The technological jump from no functional aeroplane to the first serious military fighter occurred in a mere 10 years. The Wright brothers conducted their first flight in late 1903 and by 1914 WWI broke out with an associated expansion in military flying. This expansion occurred almost entirely without the benefits of organised science in formal institutions and universities, and was led predominantly by tinkering aviators. Aircraft pioneers were often gifted flying-buffs or sporting daredevils, but very few of them had any real theoretical knowledge. This proved to be sufficient for the early developments, when flying was mostly a matter of strapping a powerful and lightweight engine to a basic flying design, and having the skills to keep the aircraft aloft and stable. Many pioneers, like Charles Rolls, paid with their lives for this mindset and it took many accidents from stalls and spins to figure out that something was amiss.

The specifications and operating environment of aeroplanes was, of course, entirely different from either cars or trains. Particularly the design requirements for reliable yet lightweight construction posed a conundrum for early aerospace engineers. To make something stronger, a rule of thumb is to add more material. For aircraft this means increasing the wall-thickness of the beams, frames and plates that comprise the aircraft. Of course, by making components thicker, the structure becomes heavier and less likely to fly. Furthermore, thicker structures are stiffer, which causes loads to be redirected within the structure, and rather counter-intuitively, can make the aircraft more likely to fail.

This counter-intuitive finding was played-out during the discovery of wing twisting. Wings are predominantly subject to bending forces due to aerodynamic lift that keeps the aircraft aloft. As this is entirely obvious, and since there was a great deal of acquired expertise in bridge building, wing bending loads were supported quite reliably by beams (spars) running along the length of the wing. The wing is, however, also subject to large twisting forces, and if these are not accounted for, the wing will twist-off the fuselage.

Spars running along the length of the wing and connected by a series of ribs

By 1917, the Allies had developed a certain degree of air superiority over the Western Front of WWI by means of better biplane construction. Out of necessity the Dutch engineer Anthony Fokker, working in Germany at the time, was developing a more advanced monoplane design with performance specifications better than anything the Allies had to offer. While biplanes are very light and were the preferred type of construction up to that point, their flying performance in terms of nimbleness and speed is limited due to the high drag induced by the aerodynamic interference of the two separate wings. There was thus a strong incentive to build faster monoplane aeroplanes. But since the fateful crash of Samuel Langley into the Potomac River in 1903, monoplanes had the reputation of being entirely unreliable.

Fokker D8

And indeed, as soon as Fokker’s new D8 aeroplane flew in combat situations, the wings started to snap-off as pilots pulled out of dives during dogfights. Being pressed for time, the D8 hadn’t gone through an extensive series of flying tests, and this cost many of Germany’s best pilots their lives. As a result, the German Air Force ordered a series of structural tests on the D8. As in the more standard biplanes of the time, the wings of the D8 were entirely covered by a thin fabric whose only purpose was to provide an aerodynamic profile for lift creation. The fabric itself did not carry any of the aerodynamic loads, and indeed all wing-bending loads were carried by two spars projecting from the fuselage and running along the length of the wing. The spars were connected by a series of ribs which served as attachment points for the stretched fabric. According to the testing standards of the time, the D8 aircraft was mounted upside down with weights suspended from the wings to simulate aerodynamic loads six times the weight of the aircraft. When tested this way, the wings showed absolutely no sign of weakness. When increasing the load beyond the factor of six, the wings began to fail in the aft spar such that the German authorities ordered all rear spars to be replaced by thicker and stronger ones. Unfortunately for the German military command, the accidents of the D8 become more frequent as a result of this intervention. Germany’s engineers now faced the perplexing conundrum that adding more material to the wings seemingly made them weaker!

At this point Fokker took matters into his own hands and repeated the tests in his own factory. What he found was that not only would the wings rise as a result of aerodynamic loads, but they would twist too, even though there was no obvious twisting loads being applied. Particularly important was the direction of twisting, which occurred as to twist the leading edge upwards, thereby increasing the angle of attack and the lift created by the wings, thus further increasing wing twisting, and so on in a detrimental feedback loop. As a pilot pulled up out of a dive, the extra lift needed to pull-off the manoeuvre was sufficient to initiate this catastrophic feedback loop, until the wings eventually twisted-off. Fokker had discovered the phenomenon now known as “divergence”.

But why did this divergent behaviour occur in the first place?

Imagine two horizontal and identical beams placed side by side and connected by a number ribs along their length to bridge the gap between them. One end of this assemblage is free and the other is rigidly supported (clamped). This simple construction is basically the fundamental structure of even the most modern aircraft. If a vertical load is applied exactly halfway between the two beams at the free end, then both beams will just bend upwards without any twist. However, if the vertical load is biased towards one of the beams then the assemblage will bend and twist at the same time, because the load carried by one beam is greater than the load carried by the other. The point where a load must be applied such that a structure bends without twisting is known as the flexural centre.

If a load is applied at the flexural centre (for a wing pretty much half-way between the two spars) the wing will only bend. But because the centre of pressure is located at the quarter-chord position, the wing bends and twists at the same time. The load is not applied at the flexural centre

Of course, if there are more than two beams or if the beams are of different stiffness, then the flexural centre will not be halfway between the beams. In fact, the aerodynamic lift forces are distributed across the wing and do not really act at a single point. However, the distribution of aerodynamic pressure can be summed up and represented mathematically as acting as a point load somewhere between the front and rear spars. This point is known as the centre of pressure and may shift along the length of the wing. One might assume that the centre of pressure of a wing profile is situated nicely in the middle of the two spars, but this is not what happens. The centre of pressure for most wing profiles is in fact just behind the front spar, in the vicinity of the quarter-chord position, that is 25% of the chord length behind the leading edge. Therefore it follows quite simply that if the flexural centre and centre of pressure do not coincide, the wing must twist and bend at the same time. The extent of twisting naturally depends on this mismatch and the stiffness of construction in torsion. It is the designer’s role to minimise it as much as possible, and in fact, the thick quill of a bird’s feather is located at about the quarter span to minimise twisting.

Wing lift distribution with centre of pressure at the quarter-chord. A feather features a reinforcing “spar” at the quarter-chord to prevent twisting of the feathers

In the simple fabric-covered D8 monoplane, the flexural centre and torsional stiffness of the wing depended entirely on the two wing spars. In early designs of the D8, the centre of flexure was pretty much bang in the middle between the two spars, and the fruitless attempts of beefing-up the rear spar only moved the flexural centre further to the rear and away from the centre of pressure at the quarter chord. So Fokker decided to reduce the thickness of the rear spar, thereby not only solving the problem of divergence but also making the aircraft lighter and a serious menace to the British and French biplanes.

Fokker also came up with a second design evolution that enabled monoplanes. In the early fabric-covered monoplanes the torsional stiffness of the wing is provided entirely by differential bending of the two spars. Not much can be done to improve the torsional stiffness by tinkering with the design of these spars. This was part of the reason why monoplanes were forbidden in the early days of flying. It was a safety precaution, and not a particularly unpopular one, because in practise many biplanes were not much slower than monoplanes and considerably more reliable.

An example of the shear flow around a wing box due to a vertically applied load

As a structure is sheared it creates what is called shear flow – the shearing force divided by the length of material over which it acts. Because the fabric does not carry sufficient loading, the early fabric-covered monoplane construction is considered an “open” cross-section as shear cannot flow from one spar to the other. The strutted and braced construction of the biplane, however, has the advantage of creating a closed “torsion box”. The torsion box of biplanes creates a closed cross-section and the shearing forces can flow around the material to optimally resist torsion. Torsion is therefore ideally resisted by any box or tube whose sides are continuous. The second breakthrough of monoplane construction was therefore to replace the fabric with thicker sheet-metal that could carry load. Now the closed aerodynamic surface of the wing could provide the job of resisting shear loads efficiently, while the two spars predominantly served to resist bending loads. In effect, this is an efficient division of labour concept even though it requires a much thicker and heavier wing to resist torsion.

References
[1] J.E. Gordon. Structures: Or Why Things Don’t Fall Down. DeCapo Press. 2nd Edition, 2003.

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