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When viewed from the Z axis (above or below), why are modern aircraft wings often pointed as they get towards the wingtips instead of maintaining the same surface area for their entire length?

This seems to be a design change in the last 50-60 years, as earlier designs typically featured more rectangular wings.

Extra points if you can explain why some rectangular wings feature rounded tips, with the maximum protrusion halfway between fore and aft of the wing. This design was very common for biplanes.

Wing narrows towards wingtip

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    $\begingroup$ Just to be sure: you're asking why the wing is swept back (then you already got the answer) or why the leading edge and the trailing edge are not parallel? $\endgroup$ – Marco Sanfilippo Sep 15 '15 at 8:12
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    $\begingroup$ Or are asking about the taper of wings? $\endgroup$ – ROIMaison Sep 15 '15 at 11:12
  • $\begingroup$ @MarcoSanfilippo and ROIMason, I am referring to the taper of the wings: the fact that as the wing extends towards the wingtip, the surface area decreases. $\endgroup$ – RockPaperLizard Sep 20 '15 at 8:23
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Rectangular wings are easy to build: You need just one rib size and can repeat making it several times, using the same jig. Early airplanes needed a lot of manual assembly by semi-skilled workers, and it made sense to simplify the task.

SE5a wing under construction

SE5a wing under construction (picture source)

However, to produce the least amount of induced drag, the downwash behind the wing should have the same angle over the whole wingspan. This can be achieved with washout, but then the washout needs to be tuned to one angle of attack. Change the angle of attack and your lift distribution over span is producing more drag than necessary. To overcome this problem, elliptic wing planforms were used, but they are complicated to build and prone to tip stall. This is when the wing tip loses lift first during a stall and causes the aircraft to roll violently. If this happens close to the ground, a crash is inevitable.

Therefore, designers soon settled for something wich resembles the elliptic planform, but leaves more area at the tip such that it has less loading and more stall margin. Especially when this wing is covered with sheet metal, it makes sense to have only one direction of curvature, thus trapezoidal planforms soon became the preferred way of building wings once aluminium became the primary structural material for aircraft.

SB-11 side view

The SB-11 glider uses a rectangular inner wing and a trapezoidal outer wing. This way, the mould for the inner wing could be used for the left and right side, making construction easier (picture source).

The trapezoidal wing is also helpful in another respect: Cantilever designs have high bending moments at the wing root. If the root has more chord, the spar can be made thicker, and if the area at the tips is smaller, less bending moment is created for the same lift. The bracing of biplanes takes care of root bending moment, but when monoplanes emerged, the rectangular wing lost most of its benefits.

Now for the rounded wingtips: They are an attempt to get the wing closer to the ideal elliptic planform without losing the benefit of a constant-chord wing over most of the span. Much of the wingtip design is also about aesthetics, and some people hold quasi-religious beliefs about the benefits of a particular wing tip shape. For metal wings, wingtips can be made by pressing the aluminium sheets for the top and bottom part in shape and riveting them together since the aerodynamic loads on the wing tip are low. Wingtips and fairings were also among the first parts on aircraft to be made with composite materials, which make three-dimensional shaping much easier. Closer to the root the wing needs much more strength, and here the trapezoidal planform is still the best compromise today.

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The wings are pointed towards the wing tips because most of the aircraft flying today use swept wings.

The swept wing, where the wing is swept or the wing chord reduces towards the wingtip is to reduce the wave drag. This is mainly seen in the aircraft flying in transonic (civil airliners) and supersonic (combat aircraft), while rectangular wings are used in low speed general aviation aircraft.

Sweeping the wing has the effect of reducing the normal velocity of the airflow as seen by the wing, by the cosine of the angle of sweep.

Swept wing

Source: history.nasa.gov

This has the effect of increasing the critical Mach number, above which the wave drag increases significantly.

Wing sweep drag

Source: history.nasa.gov

Some rectangular wing tips are rounded off for the same reason- to reduce drag, though in this case ,they are there to reduce induce drag.

Types of Wing tips

Source: Sport Aviation

However, the effect is marginal, so quite a few aircraft go without it.

Comparison of wingtips

Source: Sport Aviation

Another reason for airliner wings becoming 'pointed' towards the tip is structural- The wing is practically like a cantilever beam, and reducing the cross section (of the large and long wings) towards the tip reduces the root end bending moments.

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Another reason for the "pointy" design on modern wings is the incorporation of "winglets". Instead of ending in a stubby rectangle, the wing extends to a near point, which arcs upwards.

enter image description here

Winglets basically reduce the drag by keeping the air smoothly running over the wing, even near the tip. It can increase fuel efficiency by around 5%, which is pretty astounding.

You can read more about it here: http://www.nytimes.com/2013/10/24/business/eye-catching-wingtips-but-they-arent-for-show.html

This paired with the general use of swept wings leads to a more "pointy" wing design that you might be referring to.

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