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Aerodynamics of the Tailless Wing

Updated 17 Aug 2021

This tale is still emerging. While my cognizance of it at present lags even further, a bold and challenging thesis is suggesting itself. At present it smells rather of the modern fashion for post-truth journalism, being somewhat rude about the establishment in favour of one's chosen maverick. Like you, that is the bit that troubles me most, but it is an honest representation of my investigations to date and I would not hide it; it is my goad to do better. Besides, there have indeed been issues over which the establishment were, with hindsight, demonstrably pig-headed. With luck, this story will continue to grow in completeness, coherence and (who knows?) conviction.

Contents

Introduction
Flying without a tail
The Zanonia fallacy
JW Dunne
The new misdirection
The German mavericks
NASA
Conclusion
Bibliography

Introduction

"But the aeroplane does do these things, and if the theory does not give warranty to the practice, then it is the theory which is wrong." — JW Dunne to the Aeronautical Society of Great Britain, 23 April 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. Although the latter does not seem to be aware of the former, the connectioin between their work is deep and compelling.

JW Dunne built the world's first certified stable aeroplane, the D.5, to much acclaim. It had a tailless swept wing, flew as far back as 1910, used its wing endplates not as stabilising fins but winglets, and needed no rudder. His design theory became public knowledge in 1913. None of the 27 or so Dunne aeroplanes flown ever killed anybody (a remarkable achievement for the pioneer era). In stark contrast, almost all subsequent designs have had unsafe characteristics to a greater or lesser extent and needed stabilising fins. The GAL.56 of 1944 was declared by the world's most prolific test pilot Eric "Winkle" Brown to be the most dangerous aeroplane he had ever flown; it went on to kill the world's most experienced tailless pilot, Robert Kronfeld. What did Dunne know that the world so soon chose to forget?

A generation later Reimar Horten worked steadily on the problem throughout the 1930s to the 1980s and rediscovered much that had been forgotten. Like Dunne, he was studiously ignored by the mainstream and his discoveries all but forgotten once more. What on Earth did Dunne and Horten's colleagues and successors in the field think they had been doing for the century following Dunne's widely publicised first official certification?

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 somewhat more formal analysis coupled to that same intuition and created the first viable jet flying wing, though the evidence suggests 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. The trail of dead test pilots they left in their wake is frankly horrific. Their global dominance amounts to a breathtaking institutionalised incompetence.

Then, over 80 years after Dunne rose to prominence, 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 Dunne anticipated pretty much all of it, and perhaps more. His understanding is now largely vindicated by computer analyses and experimental drones, while some of his key discoveries still await 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 the unswept flying wing and the likes of Charles Fauvel, 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 must, if it is to handle safely, be stable and controllable about 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 has been called an all-wing design (the original German term, nurflügel, means "wing-only"). 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 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 minimal side area which, were it the only trick up his sleeve, 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 raise thge nose, to dive it is moved back to lower the nose. 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. Conveniently, by adding a tail to provide the counteracting force, the plane as a whole can easily be stabilised. The tail plane must typically be set at a reduced angle of attack (AoA) to the airflow. If there is no tail then there are several ways in which the wing itself can be made stable:

Of these solutions, 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.

Longitudinal trim

Any practical flying machine must be able to accommodate a range of loading conditions. Throughout the flight, as payload shifts or is dropped, and fuel from various scattered tanks is burned, its centre of gravity moves around. At the same time, its centre of lift moves under the influence of varying flight conditions. For stable flight, these two centres must be kept in close alignment. The plane must be trimmed for level flight on takeoff and preiodically adjusted throughout the flight. Like the elevators, the trim tabs need a good moment arm to act effectively. Indeed, the small trim tabs necessary are usually fitted to the larger elevators, or the whole elevator used for trimming.

But if there is no tail, how can this be done? Often it cannot, and many tailless aircraft suffer from a narrow CG range. They must be carefully loaded, the fuel tanks used up, munitions dropped in the right order, and so on. In other words, they are of limited practicality.

The usual solution is to sweep the wings sharply, typically backwards, so that the wing tips can be far enough off-centre to act as a "tail at the end of the wing". But sharp sweepback brings other problems of sideways airflow, especially at subsonic speeds. And even Concorde had to pump fuel to and fro to stay on an even keel. Another solution is to adjust the angle of wing sweep in flight. It has been done, but carries a significant weight penalty.

The problem of CG range and trim remains a severe limitation on the subsonic tailless aeroplane.

Directional stability

When you look at all the so-called tailless aeroplanes, primarily those of GTR Hill with his Pterodactyls, Alexander Lippisch with his Storks and Deltas, and Jack Northrop in the US, they almost 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 a pure wing is not very practical and various excrescences must be added. Anything added to the front, such as a nacelle for the pilot, 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 enhance 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 little or no sweep behave in roll and yaw like any ordinary aeroplane of the same span, which may be quite large. However flying wings 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 that is quick, agile and sensitive 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 the 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 and responsively, 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 automatic drag rudder. They are commonplace and they do help a lot, but they can seldom 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 treated it as something of a Holy Grail, eagerly sought but ever out of reach since the day it was lost, and believed by many not to exist. For yes, it was once used and was 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 will not work and 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 and the aileron to lose control authority.

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. However designers often reduce the camber at the tip, thus exacerbating the problems, in order to reduce drag during the cruise.

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 rose to high office and honour in the Society, sitting on its ruling Council and earning too its first ever Certifiate of Fellowship (now in the Science Museum archives). He himself had a unique grasp of the theory at that time, which he expounded to the Aeronautical Society of Great Britain in 1913. It quickly became public knowledge, published not only in the Society's own journal but also serialised in Flight a few months later. 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 in the ensuing extended discussion that, "The aeroplane does do 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 caused 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.

More astonishingly, his 1913 lecture even goes so far as to recognises the existence of forward thrust or negative drag from the wing outer sections at increased angles of attack, where washout is only slightly negative but the lift is still positive. He called it the reserve tangential device or effect and it is depicted in Fig.14 of his transcript (see right). This phenomenon would sink without trace and fail to be rediscovered for the next hundred years! But even the most recent and enlightened researchers do not seem to have yet realised how profoundly this affects the wing's behaviour in the approach to the stall, to render it far more benign that it might otherwise have been; this one is a hundred and eight years later and counting!

Since Dunne's aeroplanes were longitudinally stable they needed no tail plane, and since they were also directionally stable they needed neither fin nor rudder. The elevons moving together acted as elevators, while moving them differentially made them act as ailerons to roll the aircraft; carefully-balanced proverse yaw then took the plane into and round the turn.

One should acknowledge that Dunne had one determined blind spot. He was convinced that his two-lever control system was the safest that could be contrived. He was fully aware that it offered no ability to sideslip and that therefore takeoff and landing must always be made into the wind. He himself crashed at least one plane in a crosswind landing and it became a common cause of accidents with the Dunne type. But he never accepted that a rudder and foot pedals would make the plane safer for the inexperienced pilot.

Most of Dunne's biplanes featured end plates at the tips and these are often mistaken for stabilising fins, even assumed by eminent authors to be fitted with rudders (No, I shan't embarrass you here). 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 unswept aeroplanes such as the Bristol Boxkite, and in none of those aeroplanes could 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; the fins only made that worse. 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", what we would nowadays call wing fences, 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; the red line in the drawing shows the subtle reflex camber as the line flattens out towards the trailing edge. Hill used RAF 34 in his later Pterodactyls.

My thesis here is that in doing this 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 tailles 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; in the pioneer days they had even tried to poach him from Britain with promises to put a 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 (but for other reasons) 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, even with vertical fins. Many other advanced projects, drawing on his delta- and swept-wing work, appeared in German design offices around this time, but one has to question their viability. For example after the war Messerschmitt designed the Spanish Hispano HA P-300 tailless delta glider, prototype for a supersonic fighter; the glider proved unstable in flight and when the jet project was moved to Egypt as the Helwan HA-300, Messerschmitt had to add a tailplane to make it fly right.

Meanwhile Jack Northrop in America had been 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.

The German mavericks

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 track it down and 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, broadly followed suit. 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.

Blohm & Voss and Richard Vogt

But one German design team became well aware of proverse yaw. Working at Blohm & Voss during WWII, Chief Designer Richard Vogt and colleagues developed a semi-tailless wing in which the tips were moved aft on short booms to act as outboard horizontal stabilisers (OHS). While not a pure tailless form, such close-coupled outboard tails share many of the same issues. Their first was for a single-engined pusher fighter, Projekt 208, which had no vertical fin or rudder. Voght's deputy Hermann Pohlmann (1979) explains:

"The outer horizontal control surfaces can also be used as ailerons ... By angling the tail planes — they have to be adjusted downwards in anhedral and lift — the elevator can also take over the function of the rudder."
(»Die außen liegenden Höhenleitwerke lassen sich gleichzeitig als Querruder mitbenutzen ... Durch Schrägstellung der Höhenleitwerke — sie müssen sinn- und wirkungsrichtig nach unten gestellt werden — kann das Höhenruder auch noch die Funktion des Seitenruders mit übernehmen.«)

Vogt and his head of wing design George Haag went to the trouble of commissioning a test aircraft for its control system from the Czech designer Skoda Kauba.

These B&V designs have recently come under significant scrutiny. I have yet to get hold of Tipton (1995). Muller (2002) and Hagen (2019) concluded that the P 208 had insufficient vertical tail area. This conclusion implies that a serious fighter design presented to the authorities in fact failed in the basic necessities of flight. Yet it seems unlikely that B&V would not have obtained wind tunnel data to inform the aerodynamic design or would not have resolved any critical stability issues before putting their reputation behind the design. One must question whether such limited modern simulations, based on minimal historical data and not validated in the wind tunnel, are sufficiently convincing.

By contrast, Hagen also found that the P 208 would have exhibited proverse yaw in the turn. Given that the radical lateral control system would have needed sufficient authority to overcome adverse yaw in a dogfight, the presence of proverse yaw might be seen as a necessity and its endorsement adds credibility to its conscious inclusion. The downturning of the tail in both pitch and anhedral are known to be the necessary features for proverse yaw. But the problem is that they couple aileron and rudder action together ( aproblem which Dunne regarded as an advantage, but that is another story). So a pure yawing command would require some form of drag rudder. Pohlman's remark makes more sense if it is referring to their action as proverse-yaw "rudders" in the turn. But we know neither the exact control provision for yaw, nor what Pohlmann intended to say. Also, we do not know the extent to which the B&V team were or were not aware of Prandtl's work but, given their very similar remarks on structural and aerodynamic efficiency, if they were not then they did a darn good job of rediscovering it and taking it a step forwards.

A series of jet-powered projects followed. To make room for the air intake these had larger noses. Moreover the stabilising effect of the pusher propeller's side area was now absent. These changes both had destabilising effects. The first, the P 209, was indeed found by Barnes (2012) to be directionally unstable. However giving it a modest increase in dihedral would have restored acceptable flying qualities. We do know that wind tunnel models of the next in the line, the P 212, were tested with and without small vertical fins added, and as a result it did end up with vestigial fins. Again, although the accuracy of limited modern analyses is arguable, the principles and tradeoffs were very evidently understood to a fair depth by B&V (Indeed one migh argue that it was the obvious presence of this understanding, suggested so strongly by the designs and contemporary claims, which attracted the modern researchers).

At the end of the war, Vogt and his Head of Advanced Projects Hans Amtmann were hoovered up by the American "Operation Paperclip". However their outboard tail was studied principally for its drag-reducing primarily, especially in supersonic flight, and their work on proverse yaw faded once again into history. Since Pohlmann and others failed to comment on proverse yaw, and later designs omitted the tail anhedral in favour of fins, one must wonder whether anyone at B&V understood its presence and significance.

NASA

The Convair deltas

America's first delta-winged jet appeared almost by accident. In response to a 1945 USAAF requirement, Convair proposed a swept-wing design with a V tail. They then found that lengthening the root chord improved it and led directly to a thin-wing delta. With a symmetrical aerofoil, no tail plane would be needed, just a huge fin. Lippisch was involved in some of the discussions, but it seems that his role was more one of offering moral support than technical originality. A research prototype emerged as the XF-92A and flew in 1948.

By then, already in 1947 but too late for the XF-92A, Robert T. Jones at NACA (as NASA was originally called) had suggested giving the delta wing some camber and twist, and especially leading-edge camber, in order to reduce drag at both high and low speeds. The idea rapidly developed into the notion of conical camber, applied initially to the whole wing in classic biconical form but then refined down to only the leading edge. On a sharp-tipped delta this conical profile caused the trailing edge to curl downward at the tips, and this effect can be seen on Convair's subsequent F-102 Delta Dagger, F-106 Delta Dart and B-58 Hustler supersonic deltas.

Recalling how closely this follows Dunne's prescription, we need not be too surprised to learn that this conical treatment also helped with the inherently unpleasant stall behaviour of the symmetrical swept wing at low speeds. However there is nothing to suggest that Jones and his colleagues knew anything of their predecessor, and indeed they arrived at the design via a very different route.

Robert T. Jones and Prandtl

In 1950, around the time that Reimar Horten seems to have been making some modest advances in proverse yaw and with conical camber yet to appear on the F-102, Jones made a related rediscovery and further advance. He 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. He thus effectively rediscovered Prandtl's curve (of which he apparently had no knowledge).

Jones also went a step further beyond Prandtl, considering the induced drag in greater detail and deriving its spanwise distribution – the first time this is known to have been done.

Bowers and the Prandtl-D

Several decades after Jones, Albion Bowers and colleagues at the NASA Armstrong Flight Research Center began revisiting the bell lift distribution and the swept flying wing. Bowers, motivated by the need for efficient flight in minimising impact on the environment, had followed the example of so many early pioneers and gone back to bascis, first studying bird flight. Like Dunne before him, he put the observed behaviour ahead of the current 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. Presently he unearthed Prandtl's forgotten bell curve.

By 1994 Bowers had realised that a bell distribution could in theory imbue a swept wing with proverse yaw in the turn, making a fin unnecessary. In 2013 he and his colleagues flew an experimental all-wing drone, the first "Prandtl-D", which successfully demonstrated its ability to fly stably and controllably, taking advantage of negative drag and proverse yaw to dispense with any tail surface whatsoever. More drones followed.

Bowers has stated his belief that none of his predecessors, not even Dunne, had seen the possibility of proverse yaw in the bell-shaped lift distribution. consequently he does not believe that he has been beaten to its practical realisation – in a manned aeroplane to boot – by just over a century. So please treat my own arguments with a touch of scepticism.

Where Dunne sought inherent stability, Bowers sought efficiency. His analyses have certainly taken our understanding forwards, not only in systematising, confirming and quantifying Dunne's empiricism and intuitions but also in refining his rather crude arguments requiring downforce at the tips to a more nuanced relationship between airflow deflection, washout and the resulting lift and drag. The Prandtl-D was the first aircraft ever to embody Prandtl's mathematical description of Dunne's experimental discoveries. In this, Bowers has succeeded in unifying the solution to the two parallel, century-long quests for stability and efficiency.

And yet Bowers complains of another of Dunne's bugbears – no matter his professional standing, the mainstream refuse to take his discoveries seriously. This despite his rising to become the research centre's Chief Scientist (just as Dunne sat on the ruling Council of the Aeronautical Society of Great Britain). It's the same old story; we don't quite understand what you insist on banging on about, we can't believe the benefits you claim, here is a list of the same old objections you just debunked, the idea needs more research anyway. He has described it as "a lost cause". All this despite a century of international research, the demonstrable success of tailless supersonic aircraft and the rock-solid data gathered by Bowers.

There is at least a ray of hope. Bowers's social skills appear more effective than Dunne or Horten's. He built a community of interns who will hopefully, as their careers percolate through the mainstream of aeronautics, take the truth with them.

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 the truth about 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 learned to fly downwind of his landing site, then turn into the wind for the run in. 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, would have been 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 tailless 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' 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. Moreover, the planes would have lasted longer and the acute shortage relieved far sooner. Had his principles been incorporated in the bombers and reconnaissance types, with or without tails (and he patented both), 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, might 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 more than lip service to his theories and achievements. It was an utterly avoidable waste. The wilful institutional ignorance of Dunne's life-saving 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, nowadays most if not all of the desired flight characteristics can be programmed into a flight control system. Some years after Northrop's death, his company succeeded with the B-2 stealth bomber by using computers to make up for its aerodynamic shortfalls. So why bother with the aerodynamic subtleties any more?

The technical answer is threefold. Firstly, 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, lowest operating cost and least damage to the environment with any given engine. Secondly, in the absence of complex, expensive and error-prone digital flight 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. This can significantly reduce the workload demanded of the control computer, yielding a faster time to market and a lighter, cheaper system. Thirdly, the military quest for stealth is also the quest to remove any and every extraneous feature from the physical shape. That includes not only the tail, but also the flashes of reflection produced by control surfaces. Proverse yaw helps significantly in this last, while tailless is better than tailed, the flying wing better still, the finless all-wing stealthiest of all.

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

While Dunne lacked in mindset, Prandtl and Jones 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. He has since retired, but others are already beginning to fly drones and push his work forwards.

Where ignoring Dunne cost thousands of lives throughout WWI and on into the jet age, ignoring Bowers is costing the environment every day from here on in. In an age where Greta Thunberg can become a superstar just by telling the truth, this century-long institutional cold-shouldering, of the safety and wellbeing of humankind and planet, becomes an ever-increasing embarrassment to the mainstream aeronautical community.

Postscript

The beauty of Bowers' solution reminds me of yet another shunned genius, of Barnes Walls and his "wing-controlled aerodyne", a tailless variable-geometry concept which did away with not only the fin and rudder, but all supplementary control surfaces, with the wings and fuselage themselves interacting to provide all the control that was necessary. He flew two successful families of drone, Wild Goose and Swallow (pioneering drone technology in the process, but that is by the by). While his designs have received great fame, it is superficial; his paper on the theory, which goes all the way back to his airship days, is yet another forgotten gem, though one which I have still to dig out. The independent and closely related discoveries in this field of his contemporary and fellow countryman LE Baynes are even less acknowledged.

The presence of a fuselage and variable wing sweep resolves the tailless wing's inherent practical problems of payload and trim (It was used by Hill on one of his Pterodactyls). I am minded too of the seagull, which tucks its tail out of the way while soaring and only deployes it when manoevring sharply, an approach somewhat echoed by Baynes. While we may now have ultimate safety and ultimate efficiency combined, Nature teaches us that the practicalities of life demand a subtle compromise. The story of high promise and wilful ignorance may not be over yet.

Bibliography

In order to follow the text, this (somewhat incomplete) 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.

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

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

Hermann Pohlmann; Chronik Eines Flugzeugwerkes (Story of an Aircraft Manufacturer), Motorbuch, 1979. (In German)

Karl R. Pawlas; "Blohm & Voss P 208: SchnellstJäger" (Blohm & Voss P 208: Highest-Speed Fighter), Luftfahrt International, No. 15, May/June 1976, pp.2325-2340. (in German)

Karl R. Pawlas; "Blohm & Voss BV P 212", Luftfahrt International, No. 5, Sept/Oct 1974, pp.715-730. (in German)

B. Tipton, "The preliminary design analysis of a unique semi-tailless aircraft configuration", MSc Dissertation, University of Oklahoma, Norman, Ok, 1995. (Not seen)

Kurt W. Muller; Analysis of a Semi-Tailless Aircraft Design, Master's thesis, Naval Postgraduate School, US, 2002.

Kevin Hagen; "Semi-tailless aircraft concept with variable cant stabilizers applied to small UAVS", Master's thesis, Wichita State University, 2019.

Phil Barnes; "Aerodynamic Study of the German Jets and Engines", HowFliesTheAlbatross.com, 2012.

Robert T. Jones; "Estimated Lift-Drag Ratios at Supersonic Speeds", Technical Note 1350, NACA, 1 July 1947.

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.

Jeff Ayers; "NASA Chief Scientist Albion Bowers", Interview Transcript, Fueled by Death Cast, 2019.