say the question is resolved, but I’m a naval architect/marine engineer by training and some design and operating work experience though long ago. Although my hands on experience was with merchant ships. OTOH warship propulsion plants are also an interest of mine (as in posting recently about the difference in plant arrangement and fuel economy of the early US dreadnoughts, that kind of stuff).
So, I’ve never been down the shaft alley on a post WWII a/c carrier. But, if they have flexible couplings connecting the lineshaft sections or reduction gear to the shafting, that would be really surprising. 
That’s definitely not the case of merchant ships or older warships and I don’t see a reason for such a practice. Again flexible couplings are typically applied between engines and gears, and not typically at all in steam turbine surface ships. In steam turbine surface ships you just align everything rigidly, accurately enough for it to work properly. And the hull is relatively stiff, lots of steel in the foundations to be sure it is. So it does work.
So the explanation being that the lineshaft couplings are flexible couplings is very unconvincing to me. And regular couplings basically don’t deflect at all, the bolt has smooth sides which just fit into the flange holes.
But maybe somebody who claims the deflection is the larger type of number can explain it design terms, as some other reason perhaps but I didn’t think of it or very unique to the carrier plants and not well known. But OTOH IME in many cases, not casting personal espersions, I’ve often heard ‘first hand’ stuff about ships, even ships I sailed on myself by other people on the ship, I knew were not correct from a design standpoint.
Even if there were some play in the joints between the sections, the play wouldn’t be elastic. When you torqued up the engine, all of the joints would twist up to their maximum, and there would still be torsional stresses, and so the rest of the shaft would still twist until the strain corresponded to the stress.
not actually about the prop shafts, but the Nimitz finished a major overhaul in 2017 and the Navy published a series of videos detailing much of the work. Fascinating.
Episode 7, the heavy work, shows them removing the rudders. Those are some big pins!
