The B-17's wing produces less lift more drag pr. area than the U-2's wing, first of all because of it's lower AR, making it a less efficient wing than the U-2's. Furthermore the engine placement on the B-17's wing disturbs the span wise lift distribution over it and creates additional drag, both induced and parasite drag, making it even more inefficient.
Soren - you missed the point in contrasting U-2 to B-17 with lower wing loading and lower aspect ratio, and contrasting the U-2 with a B-29 which had a higher wing loading and higher aspect ratio.
You keep trying to tie 'efficiency' of a wing to a nebulous concept of stream tube whose diameter is the same as a wing span - then traipse off into concepts not in fact, and forgetting what you demonstrated you once knew.
Namely -
1. Induced Drag = drag created by the lift acting on the airfoil.
The equation for induced drag is
independent of span.
It is (1/k)^^2*CL^^2/(pi*AR*e) where 1/k = 1/2*rho*V^^2. At same altitude and engagement speed 1/k may be removed from the comparisons to arrive at proportional relationships.
2. The CL of all these a/c at the same engagement speed, same altitude and same place is proportional to:
F-14 Extended Wing -----> CL proportional to L/S ---> 61,000/565---> 108
F-14 Swept Wing --------> CL proportional to L/S ---> 61,000/565 ---> 108
Wing area the same but one swept and one not)
AR=2.55 and 7.2
F-15 Wing ---------------> CL proportional to L/S --->44,500/608 ----> 73
AR=2.9
F-16 Wing ---------------> CL proportional to L/S --->26,500/300 -----> 88
AR=3.4
This says nothing about L/D of the respective ships or the 'efficiency'
3. Back to 1. to compare CDi for each ship at same entry speed, altitude and location (drop 1/2*rho*V^^2 as they are all the same. If 'e' is approximately the same for swept, then"
CDi is proportional to CL**2/(pi*AR)
F-14 Induced Drag proportional to (108^^2)/AR = (108^^2)/2.55----> 4574
F-14 Induced Drag for extended (108^^2)/7.2------> 1620
F-15 Induced Drag proportional to (73^^2)/AR = (73^^2)/2.9 -------> 1837
F-16 Induced Drag proportional to (88^^2)/AR = (88^^2)/3.4 -------> 2277
So, for these simplistic events, level, same altitude, same entry speed, same relative wing efficiency factor 'e'.
The F-14 in lower speed range with extended wings has ~ 88% CDi of F-15 and 71% of the F-16 -
With Swept wings the F-14 is at a huge disadvantage to both the F-15 and F-16 with ~ 4574/1837 ~ 2.48 x CDi of F-15 and 4574/2277 ~ 2.0 x Cdi of the F-16.
This helps a little bit as we know that the swept wing F-14 has a lot more induced drag at the same velocities of the other two ships, but -
CD parasite should dominate higher speeds including even 350kts range but your thesis has been all about vortex strength/tip vortex advantage of the F-14 because of a 'larger stream tube' presumably of the extended wing and it has NOTHING to do with span but everything to do with lift loading and aspect ratio -
IF
the Cl/Cd for all the a/c are equal.
If not the case you have to look at the data for each ship carefully to predict performance.
Induced Drag is all about the drag created by Lift. The 'downwash' vector is all about the strength of the circulation, the characteristics of the spanwise lift distribution and the effects of a three dimensional wing. If you look at most CL/CD polars and/or the d(CL)/d(AoA) slope ( the derivative of CL with respect to AoA) , the effects of AR between 1 and say 5 are very significant in improving the slope, beyond that the increase of the CL slope is not changed so much with increases in AR.. You'll find that to be true if you examine a lot of airfoil data corrected by AR. Airfoil section data absent AR corrections is for a 'perfect wing' of infinite AR and no induced drag.
If you don't KNOW L/D for each then you can only
speculate from your belief system which a/c is 'more efficient'. That was why I drew you into a discussion comparing different a/c with same wing span but different Lift Loadings at 1 g, as well as different a/c with different (but reversed) AR and Lift Loadings.
But please apply your stream tube philosophy to calculate wingefficiency, induced drag and manuever relevance.