# Is a winglet better than an equal span extension?

Is there indisputable evidence that a winglet improves performance over an equal span extension? Please note: I am only interested in L/D improvements.

Winglets do improve roll performance, that is not what I am looking for. Also, if span is restricted, winglets improve L/D over straight wings. Again, that is not what I am looking for.

Boeing and Airbus use fancy wingtip designs to demonstrate technological sophistication and make incredible-sounding claims about them. This is not the kind of proof I ask for. Is there theoretical or practical evidence comparing winglets with span extensions of equal wetted surface which show that the winglet produces better L/D values at any point of the polar?

Bonus points for a comparison of net lift to drag comparison, so the structural impact of both wing extension and winglet get subtracted from the generated lift. This should be the fairest way to compare both, but it seems such research is not published at all.

• would you believe NASA? – ratchet freak Sep 12 '14 at 8:17
• @ratchetfreak: Yes, if they compare them to equal span extensions, which they do not in the linked page. – Peter Kämpf Sep 12 '14 at 8:27
• May I argue you should not focus only on L/D but take into account the construction weight as well. My feeling is that an equal span extension would generate a higher bending moment in the wing root, requiring a heavier construction. What you should compare is the "nett L"/D which is the aerodynamic lift minus the weight of the wing construction divided by the drag. That gives a fair comparison. – DeltaLima Sep 12 '14 at 12:03
• @DeltaLima: Yes, you are absolutely correct. But it is hard enough to find just a fair aerodynamic comparison. All papers look at the winglet in comparison to the naked wing, without extension. That's why I wanted to reduce the complexity of the problem. – Peter Kämpf Sep 12 '14 at 12:26
• and even if they weren't "better" for some aircraft increasing wing span is no option as it'd mean they wouldn't fit on taxiways and parking spots. – jwenting Sep 17 '14 at 4:33

In the absence of a span restriction, the evidence is that a winglet is definitely inferior to a span extension of the same size when structural effects are included with induced, viscous and compressibilty drag.

The University of Michigan MDO (Multidisciplinary Design Optimization) Lab has done extensive research into the effects of structural weight in the optimization of wing lift/drag. Aerostructural optimization of non-planar lifting surfaces directly addresses this question. It describes a series of numerical optimizations on a b737-900 class generic aircraft with a NACA 64A212 airfoil, including the following representation of a structural model.

A gradient free optimizer is allowed to develop wing configurations to satisfy various constraints. The wing is represented by up to four segments. The geometry of each segment is defined by six design variables: span, area, taper, twist, sweep and dihedral. Shown are four possible wing geometries.

For the aerodynamic optimization, box-wing or joined-wing configurations were found to be optimal when only induced drag was considered. When viscous drag was added, these configurations incurred a drag penalty due to the large surface area, and a C-wing configuration was preferred. The reduction in drag was similar for these cases, ranging from 26% for the joined wing to 22% for the C-wing configuration. Ignoring structural effects makes many solutions appear attractive.

Allowing the optimizer to perform trade offs between aerodynamics and structure is a significant improvement over previous approaches, where structural performance was considered by simply constraining the root bending moment. When structure, induced drag, viscous drag, and compressibility are all considered, a raked wingtip is the optimal solution when span is not constrained. It produces 2.2% better range than the second best alternative, a winglet design. When span is constrained and the same factors are considered, a winglet design is superior.

Here is what I think you need to come to your own conclusion. First I will give a very general overview over lift creation, and then I will look at three wings:

1. An unmodified wing
2. This wing plus a winglet
3. This wing plus the winglet, but this time folded down into the plane of the wing.

For each I will plot the lift and bending moment distribution. I will assume an elliptic circulation, fully knowing that this is not what most aircraft use. But I have to pick a distribution to make all three cases comparable, and the elliptic one makes things easier. The conclusions can be generalized for other distributions.

This will be a lengthy post (you should know me by now), so thanks to all who persevere through all of it.

Lift creation and induced drag

This topic had been covered before, and I mention it again to show a very simple and elegant way to explain induced drag that does not need vortices. I want to dispel the myth that induced drag is caused by air flowing around the wingtip, and winglets somehow magically can suppress this flow.

Consider a wing with elliptic circulation over span (think of circulation as the product of the local lift coefficient $c_l$ and local chord; it is basically the lift per spanwise increment). The wing bends the air through which it flows slightly downwards, and creates an opposite upwards force, namely lift (Newton's second law). I choose an elliptic distribution because then the downwash is constant over span, which makes the following calculations easier.

The sheet of air coming off behind the wing looks trough-shaped and moves downwards, thereby pressing other air below out of the way and allowing air above to flow inwards and to fill up the vacated volume. That is how the free vortex is created, and air flowing around the wingtips has only a small part in this.

Induced drag is the consequence of the wing bending the airflow downwards. To simplify things, let's assume the wing is just acting on the air with the density $\rho$ flowing with the speed $v$ through a circle with a diameter equal to the span $b$ of the wing. If we just look at this stream tube, the mass flow is $$\frac{dm}{dt} = \frac{b^2}{4}\cdot\pi\cdot\rho\cdot v$$

Lift $L$ is then the impulse change which is caused by the wing. With the downward air speed $v_z$ imparted by the wing, lift is: $$L = \frac{b^2}{4}\cdot\pi\cdot\rho\cdot v\cdot v_z = S\cdot c_L\cdot\frac{v^2}{2}\cdot\rho$$

$S$ is the wing area and $c_L$ the overall lift coefficient. If we now solve for the vertical air speed, we get $$v_z = \frac{S\cdot c_L\cdot\frac{v^2}{2}\cdot\rho}{\frac{b^2}{4}\cdot\pi\cdot\rho\cdot v} = \frac{2\cdot c_L\cdot v}{\pi\cdot AR}$$ with $AR = \frac{b^2}{S}$ the aspect ratio of the wing. Now we can divide the vertical speed by the air speed to calculate the angle by which the air has been deflected by the wing. Let's call it $\alpha_w$: $$\alpha_w = arctan\left(\frac{v_z}{v}\right) = arctan \left(\frac{2\cdot c_L}{\pi\cdot AR}\right)$$

The deflection happens gradually along the wing chord, so the mean local flow angle along the chord is just $\alpha_w / 2$. Lift acts perpendicularly to this local flow, thus is tilted backwards by $\alpha_w / 2$. In coefficients, lift is $c_L$, and the backwards component is $\alpha_w / 2 \cdot c_L$. Let's call this component $c_{Di}$: $$c_{Di} = arctan \left(\frac{c_L}{\pi\cdot AR}\right)\cdot c_L$$

For small $\alpha_w$s the arcus tangens can be neglected, and we get this familiar looking equation for the backwards-pointing component of the reaction force: $$c_{Di} = \frac{c_L^2}{\pi\cdot AR}$$

If the circulation over span has an elliptic distribution, the local change in circulation times the local amount of circulation is constant, and the induced drag $c_{Di}$ is at its minimum. If this would be different, a higher local $v_z$ causes a quadratic increase in local induced drag, so the whole wing will create its lift less efficiently.

Now we know we can calculate induced drag and we understand why the vortex sheet behind the wing rolls up, producing two counter-rotating vortices, all without looking at the details of the wingtip. What counts is that the wing is of finite span, so the stream tube which is influenced by the wing is of finite diameter as well. Of course, in reality there is no clear boundary between air which is affected by the wing and other air which is not. There is a diffuse transition the more one moves away from the wing.

Comparison of wingtips

First the geometries: Here are three wingtips in top and front views for comparison:

Now let's look at the circulation distribution of the simple wing tip:

Again, I choose the elliptic distribution for simplicity. The corresponding bending moment looks like that:

No surprises so far. Now we add a winglet and make it work as best as possible. This means we have to give it an angle of attack where it carries the circulation from the wing over on the winglet and completes the elliptic tapering of circulation down to 0 at the tip:

The grey dashed line is the circulation of the original wing. I adjusted the circulation such that both wings produce the same lift. $b_{WL}$ is the span at the winglet tip, and for the bending moment plot I have folded the spanwise coordinate down on the y axis:

Now the bending moment starts at the wingtip with a nonzero value. Since the sideways force of the winglet is parallel to the wing spar, this bending moment contribution is constant over span. But there is more: Now also circulation at the old wingtip location is nonzero, and we get a substantial lift increase at the outer wing stations. This effect is what causes the additional lift and gives the better aileron response that winglets make possible. But it also increases the root bending moment, because this additional lift acts with the lever arm of the outer wing.

How can we compare the induced drag of the wing with winglets to the original wing? The circulation gradient is lower, that helps. Also the diameter of that stream tube is larger, but it is hard to say by how much. The sideways force on the winglet is created by pushing the vortex sheet aft of the winglet sideways out, so the trough-shaped area should become wider. Empirical evidence hints at an increase in diameter of 45% of the winglet span (see chapter 6 for a discussion of several papers on the topic).

Just for the heck of it, let's assume that the diameter really increases in line with winglet span. Then let's compare that to the straight wing extension, where the same diameter can be assumed with much more certainty:

Now also the lift on the folded-down winglet acts upwards, so the circulation at the center of the wing can be reduced even further. However, now it adds a linearly increasing part to the bending moment, and the outer wing section creates more lift, as before with the wing with winglet:

Here, the root bending moment is higher than in the winglet case. This is a second advantage of winglets: They allow to increase maximum lift with less bending moment increase than a wing extension. But the wing extension puts all parts towards the creation of lift, and not some to the useless creation of side force. Both the extended and the winglet-wing have the same surface friction and (when we assume the same diameter of the hypothetical stream tube) the same induced drag. But since the winglet creates some side force, the remaining wing needs to fly at a higher lift coefficient. Also, the intersection of wing and winglet might be as well rounded as possible, this is where early separation starts at higher angles of attack. None of this affects the straight wing extension.

Most evidence shows that winglets improve L/D over the original wing, but folding the winglet down will more than double its effectiveness in lowering drag. Even if we assume that the winglet is just as good as an equal span extension, still the span extension comes out ahead in L/D improvement because all its lift contributes to overall lift, whereas the winglet produces a side force instead. If no separation occurs at the wing-winglet intersection, both will create the same induced and profile drag (pressure and friction), because both have the same wetted surface and the same local circulation. Again, this gives winglets the benefit of equally low induced drag, which is not supported by most measurements.

The extended wingtip in the example above has interesting characteristics. It is a sweptback (raked) wingtip, which causes the local lift curve slope to be lower than that of the straight wing. This increases its maximum angle of attack and - assuming that the local area is bigger than what an elliptic wing shape would dictate - makes it possible to keep a nearly elliptic circulation distribution over a wider angle of attack range. The bigger local area is a sensible precaution against the wing tip stalling first, so a raked wing tip will combine benign stall characteristics and very low induced drag.

Compare this to the winglet, which has to be tailored for one polar point: Since changes in wing angle of attack will not change the incidence of the winglet, it cannot adapt as well to different flow conditions as can the extended wing. In sideslip the winglet will mess up the circulation distribution on the wingtip and will act like a deflected spoiler.

Conclusion

Comparing equal winglets and wing extensions gives these basic characteristics:

• Both have the same viscous drag at low angle of attack.
• Both can create more maximum lift, and both lower induced drag.
• The wing extension can create most lift for the given increase in wetted surface.
• The wing extension is more than twice as effective in lowering induced drag.
• The wing extension gives a better circulation distribution at off-design angle of attack.
• The wing extension produces the highest root bending moment for a given amount of lift.

How much the bending moment increase will drive up structural mass depends on the aspect ratio of the original wing. Low aspect ratio wings will not suffer much, but stretching high aspect ratio wings will drive up spar mass considerably. But please note that the winglet also causes higher root bending moments, and it creates less bending moment than the wing extension because it creates some side force instead of pure, useful lift.

• Hi Peter, thank you very much for this interesting article. It makes all my aerodynamic classes come back from deep memory. I agree with your conclusions. It would be nice if the structural weight penalty for the additional bending moment could be quantified. Food for thought, thanks for that! – DeltaLima Sep 13 '14 at 21:14
• @DeltaLima: Thanks for your kind words! The structural penalty can be quantified for a particular wing, but unfortunately not in a general way. – Peter Kämpf Sep 14 '14 at 8:28
• I've been thinking about the winglet a bit more. What is the local direction of flow above the wingtip? I assume it is slightly inward as the vortex sheet starts to roll up there. This means that the lift vector of the winglet would be slightly tilted forward, causing a negative induced drag. – DeltaLima Sep 14 '14 at 9:38
• @DeltaLima that would be what also my fluidynamics/aerodynamics lecture notes say. --- Peter so, in the absence of span restriction, basing on your conclusion, there is still no black&white answer: if you modify an existing wing, probably a winglet is better (less bending moment) [A320 style], but if you design a new wing, raked wingtip [B787]. do I read you correctly? – Federico Sep 14 '14 at 11:39
• @DeltaLima: The winglet needs to carry over the circulation of the wing, thus creating an inward-pointing force. This deflects the airflow aft of the winglet outward, and the lift (better: Side force) vector is pointing slightly backwards, like that of the wing itself. The winglet will produce much the same drag as the span extension, but will contribute less lift. – Peter Kämpf Sep 14 '14 at 19:12

In addition to the principles and research of other answers, here is a look at the winglet design chosen on different aircraft. Is a winglet always preferred, or only in certain circumstances?

In this answer, it is mentioned that it can make sense to add a winglet when span is restricted. Therefore, it is important to understand reasons why span may be restricted on an airliner.

Wingspan is limited structurally because bending moments place increased stress on the wing structure as the distance from the wing root increases. This means increased material and weight to handle the stress, which reduces some of the benefits of the increased span. These limits will depend on the wing structure, which varies between aircraft, so they will not be focused on here.

Wingspan is also limited by regulations. In AC 150/5300-13A by the FAA, on page 13, Table 1-2 lists six Airplane Design Groups into which aircraft are categorized based on tail height and wingspan. ICAO Annex 14 has these same groups but labeled A-F. Aside from clearance at gates and on taxiways, the group also affects other airport facilities. In most cases the wingspan is more critical than the tail height, so wingspan will be focused on here.

Group #     Wingspan (ft)
I           <49
II          49-<79
III         79-<118
IV          118-<171
V           171-<214
VI          214-<262


Below are different aircraft, and the groups in which the wingspan is categorized (values from Wikipedia). Lengths are rounded down to the nearest foot to compare against the limits. This focuses on aircraft that come with winglets as designed. Winglets available as retrofits improve performance, but the question is whether a wingspan extension would be better, which will depend on each aircraft's design.

You will see that aircraft at the upper limit of wingspan in a certain group tend to have winglets, whereas aircraft not at the limit do not. There are some exceptions to this. The LR/ER versions of the 777 reached the wingspan limit of Group V, but opted for raked tips instead of winglets. The A330/340 are below the limit of Group V but use winglets, though newer versions of the A340 do reach the limit, and all are at the upper end of the group.

An interesting case is the P-8, which is an ASW aircraft based on the 737-800. The military is less concerned with wingspan classes than commercial carriers, and endurance is an important design goal for this role. The design opted to increase wingspan and use raked tips rather than retain or add the winglets of the 737-800.

From this it seems that winglets are more useful when at a limit in wingspan. It suggests that winglets are less useful when not limited in wingspan, but is certainly not conclusive.

A380-800
Wingspan: 261 ft (Group VI)
Group Max: yes
Winglets: yes

B777-8X/9X
Wingspan: 235 ft (Group VI), fold to 212 ft (Group V)
Group Max: no
Winglets: no

B747-8
Wingspan: 224 ft (Group VI)
Group Max: no
Winglets: no

A350
Wingspan: 213 ft (Group V)
Group Max: yes
Winglets: yes

B777-200LR/300ER
Wingspan: 212 feet (Group V)
Group Max: yes
Winglets: no

B747-400
Wingspan: 211 ft (Group V)
Group Max: yes
Winglets: yes

A340-500/600
Wingspan: 208 ft (Group V)
Group Max: yes
Winglets: yes

B777
Wingspan: 199 ft (Group V)
Group Max: no
Winglets: no

B787-8/9/10
Wingspan: 197 ft (Group V)
Group Max: no
Winglets: no

A340-200/300
Wingspan: 197 ft (Group V)
Group Max: no
Winglets: yes

A330
Wingspan: 197 ft (Group V)
Group Max: no
Winglets: yes

P-8 (Based on 737-800)
Wingspan: 123 ft (Group IV)
Group Max: no
Winglets: no

A320/neo
Wingspan: 111 ft (117 ft with sharklets) (Group III)
Group Max: yes
Winglets: yes

B737 NG/MAX
Wingspan: 117 ft (with winglets) (Group III)
Group Max: yes
Winglets: yes

B737 Classic
Wingspan: 94 ft (Group III)
Group Max: no
Winglets: no

E170/175/190/195
Wingspan: 85 ft (E170/175) 94 ft (E190/195) (Group III)
Group Max: no
Winglets: yes

Less common aircraft:

SSJ 100
Wingspan: 91 ft (Group III)
Group Max: no
Winglets: no

IL96
Wingspan: 197 ft (Group V)
Group Max: no
Winglets: yes

CS100/300
Wingspan: 115 ft (Group III)
Group Max: yes
Winglets: yes

• Another interesting data point to suggest that span increases are better: Boeing is going with span increases that fold up for parking on the 777X. Best of both worlds that way, I guess. – reirab May 7 '15 at 20:46
• "Wingspan is also limited by regulations." The regulation is not the limitation. It is merely a formal classification which allows manufacturers, airports and possibly others to design compatible products. – Pilothead Sep 29 '18 at 13:05
• So a Zeppelin-Staaken R.VI family (1917) would be in Group IV family with the B-29. The largest of the WWI giants would be in group V. Just to put things in perspective. – Harper - Reinstate Monica Dec 17 '18 at 22:08

This paper from 2005 states that is not a settled question:

When the geometric span of the wing is constrained, well-designed winglets do provide significant reductions in airplane drag and have now been incorporated on aircraft ranging from sailplanes to business jets and large commercial transports.

(and I understand you agree with the above)

The justification for winglets as opposed to span extensions for aircraft that are not explicitly span-limited is less clear. Studies at NASA Langley that compared these two concepts with constrained root bending moment concluded that winglets were to be preferred over span extensions. (Theoretical parametric study of the relative advantages of winglets and wing-tip extensions - Heyson, 1977 - NASA TP 1020). Studies with constraints on integrated bending moment suggested that the two approaches were almost identical in these respects. (Effect of winglets on the induced drag of ideal wing shapes - Jones, 1980 - NASA NASA TM 81230). A somewhat better weight model (which includes the effects of changes in wing chord on structural efficiency) leads to very similar conclusions as shown in figure 9. The conclusion is that the complexity of the structural model and constraints limits the general applicability of any such conclusions.

In particular

The evaluation of optimal winglet height and dihedral, depends on the details of the wing structure, whether the wing is gust critical or maneuver critical, whether large regions of the wing are sized based on minimum skin gauge, and whether the design is new or a modification of an existing design. The evaluation of wing tip device advantages must be undertaken for each design and include an array of multidisciplinary considerations. These include the effect on aeroelastic deflections and loads, flutter speed, aircraft trim, stability and control effects (especially lateral characteristics), off-design operation and effects on maximum lift, and finally, marketing considerations.

To conclude:

There is no clear answer to the optimal configuration, and even when winglets are adopted, the geometries vary widely.

What I understand from the above is that if you include no structural or a simple structural limitation, a winglet is better than a span extension (NASA TP 1020 referred above) otherwise you will have to search for a case-by-case answer.

There is also this other paper (behind paywall) from 2010 (5 years later than the above paper) that in its abstract reports similar conclusions:

When only aerodynamics are considered, closed lifting-surface configurations, such as the box wing and joined wing, are found to be optimal. When aerostructural optimization is performed, a winglet configuration is found to be optimal when the overall span is constrained, and a wing with a raked wingtip is optimal when there is no such constraint

• if you include no structural or a simple structural limitation, a winglet is better than a span extension No, the opposite is true. – Peter Kämpf Sep 13 '14 at 18:31
• I'm guessing he's saying that without structural limitations, a span extension is preferable. – falstro Sep 16 '14 at 19:05

Yes because a winglet reduces the drag caused by the lower part of the wing comes onto the higher part of the wing and rotates forming a vortex called wing tip vortex and the winglet reduces the strength of the vortex reduces the drag also makes it more efficient and has extra range from the winglet. So its better to have a winglet than no winglet