# Why does the mass penalty of cantilever vs externally braced wing decrease with aircraft size?

From Wikipedia Cantilever wings require a much heavier spar than would otherwise be needed in cable-stayed designs. However, as the size of an aircraft increases, the additional weight penalty decreases. Why? The article does not have a citation there.

• Speculating that the increase in spar size to cantilever a large wing vs having it cable-stayed is much smaller than the increase in spar size to cantilever a small wing vs cable-stayed? i.e. the difference in size and weight of the spar isn't that much when the wing is large, especially when offset by the lack of drag and weight of the stays. Commented May 21, 2020 at 13:09
• My guess is that Wikipedia is wrong here, I'll add a "citation needed" tag to that claim. Recall that the Gossamer Condor and Gossamer Albatross man-powered monoplanes had large spans and still had to be wire-braced. Commented May 21, 2020 at 13:34
• While adding a citation tag I noticed that the whole section of the article has been tagged as unreliable and, reading it through, it is full of little mistakes and muddles. I'll try and give it a proper makeover if I can find the time, meanwhile I'll give a provisional answer here. Commented May 21, 2020 at 13:43

I think the Wikipedia article is wrong. Scaling the structure has other issues, but spar weight is not one of them.

The correct approach is to compare the scaling-up of a cantilevered monoplane wing with the same scaling-up of the equivalent wire-braced monoplane design.

In both cases, structural weight rises with the square of the linear scaling, for example doubling the length and span will give a fourfold increase in structural weight. The designer's challenge is to maintain the same weight of structure per unit of wing area, called wing loading, at scale.

The real difference comes not with scale but with speed. As the speed rises, the drag of the bracing rises more sharply, while the aerodynamic forces on the wing demand a stronger structure, especially thicker skinning. Eventually you reach a point, at around 200 mph (300 kph), where the drag of the bracing becomes excessive and the strength of the airframe will admit a cantilever construction without excessive additional weight penalty.

This was what triggered the historic change in design habits which the Wikipedia author was trying to explain and is, I suspect, what they would have said had they known better.

I have now substantially reworked that section of the Wikipedia article (current version here) and added a couple of citations.

• so higher speed=thicker skin=stronger wing. right? Commented May 21, 2020 at 15:03
• Well, it's half-right. Things like the resistance of the skinning to local knocks, scuffs and wrinkles can also be important. These matter more when the skin is structural. If your wing skinning can take that kind of treatment at 200 mph then you are more than half way to a stressed-skin cantilever: it's worth going the rest of the way. Commented May 21, 2020 at 16:35
• @Guy Inchbald appreciate your excellent work. Please check "maintain...wing loading at scale". This is not possible unless it is accompanied by an increase in speed. Hence, higher G loads when maneuvering lead to the need for a stronger spar. Late 1930s aircraft were literally ripping their wings off in high G maneuvers, sadly, in some cases, this lead to a trend toward smaller tails. But the spars did get stronger. Commented May 21, 2020 at 19:17
• @RobertDiGiovanni. Sorry, that appears totally confused. It is well known that the square law in scaling apples at constant airspeed. Commented May 21, 2020 at 19:49
• You appear to misunderstand what wing loading is: it is the weight supported by a unit area of wing. Or, if you like, wing loading = aircraft weight divided by overall wing area. You'd need to ask a new question to get a fuller answer. Commented May 22, 2020 at 5:18

Interesting, because the largest bridges are cable stayed. Any design depends on anticipated G loading and top speed. Not sure if this "engineering by rote" maxim belongs in anyone's concept toolbox.

Stayed cable designs suffer from increased drag with increasing speed, but the major penalty is the inefficiency of 2 wings compared to one, and the further penalty of having to carry a heavier, more powerful engine for similar cruise performance, with another penalty of having to carry more fuel to get the same range.

Larger planes are generally not designed for fighter plane-like G loading, and a slightly heavier internal spar on a more efficient single wing become advantageous.

• Hey, thanks for the answe. Boeing SUGAR has a strut-braced wing. With jury struts too. Commented May 21, 2020 at 11:31
• The difference in g-loading is due to the lower roll/pitch/turn rate? Commented May 21, 2020 at 11:32
• @Abdullah yes, sort of like driving the family car instead of racing around. These planes can be built to save weight and drag. Higher aspect wings too. Commented May 21, 2020 at 17:17