After a rigorous German education in the physical sciences, young Ludwig Wittgenstein entered Manchester University as an aeronautical engineering research student. There he devised and patented a novel aero-engine employing an airscrew propeller driven by blade tip-jets. Within the context of the growth of English aviation during the first half of the twentieth century (including the contributions of many Fellows of the Royal Society) and taking into account related aspects of his life, this paper examines an unfulfilled engineering aspiration. In enlarging upon what Wittgenstein might have accomplished during his stay at Manchester, it contrasts his invention with later comparable proven designs, albeit applied to hybrid rotorcraft. His engine employed centrifugal flow compression and arguably was a precursor of Sir Frank Whittle's gas turbine. In conclusion, reasons are given for Wittgenstein's departure from Manchester.
From Vienna to Manchester
Ludwig Wittgenstein (1889–1951) is recognized as one of the western world's most influential philosophers. Yet in 1908, when he first came to England at the age of 19 years, it was not to engage in broadly speaking analytical philosophy, but to enrol as a research student in aeronautics at Manchester University. His father, an extremely wealthy Viennese steel magnate, desired the youngest son to follow in his own industrial footsteps. Thus Ludwig received his secondary education in a vocational school, the Realschule at Linz. During this phase Wittgenstein read works by Heinrich Hertz and Ludwig Boltzmann ForMemRS, engendering interests in mechanical engineering, physics and the philosophy of science. Hertz's rigorous approach to science argued for in his book The principles of mechanics much impressed Wittgenstein. Had it not been for Boltzmann's suicide (1906), Wittgenstein would probably have remained in Vienna, completing his education there. Instead he went to the Technische Hochschule, Charlottenberg, studying mechanical engineering which in the then German educational tradition encompassed ‘…a thorough intellectual grasp of theoretical physics, especially Newtonian mechanics [and] a proper understanding of mathematics in ‘its relation to physics’.1 Lecturing in 1894, Boltzmann had stated that the most promising line of development in aeronautics lay with the airscrew-powered aeroplane, not with the dirigible airship. He opined that the task required the courage and intelligence of a Christopher Columbus.2 One Wittgenstein biographer extends this to a ‘task for a genius’.3
By 1908 the Wright brothers had developed their Flyer to the point of commercial sales.4,5 Their flimsy biplane with its forward-mounted canard elevator and unconventional controls (by modern standards) required skilful piloting. As it was an unforgiving aircraft, Orville was lucky to survive a serious crash—his passenger was killed. In 1910, during an English flying tournament, the Hon. C. S. Rolls, patrician motor pioneer and early aviator, piloting a modified Wright Flyer, also came to grief. When he departed Manchester for Cambridge, Wittgenstein was to ask Bertrand Russell FRS whether he [Ludwig] was ‘a complete idiot or not—because if I am I shall become an aeronaut but if not I shall become a philosopher.’ Russell in reply suggested that Ludwig write something on a philosophical subject. The resulting piece was sufficient for Russell: ‘No, you must not become an aeronaut.’6 The idiocy of this novel alternative career was not unfounded. In those days it was truly unwise to become an aeronaut. To advance the study of aeronautics and to take up the risky challenge of becoming an aviator—these were indeed tasks for a genius.
A brilliant academic body
The eponymous university of a vibrant industrial city was an appropriate institution for studies in higher engineering; his father counselled Ludwig to go to Manchester. At the time, English aeronautics was transforming itself from a fledgling, essentially empirical, science to one grounded on firmer principles, taking forward the perceptive concepts of powered aeroplane flight set down by Sir George Cayley a century earlier. Frederick William Lanchester (FRS 1922), who disapproved of trial and error methods, had produced his theoretical calculations for the lift acting on an aircraft wing. His book Aerodynamics was the standard text to be consulted on the subject.
The university had not long been formed from the incorporation of two higher education establishments, Owen's College and Victoria University. It inherited a brilliant academic staff. The Professor of Mathematics was Horace (later Sir Horace) Lamb FRS.7 His classic work Hydrodynamics underpinned the solution of numerous problems arising from the dynamics of an aircraft in flight. A lecturer under Lamb was J. E. Littlewood (FRS 1916), who after spending an unhappy three years at Manchester (1907–10) returned to Cambridge.8 Wittgenstein attended Littlewood's lectures and eventually met up with him again at Cambridge on equal professorial terms.
Another notable at Manchester had been Osborne Reynolds FRS, a longstanding Professor of Engineering who retired a few years before Wittgenstein's arrival but whose work on kinematic viscosity resulted in the Reynolds number, a parameter of vital importance with regard to the onset of turbulent flow within the boundary layer on the surface of an aerofoil. Reynolds's successor, Ernest Petavel FRS, a distinguished physicist, actually learned to fly; in consequence he underwent a severe flying accident.9 In due course he took up the post of Director of the National Physical Laboratory (NPL), an organization also becoming involved with aviation activities, for instance constructing wind tunnels to test models.5 In 1908 the contributions of these Manchester academics to aeronautics were yet to be fully realized.
Initially Wittgenstein worked under Professor of Physics Arthur (later Sir Arthur) Schuster FRS, a renowned Manchester physicist and incidentally an old friend of Hertz. Although retired (1907), Schuster still supervised the Upper Atmosphere Research Station at Glossop, some 13 miles southeast of Manchester in the foothills of the Peak district.9 (Schuster's celebrated successor to his chair was Ernest Rutherford FRS.) Here Ludwig's interest lay in the dynamics of kite flight and its relationship to wing design. In similar respects the Wright brothers had chosen one of the United States's statistically windiest spots, Kitty Hawk off the North Carolina Atlantic coast. They launched their embryo aircraft from convenient sand dunes, flying it virtually as an unpowered tethered kite, and improved on wing design accordingly. Glossop Moor (1100 feet) was one of several nationally distributed research stations run under the aegis of the Royal Meteorological Society. Meteorological research and investigation into the ionization of the upper atmosphere was conducted with scientific instrumentation suspended from balloons or kites. At one Society meeting and after the delivery of a paper, ‘Electrical state of the upper atmosphere’, the ill-fated Hon. C. S. Rolls, a member of the audience, asked if St Elmo's fire had been observed at altitude, no doubt seeing this as a possible future hazard to manned flight. There was a positive reply: ‘at night in a strong 20 m.p.h. wind a balloon at 3000–5000 ft had been observed displaying the effect’.10
Petavel, ex-lecturer in meteorology and an ingenious designer of machinery, personally improved the winch used for flying the kites.9
The box kite was the invention of the Australian Lawrence Hargrave. Heavy but inherently fragile, it required delicate handling.11 Its excellent stability, steep ascent and lifting power, provided there was sufficient wind, made it the kite of choice.12 William Eccles, a fellow engineering student who became a long-standing friend—being a friend of a person with Ludwig's temperament was a demanding and forbearing task—notes that Wittgenstein ‘arrived to do research on aeroplane design using kites for the purpose’.13 Not short of money, he was able to finance his stay at Manchester, much of his kite experimentation and later his engine researches.
The generally accepted challenge to aviation was to produce an engine high in power and light in weight. To meet the challenge the Wrights had been obliged to design their own engine, a four-cylinder in-line, producing 10 horsepower at 1100 r.p.m. Ludwig, also realizing that an aeroplane was as good as its engine, soon switched from what can loosely be described as experimental aerodynamics to powerplant design.
What exactly did Wittgenstein do in the way of engine design to meet the challenge? One author overenthusiastically states that he ‘[experimented] with rocket propulsion … conducted on a stretch of railway track just south of Manchester’.14 The statement has been toned down by others, for example ‘…tests on an unused railway track in the Manchester area which suggests a fair degree of development’.15 Unfortunately the exact location is never given. Eccles has little to say about this or other laboratory engine tests, although he does mention the excellent relations that Wittgenstein had with laboratory technicians who helped him in his work. Ludwig himself refers to one as ‘…one of the very few people I got on with during my Manchester period’.13 (Ludwig's ‘nervous disposition’ was not very helpful when things went wrong.) Eccles correctly names Wittgenstein's work as ‘jet engine experiments’, which are not to be confused with the jet engine we recognize today.
In explaining Wittgenstein's researches it is best to begin with a description of their culmination—a patent taken out in 191016—a short document, about 90 lines (figure 1). Basically, air and vaporized fuel fed through the hub of a radially armed motor are driven along each arm into a small terminating combustion chamber whose exit nozzle emits a resulting pressurized jet. The arms are described as tubular and formed or fitted with an airscrew propeller blade. The exact wording for the complete specification states that ‘The air and gas admitted at the hub is forced along the arms A to the combustion chambers C and therein compressed by the centrifugal force exerted by the revolving arms, and ignited.’ One assumes that the same centrifugal effects also act in ‘forcing’ the mixture along the arms. There is no mention of any air compressor being mounted before the input (about which more later). In principle the operation is not unlike that of a centrifugal flow gas turbine, although in the latter only air passes through a compressor stage. The twin-blade propeller turns in a vertical plane and the respective combustion chambers are mounted tangential to a blade tip's circular path in the plane of rotation. The patent also provides for multiple-blade propellers with tip-jets. Although Wittgenstein states that the fuel–air mixture is ignited in the combustion chambers, the means of doing so is not described or illustrated. The hub is fitted with suitable inlet valves by which the admission of air and gas can be regulated, again by means not described. One problem would be that of feeding the fuel–air mixture through rotating ports. According to one biographer the idea was ‘fundamentally flawed and quite impractical for propelling an air plane’.17 No reason for the statement is given; in principle the scheme is sound.
It is known that an outside contractor manufactured a combustion chamber (also described as a ‘variable volume combustion chamber’) that was used to experiment with various discharge nozzles, the hot gas discharge arranged to impinge on a deflector plate where its reaction could be measured.18 Apparently the combustion chamber operated successfully and designs plus other documents are said to have been deposited in the Manchester University Library.19 (Enquiries have been made of The John Rylands University Library, who report that they have no record of this material being deposited with them.) Wolfe Mays, a student of Professor Wittgenstein at Cambridge with personal knowledge of him, wrote a number of articles on the Manchester period.20–22 Biographers of Wittgenstein often quote him as a prime source. Mays wrote21 that W. Eccles placed Wittgenstein documents at his disposal. Curiously, in expanding upon Wittgenstein's experimental work,22 Mays made no mention of the patent and the proposed use of centrifugal forces, nor of the railway tests. A tribute to Mays23 includes the statement: ‘[Mays] was particularly proud of the fact that he had been able to locate the plans of the jet engine [sic] which Wittgenstein had constructed.’ A biography24 (in German) contains a poor photographic illustration of a Wittgenstein engineering drawing.
One article on Wittgenstein's ‘early years’25 states that ‘[the propeller was] driven by repulsion jets on the propeller tips—initially from a variable combustion chamber arranged centrally on the propeller shaft, later with combustion chambers in the jets themselves’ (emphasis added). This again raises the question of what was actually tested on the unused railway track. Did the jet emission from a single combustion chamber, duly directed and of sufficient thrust to at least maintain motion of the supporting rail vehicle, act as an elementary jet reaction engine, or did the combustion chamber, initially ‘centrally mounted’, drive propeller tip-jet exhausts by means of internal feed lines? In the latter case did this give Wittgenstein the confidence to rely on centrifugal forces alone in the feeds (no independent compressor) to provide adequate compression within tip-mounted combustion chambers? Did he achieve this and apply for a patent on these lines (or did he not, and apply for the patent anyway)? In all cases the injection of both air and fuel is required, plus ignition arrangements. Within the laboratory one technician had ‘helped him install some heavy apparatus—a heavy duty compressor’.15 Presumably this device was also used to impel air into the ‘centrally mounted’ combustion chamber.
Contemporary propeller construction techniques (ca. 1910)26–28 did not marry well with the unusual demands placed on a blade satisfying Wittgenstein's patent requirements, namely the inclusion of internal feed pipe(s) plus a small but possibly weighty combustion chamber fitted to the tip. Until the early 1920s blade material was universally wood, generally manufactured from laminations glued together, the tip protected by a metal sheath. (The Wright brothers' blades were constructed from spruce laminations, the composite coated with aluminium paint.) Typically, modern blades, having to cope with ever-increasing stresses, are made from pressed steel laminates as separate halves, the pair then welded together giving a hollow interior. Such a construction would have been ideal for Wittgenstein, allowing the accommodation of his internal feeds.
Late nineteenth-century work on propeller design was mainly devoted to the marine screw. For the airscrew, when Wittgenstein entered the field, there existed the so-called ‘momentum theory’ developed in 1865 by W. J. M. Rankine FRS and further modified by R. E. Fraude. On the basis of the hydrodynamics of a perfect non-viscous fluid, the theory assumed a propeller blade to be composed of an infinite number of segments acting together as a continuous advancing disc. The perfect streamline airflow, continuous through the hypothetical disc, produced a pressure differential across the disc, giving rise to the thrust. The alternative ‘blade element theory’ proposed by Fraude (1878) and independently by Drzewiecki (1890), considered the blade as a twisted airfoil divided into a large number of elements, each an individual airfoil, giving the equivalent of lift in the horizontal direction, an aerodynamic method. Lanchester (1907), with no knowledge of the latter work, put forward a more advanced version soon to be formalized by Prandtl. The Wright brothers had obeyed Lanchester's maxim, namely methodical development. Their approach to designing a propeller, one similar to the blade element method mentioned above, enabled them to hone it into optimum profile.
The efficiency of an airscrew is also related to the power and rotational speed of the engine and requires optimization in these respects. The various analytical treatments did not involve complex mathematics. More advanced mathematical analysis applicable to airscrew design was to come. It is often stated that Wittgenstein's attention to propeller profile design led to a wider interest in mathematics and from that to the broader theme of mathematical logic. In a letter to his sister Hermine, Ludwig recalls a conversation he had with Lamb regarding solutions to equations, that ‘he [Ludwig] had come up with. [Lamb] didn't know for certain whether they are altogether solvable with today's methods’.15,29 (Note that Wittgenstein does not record any negative comment from Lamb on the engine.) Much later, Lamb became President of the British Association for the Advancement of Science (1925–26) and in his Presidential Address remarked that the mathematics of hydrodynamics ‘is even being applied to the still perplexing problem of the screw propeller’, mentioning Prandtl's ‘recent’ work.7
Additionally Ludwig's ‘equations’ may have applied to what one again assumes is a proposed use of centrifugal forces to impel the fuel–air mixture within and along the length of a blade, a problem eminently suitable for discussion with an acknowledged expert on such matters. Attending serious mathematics lectures by a Littlewood or a Lamb together with a growing independent interest in the subject (including a reading of Bertrand Russell's Principles of mathematics published some five years earlier), all of this would more than equally transfer his attention to mathematics for its own sake.
A comparison with later tip-jet-propelled rotorcraft
The concept of tip-jet propulsion goes back to Hero of Alexander (fl. 60 AD) and his steam-driven ‘aelopile’ (figure 2). Nevertheless, for early twentieth-century aeronautics Wittgenstein's idea was innovative and in the true meaning of the word anticipated operational tip-jet schemes, though applied to hybrid rotorcraft, which were to emerge quite independently many years later. Some insight into the problems he faced, apart from the ‘interesting mathematics’ of propeller design, become apparent when considering the complex engineering involved in these future tip-jet schemes.
In the 1940s Friedrich von Doblhoff, a fellow Austrian, used an airscrew piston engine mounted at the rear of his aircraft's fuselage to drive an air compressor (figure 3).30 The compressed air, mixed with fuel, flowed into hollow rotor blades through a short pylon. The mixture finally entered steel chrome combustion chambers mounted on the rotor blade tips. In this operational mode with the airscrew disengaged, the aircraft acted as a helicopter, allowing vertical take-off and landing or hovering. For forward flight the engine powered the airscrew by means of a crankshaft in a conventional manner, the aircraft then transforming into an autogyro. An extended tail beyond the ‘pusher’ airscrew terminated in a vertical rudder. Unlike customary single-rotor helicopters, tip-jet operation has a torqueless reaction on the fuselage: no compensating auxiliary lateral thrust at the tail is necessary. Another Austrian engineer who had been associated with Doblhoff was A. Stepan. He writes that the fuel was injected into the tip-located burners (not part of a mixture).31
Stepan distinguished between three types of tip-jet drive:32
pure tip-jet, with the whole powerplant unit on the rotor blade tip;
pressure-jet drive, with the powerplant stationed in the fuselage; and
tip-located ramjet (or pulse jet).
In the 1950s rotorcraft of type (iii) were constructed by the US manufacturer Hiller.33 An auxiliary petrol engine was required to get the rotor up to 150 r.p.m. to start the process. In 1967 Dornier produced the DO-137, which employed a two-bladed rotor with hot-gas tip-jets fed from a MAN 22 hot-gas generator through the rotor head and blades—an example of type (ii).34 A scheme on the lines of type (i) seems less likely, although Wittgenstein's does approach it in that his ‘compressor’ is integrated within the propeller blades.
After the war Stepan joined Fairey Aviation and no doubt helped inspire development of the Fairey Gyrodyne, similar to the Doblhoff machine. Next came the Fairey Rotodyne, a compound helicopter/aeroplane (figure 4).35 Below a forward speed of about 80 knots, pitch control of the four rotor blades enabled the aircraft to perform as a helicopter during take-off or landing. In forward flight the rotor autorotated, substantially adding to the lift provided by a pair of stubby wings and a large tailplane. Again, a tail rotor was unnecessary. A brief consideration of the Rotodyne gives some indication of the difficult task embarked upon by Wittgenstein.
The Rotodyne's prime propulsion units consisted of a pair of turboprop engines, one on each wing. In the helicopter mode they partly drove an auxiliary air compressor by means of a hydraulic clutch. The regulated compressed air supply passed through stainless steel ducts in the wings' leading edges, then up two concentric ducts in the pylon to the rotor hub, directionally opposite rotors being fed from the same compressor. Pipes within the rotor blades connected to each tip-jet combustion chamber. Fuel, separately regulated according to the required rotor speed, was also supplied to each pair of combustion chambers. To provide steering, the Rotodyne's wing-mounted propellers, never fully decoupled, could be individually controlled in pitch. The rotor head supporting the 90-foot diameter four-blade rotor (it was a large aircraft capable of taking 40 passengers in a capacious fuselage) had, in addition to the complex helicopter hub mechanism, the complications of accommodating the air and fuel lines plus a low-voltage supply, the latter by means of slip rings for ignition purposes. The low-drag combustion chambers with their small exit nozzles were not conducive to ease of mass flow through the blades. The flow was also subject to Coriolis forces, further contributing to combustion problems. ‘There was “much mechanical ingenuity and complexity”’, it has been truthfully said.36 Any weight saving, mainly obtained by the elimination of a tail rotor and long drive shaft, was more than offset by high fuel consumption, making it an inefficient aircraft. Like most tip-jet schemes it was very noisy.
In one respect, by having no helicopter main rotor hub mechanism, Wittgenstein's engine/propeller is mechanically less complex. It should also be remembered that his propeller rotated in the vertical plane. Otherwise the significant differences are: first, that the propeller, probably about 10 feet in length, would need to revolve at, say, 2000 r.p.m. to achieve adequate thrust (by comparison, a helicopter rotor's speed is an order of magnitude smaller); second, there are the unknown tip-loss effects on propeller performance caused by further airflow disturbance (vortices) at the blade tips as a result of the addition of the combustion chambers; and last, but not least, there is the employment of centrifugal forces for compression purposes. These forces do not seem to be of significance within the slower-rotating blades of the Rotodyne (perhaps an added embarrassment). For a presumed 10-fold higher radial velocity of the Wittgenstein propeller the forces increase 100-fold. However, there will also be a decrease in inverse ratio to blade length, roughly a factor of 1/10. In addition, for a single internal feed within a blade the air and gaseous fuel molecules of differing relative densities will be propelled at different rates, with resulting problems in controlling the richness of the compressed mixture entering the combustion chambers. The use of separate pipelines might make for easier regulation of the mixture composition, but constricted feed-line diameters would introduce viscosity effects.
The proposal was ahead of its time. Twenty years after Wittgenstein's patent was taken out, Frank (later Sir Frank) Whittle (FRS 1947) lodged his, for a gas-turbine jet engine using a centrifugal flow air compressor (the impeller) ahead of the combustion chambers. Figure 5 compares the basic operation of the two tip-jet schemes discussed above with that of the Whittle engine. Centrifugal force compression along the Wittgenstein blades is assumed. (Note that the use of a separate compressor would also partly compromise the objective of a lightweight engine.) Then one can say that, as for the Whittle engine, mechanical feedback (in Wittgenstein's engine, the propeller is equivalent to Whittle's output turbine) drives a unique ‘impeller’ arrangement. As he was to remark to G. H. Von Wright (an ex-student of Wittgenstein and successor to G. E. Moore's Cambridge Chair in Philosophy) and as later recorded by Von Wright, ‘the problem on which he worked during his Manchester years has since become very urgent’.19 Von Wright assumes that Wittgenstein ‘was thinking of the role that reaction engines have recently come to play especially in aeronautics’. In 1944 the jet engine emerged from wartime secrecy into the public domain. The rival attractions of mathematics apart, did Ludwig in 1910, the magnitude of his task becoming apparent, decide not to persevere with the engine? Did he become disenchanted with the task?29 It took Whittle a decade to perfect his jet engine from first patent (1930) to its first operational use powering the Gloster Whittle jet aeroplane (1941).
To recapitulate, the received biography relating to the Manchester period is as follows. Mainly at his father's behest, Ludwig Wittgenstein, well educated for the purpose, embarked on an engineering career. In 1908, aged 19 years, he enrolled in the university as a research student in aeronautics, then an infant discipline. His activities culminated in a novel design for an aero-engine that employed reaction jets mounted on the tips of an airscrew propeller's blades. The practical realization of his scheme gave rise to a growing disenchantment with engineering and fuelled an ongoing interest in mathematics, especially its logical foundations. Ludwig switched vocations, but not without regret.
Well over three decades later, tip-jet technology was rediscovered by German and British engineers. Successful, if short-lived, hybrid rotorcraft resulted. His ideas also had an underlying potential to forward one important aspect of aero-engine design, the concept of centrifugal flow compression. Those philosophy academics who mistakenly refer to Wittgenstein's work as jet-engine research may have been nearer than they realized to what could have emerged with time had he persevered.
Frank Whittle showed ‘brilliance, charm and charisma’. He epitomized Samuel Smiles's view that ‘major technological development flows uniquely from a single person's individual genius and persistence’.37 Wittgenstein could be both well-mannered and dominating and, to his many followers, charismatic, but to all he was truly a genius. Maybe the persistence was lacking where engineering development was concerned. As McGuiness writes, ‘he had no determination to carry the whole thing through to a finish’.38
I am grateful to Dr John Cater of the Engineering Department, Queen Mary, University of London, for his useful comments on engineering aspects of this paper. Mrs Hazel Jones (Library, Institution of Engineering and Technology) provided valuable assistance in preparing this paper for publication.
Wittgenstein retained throughout his life an interest in the logic of machines.39 Engineering is not absent from his later philosophical writings, for example when using metaphors to get over his linguistic ideas. A personal friend of Wittgenstein's at Cambridge, David Pinsent, records how in October 1912 at sea during their tour of Iceland, they visited the ship's engines. ‘Wittgenstein (who has spent a lot of time studying engineering at Manchester University) explained them to me. Very interesting.’ On returning to the Firth of Forth, ‘one or two naval aeroplanes were sailing about and caused a great sensation aboard’. (Another Horace Lamb activity was to advise on the limiting dimensions of a tank erected at Farnborough for testing seaplane models.7) Six months later Pinsent accompanied Ludwig on a visit to the Science Museum (South Kensington): ‘went over part of the machinery department. Wittgenstein who of course knows a lot about it explained it all.’40
Pinsent was a Cambridge mathematician. In 1918 he joined other Cambridge scientists conducting aeronautical research at the Royal Aircraft Factory (before 1914 it was the ‘H.M. Balloon Factory’ and precursor to the Royal Aircraft Establishment (RAE)). They included future Nobel laureates G. P. (later Sir George) Thomson (FRS 1930) and F. W. Aston (FRS 1921). F. A. Lindemann (FRS 1920; later Lord Cherwell) and W. S. (later Sir William) Farren (FRS 1945; later Director of the RAE) both learned to fly (figure A1). Results from experimental flights would be communicated to the NPL. Lindemann courageously put into practice his theories for recovering a stalled aircraft from the ensuing spinning dive—a not infrequent occurrence for aircraft of that period.41 In May 1918 Pinsent was killed in an aeroplane accident at the RAE. Wittgenstein dedicated the Tractatus Logico-Philosophicus to him.
- © 2006 The Royal Society