More about aerospace >

Aerodynamics of the Tailless Wing

Updated 10 Jan 2021

This tale is still emerging. While my cognizance of it at present lags even further, a remarkable thesis is suggesting itself. With luck, this page will continue to grow in completeness, coherence and (who knows?) conviction.

Introduction

"But the aeroplane does these things, and if the theory does not give warranty to the practice, then it is the theory which is wrong" — JW Dunne, 1913.

The tale of the tailless aeroplane is an extraordinary one of unsung genius, wilful ignorance, missed opportunities and seemingly avoidable tragedy. Only recently has it become possible to answer some of the questions that have long been in my mind and crystallise my suspicions, thanks largely to two resources; the purchase of the JW Dunne archive by the Science Museum and the tireless dedication of one of NASA's Chief Scientists, Albion Bowers.

JW Dunne built the world's first certified stable aeroplane, the D.5. He rose to high office and honour in the Society, sitting on its ruling Council and earning its first ever certifiate of Fellowship. It is an astonishing fact that, although his D.5 had a talless swept wing, flew as far back as 1910, used its wing endplates not as stabilising fins but winglets, needed no rudder, and none of the 27 or so Dunne aeroplanes flown ever killed anybody (a remarkable achievement for the pioneer era), almost all subsequent designs have had unsafe characteristics to a greater or lesser extent and needed stabilising fins, with one even being declared to be the nastiest aeroplane ever before killing the world's most experienced tailless pilot Robert Kronfeld. What did Dunne know that the world so soon forgot?

A generation later Reimar Horten worked steadily on the problem throughout the 1930s to the 1980s but he, like Dunne, was studiously ignored by the mainstream and his discoveries all but forgotten. What on Earth did their colleagues and successors in the field think they had been doing for the century passed between Dunne's lecture to the Aeronautical Society and the recent re-evaluation of Bowers – and for the most part are still thinking?

Only a tiny handful of designers ever really knew what they were facing, understood the nature of the beast and kept safely within the limits of their own ignorance. Perhaps only Dunne achieved all three. He built that first certified stable machine largely through intuition driven by trial-and-error. Reimar Horten rediscoverd many of its secrets through more formal analysis coupled to that same intuition and created the first viable jet flying wing, though the evidence is suggesting that he never quite cracked the secret of the safe and stable aeroplane.

The rest of those famous tailless names – GTR Hill, Alexander Lippisch, Jack Northrop and their ilk – remained unaccountably blind to the lessons of their forebears and contemporaries. Following the lead not of Dunne but of his debunked theoretical opponents Jose Weiss, Handley Page and Igor Etrich, their tailless aeroplanes never lost the need for a tail fin and, despite the presence of one or more such, gained the whole concept a reputation not for safety and stability but for caprice and lethality. Their dominance amounts to a breathtaking institutionalised incompetence.

Then, over 80 years after Dunne's theory was published, Bowers and his colleagues once more recognised the potential of the tailless wing, with a little help from an equally forgotten 1933 paper of Ludwig Prandtl, and began to re-evaluate, rediscover and advance the theory once more. The extent to which Horten presaged Bowers' findings is a topic of active debate. However much of Dunne's intuition is now vindicated by computer analyses and experimental drones, while the rest still awaits rediscovery and re-evaluation.

At least, that is the thesis which I am exploring and building here. There is a parallel tale to unravel of Charles Fauvel and the unswept flying wing, but please, one thing at a time. My main thesis is already edgy enough and demanding of extraordinary evidence. Well, we shall have to see how it all pans out.

Flying without a tail

Any aeroplane relying on a human pilot, especially if it is to handle safely, must be stable and controllable in all three axes. Two of these, pitch (longitudinal) and yaw (directional), generally require additional stabilising tail surfaces, with control surfaces attached. But these add drag and complexity. It seems far more elegant to do away with that clumsy tail and set the wing free. A plane with no horizontal stabiliser (tailplane or foreplane) is described as tailless. A tailless aeroplane without a big fuselage to pack stuff into is a flying wing. Both these types usually keep one or more vertical fins. A flying wing without fins or anything more than a few small bulges to mar its lines may be called an all-wing design. All such tailless types still have to maintain stability and control in both pitch and yaw, without a tail. Banking a tailless plane into a turn brings its own special problem.

Only a very few designers have been able to do away with all such aids. Pioneer Lt. JW Dunne built his he D.1 biplane glider at Farnborough and it was flown by his commanding officer Col. "Jack" Capper at Blair Atholl in 1907. Dunne's subsequent monoplanes had only partially-downturned wingtips. A generation later the Horten brothers produced a series of very clean monoplane flying-wing gliders, designed principally by Reimar and culminating in the Gotha/Horten 660 jet fighter. Most recently the Prandtl-D experimental drone has been flown by NASA engineers. None of these had any vertical surfaces. Even the wingtips of the Dunne monoplanes yielded only minimal side area which was quite insufficient in itself to provide stability, as Northrop found out the hard way with his XP-56 "Black Bullet".

Longitudinal stability

For an aircraft to fly level, its centre of pressure (CP) must coincide with its centre of gravity. To climb, the CP is moved forward, to dive it is moved back. To be stable, any small deflection must move the CP in the right direction to set up a counteracting force that tips the plane back onto an even keel. Unfortunately, standard aerofoils have a feature called camber, an upward bowing in the middle, which makes them inherently unstable. Luckily, by adding a tail to provide the counteracting force, the plane as a whole can easily be stabilised. If there is no tail then there are several ways in which the wing itself can be made stable:

Of these, symmetrical aerofoils are not very efficient, though they have for other reasons been used on some aerobatic and early supersonic types, while forward sweep also has some inherently undesirable characteristics, such as directional instability, which prevent its widespread use. A straight (unswept) tailless wing must be either symmetrical or reverse-cambered. However more often reverse camber, sweep and washout are used in combination, with results that form the technical meat of this story.

Directional stability

When you look at all the so-called tailless aeroplanes, primarily those of GTR Hill with his Pterodactyls, Alexander Lippisch with his Deltas and Jack Northrop in the US, they invariably have to keep their stabilising fins or some equivalent surface. Yet sweepback in principle confers stability.

A straight (unswept) tailless wing with a symmetrical aerofoil has neutral stability in yaw. Usually there will be some sort of bulge at the front for the pilot's cockpit, and this forward side area creates instability. The use of tail fins provides the necessary side area behind the centre of gravity to counterbalance it. However there is nowhere very far back on a straight wing, so the fins are not very effective and must be overlarge. All in all, the end result is difficult to achieve and inherently inefficient. (Nevertheless, exponents such as Charles Fauvel had some degree of success with it).

Sweeping the wing back makes life a lot easier. When it yaws the forward wing widens in effective span, increasing drag, while the rearward wing reduces in span and the accompanying drag, so the plane straightens itself out. But the effect is small and adding a forward nacelle for the cockpit and other such issues can easily destabilise the wing again. One solution, discussed later, is to combine washout with droop (anhedral) at the tips, so that the surface actually creates a small amount of downforce. When the plane yaws, or is met by a side gust, the downforce and associated drag increase on the forward tip and decrease on the rearward tip, significantly enhancing the wing's natural stability.

Then there is the problem of control. With no fin, there is nowhere to put a conventional rudder, and even with a fin it is too far forward to have much effect. The answer is the drag rudder. A device capable of creating drag when operated is installed near each wing tip. Increasing the drag on one side then pulls that wing back, yawing the plane as required.

Control balance

Tailless aeroplanes with a modest sweep, and especially flying wings, behave in roll and yaw like any ordinary aeroplane of the same span, which may be quite large. However they behave in pitch like any small aeroplane of the same overal length as the wing. The pilot must handle a big, lumbering thing slow to respond in roll and yaw, but also a sprightly little thing quick and agile in pitch.

When performing a turn, it is necessary to smoothly coordinate pitch and roll, along with a touch of yaw (see later). The widely varying characteristics about each axis make the tailless aeroplane difficult to handle in the turn, and even more difficult to design for safe handling while turning and manoeuvring generally. Without any correction to the imbalance, the plane will be badly affected by Dutch roll and similar unpleasantnesses. Some palliative can be applied by making the roll control sensitive and powerful, with the pitch control sluggish and insensitive, but achieveing these contrasting characteristics with a single pair of elevons can tax the less ingenious designer. Some successful high-performance sailplanes have followed this route, but such competition thoroughbreds are almost always a handful to fly and sailplane pilots must develop a high degree of expertise before they are safe in the things.

The sharper the sweep angle, the easier things become, but the less efficient the wing is aerodynamically.

Adverse and proverse yaw in the turn

When banking into a turn, most aeroplanes suffer from a phenomenon known as adverse yaw. The pilot operates their controls to lower the outer aileron and raise the inner. As the outer one is lowered this increases lift to raise the wing. But it also increases the associated drag, pulling the wing back. The inner wing behaves in the opposite way; raising its aileron reduces both lift and drag, so that wing skids forwards as it dips. The net effect is to yaw the nose away from the turn. This is adverse yaw.

For the plane to turn safely, it needs to head into the turn not away from it. The traditional solution is to provide a tail fin with a rudder. The fin helps to check the yawing motion, while the pilot uses the rudder to compensate for the adverse yaw and direct the nose into the turn.

Frise ailerons have a short projection of the lower surface, forward of the hinge. When the aileron is raised, the forward projection lowers into the airstream and creates drag. But when the aileron is lowered, the projection tucks up into the wing and the gap below it creates far less drag. Thus, the Frise aieron incorporates its own drag rudder. They are commonplace, but can seldon fully counter the adverse yaw from their main surface.

A better solution is to arrange for the main aileron surface to provide a small amount of proverse yaw, in which the banking action has the opposite effect to the adverse phenomenon. Indeed, the quest for proverse yaw has found it to be someting of a Holy Grail, desperately sought but ever out of reach since the day it was lost. For yes, it was found and lost.

Stalling and spinning

When a wing struggles to create enough lift, its nose goes up until the airflow can no longer follow it round and breaks away in turbulence so that the wing immediately loses lift, a phenomenon known as the stall. It is vital that the control surfaces remain outside the turbulent region or they cannot be used to recover from the stall. Often one wing stalls before the other, causing it to drop and the plane to enter a spin, a spiral dive from which revcovery can be difficult or even impossible.

If you have a tail, the elevator and rudder should remain usable. You can use them to correct the wing's attitude and restore lift. But if your wing is tailless, you have only your elevons. It is therefore vital that either the stall is confined to the wing root, or that it will naturally recover without pilot intervention, preferably both.

The problem with the tapered and/or swept wing is that the tip region tends to stall first. Taper reduces the Reynolds number at the tip, changing the flow characteristics at the critical angle of attack, while sweep creates a sideways flow which accumulates towards the tip, causing the lifting flow to break away.

Two features which help delay the stall are camber and, at the tip, washout. Both work by aligning the leading edge better with the incoming flow, thus delaying the point of separation. Once the plane has entered a spin, they also help with recovery.

The Zanonia fallacy

The winged seed of the exotic Java cucumber, then known to botanists as Zanonia macrocarpa (though nowadays it is classified as an Alsomitra), has an extraordinary property. The bracts of the seed form a crescent-shaped wing, with the seed providing the nose weight needed for stable flight. Crucially, the wing is slightly curled up at the back. This creates a "washout" or reduction in the angle of incidence to the tips. Because the tips curve back from the centre section, this washout provides stability in pitch. The seeds disperse by gliding away from the parent tree.

German investigator Friedrich Ahlborn studied this naturally stable all-wing and recognised its potential for use in aeroplanes, publishinbg his study in 1897. His study inspired many early aeronauts, especially those who recognised the need for safe and manageable flying characteristics (a view which the Wright brothers disagreed with for a long time). It was soon realised that much the same upturning could be seen in the wings of the common pigeons and crows they saw flapping about.

Chief among them were José Weiss and Handley Page in the UK, and Igor Etrich in Germany. Yet when these pioneers copied such wing forms, with or without a tailplane, they found it necessary to add a tail fin before their planes would fly straight. Weiss returned to painting, Etrich to a conventional tail and Page to a conventional straight wing as well as a tail. The Zanonia agenda was proving a miserable failure.

JW Dunne

Their contemporary JW Dunne shared, even exceeded, their passion for a safe and stable aeroplane. He was a creative thinker and experimenter, not given to advanced mathematics (whatever some commentators claim). His approach was to make hundreds of small models and methodically tweak each one over and over to see how it flew. His writer friend HG Wells described them as being made of "cane, paper and elastic", though most of the later ones were just tiny paper planes less than 4 in (10 cm) in span and with one or two sewing pins for noseweight. Nevertheless in 1910 his D.5 became the world's first certified stable aeroplane, officially witnessed by none other than Orville Wright and his lawyer. He himself had a unique grasp of the theory at that time, which he expounded to the Aeronautical Society of Great Britain in 1913. Not being a mathematician, his understanding was almost wholly intuitive, born of watching seagulls, thinking everything over and experimenting with his endless models. He could confidently state, "But the aeroplane does these things, and if the theory does not give warranty to the practice, then it is the theory which is wrong." And yes, mainstream theory remained lethally wrong for the next century.

Dunne was unimpressed by Ahlborn's Zanonia seed, having gone a rather different and more thorough route. He realised that the upturned trailing edges were what made the wing directionally unstable. In the slightest wind the seeds would zigzag crazily all over the place as they flew. This was no doubt good for wider seed dispersal, or for a bird dodging in and out among the trees, but hopeless for a stable aeroplane. A better solution could be found in seagulls. These birds could soar for significant periods, making no perceptible movement of their wings, while their small tails were not needed, closed up and tucked away to minimise drag. Yet they could still manoeuvre adroitly when they wanted to. Dunne observed the gulls more closely than most, for his sister May would draw them in by feeding them, allowing him to observe their manoeuvrings from close quarters. This close-up observation revealed that they banked by dipping down the leading edge of an outer wing. This had the same effect on lift as raising a trailing aileron. Indeed, the leading edge there tended to have a permanent slight droop. This helped impart the same washout as seen on the Zanonia, but its effect on drag and directional yaw was quite different. Dunne found that, crucially, provided the wing was swept then turning down the leading edge towards the tip made it stable in both pitch and yaw.

In seeking to simplify the seagull's wing for manufacture, Dunne came up with a conical wing profile which washed out progressively along its span. He initially applied it to the delta wing, thus discovering late in 1904 what we now call the Rogallo delta. But such a delta is not very efficient. So in 1905 he successfully applied it to a swept wing of constant chord. In fact he applied two cones on each side, one to set the washout of the outer leading edge and the other to set a "wash-in" to the inner trailing edge. This latter greatly helped in automatic recovery from the stall.

For control, rather than have adjustable leading edges like a seagull, or wing warping like the Wright brothers, he tried trailing-edge ailerons. Turning down the leading edge even further at the tip produced a downforce, negative lift. Now in a turn, when the outer aileron was lowered it reduced the downforce and accompanying drag so the wing slewed forwards, while raising the inner cause both the downforce and drag to increase, holding it back. The nose automatically swung into the turn. Proverse yaw had been discovered. By 1906 he was ready to build a full-size aeroplane, was taken on at Farnborough and his first manned glider flew as a military secret in 1907.

His 1909 patent, taken out as soon as the secret was declassifed, shows how the conical development can be applied to both delta and swept planforms. All of his aeroplanes (save one civilian example designed while the cone was still secret) incorporated this swept wing with conical washout and negative lift at the tips, thus also possessing proverse yaw in the turn and a remarkable ability to recover unaided when thrown about the sky.

Since they were longitudinally stable they needed no tail plane, and since they were also directionally stable they needed neither fin nor rudder. The ailerons inherently provided the rudder effect, while moving them together in the same direction made tham act as elevators.

Most of Dunne's biplanes featured end plates at the tips and these are often mistaken for stabilising fins, even assumed to be fitted with rudders. That understanding is quite false. His first successful biplane, the D.1, had no such endplates and demonstrated stable flight in 1907. One must recall that such surfaces characterise the boxkite, which had flown in the previous century, and some tailed aeroplanes such as the Bristol Boxkite, and in none of the examples did the vertical wingtip surface contribute to stability. Dunne acknowledged that in the case of his swept wing the endplates did add stability, but his biplanes were on the whole criticised for being excessively stable; they did not need fins. He added endplates to his later biplanes in part for the same reasons that Bristol would, to reduce tip losses, but mainly because he was concerned with the effects of sideways flow induced by the wing sweep. He thought of these vertical surfaces as "side curtains" to check the sideways flow. This both improved the overall efficiency of the wing and enhanced the effectiveness of the tip section, which included the control surfaces. The turning-down of the monoplane wing tips had a similar effect, although here he acknowledged that the additional side area was useful. While he only hazily understood sideways flow and some of his intuitions have proved incorrect, he was nevertheless the first to both recognise the problem of sideways flow and develop a practical solution; his side curtains were the earliest precursors of what were later to be reinvented as wing fences and winglets.

The new misdirection: Hill, Lippisch and Northrop

Instinctive reflex

There was another reason why Dunne had wanted to do away with the tailplane. The stall happens suddenly when the airflow over much of the wing transitions to a turbulent state. The tailplane provides a separate surface, insulated from the chaos. If there were one continuous, graded surface then one end would stall while the other remained under control. The stall would not be sudden and catastrophic but progressive and correctable. No other means of recovering from a stall was then known, and even after WWI it was a haphazard procedure strictly for daredevils. So a plane that could automatically recover itself without pilot intervention would be even better, and this was also one of his goals. His biplanes achieved such automatic stability, while his monoplanes would initially "pancake" down in the stall and he never dared stall one above 60 ft (20 m) or so for fear of it failing to recover and killing him. As it was, he destroyed several examples while investigating the phenomenon.

GTR Hill left his time as a pilot in WWI with a profound sense of waste at the numbers of pilots killed in uncontrolled aircraft crashes, typically following a stall. He studied aeronautics and determined to resurrect Dunne's quest for the safe aeroplane. He contacted Dunne, who sent him a drawing and a model. His first Pterodactyl followed Dunne's general plan but differed in much detail, abandoning the wingtip droop among other things. He wanted a wing aerofoil which was more inherently stable and did not need all of Dunne's complicated subtleties. He knew from the work of Handley Page and others that turing up the trailing edge - reverse camber - was the only way to do this without using an inherently inefficient symmetrical aerofoil. So he developed a mathematical technique for designing aerofoils with positive camber forward and reflex camber aft, to yield a stationary centre of pressure. Aerofoils such as RAF 34 were soon developed along these principles and he used them extensively in his later Pterodactyls.

My thesis here is that he discarded too much of Dunne and his seagulls, turning instead to Handley Page's unstable crow inheritance. Despite working right through until the 1950s, he never designed another machine that did not need a tail fin. When Page's company returned to the talles Manx, they too fell back into their old ways.

The rot soon spread. Hermann Glauert was a German aerodynamicist who came to work in the UK for some time after the war, and there he came across Hill's methods. He subsequently took them with him back to Germany and there he and Walter Birnbaum further developed the theory. Meanwhile an up-and-coming Alexander Lippisch had dreams of high-speed flying wings and had been introduced to the basics by Friedrich Wenk, whom he had helped build the revolutionary Weltensegler flying-wing sailplane. The timing was just right, for Lippisch was able to pick up on Glauert and Birnbaum's work for his own tailless project, the Delta 1.

But Germany missed a trick. Dunne was a great idol of the early German aeronauts; they had even tried to poach him in Edwardian times from Britain with promises to put a rage design office and a whole factory at his disposal, and when he had refused to license his patents to them, they had gone ahead anyway (though they always kept the tail). But for the new generation of German engineers he had become a semi-mythical figure from the past. The excising of his subtleties, perpetrated by Hill, was not noticed and the crow still laughed at them from its perch.

Stubborn instinct

Lippisch would go on to abandon reflex camber and become the "father of the delta aeroplane" and designer of the tailless swept-wing Messerschmitt Me 163 Komet rocket fighter of WWII. Nevertheless he continued to encounter many intractable problems and never really conquered the stability and handling issues, vertical fins or no.

Meanwhile Jack Northrop in America began pursuing his own dream of the tailless swept flying wing. Although in occasional contact, even cooperation with his European counterparts, he followed his own ideas. When he eventually dared remove the tail, like Lippisch he never really conquered the intractable problems, vertical fins or no. His company would eventually resort to fly-by-wire computers to make the thing flyable.

Prandtl's near-miss

In 1920, Ludwig Prandtl had famously published his elliptical lift distribution curve, which minimised induced drag and gave the maximum efficiency to a wing of a given span. It had quickly become a byword in design circles and remains established dogma to this day. But then in 1933 he published the answer to a subtly different question; what is the optimal lift distribution giving the lowest induced drag for a given amount of lift rather than a given span? In other words, what was the most aerodynamically efficient, regardless of span? It turned out to be not elliptical but bell-shaped, with the lift tailing off to amlost nothing before it reached the very tip. Moving some of the lift inboard in this way meant that the structural forces on the wing were reduced and it could be made lighter, reducing overall weight and the lift needed to counter it, and thus also the reducing the drag induced by that lift - a double-whammy on drag reduction. Lifting capacity is generally a greater determinant of a wing than its absolute span, while light weight is always high on everybody's agenda, so this curve was actually more significant than the elliptical one.

However Prandtl stopped at calculating the total induced drag, he did not go on to consider its distribution along the wing as he did for the lift. In this, he once again missed a forgotten subtlety of Dunne's - proverse yaw. Another point wirth noting is that he applied his analysis essentially to a straight wing, tacitly assumed to have a tail, rather than to the tailles swept type.

Some recent writers have suggested that Beverley Shenstone, the aerodynamicist in charge of the Spitfire wing, recognised the importance of Prandtl's bell-shaped lift and designed it in. The wing itself was undeniably elliptical in shape, but its lift was not distributed that way. For a start its proportions thinned as low as 6% thickness at the tips, reducing the loading as it thinned. More unusually it also washed out progressively, to a small negative angle of -1/2 deg at the tips, so the lift distribution would have been closer to the bell shape than the elliptical. Shenstone was well travelled and well connected, he probably knew of Prandtl's work. However mainstrean sources show no hint of any such overt design strategy, noting instead the benevolent stall characteristics the solution imbued. Frise ailerons were adopted to mitigate adverse yaw in their own right. It is conceivable that some deliberate disinformation was indulged in, to conflate the planform with the aerodynamics in a bid to keep the Spitfire's secret from the light of day. Shenstone himself was capable of pointing at the "ideal" wing shape while in the next breath explaining how its thickness and washout changed things, so that everybody has known ever since that the elliptical wing was what gave the Spitfire its superior performance and handling. Only, it wasn't the ellipse, it was the lift distribution dervied from those more subtle features. However, Shenstone may well have stumbled on a broadly similar lift distribution through a process of convergent evolution or unconscious emulation rather than any directed plan, and just not bothered to explode the "ideal" tag which so conveniently offered. We may never know.

Reimar Horten

The Horten brothers were passionate about flying wings. Reimar Horten studied under Prandtl in the 1920s. He designed and built his first flying wing in 1933, the same year that Prandtl published his bell-shaped curve. However Horten was not an able enough mathematician to employ the theory until Alexander Lippisch published a design method for a simplified version. In at least one significant aspect Horten went a step further, considering not just the distribution of lift across the span, but also that of the accompanying induced drag. He continually refined his theories and his designs, battling with the principlesd of stability and proverse yaw, and leading to the Horten Ho 229 jet fighter prototypes of 1945. None of these designs ever needed fins, although it has to be said that some did not behave well and his successes with proverse yaw relied mainly on the drag properties of Frise ailerons. While in an Allied prison in 1945, it is said that he wrote his doctoral thesis on the subject of span loading and proverse yaw. I have yet to confirm whether this is true, but if it is then it was the first real step in understanding since the days of Dunne.

After the war, Reimar Horten applied to join the "paperclip" expatriate technologists in the US, and also in the UK, but was refused both. This despite working for the British for a time in Germany, in the immediate aftermath of war, and being interviewed by many in the UK industry. His rejection must in part be down to an unsympathetic summary of his knowledge by a British official interviewer. Sir Richard Fairey liked what he saw but his colleagues at Fairey Aviation refused to work with a German.

On the other hand, Lippisch was readily accepted into the US. One reason for this difference in perception of the two rivals was that Lippisch had fifteen years of solid financial backing and academic research programmes behind him, leading to a large pile of materials attesting to his standing, not to mention a revolutionary warplane. By comparison the Hortens had always struggled and much of their accumulated expertise was never given the resources to be properly written up, remaining in Reimar's head or notes. Wind tunnel funding had not been forthcoming so they had had to be replaced by glider flights, leading to the circular criticism that the use of gliders showed his work to be too trivial for a wind tunnel. His rather high-handed "I don't need experts, I am the expert" attitude may have had some truth to it, but it lacked a visible evidential base and consequently was not believed.

In part due to the recent release of classified reports, the claim has arisen that Horten was able to design proverse yaw into his flying wings. Together with sweepback, this created a plane that was directionally stable. None of his earlier designs used fins and some were indeed tame enough. Those of Lippisch and Northrop suffered from adverse yaw - a tendency to shy off course when banked into a turn - hence their constant need for fins. However Horten's mileage varied with different designs, only sometimes deliberately, and later in life he was not above providing fins where necessary. His own accounts are somewhat self-contradictory, but then he liked to keep his little trade secrets and gave them out only reluctantly.

A comparison of wing root sections, found in technical drawings of their various designs, reveals that both Lippisch and Horten originally opted for reflex camber but, in the pursuite of transonic performance, by 1944 had joined Northrop in adopting symmetrical profiles. Junkers, whose flying wings originated back in the pioneer days and who occasionally still dabbled, gave their proposed EF 128 tailles swept jet fighter's wing conventional camber with washout. When Horten returned to sailplanes after the war, he also returned to reflex camber. In all this, Horten does not stand out from the general German wartime picture as unusually insightful.

If he was, as claimed and contrary to appearances, able to design proverse yaw into the wing itself and wrote his Ph.D thesis on the subject, that would mark him out as the first designer since pioneer JW Dunne to conquer the stability of the finless aeroplane. But his track record on safety unarguably falls short of Dunne's. Was this through lack of understanding or because, as so many high-performance competition aircraft designers have done, he deliberately put ultimate performance ahead of safety?

He would continue to refine his understanding and to design aircraft until the end of the 1980s. It is perhaps telling that one of his last, but unbuilt designs, the Piernifero 3 ultralight sailplane, had turned-down wingtips; his formula to date had eveidently not entirely satisfied him, but had light finally dawned? Perhaps the persistence of the Zanonia's reflex camber in its aerofoil answers that question.

NASA

In 1950, around the time Reimar Horten seems to have been making some further advances in proverse yaw, RT Jones at NACA revisited the span loading problem according to various criteria, among other results deriving a bell-shaped curve similar to Prandtl's and with broadly similar criteria. In particular, he derived the lift distribution for minimum induced drag, for a given total lift and structural bending moment, while allowing the span to vary. Besides thus effectively re-discovering Prandtl's curve (of which he apparently had no knowledge), he also derived the induced drag distribution - the first time this is known to have been done.

Albion Bowers and colleagues at the NASA Armstrong Flight Research Center subsequently revisited the bell lift distribution and the swept flying wing. Bowers had gone back to bascis and studied bird flight. Like Dunne before him, he put the observed behaviour ahead of the theory. He realised that the accumulated data gave the lie to the traditional mantra of elliptical lift distribution, nor could the latter explain how birds can turn well without a vertical tail fin. At some point he also unearthed Prandtl's forgotten bell curve and by 1994 had realised that it could in theory imbue a swept wing with proverse yaw in the turn, making the fin unnecessary. At last a mainstream researcher had rediscovered what Dunne had worked out by 1906, patented in 1909 and and published in 1913. In 2013 Bowers and colleagues flew an experimental all-wing drone, the Prandtl-D, which successfully demonstrated its ability to fly stably and controllably, taking advantage of proverse yaw to dispense with any tail surface whatsoever. More drones followed.

Bowers remained (and as far as I know still remains) unaware that he had been beaten to the discovery of proverse yaw by almost 90 years and to its practical realisation by exactly one century, believing that none of his predecessors had seen its possibility in the bell-shaped distribution.

His analyses have certainly taken our understanding forwards, refining Dunne's rather crude arguments requiring downforce at the tips to a more nuanced relationship between airflow deflection, washout and the resulting lift and drag.

Conclusion

The benefits of stable flight are obvious enough. But ultimately, what are the benefits of proverse yaw? Dunne's "safety plane" could automatically recover to level flight from being thrown about the sky in any attitude whatsoever. His biplanes proved unstallable in normal flight and it was even known for the pilot to lock the controls, climb out of the cockpit and go wing-walking. While he never dared attempt to stall his monoplanes at any height, they were aerodynamically pure flying wings, with only the structural cagework and bracing to spoil their lines.

Horten's unbraced monoplanes seemingly took Dunne's formula to its ultimate conclusion. Yet unlike Dunne he never really conquered proverse yaw, relying on Frise ailerons and drag rudders to coordinate turns. His understanding remains debatable. It is unfortunate that when questioned he changed his tune on occasion for one reason or another, while Lee's and Bowers' accounts of him are a little too apt to reference each other in a disturbing circularity. One needs to track down that Ph.D thesis.

Dunne's monoplanes would have benefited from drag rudders for the opposite reason, the ability not to correct but to induce sideslip. This manoeuvre is not only useful in losing height while travelling only a short distance when needed, but is also essential in landing across the wind. Dunne was forced to fly downwind of his landing site, then turn into the wind for his landing run. On occasion he was forced into a crosswind landing and, unable to stop his plane crabbing sideways over the ground, crash-landed badly. The obvious solution on his biplanes, so obvious that many assume it to have been done as a matter of course, was to add independent rudders to the endplates. Swinging one rudder out would induce both a side force and a drag force (Some successful twin-finned aircraft have since had such an arragement). But he was too fixated on simplicity of control for the untrained pilot, ever to consider adding a rudder bar.

It took Bowers' mainstream academic background, allied to many other modern advances, to finally understand bird flight and reveal the technical secrets of the all-wing and proverse yaw. They go a long way to explaining the unexpected "firecracker" performance of Dunne's monoplanes and give the lie to the contemporary criticism, still raised today, that the downforce and wide span must render the wing inherently inefficient.

Can the death toll in tailless aeroplanes tell us anything? Dunne and Hill killed nobody. Lippisch, Horten, Northrop and a good many imitators - well into the supersonic era - have far sorrier track records. There is a certain correlation between understanding and fatalities, but I have yet to find the case overwhelming. What is crystal clear is that the establishment's cold-shouldering of the stable, unstallable aeroplane and of the underlying theory has resulted in countless thousands of avoidable deaths. Had Dunne types been used as primary trainers in WWI, as he proposed, the huge death toll among trainee pilots would have been drastically cut. Had his principles been incorprated in the bombers and reconnaissance types, with or without tails, further great savings would have been made. Fighting scouts are more of a moot point, for the manoeuvrability of the safe wing has never been properly investigated. Then, all those individuals who lost their lives testing badly-conceived tailless experiements, throughout the mid-twentieth century, would have been saved. A Dunne machine was the first to fly through a storm and arrive at its destination unscathed, crossing the English Channel and making headlines around the world in 1913, only four years after Blériot first did so on the calmest of days. No Dunne machine ever lost pilot, passenger or bystander. Nor did anybody in his wake need to, if they had only paid attention to his theories and achievements, it was an utterly avoidable waste. The institutional airbrushing-out of Dunne's discoveries, generation after generation after generation, is the truly shocking scandal of the whole affair.

Whether tailed or fuselaged or no, provided the basic design is viable most of the desired flight characteristics can nowadays be programmed into a flight control system, so why bother with the aerodynamic subtleties any more?

The technical answer is that the quest for ultimate aerodynamic cleanliness is also the quest for ultimate efficiency, yielding the lightest weight and lowest drag for any given payload - and hence also the maximum speed and range and lowest operating cost with any given engine. Second, in the absence of expensive, weighty and unreliable digital control systems, proverse yaw can greatly improve the handling characeristics of such highly efficient airframes, especially when safety is paramount, such as in the stall or when landing in a crosswind. For a drone, this can greatly reduce the workload demanded of the control computer, yielding a faster time to market and a lighter system allowing greater payload capacity and/or performance. Tailless is better than tailed, the flying wing better still, the finless all-wing best of all.

But perhaps there is another reason, one which stirs the deepest passions and drives its protagonists the hardest whether of mathematical or practical bent. It is, simply, the sheer beauty that arises through the conceptual simplicity of the all-wing form and the elegance of its ultimate realisation.

While Dunne lacked in mindset, Prandtl lacked in interest and Horten may or may not have lacked in application, the truly practical all-wing aircraft remained elusive. Bowers has brought the all-wing closer to its ultimate perfection, in which only the inherent drawbacks of fitting everything inside a slim aerofoil, and then balancing it within a very narrow range, now restrict the roles in which it can at last fulfil its promise.

The beauty of Bowers' solution reminds me of yet another shunned genius, of Barnes Walls and his wing-controlled aerodyne, a tailless vairable-geometry concept which did away with not only the fin and rudder, but all supplementary control surfaces, with the wings themselves providing all the control that was necessary. He flew two successful drones, Wild Goose and Swallow. His paper on the theory is yet another forgotten gem, though one which I have still to dig out. The independent discoveries in this field of his contemporary LE Baynes are even less acknowledged. The story may not be over yet.

Bibliography

In order to follow the text, this bibliography is presented in broadly chronological order of subject, rather than the usual alphabetical by author.

Friedrich Ahlborn; "Über die Stabilität der Flugapparate" (On the Stability of Flying Machines), Friederichsen, 1897.

J.W. Dunne, "The Theory of the Dunne Aeroplane", Aeronautical Journal, Vol 17 No 66 April 1913 pp.83-102. Serialised in Flight, 16 Aug to 13 Sept 1913.

Alexander Lippisch (Trans. Gertrude L. Lippisch); The Delta Wing, Iowa State University Press, 1981.

Alfred Price; The Spitfire Story, Jane's, 1982.

Dan Sharp; Secret Projects of the Luftwaffe: Volume 1, Jet Fighters 1939-1945, Tempest, 2020.

Russell E. Lee; Only the Wing: Reimar Horten's Epic Quest, 2nd Edn, Smithsonian, 2020.

Robert T. Jones; "The Spanwise Distribution of Lift for Minimum Induced Drag of Wings Having a Given Lift and a Given bending Moment", Technical Note 2249, NACA, December 1950.

A.H. Bowers; "Flying Wing Aerodynamics", discussion, rec.aviation.military newsgroup, 1999.Archive copy.

A.H. Bowers, O.J. Murillo, R. Jensen, B. Eslinger and C. Gelzer; "On Wings of the Minimum Induced Drag: Spanload Implications for Aircraft and Birds", NASA/TP—2016–219072, NASA Armstrong Flight Research Center. NTRS, March 2016.