I have often wondered what aerodynamic penalty, if any, the N series designs would have to pay for that sloping breadth of the lower stages due to the stacked sphere design.
Note that the slope is not so much just because the fuel sphere is above the larger oxygen sphere, but rather because the upper stage must nest atop the lower and must be smaller, so its oxygen sphere must have a lower radius. We could easily get away from two spheres per stage by putting the fuel in non-spherical tankage--I envision in the awkwardly shaped space below the oxygen sphere. But this would actually worsen the slope of a smooth conical line enclosing the second stage, if it too had an oxygen sphere "floating" on top of a cup of kerosene tankage! By bringing the centers of the two oxidant spheres closer together, the difference in radii reflecting the cube root of the differences in gross mass would be accented; given that one chooses to hold the cryogenic and dense oxygen in a sphere, the apparent drawback of doing the same for the fuel is offset.
If that is one supposes it is important to minimize the slope. Given that the craft will be plowing through significant atmospheric densities at multiples of the speed of sound I suppose that overall one wants something like a Sears-Haack body (V-2 was a close approximation, with the flame of exhaust substituting for the trailing pointy end) and a fair approximation is achieved with a pointy nose cone and either a purely cylindrical body for most bulk, or a gradually expanding one as with Saturn V. Having the bottom flare out so the whole thing looks like a golf tee turned upside-down would hardly be anyone's recommendation--or would it?
One approach to drag reduction tried on some ICBM models (submarine launched, actually IIRC) is putting a spike on a rather blunt warhead; apparently the shock wave forms around the tip of the spike, and the body of the missile within the shock wave cone can deviate pretty far from supersonic ideal streamline shapes and not make much difference. The N series layout might be just fine if the lower rim of the lowest stage lies within that shock cone, with the upper stages serving as the "spike". We might then actually want to go for a wider flaring, which could be achieved by monkeying around with the fuel tank shape.
Now if i understand supersonic drag at all correctly, what happens first is the formation of shock waves, since these produce irreversible heating of the air they draw a lot of power out of the motion of the object, which takes the form of powerful drag pressures on the surfaces where the shocks form--on a rocket, the tip. Then air flows between the forward shock or shocks at subsonic but high speed (bearing in mind the speed of sound is raised by the shock heating) so decent shaping and smoothing of the surfaces behind the shock tip is still a design consideration. Somewhere more or less attached to the back end of the object is a countershock; along its conical surface the air that has been shock-accelerated by the forward shock wave or waves and raised in temperature and density as well "snaps back" to approximately ambient conditions, but irreversibly heated a bit (cooler than what was flowing past the body but warmer than before the body came by) and I would guess retaining some transferred momentum along the body's direction of motion as well. so there would be a plume of air trying to follow the rocket up (or would be, if it weren't blasted down by the rocket exhaust!

) That sort of turbulent tail following an aircraft happens at subsonic speeds too.
The slope of the lower portion outward would be draggy in the subsonic flow entrained, and also I'd think another shock wave would form on its edge--but this might be mixed up with the formation of the countershock. Also the rocket engines (24 on "standard" N-1, 14 on my midsize mini version, 8 on a standard N-2) mounted on the rim would change the flow pattern to be different than if some magic exterior force were dragging the rocket along somehow, and more like there was an afterbody. I don't know just what effect the lack of rockets in the middle of the bottom disk would have but I'd expect it to be a turbulent low-pressure zone.
It would seem the drag must be higher than if the whole rocket occupied a uniform diameter cylinder, but that would clearly depend on just how long and broad that cylinder would be. I suppose one reason multi-stage rockets tend to be so very slim is that when the lowest stage, which is generally largest, sloughs off, the remainder is much squatter in proportion, and goes at an even higher Mach factor before the air drag becomes negligible too, so while broader proportions might be OK, they apply to the upper stack, not upper plus lower.
I will mention that the conical form of the N series lower stages actually sidesteps that consideration, in three ways--first because in the conical lower stages the proportions remain the same there; second because the broad base of each one is narrower than the prior stage so overall, with the upper cylindrical part becoming an increasingly large proportion of the height, overall the form is narrowing or anyway getting no worse, and finally because the spread-out form holds more volume per unit length the farther down you go, so that the conical stages are considerably shorter than they would be if fixed at some intermediate diameter.
Also that a lot of Soviet designs seem to violate the Western ideal of a long slim form one way or another; consider the conical, and angularly scalloped, form of the classic R-7.
Suggesting that rockets need not be as skinny as Western models tend to be (at least when stripped of the boosters or parallel liquid burning stages they tend more and more to be launched with) seems borne out by the relatively broad and short forms of the STS and Energia propellent tanks; with the same tank being driven through the air all the way to full orbital speed, it doesn't get relatively shorter.
So-the N form looks as though it must create somewhat more drag than say a Saturn rocket. But does anyone know how much worse it is? A small increment as I would guess, or a lot more? And how would it compare to say the STS tank, with its added interference from the boosters and the Orbiter itself, or even bare?
I'd be interested in a proof that the angle off the centerline could actually be greater, since that might allow for moving the kerosene fuel into complex-form non-spherical tanks under the oxygen sphere, and select a slope that right-sizes the upper stages, while allowing the broader based first stage to atmospherically brake and then parachute and rocket to a soft landing on the downrange steppes, to be recovered and reused.