Nose shape on fuselages
Fuselage noses of airliners hold the antenna of the weather radar, and a blunter nose will put the least amount of material in the way of the electromagnetic waves. On a three-dimensional body the shape of the nose is of less importance and sometimes used to express a brand image. In subsonic flow, sharp changes in the contour must be avoided: Here, air would have to change direction abruptly which requires strong pressure gradients. Therefore, curvature along any flow path should change gradually. This favors an elliptic body shape. If you want to have no jump even in the second derivative, use a lemniscatic function.
A hemispherical nose would have constant curvature followed by no curvature along the cylindrical portion of the fuselage. The sudden change in curvature at the transition between the rounded nose and the cylinder would require a sudden jump in pressure which causes more drag than the gradual reduction of curvature (causing a gradual increase of pressure) of an elliptic nose.
Edit 2: basically, why does No 2 in the following have less drag than No 5?
Because the sharp corner at the base of the cone in No. 5 will cause a suction peak which in turn will cause a jump in boundary layer thickness. The hemispherical nose of No. 2 is better, but best is the elliptical nose in No. 1.
A blunter ellipse will have lower overall surface but a steeper change in pressure - here, as so often, the optimum is a compromise which needs to include the Mach and Reynolds numbers as well as structural considerations. Since the optimum is flat, there is considerable space for individual solutions.
What if No 5 had a smoother “ridge” (cone to cylinder transition) but was still pointy? Say, if No 1 ended in a point?
The pointy tip would not "fix" the stagnation point to that point - rather, it would still move with the angle of attack, but the part of the flow negotiating this tip would exhibit a strong suction peak and "smooth out" the contour by means of a local separation. This would place more strain on the boundary layer and increase its thickness downstream. Any hope for laminar flow over this nose past such a tip would be destroyed by this, of course.
The smoother ridge would be better, so the elliptical nose with a pointy tip would improve things like No. 4 does over No. 5. On No. 4 the sharp ridge will most likely produce a separation on the ridge which will make the whole body look larger to the oncoming flow. The bisection of the drag coefficient in No. 4 indicates to me that the separation is much smaller. Note that this is all only valid in subsonic flow! In supersonic flow No. 4 would look best.
Nose shape on wings
On wings, however, the nose shape is extremely important - witness the jumps im performance that sometimes were achieved by optimizing the nose shape. To get to the bottom of the wing nose shape, we need to talk about boundary layers, Mach effects and much more, so be prepared for a long answer.
Glider airfoils can afford to use small nose radii because they fly at low Mach numbers. Airliners, on the other hand, need to keep local Mach numbers low which favors a larger nose radius. If you are happy with this answer, better stop reading now.
At the Symposium Transsonicum of the International Union of Theoretical and Applied Mechanics (IUTAM) in 1964, E.V. Laitone presented something like a magic number for transsonic flow:
$$Ma = \sqrt{\frac{1}{\gamma - 1}} = 1.581$$
with $\gamma$ the ratio of specific heats of a fluid. Once the local suction peak at the nose of an airfoil reaches such a speed, lift stops growing any further. With stall speeds of around 120 knots, the early jet airliners routinely hit this limit using the 6-series NACA airfoils of that time.
Below you see the pressure distribution on a flapped airfoil near maximum lift (picture source). The specifics of the airfoil don't matter much; important is the suction peak at the nose which is made possible by a large angle of attack and a flap with a ventilated gap between wing and flap.
In such a case, a small nose radius creates a very strong but narrow suction peak because a very strong pressure gradient is needed to force the flow around the tight nose contour. If the nose is blunter, the suction peak can spread out lengthwise and becomes less peaky, simply because the trajectory change of the flow around the nose is becoming more gradual. Since there is a direct relationship between local suction and local Mach number, those suction peaks must be spread out and flatter in order to allow higher angles of attack. That is the main reason why supercritical airfoils have blunter noses - they will tolerate higher lift coefficients made possible with powerful flaps.
Initial glider airfoils used rather blunt noses and high camber. With composite technology the smoothness of wings could be improved and early numerical codes helped to shape the pressure distribution such that a fairly wide angle of attack range can be covered without incurring sharp suction peaks on either surface. The Eppler code of Richard Eppler was the first such tool and by prescribing pressure levels over sections of the airfoil at specified angles of attack it made laminar airfoils easy to design on the low-power computers of that time. The result are contours with a small nose radius which would produce a sharp suction peak once the specified angle of attack range was exceeded. By suppressing the suction peak over that specified angle of attack range, the laminar bucket could be maximized in a way that a blunter nose would not allow.
Now for that promised excursion into boundary layer theory: A laminar boundary layer is stabilized by a positive speed gradient (accelerating flow) but a negative speed gradient will trip the transition to turbulent flow rather quickly, especially at higher Reynolds numbers. The back side of a suction peak has just such a negative gradient; therefore suction peaks must be avoided in order to keep the flow laminar over much of the wing chord of gliders. In addition, using camber flaps allows to shift the laminar bucket up and down on the lift coefficient scale, so the combination of a small nose radius and a camber flap will allow laminar flow over a large lift coefficient range.
Airliners cannot do the same: The Reynolds number on their wings is so large that turbulent transition happens near the nose regardless of the local pressure distribution. Therefore, they are not concerned with laminar buckets and will happily tolerate the suction peaks that come with higher angles of attack. In cruise, when managing the pressure distribution is essential to reduce shocks, the angle of attack range is extremely narrow, so the blunt nose produces no disadvantage. However, this transsonic pressure distribution demands very little camber in the forward part of the airfoil, so in order to tolerate high angles of attack during approach and landing, they need a blunt nose. The larger nose radius also helps to integrate leading edge devices like slats and Krüger flaps, which is another advantage at low speed.
According to the image (I’ve yet to read the source, I’m on it!) there’s less pressure drag, but according to an answer by aeroalias to a related question, there’s less friction drag:
Why/when is the blunt nose better?
Which one is it? Both? Which one is most relevant? Or are both irrelevant in reality? Peter Kämpf’s answer makes no mention of either alternative, only arguing about the AOA and stagnation point.
