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A Commentary by Dr F Starr FIMMM, MI.MechE, C Eng. on FUTURE DEVELOPMENTS IN AIRCRAFT DESIGN A Thesis by Officer Cadet Frank Whittle, Cranwell 1928

1. Introduction

This paper reviews the thesis that Officer Cadet Frank Whittle wrote when he was a student at RAF Cranwell in 1928, during his fourth and final term. With this thesis, Whittle began to consider what type of engine would be best suited for high speed flight at high altitude (1, 2). This put him on the road to jet propulsion, as we now know it, and he was able to file a patent in 1930. As will be seen, although Whittle makes use of the concept of the gas turbine, at this stage he was using it to drive a high speed propeller.

An invention does not suddenly appear out of thin air; rather, it almost always involves false starts. So it was with Whittle’s invention of the jet engine. The thesis illustrates his first tentative steps towards eventual success, but, just as important, it shows how Whittle was beginning to develop as a professional engineer. It culminated with him being able to build and run his first engine, the WU, in 1937. Whittle was indeed a unique individual. To paraphrase what James St Peter says of him:- Sir Frank Whittle was perhaps the last of the individual innovator-inventors, who combined the hands-on skill of a mechanic and pilot, with the acquired knowledge of the trained engineer and aerodynamicist (3).

At this point it is worth addressing the claim that the German, Hans von Ohain should be given equal status with Whittle. This is largely done on basis that the first jet aircraft that flew, the Heinkel He 178, was powered by an engine based on Ohain’s approach. A more objective analysis would be that this engine, the HeS 3B was something that simply (4) demonstrated the principle of jet propulsion . It was still suffering from difficulties with the burners, a persistent problem during all through the bench testing, from the 1937 HeS 2 prototype onwards. Accordingly, start up was with hydrogen, before the burners got hot (5) enough to vaporise the liquid fuel .

The configuration that Ohain used, and those that followed, had no development potential or commercial future. The underlying weakness was the use of a radial inflow turbine, which is fine for small engines of low thrust and output. But as engine size increases, a high temperature radial turbine is beset with ever increasing thermal stress and fatigue (6). By 1942 the Ohain team had switched all work onto a conventional axial flow compressor/axial flow turbine, the HeS 011, of which there was only a prototype. He was being bypassed by what was happening elsewhere in Germany.

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One must compare this to Whittle’s contribution. His design, which utilised a double sided centrifugal impeller and an axial turbine, was the basis of his experimental and flight trials’ engines. This approach became the basis of the Rolls Royce Welland, Derwent, Nene and Tay.

The Nene, although rather neglected in Britain, was taken up and built under licence in the USA, France, Canada and Australia. The design was pirated and improved by the Russian as (7) the VK-1. Around 50,000 were built by the Russians and their allies, the Chinese . The Nene, and its clones, served as a teaching aid to companies wishing to get into the gas turbine field. This makes Frank Whittle the real person behind the “Jet Engine Revolution”.

This paper is presented in four parts. This commentary is non-technical and outlines the background to the writing of the thesis. It also summarises the content of the thesis without detailing the mathematics and thermodynamics in the document. The second part, Appendix 1, is a facsimile of the handwritten thesis itself. The third, Appendix 2, is a transcript of the thesis, including the original hand-drawn diagrams as necessary. Finally, for those wishing to explore the technical content of the thesis, Appendix 3 is an annotated version of the thesis with the mathematics and re-drawn diagrams in full.

2. The thesis and long range flight

Cranwell students were required to produce a thesis each term during their course. The 1928 thesis, hand written by Cadet Whittle, needs to be considered as a piece of extended homework that had been set by an instructor on the Cranwell course, Professor Sinnatt, who had recognised his student-officer’s potential (8).

For many years the exercise book in which Sir Frank wrote the thesis was on display in the Science Museum. It now resides at Wroughton, near Swindon, among the Science Museum archives. There is a copy in the National Archives at Kew, in London. The copy used here derives from a photocopy of the original, which belongs to Sir Frank’s son, Ian Whittle. This was made for Sir Frank when he bequeathed the exercise book to the Science Museum. The author is indebted to Ian for allowing the use and reproduction of his copy.

Why has it taken so long to turn the contents of the exercise book into a typescript? Perhaps the most important reason is that it does not meet the expectation that it explains the concept of jet propulsion, and possibly contains a drawing of a jet engine in schematic form. Even a casual inspection of the thesis shows that it contains nothing of this nature.

Furthermore, it becomes clear, early on in the thesis, that although Sir Frank’s concept is to use a gas turbine to drive a propeller, it is not a turboprop as we understand it. Only towards the end are we told that the system involves a piston engine driving a medium pressure reciprocating compressor, as well as an ‘air turbine’ as it is called. The exhaust gases from the piston engine are mixed with the air from the compressor, which are then fed to the turbine. This drives a high revving propeller, designed for an aircraft that would fly at 600 mph and 120,000 ft.

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The early part of the thesis explains why, for a long range aircraft, flying at high speed and altitude is essential. Sir Frank argues that a new type of power unit will be needed, capable of high rotational speed and excellent altitude capability. The remaining parts of the thesis are essentially a basic thermodynamic assessment of the power unit. Although not difficult in themselves, the equations that Sir Frank deploys do imply the need to have a good grasp of elementary calculus. Sir Frank, unfortunately, has made life difficult for those of us who do not have his insight in moving from one equation to another. There are some pages which have been lost, which does not help, although it is possible to surmise what they might have contained.

Here one needs to keep in mind the likely circumstances under which the thesis was written. Sir Frank was an Officer Cadet undergoing academic training, as well as learning to fly and become an officer (9). Furthermore, he was not writing the thesis for publication. It was from him to Professor Sinnatt. Hence a major object was to show that he understood what had been formally taught in the classroom. Accordingly, the early part contains some rather strange material on 'why does an aircraft fly’.

One also gets the impression that Whittle had to write the thesis in his spare time, in which equal, if not more important, priorities would be to show that he could look after his kit, and dress and act an officer. As a result, the thesis is somewhat disjointed, reading more like a first draft than a coherent effort. Graphs and sketches are drawn in a rather hurried freehand, and it is not always clear how the figures are referred to in the text.

Nevertheless, one can see why Whittle’s tutor was impressed. Whittle’s thinking about what was needed from an aircraft of the future was quite beyond what anyone was then envisaging. In that period, a high speed for a commercial transport was 150 mph. Range was around 500 miles (10, 11). And the idea of driving a propeller directly from a turbine was quite novel. Whittle’s proposed power unit was patentable and could have been built, even with the technology of the 1920s.

The reason Whittle suggested flight at an altitude of 120,000 feet was that current aircraft used short grass airfields which required a low stalling speed. This in turn limited the maximum Indicated Air Speed (IAS) that was achievable. To attain a high True Air Speed (TAS) the aircraft had to fly at an altitude where the density of the air was a small fraction of that at sea level, so that the high TAS was associated with a low IAS. Whittle chose a density of 1% of sea level, to give a TAS ten times the IAS. In 1928 there were no tables of atmospheric density at great heights, and he estimated he would need a height of 120,000 feet. A modern table of atmospheric density shows that a height of about 106,000 feet is required. In addition, in 1928 variable pitch propellers were not generally available. With a fixed pitch propeller, as the TAS of the aircraft increased, the rate of rotation of the propeller would have to increase to maintain the correct incidence of the blades.

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3. The proposed power unit

It was to drive the propeller at a variable and high speed that Whittle proposed to use a gas turbine. He was not aware of the effects of compressibility on the efficiency of a fast-turning propeller.

The powerplant that Whittle proposed is shown in Figure 1. The propeller is driven directly by a turbine, which in turn is driven by a stream of gas from a reciprocating engine which drives an air pump. There is an ‘engine bank’ comprising a reciprocating air compressor and a piston engine to drive it. The exhaust gases from the piston engine and air from the compressor lead into a pressurised tank. Whittle refers to the tank as the ‘boiler’, but a more appropriate analogy would be that of a steam drum, as all it does is hold a hot fluid. The hot pressurised mixture of gases flows out of the tank and is then guided through nozzle blades into the impulse turbine, providing the power to drive the propeller.

Figure 1 Whittle’s initial concept for an advanced gas turbine based aircraft power plant

Calculations in the Appendix show that at sea level the tank pressure would be 109.7 lb/in2, or as Whittle expresses it, 15,800 lb/ft2, with the temperature of the mixture being in the range 500 – 527 º C.

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Although the piston engine and compressor could be separate items, Whittle shows them to be in the same engine block. This is sensible. There would be a saving in weight, and a multi-cylinder arrangement would make it easy to balance the pistons and crankshaft.

Others starting from the same point as Whittle, and needing to say something new about aircraft and engine design, might have come up with similar ideas. What marks out Whittle, was the ability to do a technical analysis of his concept. He commences using ideas from steam turbine technology to show that it is the mechanical properties of the turbine that would limit its power. But further through the thesis, and particularly in the Appendix to the thesis (pages 43 onwards), he turned to a thermodynamics based approach. He could then estimate the maximum power he could get from his combination of piston engine, reciprocating compressor and gas turbine. On the basis of a turbine inlet temperature of 527 º C, calculation enabled Whittle to derive an optimum pressure ratio of 7.51/1. He was also able to state that the work output, to the propeller, was equivalent to 100 hp per pound of airflow per second. At high altitude, he asserted this would rise to 118hp/ lb/sec. In terms of “gas horse power” these figures are in the same ballpark as early jet engines. Whittle’s thermodynamic approach was a very modern way of doing things (12).

Whittle used as his bible Aurel Stodola’s great work on steam and gas turbines, first published in 1903 (13). However, given that the gas turbine was at that time in its nascent stages as a practical piece of engineering, Stodola limited this subject to a very short appendix. Hence Whittle, it can be argued, had to go beyond Stodola (14). Unfortunately, even in typescript, the thesis is difficult to follow, so the author has drafted an annotated version of the thesis, to make the ideas in the thesis more accessible. In addition, some historical background is added to help explain why Whittle was taking a particular approach. For example, variable pitch propellers were becoming essential as flight speeds increased, but there was nothing on the commercial market (15). It also explains how Whittle used pressure- volume diagrams and the related equations to calculate the performance of his proposed power unit.

Quite quickly, Whittle came to realise that this scheme was impractical. The combination of a piston engine and a reciprocating compressor would have been impossibly heavy for an aircraft. Writing the thesis, however, provided him with the mathematical tools and engineering insights to bring forth the jet engine as we know it. That is, a compressor being driven by a gas turbine, with the exhaust being used for jet propulsion.

To get to the idea of the turbojet took another 18 months, with Whittle coming up with a jet propulsion concept similar to the Caproni-Capani N1 piston engine-jet combination, which, one can surmise, he was by then able to reject on theoretical grounds (16, 17). It was indeed a fairly obvious idea that had been thought about by others, including the Americans (18).

An attempt has been made in the annotated version of the thesis (Appendix 3 of this paper), without overstating Whittle’s intentions, to highlight those aspects in the thesis that would have pointed Whittle towards the jet engine. The process of invention has to start somewhere

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Journal of Aeronautical History Paper No. 2019/01 and, for jet propulsion, it was at Cranwell in 1928, by a then unknown Officer Cadet when he began to consider “Future Developments in Aircraft Design”

4. Conclusions

On page 46 of the thesis the Staff Tutor commented:- “It would be difficult to comment without rewriting the thesis. The thesis shows much careful and original thought and also a good deal of private reading”

The author of this Commentary is more than sympathetic to the carefully chosen words of the staff tutor. Reviewing and transcribing the thesis has not been easy, because of the lack of consistency in the use of symbols, the sudden changes in direction, and the assumption that the reader has Whittle’s grasp of higher mathematics and knowledge of thermodynamics. Putting all that to one side, what Whittle has done is extremely impressive. But contrary to what most people think, the thesis does not describe the jet engine, or even give any real recognition of jet propulsion as a viable means of powering aeroplanes. Nor does it describe the turboprop, as it is now understood. What Whittle invented was a unique method of combining the best characteristics of the piston engine with the gas turbine, thereby avoiding what would have been, at the time, insuperable materials problems.

The title of the thesis is “Future Developments in Aircraft Design”. Accordingly, it is reasonable to say that Whittle took a systems approach to the subject. He recognised that long range flight was best done at very high altitudes, where air density was low. This would reduce drag and allow flight at what were then unimaginable speeds. Flying at very high altitude also permitted stalling speeds at sea level to be kept low; an absolutely vital requirement in an era in which there were no long concrete runways. Furthermore, Whittle also recognised that high speed flight required a propeller turning at a very high rate, with the best means of driving it being a gas turbine. As an aside, Whittle mentioned the need for a fully pressurised cockpit, at a time when these were in the experimental stage.

Having lighted on the concept of a direct drive from a turbine wheel to the propeller, Whittle then had to find a method of powering the turbine. The most obvious solution was to use the exhaust from a piston engine, but the temperatures involved would have been far beyond the capabilities of the materials of the time. Instead Whittle used the piston engine to compress air which was then mixed with the exhaust gases, to give a very acceptable turbine inlet temperature of 527 ° C. In this way he also bypassed the issue of having to develop a high pressure burner, something which turned out to be a real obstacle in the development of the jet engine. Adding in a stream of compressed air increased the mass flow through the turbine, which more detailed design work would have shown to be a significant benefit. And finally, apart from the heat losses associated with the cooling of the piston engine, almost all of the energy in its fuel was passing through the gas turbine as a hot pressurised stream of air and combustion products.

Others might have come up with a similar concept, but not many would have had the capability to carry through a thermodynamic assessment of the idea. Whittle’s calculations

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Journal of Aeronautical History Paper No. 2019/01 about optimum pressure ratio, and specific work per pound of air flow, would permit estimates to be made of fuel consumption and power plant weights. These figures would govern the size of the proposed long range aeroplane. Given the very adverse circumstances in which a very youthful Whittle composed this ground breaking piece of work, no praise can be too high.

If a criticism is to be made about the thermodynamic calculations, it is the assumption that the concept is thermodynamically perfect. The compressor and turbine have isentropic efficiencies of 100%, there are no pressure drops in the pipework or entry and exit losses into the tank, or boiler as he describes it. The author considers these points should be given no weight. To have begun to include these details would resulted in Whittle doing a PhD, rather than a piece of homework that had to be done over a few nights or weekends.

Further investigations and study would, however, begin to show the main shortcomings of this approach. Although the single stage gas turbine itself would have been quite light, the overall weight of the power plant, because of the piston engine, reciprocating compressor and pressurised tank would have been unacceptable. A more fundamental issue is the fall off in power of the piston engine at high altitudes, probably limiting the proposed aircraft to not much more than 40,000 feet, a long way from the 120,000 ft. that was proposed.

The thesis was critical in the development of the concept of jet propulsion. From his own account, Whittle’s next step was to conceive a form of jet propulsion with the compressor being driven directly from a piston engine. This was quickly rejected, with Whittle moving to jet propulsion as we know it. Here again, others could have taken these conceptual steps, but as this thesis shows, Whittle had the mathematical background and enough working knowledge of the gas turbine to flesh out his ideas. The jet engine was, literally, just around the corner.

Whittle obtained a patent for the concept of a jet engine in 1930 (19), and in 1931 published a major paper on turbo-compressors for supercharging in the Journal of the Royal Aeronautical Society (20), showing his detailed knowledge of compressors suitable for the intakes of aero engines, both reciprocating and turbine. His WU technology demonstrator engine first ran on a test bench on 12th April1937.

References 1. Sir Frank Whittle Jet- The Story of a Pioneer pp 20-21, Frederick Muller, London, 1953 2. Air Commodore Frank Whittle The Early History of the Whittle Jet Propulsion Gas Turbine pp 419-435, Proc I.Mech.E., London, Jan – Dec 1945 3. James St. Peter Sir Frank Whittle and the First British Aircraft Gas Turbine Chapter 1, pp 3-39 “The History of Aircraft Gas Turbine Engine Development in the United States” published by the International Gas Turbine Institute of the ASME 1999 4 Ibid Dr Hans von Ohain and the First German Aircraft Turbine Chapter 2, pp 41-57 5. Wolfgang Wagner The First Jet Aircraft (The History of German Aviation) pp14-27 Schiffer Publishing Inc, Atglen PA 1998

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6. D. G. Wilson The Thermodynamics of Gas-Turbine Power Cycles p 345, MIT Press, Cambridge, Massachusetts, 1984 7. Bill Gunston The Development of Jet and Turbine Aeroengines” pp 136-37, Patrick Stephens, Somerset, UK, 1997 8. J. Golley Whittle - The True Story p 23, Airlife, Hillingdon, Middlesex, 1987 9. Ibid Chapter 3 RAF Cranwell 1923-26 and Chapter 4 Pilot and Prodigy 10. P. W. Brooks The First Transport Aeroplanes pp 36-66, chapter in The Modern Airliner - Its Origins and Development, Putnam, London, 1961 11. R. E. G. Davies The Romance of Early Air Travel pp 81-94, chapter in Fallacies and Fantasies of Air Transport History Airlife, Hillingdon, Middlesex, 1994 12. D. G. Wilson The Thermodynamics of Gas-Turbine Power Cycles pp 101-140, Chapter 3 in The Design of High-Efficiency Turbomachinery and Gas Turbines MIT Press, Cambridge, Massachusetts, 1984 13. Ian Whittle has emphasised to me that his father’s “bible” was Stodola 14. A. Stodola Steam Turbines with an Appendix on Gas Turbines and the Future of Heat Engines 2nd edition, trans Loewenstein, Van Nostrand, NewYork, and Archibald Constable, Edinburgh, 1905 15. R. Miller and D. Sawers The Variable Pitch Propeller pp 71-79, in The Technical Development of Modern Aviation Routledge and Kegan Paul, London, 1968 16. Sir F. Whittle Jet - The Story of a Pioneer pp 24, Frederick Muller, London, 1953 17. G. G. Smith Gas Turbines and Jet Propulsion for Aircraft pp 45-47, 6th Edition, Iliffe, London, 1955 18. E. Buckingham Jet Propulsion for Airplanes Report No 159, US Bureau of Standards, Washington DC, 1922 19. F. Whittle Improvements relating to the propulsion of aircraft and other vehicles British Patent Application Number 347,206, filed 16 Jan. 1930, granted 16 March 1930 20. F. Whittle The turbo - compressor and the supercharging of aero engines JRAeS pp 1047-1074, Royal Aeronautical Society, London, 1931

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Appendix 1

A facsimile of Whittle’s 1928 Cranwell thesis

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Page 1 Page 3

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Page 43 Appendix Page 45

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Page 47 Page 49

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Appendix 2

FUTURE DEVELOPMENTS IN AIRCRAFT DESIGN A Thesis by Officer Cadet Frank Whittle, Cranwell 1928

[Page 1] Introductory

The flight of the aeroplane “Southern Cross” from San Francisco to Sidney via Honolulu and Suva marks the latest step in aircraft performance, yet it is less than a score of years since the crossing of the Channel by Bleriot was acclaimed as a marvellous feat. The development of aircraft has made some astounding strides, and it is reasonable to suppose that this development is going to continue. It is a hazardous business to forecast the future, especially in these days of discovery, where science may at any moment make revolutionary discoveries. There are three ways of speculating on the future. There is the immediate future, the further future, and the far future. The object of the work is to discuss the “middle” future, with a certain amount of [page 3] speculation which probably overlap the immediate future.

Development will take place along the following lines. 1) Increase of range 2) Increase of speed 3) Increase of reliability 4) Decrease of structural weight 5) More economical flight 6) Increase of ceiling 7) Increase of load carrying capacity 8) Greater ability to withstand the elements

Many of these will be interdependent, for instance, a decrease in structural weight will result in increased range, etc.

The World

This may seem a strange heading considering the nature of the article, but there are certain properties of the world which must be taken into [page 5] account in aviation, such as gravity, and the earth’s magnetic field, on which navigation depends.

To what extent does centrifugal force affect weight? The answer is “not much!” The earth’s rate of rotation is 2 π radians in 24 hours, and the angular velocity being so small, the centrifugal force small in spite of the large radius.

If an aeroplane weighing 1000 lbs at rest in space would weigh 986 lbs at rest on the earth and 940 lbs if travelling at 1000 mph in the direction of the earth’s rotation (On the equator).

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How is ‘g’ affected by height? The answer is again “not much!” The value of g varies inversely with the square of the distance from the centre of the earth. Calculation shows that if an aeroplane wt [weighing] 1000 lbs at the surface of the earth, went to a height of 100 miles, the weight would be approximately 953 lbs.

Fig 1 [page 6]

No other way of reducing ‘g’ is known [page 7] to science at present. The only means of obtaining flight is by means of producing a force equal to, and directly opposing the weight.

Methods of Obtaining Lift

Methods of obtaining lift may be divided into two classes, both dependent on the atmosphere, (a) The principle of buoyancy (b) The downward displacement of air.

As this article is only intended to deal with heavier-than-air craft, only the latter will be considered.

Fig 1. illustrates the principle of the aerofoil. If a weight of air W lbs per second, travelling at V ft.p.sec be deflected down, so that it has a velocity V in a direction making an angle α with its original direction of flow, the vertical, i.e. lift component of change of velocity = V sin α and

Lift = (W/g) x V sin α

W/sec will be proportional to V and α

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[page 8]

B

B B

[page 9] i.e. W lbs/sec = K ρ V Lift = K (ρ/g) V 2 sin α

This agrees with the empirical formula obtained in the wind tunnel, ie 2 L = K L (ρ/g) A V

Aerofoils are now of high efficiency having attained in some as high an L/D of 21. It doesn’t seem likely that a more efficient method of lift is likely to be evolved.

It is possible that the Bernouilli principle may be employed. For instance if two plates (fig 2) curved as shown and having the distance at B less than at A, be forced through the air, the air passing between them would be given both a change of direction and a change of speed, i.e. V 1 would be greater than V, and for the air passing between the plates the change of velocity would be represented by V 2

Range

Assumptions:- Engine efficiency 25% (thermal) Airscrew efficiency 70% η = Aeroplane’s Lift drag ratio [page 11] W = wt of aircraft (lbs) , D = drag in lbs, w = Wt of fuel per thousand miles (air miles), V = Velocity in ft/sec Calorific value of fuel = 19000 BTU H.P. necessary to maintain aeroplane Wt, (weighing) W lbs in level flight VD / 550 D = W / η HP = V W / 550 η In one hour machine will travel 15 / 22 V miles. Total efficiency of airscrew and engine = 0.7 x 25% = 17.5% Fuel required per HP hr = (33000 x 60) / (0.175 x 778 x 19000) = 0.765 lbs Fuel required per hr = 0.765 VW / (550 x η) Fuel required per mile = 0.765 VW / (550 x η) x 22 /15 V = 0.00182 W / η Fuel required per 1000 miles = 1.82 W / η

Thus range depends on weight of fuel and wt of fuel in turn is proportional to wt of aircraft and inversely proportional to the overall efficiency of the aircraft. Thus improvements in [page 13]

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Journal of Aeronautical History Paper 2019/01 streamline and aerofoil sections and reductions in structural weights are the means by which greater ranges will be obtained.

A more general formula would be Wt of fuel per thousand miles = K W/ E e η Where E = thermal efficiency of engine e = efficiency of airscrew

This does not allow for the decrease of W due to fuel consumption.

Increase of Speed

Except for saving [life saving] purposes it is not likely that increases of speed will be sought at normal altitudes, as increase in speed means a lower overall L/D ratio owing to the increase of the proportion of passive drag, and, as shown above, decreased η means decreased range, also the greater power required means larger engine units and consequently increased weight. I intend to show that greater speed will probably attained by very high altitude flight.

[page 15] Reliability

The reliability of an aeroplane is the reliability of the power unit, and already it is being realised that it is much safer to use two or more power units, than to rely entirely on one, also the distributed weight of several power units will lead to reductions in structural weight, as I hope to show below.

Decrease of Structural Weight

It is natural to suppose that aeroplanes are going to increase in size. If so the arrangement of weights will have to be somewhat different from the present practice. For instance, if a Bristol Fighter be made exactly twice as large as it is at present, then the area of the planes having increased four times, the loading on all members for a given speed would be increased four times, and a flying wire (say) would have to have four times the cross section, and its length twice as much as the original, its weight would be eight times.

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[page 17] and C is the value of √  o / at that altitude.

Similarly HP required for level flight = C HP o where HP o is the horsepower required for level flight at ground level.

Also airscrew revs = C n o where n o equals airscrew revs at ground level Thus it may be seen that if practical difficulties could be overcome an aeroplane which would fly at 60 mph at ground level would be able to fly at 600mph at 120,000 ft if the horsepower was available.

It is clear that the aeroplane will have reached its ceiling when C HP o equals the available horsepower.

At present the available horsepower of an engine falls off with height unless supercharged and supercharging is at present inadequate for greater altitudes than 30000 ft.

Also an airscrew designed to work efficiently at low altitudes becomes hopelessly unsuitable at great [page 19] altitudes as to give proportionate thrust at any altitude its rpm must increase to C n o. The only way out of the airscrew difficulty is gearing, as it is impractical to increase the engine speed. A variation in pitch would be quite inadequate.

Of course at altitudes greater than 30000 ft, or even less, a totally enclosed cockpit into which warmed air is pressure fed would be necessary.

Another great advantage, which would be obtained from long distance flying at great altitudes, would be the absence of atmospheric disturbances, as above the tropopause (33000 ft) such things as depressions do not exist, as there are no convection currents, and such winds as there are will be absolutely steady. A 100 mph wind against a machine travelling at 600 mph at 120000ft would have less effect than a 20 mph wind against the same [page 21] machine doing 60mph at 1000 ft. Thus everything indicates that designers should aim at altitude.

POWER UNITS

Before discussing various power units we will examine the “Rocket Principle”. One has read a lot about cars being propelled by rockets, and projected schemes for driving aircraft by rockets and schemes for leaving this homely planet through the same principle.

It is true that this at present seems to be the only means of exerting thrust in space, but I hope to show that for terrestrial purposes the “rocket principle” is hopelessly inefficient.

This method of drive consists in forcing gases at high velocity through a nozzle, the reaction obtained being opposite in direction to the flow of the escaping gas. [page 23] Suppose W lbs per second of gas leaves a nozzle (from a chamber in which the gas is supplied at ' pressure) with a velocity of V / sec.

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Then the force exerted on gas and (as action and reaction are equal and opposite) the thrust obtained 2 will equal (W / g) V. The kinetic energy imparted to the gas will be (W / 2g) x V ft lbs/sec. 2 i.e. power given to the gas = (W / 2g) x (V /550) HP and power developed by the reaction = (w / g) x (Vv / 550) where v is the velocity of the generating apparatus. 2 Efficiency = Output / Input (W Vv / g 5550) / (W V / 2g x 550) = 2v / V i.e. maximum efficiency would be obtained when v = ½ V As the velocity of a gas escaping from a nozzle is of the order of molecular speeds, v would have to be very great before a machine driven on the rocket principle would [page 25] become efficient.

[Figure 4]

Turbines?

It seems that, as the turbine is the most efficient prime mover known, it is possible that it will be developed for aircraft especially if some means of driving a turbine by petrol could be devised. A steam turbine is quite impractical owing to the weight of boilers, condensers etc.

A petrol driven turbine would be more efficient than a steam turbine as there need be no loss of heat through the flues, all the exhaust going through the nozzles.

The cycle for a petrol driven turbine is shown opposite. It is a constant pressure cycle. Air is compressed adiabatically (A.B) into a chamber where it is heated at constant pressure by burning petrol (i.e. air enters the chamber at the same speed as it leaves the nozzles).

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[page 27] It then expands adiabatically through the nozzles (C.D) and escaping into the atmosphere cools at constant pressure (D.A).

There is a similar relation between the velocity of the gases and the blade velocity of the rotor, as in the rocket principle. v = velocity of blade V = velocity of gas

V 2 will be the relative velocity with which the gas meets the blade, V 3 will be the velocity relative to the blade after deflection, and V 4 represents the actual velocity after deflection. It is clear that the maximum energy will have been absorbed by the blade when V 4 has no component in the direction of rotation, i.e. when it is parallel to the axis of the rotor. It is clear from the diagram that V 4 will parallel to the axis of the rotor when 2v = V 5, the component of V (velocity) in the direction of blade rotation i.e. the most efficient speed [page 29] for the blades is one half the component of the nozzle velocity in the direction of rotation.

If α is angle of nozzle axis with direction of rotation then v = ½ V cos α for maximum efficiency.

[Figure 5]

2 KE per second of gas = (W / 2g) V ft lbs /sec power (W/g = mass (lbs) per sec)

Assuming perfect deflection, change in velocity of gas = AB = 2v Force on the blades = (W / g) x 2v And Power = (W / g) x 2v x v ft lbs/sec 2 = (2W / g) x v 2 2 2 Efficiency = Output / Input = { (W / 2g) V cos α} / {(W / 2g) V } 2 = cos α

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There are two chief limitations to a petrol driven turbine (a) blade velocity (b) temperature of gases

(a) Assuming a material of ultimate tensile strength, T tons per square inch and density ρ lbs / cu.in, then the hoop stress (for a turbine disc) due to centrifugal force 2 2 2 2 = (W / g) x (r ω 2r /2) = (W / g) x r ω = (W / g) V

This cannot exceed T tons/sq in bursting speed = √ g T / W [page 31] Assuming a safety factor of 4 Then maximum stress = T / 4 and limiting speed = ½ √ g T / ρ f.s. i.e. v = ½ √ g T / ρ v = ½ V cos α

Therefore maximum nozzle velocity of gas should be {√ g T / W }/ cos α 2 i.e. maximum KE of gas/sec = { W 2 / 2 g } { g T / ρ cos α } 2 = W T / g ρ cos α W = wt/sec of gas escaping

Assuming adiabatic expansion in nozzles (i.e. assuming perfect flow), then if the gases expand from pressure P 1 to pressure P 2 the loss of heat energy is represented by area ABCD in diagram (a) opposite, this equals KE at nozzles then if figure (a) represents PV diagram for the expansion of W lbs then work represented by area

P 1 ⌠ 2 ABCD = ⌡ V dp = W T / g ρ cos α P 2 Work indicated in the complete cycle in figure (b) = EFGH

If b represents the cycle for 1lb of air, then I.H.P. = w x EFGH / 550 Where w = lbs of air per sec. [page 33] P2 will be atmospheric pressure.

My aim is to show that a turbine will be more efficient than the petrol internal combustion engine and would be more suitable for high altitude work. It is clear from the cycle diagram that the higher the altitude the more thermal efficiency will be will be obtained owing to the low temperature and lower ‘condenser’ pressure.

This cycle is very flexible and the H.P. is not dependent so much on the rpm of rotor as in the case of the petrol engine. The revs are governed by the area abcd, whereas the power depends on the weight of air per second and the area enclosed by the cycle.

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Figure 6

[Figure 7]

[Figure 8]

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The flexibility may be seen by considering a cycle for low altitude work E.F.G.H. Now as altitude increases, the weight of air which may be taken in decreases, but the cycle can be increased to LMNO owing to the lower atmospheric pressure and the addition of more [page 35] heat per lb of air. As before, the limitations to this process are when the temperature at M becomes as high as practicable, and the area QMNR reaches the maximum permissible. It is clear that with altitude the rpm of rotor being proportional to area QMNR, will increase with altitude, which for an airscrew is what is wanted.

Diagram opposite represents cycle for 1lb of air.

P ⌠ 1 r

Area EBCF = KE of 1lb of air at the nozzles = ⌡ V dp when P V = K 2 P 2 i.e. if v = velocity of gas at the nozzles

P 1 2 1/r ⌠ 1/r

then w / 2 g K ( 1 / P ) dP = 1 v = 2 ⌡ P 2

2 1/r P 1 1/r 2 ⌠ Therefore / 2 g = K ( 1 / P ) dP = T / g ρ cos α for maximum v 2 ⌡ P 2 Where T is the safe maximum tension of material of the rotor, ρ = density of material, α = angle of nozzle P 1/r ⌠ 1 1/r 2

The equation K 2 ⌡ ( 1 / P ) dP = T / g ρ cos α P 2 gives the maximum value of EBCF for an efficient turbine.

[Figure 9]

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[page 37] The principle of the turbine is shown diagramatically opposite.

Air from air pumps is compressed adiabatically until the pressure is equal to that in ‘acting boiler’ when it passes through non-return valves, it is heated by mixture from an exploding cylinder. The rate of escape through nozzles should just equal rate of admission through valves thus keeping a constant pressure.

The maximum temperature in a prime mover of this type should not exceed 500 ° C. This limiting temperature also limits the nozzle velocity, as it is shown by plotting that the energy drop from 500 ° C on any adiabatic (energy for drop to atmospheric pressure) for 1lb of air does not by any means approach that kinetic energy of gases at nozzle which would necessitate a dangerous speed of rotation to meet the condition v = ½ V cos α

[Figure 10]

The maximum temperature limits the power of which may be obtained [page 39] by heating 1 lb of air per second, but more power may be obtained by heating a larger quantity of air The limits to the quantity of air which could pass through the engine/sec is a question of experiment, but I estimate that 10 lbs /sec at ground level could be managed on one turbine. Of course the more air passing through, the lower the maximum temperature for a given power.

Such a prime mover would quite feasibly use crude oil as the heating agent with consequent reduced cost.

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Summary

Summarising one can see that the range of aircraft depends on weight and efficiency, and that it will only be increased by careful streamlining, and better structural design and also more efficient prime movers.

Speed is best achieved by attaining [page 41] great altitudes, which, in turn, can only be done by the development of a more suitable prime mover.

The prime mover which will apparently lead to the desirabilities mentioned above is an air turbine, as this gives back the energy in supercharging, has a greater efficiency at high altitudes, and is much more flexible (in rate of rotation) than present engines.

It should also have a greater efficiency than the steam turbine, which is the most efficient prime mover at present. Greater thermal efficiency obviously means greater range for a given quantity of fuel.

The most important developments, which will take place, will follow as a result of the development of a more suitable prime mover, i.e. an air turbine. Pages 12 and 14 relate to the section on range (pages 9 to 13), but do not form part of the main argument and are not used later in the thesis. They are reproduced below.

[page 12] Range allowing for Fuel Consumption if R = range and w = wt of fuel on board at any given time and W net weight of aircraft then fuel per mile = dw / dR This will equal K (W + w) / E e η Let K / E e η = k then dw / dR = k (W + w) dR / dw = 1 / k (W / w) dR = dw / k (W + w) ⌠W 1 R = 1 / k ⌡ 1 / (W + w) dw 0

Where R = Actual distance in air miles which may be flown with W 1 lbs of fuel

W 1 [page 14] R = 1 / ⌡⌠ 1 / (W + ) d k 0 w w

= 1 / k { log e (W + w) } 0

= 1 / k { log (W + w) - log W }

= 1 / k log (1 + w / W)

R = 1 / k log (1 + w / W) If η = L / D ratio W + w = total weight = thermal effy of engine  = Airscrew effy. Cal, value of fuel = 19000 BTU per lb

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Then drag = (W + w) / η lbs HP = (W + w) V / η 550 Fuel for 1 HP = 33000 x 60 / 19000 x 778 x x  Fuel / mile = fuel / hr x V x 15 / 22 = 33000 x 60 (W + w) 22 / 19000 x 778 x  xη x 550 x 15 i.e. dw /dR = 33000 x 60 (W + w) 22 / 19000 x 778 x  xη x 550 x 15 i.e. R = 33000 x 60 x 22 / 19000 x 778 x  xη x 550 x 15 Therefore 1 / k = 19000 x 778 x  xη x 550 x 15 / 33000 x 60 x 22 = 2800 η

R = 2800 η Log (1 + w / W) miles (air)

[page 43] Appendix To Find Maximum Work which may be done by subjecting 1lb of air to a constant pressure cycle given a maximum temperature limit of t° (Kelvin)

AB is the isothermal PV = Rt p1 is atmospheric pressure DE the adiabatic for the compression of atmospheric air

We want to find the value of p 2 which will make EFGD a maximum.

At point F p 2 V = R t therefore V = R t / p 2 γ Therefore equation PV = K for FG [adiabatic line]

has at F P = p 2 V = R t / P γ

therefore K = p 2 (R t / p 2 ) γ γ

i.e. equation of FG is P V = p 2 (R t / p 2 ) γ equation of ED is P V = k

k is found by substituting pressure and volume of 1 lb of air at atmospheric conditions.

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p p ⌠ 2 ⌠ 2 EFGD = V dP - V dP ⌡p ⌡p 1 γ 1 γ (P V = K) (P V = k) [page 45] p 2 p 2 1/γ ⌠ 1/ γ 1/γ⌠ 1/ γ = K ⌡ (1/P ) dP - k ⌡ (1/p ) dP p1 p 1

p p 1/γ (1 - 1/ γ) 2 1/γ (1 - 1/ γ) 2 = K { (P )/ (1 - 1/ γ) } - k { (p )/ (1 - 1/ γ) } p p 1 1

(1 - 1/ γ) (1 - 1/ γ) 1/γ 1/γ = { (p 2 - p 1 )/ (1 - 1/ γ) } { K - k }

γ Therefore Work = K = p 2 (R t / p 2 )

(1 - 1/ γ) (1 - 1/ γ) (1/ γ – 1) 1/γ = { (p 2 - p 1 ) / (1 - 1/ γ) } { p 2 Rt - k }

(1 - 1/ γ) 1/γ (1 - 1/ γ) (1/ γ - 1) 1/γ (1 - 1/ γ) = (Rt - p 2 k - p 1 p 2 Rt + k p 1 ) / (1 - 1/ γ) if γ = 1.4 1/ γ = 0.72 1 - 1/ γ = 0.28 0.28 0.72 0.28 - 0.28 0.72 0.72 Therefore Work = (Rt - p 2 k - p 1 p 2 Rt + k p 1 ) / 0.72 0.28 0.72 0.28 - 0.28 0.72 0.72 = (Rt / 0.72) – (p 2 k / 0.72) – (p 1 p 2 Rt / 0.72) + (k p 1 / 0.72) 0.72 - 0.72 0.28 - 1.28 dW / d p 2 = (- 0.28 k / 0.72) p 2 + (0.28 p 1 p 2 / 0.72) Rt 0.28 1.28 0.72 0.72 when W = max (0.39 p 1 Rt) / p 2 = 0.39 k / p 2 [Whittle appears to have made a mistake substituting values for the indices; the lines above should read 0.28 0.72 0.28 - 0.28 0.72 0.28 Work = (Rt - p 2 k - p 1 p 2 Rt + k p 1 ) / 0.28 0.28 0.72 0.28 - 0.28 0.72 0.28 = (Rt / 0.28) – (p 2 k / 0.28) – (p 1 p 2 Rt / 0.28) + (k p 1 / 0.28) 0.72 - 0.72 0.28 - 1.28 dW / d p 2 = (- 0.28 k / 0.28) p 2 + (0.28 p 1 p 2 / 0.28) Rt 0.28 1.28 0.72 0.72 when W = max p 1 Rt / p 2 = k / p 2 The following is from the original thesis]

0.72 1.28 0.28 0.72 k p 2 = p 1 p 2 Rt 0.72 0.56 0.28 k p 2 = p 1 Rt 0.56 0.28 0.72 p 2 = (p 1 Rt) / k 0.5 1.785 1.785 1.285

p 2 = (p 1 R t ) / k

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For air speed at ground level k = 65,600 R = 96

p 1 = 2120 lbs / sq.ft

[page 47]

Therefore p 2 at ground level for maximum work 1.785 1.785 1.785 = (√ 2120 / 65,600 ) x 98 t

If t = 800 o A

Then p 2 = (46 x 3550 x 151200) /1,550,000 = 15,910 sq.ft then K = 15910 (98 x 800 / 15910) 1.4 = 148300

15,910 15,910 0.72 ⌠ 1/γ 0.72⌠ 1/γ Work = 148,300 P dP - 65,600 P dP ⌡ ⌡ 2120 2120 0.72 0.28 0.72 0.28 = 148,300 P / 0.28 - 65,600 P / 0.28 { }15,910 { }15,910

= 5250 x 23.3 - 2885 x 23.3 =2120 55,000 ft lbs 2120 o i.e. Max I.H.P. for 1 lb of air / sec, limiting tem = 800 A = 100

A similar calculation shows that at altitude where ρ H / ρ o = 100 o Max I.H.P. for 1 lb of air / sec with a limiting temperature of 800 A = 118 o

note. (Temp of stratosphere assumed to be -50 C)

N.B. The only limit to the compression ratio is the temperature to which the materials may be subjected. [page 49] Effy of constant pressure cycle

p 1 V 1 = K p 1 V 4 = k

p 2 V 2 = K p 2 V 3 = k

p 1 V 1 = p 2 V 2

p 1 V 4 = p 2 V 3 Therefore V 1 / V 4 = V 2 / V 3 = R compression ratio

(γ - 1) (γ - 1) (γ - 1) T 2 = T 1 (V 1 / V 2 ) = T 1 R (γ - 1) (γ - 1) (γ - 1) T 3 = T 4 (V 4 / V 3 ) = T 4 R

Heat received = (T 3 - T 2 ) C p

Heat rejected = (T 4 - T 1 ) C p

Work done = (T 3 - T 2 ) C p - (T 4 - T 1 ) C p

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 = work done / heat received = (T 3 - T 2 + T 1 - T 4 ) / (T 3 - T 2 ) (γ - 1) (γ - 1) (γ - 1) (γ - 1) = (T 4 R - T 1 R + T 1 - T 4 ) / (T 4 R - T 1 R ) (γ - 1) (γ - 1) (γ - 1) (γ - 1) = (T 4 - T 1) ( R - 1 ) / (T 4 - T 1) R = ( R - 1 ) / R = 1 – 1 / R (γ - 1)

[Staff Tutor’s comment] It would be difficult to comment without rewriting the thesis. The thesis shows much careful and original thought and also a good deal of private reading.

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Appendix 3 An annotated version of FUTURE DEVELOPMENTS IN AIRCRAFT DESIGN A Thesis by Officer Cadet Frank Whittle, Cranwell 1928 by Dr F Starr FIMMM, MI.MechE, C Eng.

Preamble

The early part of Frank Whittle’s 1928 thesis explains why, for a long range aircraft, flying at high speed and altitude is essential. Sir Frank argues that a new type of power unit will be needed, capable of high rotational speed and excellent altitude capability. The remaining parts of the thesis are essentially a basic thermodynamic assessment of the power unit. Although not difficult in themselves, the equations that Sir Frank deploys do imply the need to have a good grasp of elementary calculus. Sir Frank, unfortunately, has made life difficult for those of us who do not have his insight in moving from one equation to another. There are some pages which have been lost, which does not help, although it is possible to surmise what they might have contained.

This annotated version of the Frank Whittle’s 1928 thesis has been written to assist the reader follow the technical content of the thesis. It is laid out to track how the thesis progresses, but there are difficulties. Some of the sections move from one idea to another, and because of this a number of subsections have been added. These are shown in italics. The original headings are shown in capitals. All of the thermodynamic PV diagrams have been redrawn. For clarity, in this Commentary, the figures are numbered in sequence. They do not always correspond to what is in the thesis or the transcript.

It is suggested that after having a look through the transcript of the thesis, identifying any points of interest the reader may have, he or she should use this annotated version of the thesis as a guide to see how Whittle develops his ideas. No two people will ever review or respond to a document of this type in the same way. However, it is hoped that what has been written will be of service to the historian of technology and will interest both amateurs and professionals in the aviation community.

INTRODUCTION PAGE 1

The opening sentence of the thesis, referring to the three stage Transpacific Flight of the “Southern Cross” by Kingsford Smith, from California to Australia, dates the thesis to after the beginning of June in 1928 (1). The flight also gives us some idea of what was state of the art in commercial aviation at the time, and how advanced Whittle’s ideas must have seemed to his tutors. The Southern Cross was a Fokker FVII/3m, powered by three Wright J-5 Whirlwind radials of about 200 hp, see Figure 1. The longest stage was from Kauai, an island in the Hawaiian chain, to Fiji, a distance of 3,155 miles (5,077km) that took over 34 hours. A modern jet would do it in seven, actually doing the kind of speed that Whittle was then. envisaging .

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Figure 1. Southern Cross, Fokker FVII/3m Source National Aerospace Library, Royal Aeronautical Society

In “Future Developments in Aircraft Design” Whittle decides to look at the ‘middle’ or ‘intermediate’ future. If the focus had been on the near future, this would have ruled out any consideration of turbine based engines. The thesis would then have been geared towards the design of aircraft, perhaps examining the merits of the biplane and monoplane and improved streamlining. These would be quite easy to write about, being covered in aircraft magazines such as Flight, and books by professional writers such as Judge and aerodynamicists like Bairstow (2, 3). Future developments with piston engines, would have required too much ‘insider knowledge’ and the best that might have been done would have been to discuss supercharging, which was becoming an accepted technique at the time. Flight itself had an article on the supercharged Bristol Jupiter (4).

What Whittle does is to highlight the amazing advances that had been made, contrasting Bleriot’s 25 mile flight across the Channel in 1908 with that of Kingsford Smith. He asks what might be done in the next twenty years. We know that by 1947 the sound barrier had been broken and the B-47 swept wing bomber had made its first flight, pointing the way to successful commercial jet transports (5, 6).

PAGE 3 Whittle ends the Introduction with the developments required to ensure that the aeroplane takes its place as a standard means of transport. These are:  Increase of range  Increase of speed  Increase of reliability

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 Decrease of structural weight  More economical flight  Increase of ceiling  Increase of load carrying capacity  Greater ability to withstand the elements

THE WORLD PAGES 3 and 5

As Whittle himself says, this is a rather strange section to have in the thesis. One can only imagine that Cranwell had found that there were some rather odd ideas among the students as to why aircraft are able to fly. Some might have thought it was because of the reduction of gravity with height. It may also have been supposed that aircraft were easier to fly nearer the equator, the hypothesis being that centrifugal force, from the earth’s rotation, outweighed gravity more than at higher latitudes.

Whittle shows that the changes in gravity and centrifugal force are insignificant and could play no part in revolutionising aircraft design. Even the force of gravity only diminishes very slowly with height. The effects of aircraft speed on centrifugal force, thereby reducing its apparent weight, would, in theory, become just about noticeable in an aircraft like Concorde, but are not taken account of in performance estimations. As Whittle says, the only method of obtaining flight is to produce a downward force equal to the weight of the aircraft. At the time, the only practical means was the wing. Helicopters and jet lift were for the future.

METHODS OF OBTAINING LIFT PAGES 7 and 9 Also Diagram on PAGE 6

After dismissing buoyancy, Whittle gives what was the then accepted explanation as to how lift is generated. It is adequate, as far as it goes. Whittle says that the air which is moving over a wing is deflected downwards, giving an upwards reaction proportional to the sine of the angle of deflection. This is not too bad a conclusion. But from the same diagram, the drag is proportional to the cosine of the deflection, which is not necessarily true at all.

What is missing, to modern eyes, is any explanation of how this deflection comes about or the origin of the drag force. Here we should understand that the leading lights in aeronautical academia in Britain, whose opinions carried considerable weight, rejected the Lanchester-Prandtl circulation theory until well after the First World War (7). It was only after the book by Glauart had been published in 1926 that the circulation theory began to be accepted in this country (8). Without going into details, the theory explains that a moving wing imposes a circulatory flow on the air, increasing the velocity over the top of the wing and slowing it on the underside. From Bernoulli’s principle, the pressure over the top of the wing falls, whereas that on the underside rises. Hence a lift force is developed. But as a result of a “circulation” being added to the airflow, the air is deflected downwards, as Whittle shows in Figure 2.

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Figure 2. Whittle’s original drawing showing the passage of air over an aerofoil. The velocity triangles show the net reactions. The very faint small triangle subdivides the net reaction R and could be made to show the lift and drag.

Direct measurements of lift and drag could be obtained in the wind tunnel, and allowed Whittle to say that the best aerofoils were giving L/D ratios of 21 and were hardly likely to be bettered. The results from thin cambered aerofoils, like RAF 15, would have been what he was thinking about (9).

Knowing what was a good lift to drag ratio for a wing, which is a streamlined shape, would have allowed Whittle to estimate the power required and the range attainable by a well-designed aircraft. He was obviously hoping for an overall L/D ratio of around 20, which is only a little higher than that of a jet transport such as the Boeing 747 (10). He assumes that the reader (his tutor) will understand the significance, and then uses the L/D ratio in his range calculation which follows in the next section.

PAGE 9 Also Diagram on PAGE 8

Whittle does suggest a kind of jet reaction as a method by which an aircraft might be pushed upwards. The idea is that the passage of air through two curved plates would produce a jet of air deflected downwards, as in Figure 3. Although he does not mention it, such an arrangement would, as well as generating an upward vertical force, produce a horizontal jet reaction.

The Bernoulli principle is mentioned in this section, but only in the context that the narrowing of the passage through the two curves plates would result in an increase in velocity, thereby increasing the force of the jet. Although Whittle does nothing with the idea in the thesis, one of the essential ingredients of the jet engine is here in embryonic form.

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A V B

V2 V1

Figure 3. Use of a deflected stream of air to produce an upward force. Note that the area between the two plates narrows, increasing the jet velocity and the forces involved

RANGE PAGE 9,11,12 and 13

Here Whittle was endeavouring to determine the fuel consumption of an aircraft, which he gives in pounds of fuel per thousand miles. This section contains Whittle’s independent discovery of the Breguet range equation, which had been publicly announced to the Royal Aeronautical Society in 1919, by the Frenchman (11). Whittle’s version of the equation shows that for maximum range the requirements are:  The highest possible cruising speed, commensurate with a good lift to drag ratio.  A highly efficient engine, that is a low fuel consumption per horsepower hour  An efficient propeller  An aircraft in which the fuel weight is a high proportion of the loaded weight.

Modern versions of the equation for propeller and jet aircraft are given by Anderson (12). Anderson shows that maximum range for a propeller driven type solely depends on the L/D ratio. He goes on to emphasise that this is in contrast to flying for maximum endurance, whereby altitude does matter, when the aircraft has to fly at a lower speed than that for optimum lift to drag. For jet aircraft, a variation of the formula indicates that not only is altitude important, but the aircraft must fly at a higher speed than that at which L/D ratio peaks. This supports a major finding of this review which is that Whittle, at this point in time, was thinking about a sophisticated propeller driven aeroplane, not a jet.

At this juncture, it is worth remarking that one would have expected that some variant of the Breguet Range Equation to have been taught at Cranwell. Whittle affirmed several times during his life that he had formulated these ideas himself. Confirmation of Whittle’s initiative comes from Anderson, who states that although the range equation seems an obvious concept, it was not appearing in the (13) literature, only in internal reports, etc. .

The basic question is the horsepower required by the aircraft, which is a direct function of the speed and the aircraft drag. The drag is simply the aircraft weight divided by the lift to drag ratio. The

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equation that results shows horsepower increasing with flight speed and aircraft weight, but is minimised by having a high ratio of lift to drag. Note that if aircraft drag was constant regardless of the speed, horsepower would need to increase as the speed increased.

It might sound strange to assert that drag could be constant, even if speed increases. Whittle recognised that this was possible, if an aeroplane flew at high altitude. Using modern data, an aircraft flying at 150 mph at sea level, with a drag figure of 620 lb, would experience exactly the same amount of drag at a speed of 300 mph and an altitude of 40,000 ft (the IAS would still be 150 mph and the lift coefficient would be the same at both altitudes). Hence a jet engine in both cases would only need to produce a thrust of 620 lb. But if the thrust was being provided by a piston engine driving a propeller, the power needed would double from 248 hp to 496 hp, because horse power is thrust times speed, plus an additional 20 - 30% due to propeller losses. Hence Whittle would be looking for an engine capable of producing high power at altitude.

Whittle goes back to first principles in working out the weight of fuel used by the engine in driving a propeller. For this he assumes an engine efficiency of 25%, a propeller efficiency of 70% and fuel with a calorific value of 19,000 British Thermal Units per pound weight. This gives him the specific fuel consumption for the engine-propeller combination, which comes out at 0.765 lbs/hp.hr. He puts this figure into a formula that gives him the drag of the aircraft. For this he needs the aircraft weight and the lift to drag ratio.

In considering range and speed, Whittle goes beyond the usual treatment of the Breguet range equation by modern authors, which only consider flight at a constant altitude, with the focus of the discussion being on how the flight speed needs to change as fuel is consumed. Whittle highlights, in contrast, that providing an aircraft flies at a constant lift to drag ratio (ideally its best) the fuel consumption per mile and the range stay the same. This focused Whittle on the need to think about the most appropriate power unit for high speed flight at high altitude.

The determination of the maximum range for a propeller driven aircraft took Whittle’s thoughts, quite literally, into the stratosphere. It was not an obvious step. The lift to drag ratio peaks at just one indicated airspeed (14). At ground level, indicated airspeed and true airspeed are the same. However, as noted earlier, at altitude the reduction in air density means that the true airspeed becomes higher than the indicated airspeed. Thus by flying at high altitude, it is possible to maintain a high L/D ratio.

The downside of flying at high altitude and high speed is that engine power has to be increased. Whittle was aware that even supercharged engines, where the supercharger is driven by the engine, lose power as altitude increases. This was, and is, a basic fact of life. Tests done in the 1930 and 40s suggested that at 55 - 60,000 ft all of the engine power is consumed in driving the supercharger and turning the engine over, with nothing left for propulsion (15). Whittle may also have appreciated that to maintain power at high altitudes requires the supercharger to operate at very high pressure ratios. Here the standard type of centrifugal compressor, as used on aircraft engines, is seriously compromised. The impeller must operate at impossibly high tip speeds, and isentropic efficiency falls as pressure ratio increases (16). Whittle seems to have taken the view, with his concept, that since reciprocating compressors would be used, operation at very high altitudes would be feasible. As well as being capable of high pressure ratios, they would in, principle, absorb less power.

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SPEED PAGE 13

Whittle was dubious about much increase in speeds at sea level. At the time, the airspeed record was 318.6 mph (17). He ascribes the difficulty to the increase in ‘passive drag’, a combination of form and parasite drag. For most designs of the period, form drag was quite high, as structural considerations outweighed a good streamlined form. For the classic biplane, with its fixed undercarriage, uncowled radial engine, multiplicity of struts, flying wires, and fabric covering, parasite drag was dreadful. Figure 4 shows the Bristol Bulldog, an aircraft about to enter service with the RAF, which was typical in its neglect of good aerodynamic form. Top speed was 178 mph (287 km/h) (18).

Figure 4. Bristol Bulldog Mk II National Aerospace Library, Royal Aeronautical Society

Whittle reiterates that the L/D ratio will fall at higher airspeeds. From his version of the Breguet equation, range will suffer. He also states that faster speed will require a larger engine and structural weight will increase. In consequence, if long range is to be combined with high speed, this can only be obtained by flying at very high altitude.

High altitude at the time would have been considered as the point at which an oxygen mask or a pressurised suit for pilot was essential. The Handbook of Aeronautics, dating from 1931, states that above 22,000 ft “the provision of oxygen” is essential (19). This might bring a smile to seasoned air travellers. Anoxia sets in well before this, with cabin altitudes being set at a maximum of 8,000 ft, even in older jet transports. It eventually becomes clear on PAGE 15 that Whittle’s target was 120,000 ft, even today beyond what we can achieve in steady flight. It is something which can only be attained for a few seconds in a zoom climb by a supersonic fighter (20).

Why Whittle suggested such a target is discussed in the section on ‘Flight at Altitude and Power Requirements’. However, at this point it is worth noting that by the time that Whittle was about to build his first jet engine, he realised that 120,000 ft was unrealistic. The requirements for the WU,

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his first experimental engine, were based on an aircraft flying at 70,000 ft and 500 mph (21). Essentially a mid-1930s Lockheed U-2! (22)

RELIABILITY PAGE 15

Here Whittle seems to be thinking about safety rather than reliability per se, since he states that two engines give a more reliable aircraft than one. At the time this would have been a moot point, especially for long range aircraft, as P. W. Brooks says in his history of the airline industry (40). Paraphrasing slightly, Brooks states that: None of the early twin engined aircraft had any sort of single engine performance. At best, the remaining engine could be used to stretch the glide to a safer landing place. ….. Against the two-engine arrangement, there was a doubled chance of engine failure, and a larger and more complicated and expensive aeroplane to do the job. Handling characteristics when flying on one engine were rarely satisfactory.

At the time propellers were fixed pitch and could not be feathered. When not being driven such a propeller would windmill, adding off-axis drag to the aircraft and probably causing further damage to the shut-down engine. It is worth keeping in mind that commercially available propellers were all of the fixed pitch type, since it may have been the reason why Whittle was led to using a direct-drive turbine as a power source. This point will be discussed later.

Whittle mentions that the wing bending moment is reduced by mounting two engines on the wings, benefiting aircraft weight. This leads onto the next section which deals specifically with structural weight.

DECREASE OF STRUCTURAL WEIGHT PAGE 15 and Diagram on PAGE 16

Some of the section on structural weight has been lost, so that four, or possibly even six, pages of the thesis are missing. This section is possibly not too important, as it appears to be showing that an increase in aircraft size is not the solution to long range, high speed flight.

Whittle leads off with the well-known observation that a doubling in the size of an aircraft more than doubles the weight. This follows from simple application of the rules of geometry, which been recognised since the time of Galileo (24). The massive size of modern aircraft has not defeated this ‘law’. It has been bypassed to some degree by allowing wing loadings and takeoff speeds to increase and through improved materials and better structural design (25).

The section ends at this point, so what follows is conjectural, but is based in part on Whittle’s sketch of a front elevations of biplane wings. One of the sets has all the weight concentrated at the mid- point, where the fuselage would be located. The other has the weights, such as engines, fuel and bombs distributed along the wing span. In modern parlance, these weights provide relieving moments against the lift forces. Whittle writes the following note underneath his thesis sketch, which is reproduced in Figure 5. Illustrating tendency to distribute weights (power units, fuel, etc.) along lifting surface, thus reducing structural loads by neutralising loads

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Figure 5: Showing benefit of distributing weight over the span of the wings instead of concentrating it in the fuselage

Whittle would have meant neutralising aerodynamic lifting loads, of course. Today this idea is something of a commonplace (26). However, it seems to get less emphasis in modern books, possibly because the big structural issue, in hanging massive weights on wings, is the design problem associated with cut-outs of the wing structure.

The purpose of the section on structural weight may have been included in the thesis to demonstrate that Whittle understood the basic ideas in the syllabus. The comments about aircraft size and weight, and what is now called the square/cubed law, could have been part of the academic course at Cranwell, perhaps leading onto how best to design large aircraft. As Whittle says, the need to minimise bending moments does suggest the mounting of engines on the wings rather than in the fuselage.

Wasn’t it more likely that Whittle was going to show, from the square/cubed law, a large aircraft was not the best solution to long range flight? The Southern Cross was not a very large aircraft, and Lindberg’s Spirit of St Louis was even smaller.

High Speed Flight at Altitude PAGES 17, 19 and 21

There is no such section in the thesis. However, it is proposed that such a section with this sort of title must have existed in the missing pages, judging from the words at the top of page 17 in the thesis, which obviously followed on from the pages which were missing. The actual words are:

o “and C is the value of √ at that altitude.  Similarly, HP required for level flight = C.HP0 where HP0 is the horsepower required for level flight at ground level. Also, airscrew revs

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 Cn0 where n0 is the aircraft revs at ground level Thus, it may be seen that if practical difficulties could be overcome, an aeroplane which would fly at 60 mph at ground level would be able to fly at 600mph at 120000 ft. if the horsepower was available. It is clear that the aeroplane will have reached its ceiling when C.HP0 equals the available horsepower.”

It is apparent that much of the missing section must have focused on high speed flight at very high altitudes, but exactly what it was about can only be subject to intelligent guesswork.

Despite what Whittle had discovered using his version of the Breguet range equation, which appears to show that speed is not a factor, as a pilot he would have appreciated its value. Pilot fatigue, especially in the primitive cockpits of the day, would limit flight distances. The Fokker VIIB/3m trimotor, mentioned earlier in the context of the Southern Cross flight, had a cruising speed of about 95 mph with a normal range of 300 miles, indicating that a pilot would have to be at the controls for well over three hours. Even moderate headwinds meant a longer turn on duty. Hence it is reasonable to suppose that Whittle would have argued the need for higher speeds. As shown earlier, even when flying at the maximum L/D ratio, high speed requires more power and increasingly high rates of fuel consumption for each hour of flight.

Improved L/D ratios could be obtained by a reduction in wing area, but for the improvements to be significant, take off speeds and distances would have been quite unacceptable. We now use flaps to mitigate these effects, but they were not standard fixtures when Whittle was writing. In fact, flaps were ill suited to the thin, heavily cambered wing sections of the time (27). Flaps were also less effective on biplanes; the increased down flow from the top wing interfering with the lift from the lower wing (28). When most airfields were of grass, and three mile concrete runways were even beyond the science fiction of the 1920s, a low stalling speed was a critical requirement.

The supposition is that Whittle, having deposed of the idea that an increase in aircraft size or a decrease in wing area could be solutions to increasing the speed and range of aircraft, he then investigated another possibility. That is, the benefit of flying at ultra-high altitude. This would be exactly in line with that part of his academic course which would have emphasized that as altitude increases, the indicated airspeed is reduced, although the true airspeed remains constant. The converse being, of course, that with an increase in altitude, flight at a constant indicated airspeed, implies a faster true airspeed.  In the italicised section, the function √ o is the square root of the ratio of the density of air at sea  level to that of the altitude of flight. It also gives the ratio of the true air speed to the indicated air speed. As previously mentioned, Whittle refers to flight at 120,000 ft, where the reduction in air density is so great that an aircraft with a true speed of 600 mph, would have an indicated airspeed of 60 mph. In coming up with this figure he would have had to make an intelligent guess about the air density. In 1921 the UK, along with the rest of Europe, had decided to use the values provided by Toussaint, which only covered altitudes up to 10,000 metres, well below where the stratosphere starts (29). In 1924 Walter S. Diehl in the USA had published a report giving data up to 63,000 ft, which is still the basis of modern tables, but it seems doubtful if Whittle knew of this (30). He would have needed to devise a density/altitude formula that allowed him to make estimates beyond any

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published figures. This seems to have been done in an earlier thesis when he wrote on Chemistry in the Service of the RAF (31). Sadly, it is a piece of work now lost.

A modern table of “Standard Atmospheres” allows us to say that the pilot of an aircraft travelling at 600 mph at this incredible altitude would see, on his airspeed indicator, a reading of 44 mph (32). But whether the indicated airspeed was 60 mph or 44 mph, such an aircraft would have looked something like a glider or U-2. The altitude at which the TAS would be ten times the IAS is now known to be about 106,000 ft.

It was not until 1936 that Whittle was able to begin construction of a true jet engine. By that time reliable figures for density at altitude were available. As noted earlier, the design specification included flight at 70,000 ft and 500 mph. At this altitude, this would give an indicated airspeed of about 130 mph. At this height engine design thrust was 111 lb, which given the weight of the proposed aircraft of 2,000 lb, would have been quite adequate. At sea level, the design thrust of 1,389 lb was much higher, because of the increased air density (21). It is clear that Whittle was extremely exact in his calculations.

Flight at Altitude and Power Requirements

If we stay with the thesis and accept its figures, and this unique form of turboprop, Whittle states that the drag of an aircraft at 600 mph and 120,000 ft. would be the same as one flying at 60 mph at sea level. He qualifies the statement by adding, “if the horsepower were available”. It is a point of vital importance, leading Whittle to consider the need for a novel power unit. Although flying at the peak L/D ratio gives the same drag value, the horsepower is directly proportional to velocity. Hence the horsepower required for flight at 120,000 ft. and 600 mph would be ten times that at 60 mph at sea level. To give a specific example, if the drag was 420 lb at sea level, the required power would be 67.2 hp. But at 120,000 ft. and 600 mph the engine would need to be supplying 672 hp.

These results follow from the formula Horsepower = Force x Distance per second Since one horsepower = 550 ft.lb/sec Then in Imperial units the drag to engine power conversion is (Drag Force in lb x Velocity in ft/sec) / 550

These figures are indicative, of course, but it is clear that the type of aircraft of which Whittle was thinking would require an engine capable of producing some hundreds of horsepower at 120,000 ft. No such engine existed, or was even in consideration. It would certainly have to be supercharged, so as to maintain its sea level power up to extreme altitude.

What was the aero engine scene like when Whittle was writing? In 1925, a variant of the Armstrong Siddley Jaguar was the first engine equipped with a supercharger to go into production, being used in the Siskin biplane fighter. Altitude capability was limited, the engine giving 385 hp up to 9,500 ft, above which it declined (33).

Making some assumptions about what Whittle had in mind, in terms of a long range, high speed aircraft, he would have required an engine two to three times the power of the Jaguar. More importantly, power would need to be maintained at 120,000 ft, where the air density is less than one

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two hundredth of that at sea level (32), although Whittle would have assumed it to be 1% of sea level density.

High Speed Propellers

Although Whittle gets to the correct result, perhaps in the haste to get the point over, there is some muddled thinking in what is stated. He writes: Also, an airscrew designed to work efficiently at low altitudes becomes hopelessly unsuitable at great altitudes as to give proportionate thrust at any altitude its rpm must increase to Cn0. Here Whittle seems to be considering two issues. The most obvious is what, in propeller terminology, is termed the ‘advance ratio’. That is, the blades of a propeller must cut the incoming stream of air within in a fairly narrow range of angles, if useful thrust is to be produced. This requires a suitable combination of propeller blade pitch, or angle, and propeller rpm (34). High speeds require a coarser pitch.

Modern propeller-driven aircraft, which operate over a wide speed range, are able to change the pitch of their propeller blades. Although the technique was in prospect when Whittle was writing, it had yet to be introduced commercially (35). However, Whittle says, quite presciently, that given the rpm of typical engines, even the ability to change blade pitch would not be sufficient for speeds of 600 mph. In simple terms, the blade angle would be so coarse that most of the thrust from the blade would be going sideways rather than backwards. Curves of advance ratio versus blade angle support this contention, with efficiency falling above the optimum blade angle of about 45 degrees (36). Accordingly, for a very high speed aircraft, a propeller must operate at a very high rpm.

I believe this is what Whittle was trying to say, but in the back of his mind was the issue of reduced air density, which will also influence the design of the propeller. The absence of any discussion on this point seems to suggest that Whittle did not know of the book by Harris Booth, which contains an equation allowing the calculation of propeller diameter with respect to engine power, engine revs and aircraft speed (37). A rearranged version of the equation is shown below:

P = Horsepower of engine n = Propeller rpm d= Diameter of propeller in inches V = Aircraft speed in ft/sec

The equation was originally developed by H. C. Watts who states quite specifically that it is independent of altitude (38). Although the equation is quite ancient, it is quoted by Darrol Stinton, in The Design of the Aeroplane, a book intended for those planning to build, modify or fly home built aircraft (39).

Consideration of the above equation will show that for a fixed propeller diameter, the effect of an increase in velocity, with the propeller rpm in a fixed ratio to the air speed, the power varies as the cube of the aircraft speed. Given that the speed at 120,000 ft is ten times that at sea level, a simple application of the Watts’ formula would show the engine needed to produce 1,000 times more power

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than at 60mph. Whittle, quite correctly, calculated that only ten times as much power would be required.

But all that Whittle would have needed to do, if he had known of the equation, was to reduce the size of the propeller. The fact that he did not do so would suggest he was not aware of the books by Booth or Watts. They were quite advanced works intended for aircraft designers. In fact, we can say for certain that Whittle cannot have read the book by Booth, as it contains two long sections dealing with aircraft range (40). These had been developed independently of Breguet (11).

There are a couple of additional points worth making about Whittle’s few paragraphs on propeller aspects. Here was in embryonic form the bypass or turbofan jet engine, the concept patented by Whittle in 1935 (41). Furthermore, for a conventional propeller, 10,000 rpm would have pushed much of the propeller into the supersonic range. Even in the 1920s it was recognised that once propeller tips reached transonic speeds there was a marked drop in propulsive efficiency. Indeed, it was one of the first indications there was a ‘sound barrier’ (42).

Centrifugal loads on the propeller blades, which increase as the square of the rotational speed, would also have pointed to a need for a rethink of propeller design. Instead of just two long propeller blades, a much larger number of shorter blades would be necessary. It can also be shown that at reduced air densities more blades are needed. Hence, although Whittle’s turbine engine concept did not have much in common with the jet engine, if it had been realised it would have started to look, externally at least, rather like a turbofan.

Whittle ends this section with some comments on flight at high altitude. He says that an enclosed pressurised cabin would be needed, fed with warm air. He is also correct in thinking, on the whole, that flight at high altitude would be a lot smoother than close to the ground. He would not have known anything about the jet steam or clear air turbulence, but he is certainly correct in saying that the effect of a 100 mph headwind on the range of a 600 mph aircraft at 120,000 ft would be no more than one of 10 mph on an aircraft doing 60mph at a 1,000 ft.

POWER UNITS Rockets and Jet Propulsion PAGE 21, 23 and 25

Whittle begins this section by referring to rocket engines as a means of propulsion. This is the nearest we ever get, in the thesis, to jet propulsion as we know it. He only gives the subject a mention, saying: “One has read a lot about cars being propelled by rockets, and projected schemes for driving aircraft by rockets, and schemes for leaving this homely planet through the same principle”. Robert Goddard in 1920 had attracted considerable interest with his proposal for a moon rocket, and by 1928 the construction of a rocket propelled car was well advanced in Germany (43).

Whittle explains that a rocket works through the reaction to a stream of gas being forced through a nozzle, producing the force to accelerate the rocket. He then sets down a series of equations, first giving the reactive force. All of the ensuing calculations are given in Imperial units (pound weight, feet, inches, tons, seconds, etc.). The acceleration due to gravity ‘g’ figures in many of the equations, although he does not ever use the numerical quantity itself (32.2 ft./ sec2).

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The mass flow per second, W, gives the reactive force or ‘thrust’, the first time this term is used in the thesis. The kinetic energy of the jet is derived in the usual way from the mass flow multiplied by half the square of the velocity. Because ‘g’ is in the equation, although Whittle does not show it, it is possible to cancel part of the velocity and time (seconds) terms. This enables Whittle to calculate what we would term the ‘gas horsepower’ of the jet, which he calls the power given to the gas. He does this by dividing through by 550, (i.e. 1 horsepower = 550 ft.lb/sec). He also does a similar calculation for the amount of power used to drive the rocket. When the rocket is stationary, although the jet is giving thrust, it is not doing any useful work. Note that ‘work’ is force times distance, and power is work per second. As the rocket speeds up, more of the energy in the jet is being used to do useful work.

Whittle then states that the propulsive efficiency of the rocket is given by dividing the power being used to drive the rocket by the gas horsepower. After simplification, this gives him the equation, where u is the flight velocity, and V is the velocity of the exhaust: 2u Propulsive efficiency = V He concludes that the propulsive efficiency is at a maximum, i.e. 100%, when the flight velocity has reached half that of the exhaust. He says quite correctly that the exhaust velocities of rockets are at “molecular speeds” meaning that rocket engines could only be used for aircraft travelling at very high speeds.

Whittle’s derivation of propulsive efficiency would not now be regarded as being correct for rocket engines, where the peak efficiency occurs when the flight speed is exactly that of the exhaust (44). In this state where, to an external observer, the combustion products making up the rocket exhaust would appear to be stationary, they would still be producing the same propulsive thrust. For the jet engine, although there is a somewhat similar equation for efficiency, when the flight velocity reaches the exhaust velocity, jet thrust drops to zero. A somewhat impractical state of affairs, as Cumpsty remarks (45). In the book that Whittle published in 1981, on gas turbine theory, he gives the standard jet formula, making the same point as Cumpsty (46).

TURBINES PAGE 25

We are now starting on the central theme of the thesis, which is the application of the gas turbine to a propeller driven, high speed, high altitude, long range aeroplane. It is a pity that at this point Whittle did not properly state how the gas turbine was going to be used. It would have avoided a great deal of confusion in the subsequent retelling of how the jet engine came to be invented. Instead, Whittle immediately embarks on a mathematical analysis of the performance of a pure gas turbine, that is, a turbine wheel driven by pressurised combustion gases (as steam drives the single wheel of a de Laval steam turbine). Here the main aim was to estimate how much power might be produced and what this might imply for the turbine blade speeds and stresses.

It is not an easy section of the thesis to follow. The maths and thermodynamics are at Sixth Form/ Undergraduate level, the handwriting is sometimes hard to decipher, with Whittle not always making it clear what the symbols mean. This can cause problems, when for example, the upper case ‘V’ and lower case ‘v’ are used in the same equation.

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Furthermore, at the time when Whittle was writing, the only practical method of propelling aircraft was the airscrew, and he would take this to be understood. Anyone who seeks to read into the thesis jet propulsion, as we know it, will be misleading themselves. Edward Constant has shown that where jet propulsion had been seriously considered, as with the detailed study by Buckingham in 1922, it almost invariably uses a reciprocating engine to provide the jet (47, 48).

Constant goes on to make the point that by the late 1930s, in the struggle to provide flight at higher speeds and especially at higher altitudes, schemes for propeller driven aircraft with piston engines were becoming ridiculously complex. He makes the analogy of the extremely complex Ptolemaic model of the solar system with that of Copernicus. That is, the evermore complicated reciprocating engine versus the very simple jet (49).

One of the main advantages of a turbine is the high rotational speed, something that Whittle had shown was useful in a high speed aircraft, allowing a direct drive to the propeller. Whittle briefly mentions the steam turbine, but rejects it because of the weight of the boiler and condenser. He states that a ‘petrol driven’ gas turbine is lighter, and avoids what we would term the flue gas losses. That is, loss of heat through the boiler chimney or stack. In contrast, all the energy released by the combustion of the fuel passes through the gas turbine. Nevertheless, Whittle occasionally draws analogies between his ideas and the operation of steam turbines.

Here of course he is neglecting the heat energy in the exhaust. For this to be minimised the expansion ratio through the turbine has to be quite high. In a steam turbine the expansion ratio is about 100 to 1, which results in the exhaust steam exiting the turbine at just above room temperature. For various reasons this is impractical in a gas turbine.

PAGE 25 and 26 and Diagram on PAGE 24

Whittle then gives a rather sketchy outline of the constant pressure (of combustion) cycle, without naming it, which is the foundation of gas turbine theory and practice. Whereas this cycle would be a fundamental part of any engineering course today, it was not so in the 1920s, when engine technology depended on the Otto, Diesel and Rankine cycles. The book by Low, intended for undergraduates and technical students, exemplifies this, giving barely a page to the Joule or Brayton cycle, as the constant pressure variant is now called (50).

Figure 6 is a clearer version of the first Pressure-Volume or PV diagram shown on Page 24 of the thesis, keeping the lettering as Whittle decided. The power part of the cycle occurs during adiabatic expansion along the curve CD, and is Whittle’s main focus. He only briefly refers to the compression and combustion stages; in the latter he states that the petrol is burned in a pressurised chamber. He is careful to make clear that the air leaves the chamber at the same speed at which it enters, which enables him to neglect kinetic energy effects.

To make things a little clearer, a small diagram showing a gas turbine in schematic form has been added to Figure 6. Many readers will be familiar with this. But it does not really represent the Whittle concept. In a normal gas turbine, the compressor is driven by a shaft which comes from the turbine. Whittle uses a piston engine to drive the compressor. It follows that since there is no shaft linking the compressor to the turbine, all the power coming from the turbine is available to do external work. However, the same thermodynamic calculations can be applied to the Whittle

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machine as any simple type of gas turbine. The key questions being work output, efficiency and pressure ratio.

Figure 6. Brayton Cycle PV Diagram

The calculation for the work done, along CD, involves the integral of Vdp rather than the more usual Pdv, as is normally utilised in calculating output in power cycles, where the working fluid is confined by a piston within a cylinder. Vdp is the ‘flow’ form the work equation. One would guess that at the time, this variant was comparatively unknown. The equation is stated in the classic book on steam and gas turbines by Stodola (51). It was a book, as Ian Whittle has told the author on several occasions, used as a ‘bible’ by his father. Perhaps it was the first time that Sir Frank had come across this ground breaking volume.

At the beginning of his book Stodola uses St Vénant’s formula to derive Vdp in calculating gas velocity through a ‘nozzle’. ‘Nozzle’ in this case refers to the fixed blading on a turbine that directs the flow at the correct angle and accelerates it to an appropriate speed. More importantly, Stodola also uses Vdp in a very succinct section on the gas turbine at the end of the book (52, 53). Other writers, who quite naturally focused on steam turbines, did not do this. In calculating nozzle velocities, they seem to be using a combination of ideas from hydraulic engineering and the temperature entropy diagrams (54, 55). This was reasonable bearing in mind the large pressure differences and the prospect of condensation during expansion. Sir Frank saw, quite rightly, that the use of temperature entropy diagrams was an unnecessary complication for true gas turbines, where pressure ratios were quite modest and condensation impossible (56). In his later book on gas turbine theory, Sir Frank uses Vdp, incorporating density into the subsequent derivations, but most modern authors seem to approach energy calculations in gas turbines in a different way, deliberately perhaps, avoiding the Vdp or PdV arguments. 61

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Returning to the thesis itself, Whittle sees the line D to A, in which there is a reduction in volume, at constant pressure, as being equivalent to the operation of a condenser in a steam turbine plant. Of course, nothing like this happens in practice. All that happens is that fresh cold air is drawn from the atmosphere into the inlet of the compressor. Nevertheless, it is an analogy that his supervisor would have understood. It enables Whittle to argue that, just as in a steam turbine, the lower the condenser temperature, which of course, implies a lower condenser pressure, the more efficient is the gas turbine cycle. Accordingly, the gas turbine becomes more efficient as altitude increases.

All Whittle’s subsequent thermodynamic calculations to determine work output and optimum pressure ratio were done on the basis of isentropic adiabatic compression and expansion, with no pressure drops through the combustion system, etc. Although unrealistic, this is adequate for an initial examination of the potential of any gas turbine cycle. Since it is a best case scenario, if the efficiency or the work output look unpromising, there is no point in going on. Such calculations will also show that the maximum work output occurs at a pressure ratio significantly less than that at which the efficiency of the engine is at a maximum (57, 58, 59). Stodola didn’t do this type of calculation, so what Whittle was doing was quite innovative. However, it does seem likely that, at that time, Whittle may have thought that the pressure ratio for maximum work coincides with that for peak efficiency. It is a common error that those, new to gas turbine thermodynamics, make.

Velocity Diagrams and Power from an Impulse Turbine PAGE 27 and 29 and Diagram on Page 26

At this point in the thesis Whittle’s aim is to set out the factors which govern the design of an efficient single stage turbine of the impulse type. In such a design, the pressure energy in the gas is transformed into velocity or kinetic energy in the stator blades, or nozzle vanes as they are termed in the USA. Apart from frictional losses, which are small and which Whittle neglects, there is no further drop in pressure in the rotor blades or buckets.

Power is generated from the rotor blades simply through a change in the direction of the fluid. In a reaction turbine, which is more efficient than the impulse design, there is still some pressure left in the fluid after it leaves the stator or nozzle blades. The fluid continues to expand in the rotor, helping to push the rotor round. However, at this level of thinking, to have brought in the reaction turbine would have added needless complexity. Furthermore, a significant advantage of the impulse turbine is that the high level of expansion through the nozzles gives a relatively low exit temperature, ensuring that the highly stressed rotor blades run fairly cool (60, 61, 62, 63). Although this was a major consideration in the design of early gas turbines, before blade cooling was developed, it was not something Whittle made use of, explicitly at least. Later in the thesis, he stated that the turbine wheel should be limited to 500°C, but he then set 800° K (527° C) as the turbine inlet temperature for any calculations. Presumably he expected, correctly, that the wheel would run well below the gas temperature.

Figure 7 is based on the sketches on Page 26 in the thesis. It shows a schematic of the stator and rotor blades, plus a simplified version of the velocity diagrams needed to explain how the turbine operates. For an impulse turbine, Whittle shows that, at maximum efficiency, the rotor speed should be half the velocity of the gas emerging from the nozzles, multiplied by the cosine of the nozzle angle. In other words, the component of the gas velocity, in line with the periphery of the rotor, will

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then be twice that of the blade or peripheral speed. An impulse turbine will then be making the fullest use of the momentum in the gas stream. In his explanation, Whittle refers to V5 the cosine of the nozzle velocity, but accidently omits this from the diagram; he also omits V 4. These have now been included in Figure 7. Stodola gives a fuller version of the calculation, which is now included in elementary text books on turbine theory (64, 65).

Outlets from combustion chambers Cosine of Nozzle Velocity Velocity at (V5) Nozzle Exit Turbine (V) exit flow V4

Nozzle exit flow V

B on thesis page 28 diagram Ideal Flow Direction at Rotation Turbine Exit of turbine (V4)

Figure 7. Schematic of nozzle arrangement and rotor blading in impulse turbine and simplified velocity diagram

Whittle remarks that, similarly, a rocket engine is at its most efficient when the exhaust speed it twice flight velocity. Furthermore, he points out that when an impulse turbine runs at maximum efficiency, the gases leaving the turbine are directly in line with the rotor shaft. Now if Whittle had seriously been considering jet propulsion he would have put these two ideas together, it being a simple calculation to work out jet thrust. Jet thrust is given by the mass of the exhaust multiplied by its velocity (66).

There is no such mention. Instead Whittle works out the horsepower given to the turbine as a result of the change in direction and momentum of the gas. But he first calculates, in Imperial Units, what is sometime referred to as the gas horsepower, which is proportional to the square velocity of the gas in ft/sec and the weight of flow in lbs/sec. The usual values, as required by the Imperial System, ‘g’ and the horsepower conversion of 1 hp = 550 ft.lb/sec appear in the equation. This section is somewhat hard to follow, as it is easy to confuse the way in which Whittle writes ‘u’, the relative velocity of the gas to the moving blade, with a ‘v’ which could be taken for the actual velocity of the gas emerging from the nozzles. However, Whittle uses a capital ‘V’ for the latter. For optimum efficiency, as noted above, ‘u’ is equal to ½ V cos α, where α is the nozzle angle.

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Whittle states that the turbine work is maximised when the nozzle positioned at a shallow angle to 2 the turbine, the function being given by cos α. Here, it is worth pointing out that the more efficient the turbine is at extracting energy from the stream of exhaust gas, the less is available for jet thrust.

Nozzle Velocities and Stresses in the Rotor PAGE 29 and 31

Whittle then moves onto the question of the turbine stress, which eventually gives him one method of determining power output. Here, his focus is not on the stresses in the blades, which is the principal concern of gas turbine metallurgists of today, but those of the rotor. This was in keeping with steam turbine design in the 1920s, where the centrifugal stresses in the rotor disc were the critical limit. The issue was discussed by Stodola and was a feature of text books of the time (67, 68, 69).

The basis of the calculation offered by Whittle is not explicitly stated, but is that of the centrifugally induced hoop, or bursting stresses, in a thin ring. It follows the approach given by Stodola and other authors. But it does seem possible that the derivation of the formula may have been in the Cranwell course, since centrifugal stresses were limiting factors in the design of rotary engines and propellers.

The thin ring formula leads to the result that the bursting speed of a rotor is determined solely by its peripheral velocity and the strength and density of the rotor steel. Knowledge of the velocity is then used by Whittle to formulate an equation which gives the power output of the turbine. Somewhat surprisingly this is not turned into an actual quantitative figure.

Perhaps Whittle thought this was too elementary an approach and attached more significance to his later calculations based on the optimum pressure ratio for his machine. These were much more useful, in terms of developing Whittle’s thinking, since such calculations are needed during the preliminary stages of gas turbine or jet engine design. He may also have become aware, when writing the thesis, and from his reading of Stodola, that a single stage impulse turbine cannot give very high power outputs unless wheel speeds rise to unacceptable levels.

Nevertheless, it follows from this line of thinking that the ‘allowable strength’ of the rotor steel, which is the tensile strength divided by a safety factor of four* will determine:  Peripheral velocity of the disc and blade  Gas velocity at the nozzle exit  Kinetic energy in the gas stream and the power generated

He states that if the tensile strength of the disc is T tons/sq. in, and the density of the steels is W or ρ pound weight per cubic inch (Whittle switches from W to ρ part way through this section), and taking the safety factor into account, the limiting speed is given by: 1 gT ft./sec 2 

Without showing the intermediate steps Whittle states that the kinetic energy in the gas is a function of the nozzle angle, and the strength and density of the disc material. The actual steps are:

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1 gT ft. /sec = 1 V cos  2  2

* The allowable strength for steels, up to quite modern times, was the tensile strength divided by four, which is a figure which Whittle uses, or as he expresses it “T/4”. gT = V cos   gT V2 =  cos 2  2 But ½ V W2/g is the kinetic energy, where W2 is the weight of flow of air in pounds per second. Hence to obtain the kinetic energy we multiply both sides of the equation by W2/2g W2 T Hence the kinetic energy is g  cos2 

Use of Pressure Volume Diagrams in Explaining Engine Operation

In this part of the thesis Whittle explains in more detail how the various parts of the gas turbine pressure-volume diagram apply to his concept. But at this stage the arguments are essentially qualitative.

It is important to understand that the gas turbine being envisaged by Whittle is quite unlike modern equipment. This does not really become clear until just before the Appendix, when Whittle gives a description and drawing. It is then seen that it does not have the usual arrangement of a compressor, combustion chamber and turbine, with the turbine providing enough power to drive the compressor, with any excess being used to drive a propeller. As is eventually shown in the thesis, it is another part of the ‘engine’ that produces the power needed to compress the combustion air. There is no connection, mechanical, hydraulic, or aerodynamic between the turbine and the ‘compressor’. The concept is to have a completely separate, petrol fuelled, piston engine driving a set of reciprocating compressors. The exhaust gases from the piston engine mix with the compressed air in a pressurised tank, which Whittle sometimes refers to as the ‘boiler’. The mixture of compressed air and exhaust gases is what drives the turbine.

PAGE 31 and Diagram (a) on PAGE 30

Because the turbine does nothing other than drive the propeller, Whittle states that the turbine work is given by area ABCD in the PV diagram in the Figure 7a. The work is calculated using: P1 Work = Vdp P2

Where P1 is the inlet pressure to the turbine and P2 is the outlet.

This corresponds to the kinetic energy entering the turbine from the nozzles, which has been shown to be limited by the strength of the rotor, and is given by the equation:

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W T Work = 2 g  cos 2 

Figures 8a and b. Adiabatics for the turbine work and also for the complete pressure diagram for the Whittle concept. (Redrawn from PAGE 30)

PAGE 31 and 33 and Diagram (b) on PAGE 30

Whittle then moves to thinking about how the power and efficiency of the engine is governed by altitude and temperature. For diagram 8b he makes the usual comment about such diagrams, that the work done in each cycle is represented by the area EFGH. Note that because there is no pressure change during the combustion phase, EF, and also because there is no pressure change when air is taken into the engine, represented by GH, there is no work done during these parts of the cycle, either positive or negative.

It follows that that the indicated work and the indicated power output of the engine needs only to be calculated using the two adiabatic portions of the cycle. Although not stated at this point in the thesis, but shown in Figure 7b, the adiabatic curve, FG, for the turbine , corresponding to positive

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γ work, is given as PV =K1. The negative work of compression is given by the adiabatic, EH, where γ

PV =K2. Although the pressure changes in both adiabatic processes are the same, the volumes are different, because of the different temperatures experienced during expansion and compression.

Whittle wrote down the basic equation for calculating the net work or output from this cycle, as shown below p p 1 K 1 k Net work = dp - dp p p p p 2 2 He then for some reason crossed it out. There seems to be a certain amount of repetition at the bottom of Page 31 and top of Page 33, where perhaps to emphasise the point, Whittle writes: If Figure 7b represents the cycle for 1lb of air, then IHP (indicated horsepower?)

= w.EFGH 550 Where w= lbs of air per sec

P2 will be atmospheric pressure

Effect of Altitude on Power Output PAGE 33 and 35 and Diagram on PAGE 32

The next part of the thesis is intended to show that the efficiency and output of the turbine increases by flying at altitude, where the air temperature is low. He states: My aim is to show that a turbine will be more efficient than the petrol internal combustion engine and would be more suitable for high altitude work. It is clear from the cycle diagram that the higher the altitude, the more thermal efficiency (sic) will be obtained owing to the low temperature and lower ‘condenser’ pressure.

Unfortunately, the pressure volume diagram on Page 32 by which he intends to show this is not complete. The lines needed to show the cycles are not present, and in the ‘high altitude’ PV diagram, the letter ‘N’ in the air intake, or condenser part of the diagram is missing. Figure 9 below shows the completed diagram.

To me, the existing diagram, even when finished, does not really support Whittle’s arguments about the beneficial aspect of altitude, although it is quite true that the drop in temperature at altitude has a beneficial effect on the work output per pound of airflow per second and on efficiency. Obviously, providing the inlet pressure is unchanged, a low air temperature will give an increased air density and greater mass flow. However, as Wilson shows, the detailed calculations for power and efficiency are quite complex (70).

Hence it seems possible that there may have been a page at this point that showed how to calculate the PV work. Whittle may have been dissatisfied with it and taken it out, perhaps overlooking that he had lost some material. Fortunately this is not very important, since Whittle covers his approach to calculating PV work on Page 35. For this he makes use of a diagram on Page 34.

Reverting back to the thesis itself, Pages 33 and 35 deal with the question of altitude. Unless the compressor section of the engine is good enough to compensate for the effect of altitude, the power would fall away. For this to be done with a conventional piston engine, a centrifugal supercharger

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needs to turn at a higher speed as altitude increases (71). An increase in speed can be accomplished by making the drive to the supercharger of the two speed type, as was done with the later versions of the Rolls Royce Merlin (72). A better approach is to have a hydraulic drive between engine and supercharger, effectively giving a wide range of supercharger speeds, as in certain of the German DB 601 series of engines (73).

L M Q E F

H G

R N O

Figure 9. Pressure volume diagrams for the high and low altitude cases (Redrawn from PAGE 32)

Essentially Whittle asserts that Figure 9 shows that the engine will be able to provide sufficient power at altitude, since the area LMNO, corresponding to flight at altitude, is larger than that of the sea level cycle, EFGH. Whittle makes the point that because the atmospheric pressure at altitude is so low, the cycle diagram is expanded downwards, so that NO is lower than GH. There should be no argument about this. What is much less obvious is why the maximum pressure in the cycle should have increased, raising LM above EF, and why the area LMNO should be bigger than EFGH. One can only presume that at sea level the output of the engine is restricted, and as higher altitudes and speeds were attained, the power unit was ‘opened up’ in aviation parlance. Whittle also goes on to say that more heat can be added to the air to increase power. Accordingly, the line LM, which corresponds to heating the air at constant pressure, is longer than that in the sea level case, EF.

Whittle then argues that because of the increased mass flow and pressure ratio at altitude, turbine rpm will also increase as well as the power output. This is exactly the kind of performance that Whittle wanted. As previously described, the rpm of the propeller needs to increase exactly in line with the aircraft velocity. Hence a propeller turning at a modest 1,000 rpm at sea level would be turning at 10,000 rpm at 600 mph and 120,000 ft. This is a fairly reasonable assumption, although one could not expect a perfect match. As previously mentioned, if such a machine had been built, to keep propeller tip velocities at reasonable levels, a multi-bladed fan would have been needed, but this type of technology would be forty years into the future.

Even so, it seems impossible that these changes to the engine could compensate for the fall in density at 120,000 ft. An obvious problem is that the piston engine would cease to work at such an altitude. But there are other more fundamental challenges. The larger PV diagram, needed for the high altitude case, implies the need for the reciprocating compressors to work much harder. If these were to bring the boiler pressure up to just that of sea level, my own calculations imply a compression

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ratio of at least 30/1, giving a compressor outlet temperature, into the ‘boiler’, in excess of 600° C. This is in spite of the low inlet temperature at 120,000 ft. The boiler temperature would be further increased by the addition of the exhaust gases from the engine. The turbine inlet temperature would be well in excess of Whittle’s turbine inlet temperature limit of 500° C, as declared on Page 37 (a slightly higher limit of 800° K or 527° C was used in the subsequent calculations).

Further Comments on the Limits to Turbine Power PAGE 35 and Diagram on PAGE 34

On Page 35 Whittle essentially repeats the earlier parts of the thesis, where he showed that the tensile strength (with a safety factor of four) limits power and efficiency. But there are some additional points he made.

The main aim here is to express Vdp in terms of the pressure p so that the equation,

P1 Work = Vdp P2 which gives the turbine work, can be integrated. For this Whittle recognises that the adiabatic γ curves in the pressure volume diagram are given by an equation of the type PV , where γ (gamma) is the ratio of the specific heats of air. This is in contrast to isothermal curves, where the equation is PV = RT, where R is the Gas Constant and T the absolute temperature (Whittle also uses the isothermal equation in the Appendix).

A E P B 1

γ PV =K2 γ PV =K1

F P C 2 D

V (Volume)

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Figure 10. PV Diagram for calculation of turbine work (PAGE 34)

However the actual position of the adiabatic curves depends on the gas temperature, and here Whittle γ refers to the turbine work portion of the diagram EBCF, in which the adiabatic is given by PV = K 2 in Figure 10. Note that the constants K 1 and K 2 are the reverse of those shown in Figure 8b. Hence after some mathematical manipulation it can be shown that the work is given by

1 p 1 1 Work =  dP K 2 1  p2 p

w 2 This is equal to the kinetic energy of fluid being ejected by the nozzles, which is: v 2g Hence at maximum power, taking into account the strength of the turbine wheel:

1 p w 1 1 T 2   dP  Maximum power = v K2 1  2 2g p2 p g  cos 

It can be shown from dimensionless analysis that the integral term gives a set of units which correspond to the kinetic energy. The equation involving the tensile strength of the disc material 2 2 and its density is slightly more problematic, as it only simplifies to give v / t , the velocity and time aspects in the kinetic energy equation. The mass term disappears.

Nevertheless, although what has been written is a slightly misleading form of the tensile and density equation, it does enable an estimate to be made of the power of the engine. Unfortunately although Whittle says that Figure 7 represents the PV diagram of one pound of air, he does not calculate how much work is developed. One wonders if the thesis is missing more pages.

Description of Engine PAGE 37 and Diagrams on Pages 36 and 38

Figure 11 is a redrawing of the rather schematic picture provided by Whittle on Page 36 of the thesis. It might be described as an unusual form of turboprop, with a direct drive from the turbine to the propeller but not to the compressor. There is a combination of a reciprocating air compressor and the piston engine, which drives it, grouped together in an ‘engine bank’. The exhaust gases from the piston engine and the air from the compressor are led into a pressurised tank. As noted, Whittle refers to the tank as the ‘boiler’, but a more appropriate analogy would be that of a steam drum, as all it does is hold a hot fluid. The hot pressurised mixture of gases flows out of the tank through the nozzle blades into the impulse turbine, providing the power to drive the propeller.

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Figure 11. Whittle’s initial concept for an advanced gas turbine based aircraft power plant (PAGE 36)

The incomplete diagrams on page 38 appear to show an engine bank driving a propeller and also a PV diagram needed to calculate the turbine expansion work. Calculations in the Appendix show that at sea level the tank pressure would be 109.7lb/in2 (7.564 bar), or as Whittle expresses it, 15,800 lb/ft2, with the temperature of the mixture being in the range 500-527º C.

Although the piston engine and compressor could be separate items, Whittle shows them to be in the same engine block. This is sensible. There would be a saving in weight, and a multi- cylinder arrangement would make it easy to balance the pistons and crankshaft.

The drawing shows the turbine and propeller to be positioned above the ‘engine’ block, but there is no reason why they could not be located somewhere else. As in an aircraft like the P-38 Lightning, a duct could have carried the hot pressurised mixture from the engine to the turbine (74). In this way, in Whittle’s concept, the piston engine and compressor could have been placed deep within the fuselage, ensuring a good streamlined form.

The propeller would have been placed in the aircraft nose, connected to the turbine with a very short shaft. No gearbox between the two was necessary, since one of Whittle’s deeper insights was that the speed of rotation of the turbine was a good match for that of the propeller. The propeller rpm was designed for flight at 600 mph, making it a high revving, fixed pitch device, turning at transonic speed. Modern technology has given us this ability. The tip speed of the fan on the RB211 is in the range Mach 1.3 - 1.4 (75).

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A good case can be made for saying that this concept would have been patentable. The idea of using a turbine for a direct drive to a high speed propeller was unique. But the gas turbine arrangement itself was probably innovative, as the inlet temperatures to the turbine are held down to acceptable levels. This is done by diluting the exhaust gases from the piston engine with the air from the compressor, also eliminating the need to have a separate combustion system.

Turbine inlet temperature dogged the development of the gas turbine, and like Whittle, earlier inventors had to adopt various palliatives. Holzwarth, in 1905, overcame the problem with an intermittently fired combustion chamber, his machine working on a constant volume, rather than the now standard, constant pressure cycle. In so doing, the turbine blades were not constantly exposed to heat. Aegidius Elling, in Norway, used a combination of water injection into the compressor, and steam injection into the turbine, to hold down temperatures and increase power. Armengaud and Lamale adopted a somewhat similar approach, but in addition incorporated internal water cooling of the blades (76).

The use of a reciprocating compressor by Whittle is an interesting feature. It allowed him to attain the pressure ratio of 7.5/1 that the thermodynamics of his machine demanded. In the 1920s, even half of this figure would have been difficult with a centrifugal compressor. As regards the axial compressor, no one was setting their sights on this level of pressure ratio, although engineering development underway at Brown Boveri in Switzerland would provide a sound basis for future progress (77). But a pressure ratio of 7.5/1 would be 1950s capability.

Why did Whittle, when he began serious investigation of the potential of the gas turbine, drop this innovative approach to a turboprop? Its most obvious drawback is its size and weight, which Whittle, as a pilot, would have seen as a major drawback. We can also conjecture that Whittle may have become aware of another flaw, which is the use of a high speed propeller. Data was emerging to show that propulsive efficiency drops away as propeller tip speeds approach sonic velocities (78).

PAGE 37 and 39

Returning to the thesis, Whittle again states that a temperature of 500º C determines the nozzle velocity and rotational speed of the turbine blades. He refers to the adiabatic curve to support in his argument. Unfortunately his thinking is not well expressed at this point. His actual words are: The maximum temperature in a prime mover of this type should not exceed 500° C. This limiting temperature also limits the nozzle velocity, as it is shown by plotting that the energy drop from 500° C on any adiabatic (energy for drop to atmospheric pressure) for 1 lb of air does not by any means approach that kinetic energy of gases at nozzle which would necessitate a dangerous speed of rotation to meet the condition.

v = 1 V cos  2 What he seems to be saying is that the speed of rotation determines the pressure drop, but this pressure drop will be different for different inlet temperatures. For a given mass of gas, at a lower temperature, the actual volume of the gas passing through the nozzle would be reduced giving a lower velocity. This could only be offset by increasing the pressure drop through the nozzle. It follows that for each turbine inlet temperature, there would be a specific pressure ratio. Although this is true, the actual value cannot be calculated from any of the equations Whittle has used.

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There is also another issue. Up to this point, the equations only refer to the work developed by the turbine. That is, the positive work, neglecting the negative work having to be done by the piston engine in compressing the air and exhaust gases. In the Appendix, Whittle dealt with this consideration and used cycle thermodynamics to determine the optimum pressure ratio at which the work from the cycle reaches a maximum.

Design Case for Whittle’s Gas Turbine Concept PAGE 39

This part of the Commentary is based on how Whittle ended the main part of the thesis, but making use of what quantitative information was given in the Appendix. A key number, in this final section, was Whittle’s statement that it should be possible to build a turbine with a ‘swallowing’ capacity of 10 lbs of air a second. This might be taken to be the basis of his ‘design case’.

Whittle’s sketches show a turbine of the single wheel de Laval type, light in weight and having a high rotational speed. This was what was needed, the main drawback being that commercial units were not very powerful, being intended for the separation of cream from milk. Stodola quotes a few examples in the 200-300 hp range, with steam flows of around 1 lb/sec (79). But taking into account that steam turbines exhaust into a near vacuum, and that the molecular weight of steam is about two thirds that of air, Whittle’s estimate of 10 lb/sec for an air turbine seems quite practical. Flowrates in single stage turbines in the early centrifugal gas turbines were in the range of 40 - 60 lb/sec, according to Judge (80). Judge also states that the power required to drive the compressor in the Derwent jet engine corresponds to about 100 hp per 1b of air per second. Additional data for the Goblin jet engine are given by Smith who states that the power absorbed by the compressor was 5,720hp at an air mass flow rate of 60lb/sec (81).

Figures in the Appendix state that at sea level 1 lb of air flow per second would give an indicated power (i.e. without any losses at all) of 100 hp. At altitude this rises to 118 hp per lb flow. Hence, at altitude, the net indicated power of the engine on the basis of 10 lb airflow per second would be 1,180 hp. However, Whittle also shows that the indicated gross power coming from the turbine is more than twice this figure, at 2,224 hp, which for the time was amazingly high. Unlike a conventional turboprop, where much of the energy is used to drive the compressor, in the Whittle concept, the turbine is free from this burden. The compression process, which is shown by Whittle to absorb 1,222 hp for his design case, is taken care of by the piston engine and compressor combination.

This is all in theory, of course, and omits the isentropic (mainly aerodynamic) losses in the compressor and turbine, pressure drops in the boiler and ductwork, and piston and bearing friction in the piston engine and reciprocating compressor. There are more concrete objections including: a) Whether the piston engine could provide enough power at very high altitude; b) The size of the compressor needed to ‘swallow’ 10 lb/sec of air, whose density was 1% of that at sea level; c) The design of a propeller capable of absorbing around 2,000 horsepower.

Consideration of these factors, including the power needed to drive the compressor, and the weight of the piston engine and compressor, may have stimulated Whittle into thinking about other options to power his high altitude, high speed, long range aircraft. 73

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Nevertheless, accepting Whittle’s figures as they stand, it can be shown that an aircraft weighing 15,000 lb and a lift to drag ratio of 15/1, flying at 600 mph, with a propeller efficiency of about 75%, would require about 2,130 hp to be supplied to the propeller shaft by the turbine. The kind of power Whittle was thinking about. An aircraft of this weight should have been quite capable of carrying a large and complex piston engine/compressor combination. Even taking into account the inefficiencies and losses of the ‘engine’, the concept looks feasible.

The biggest weakness is that the power from piston engines falls away at very high altitude, a characteristic of all such engines, even when supercharged or turbocharged. Even the jet engine itself suffers. Whittle came to realise the issue, and in later years suggested that his first ideas about jet propulsion had involved flight at 70,000, not 120,000 ft.

SUMMARY PAGE 39 and 41

In commenting on Whittle’s summary in the thesis, it is worth reiterating that in making a forecast about ‘Future Developments in Aircraft Design’, Whittle’s aim was to identify how a long range, high speed aeroplane might evolve. He was writing at a time when, although Lindberg had flown the Atlantic non-stop from New York to Paris, it had taken almost 34 hours. Lindberg’s average speed was less than that of Alcock and Brown in 1919, eight years earlier. Whittle recognised that for practical long flight, high speed was a necessity, and asked himself how this might be achieved. He set himself a target of 600 mph, which for inter-continental travel, is actually close to the minimum acceptable.

Whittle’s summary repeats some of the main points in the thesis, but should have begun by stating he was thinking about the power unit needed for an aircraft flying at 120,000 feet and 600 mph. He should have emphasised that at such an altitude the estimated air density allows flight at high speed, but creates new challenges for the designers of aircraft engines. Whittle’s solution was to have high speed propeller driven directly by a gas turbine. This should have been made much clearer.

It is worthy of note that Whittle never uses the term ‘gas turbine’ in the whole of the thesis, although at numerous points he refers to the flow of gas or air through a turbine. The closest he gets to the modern usage is in the summary itself, where he states that an ‘air turbine’ is to be used, and then somewhat confusingly states that ‘it gives back the energy in supercharging’. In fact, in the body of the thesis, the combination of the reciprocating compressor and piston engine is never referred to as a supercharger. What they do is to provide a mixture of compressed air and hot petrol engine combustion products that drive the turbine.

Nevertheless, having made these qualifications about the Summary, it is best to let Whittle’s words speak for themselves. Let us remember, back in 1928, as a very young man, still in academic training, he wrote:

Summarising one can see that the range of aircraft depends on weight and efficiency, and that it will only be increased by careful streamlining, and better structural design and also more efficient prime movers.

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Speed is best achieved by attaining great altitudes, which, in turn, can only be done by the development of a more suitable prime mover.

The prime mover which will apparently lead to the desirabilities mentioned above is an air turbine, as this gives back the energy in supercharging, has a greater efficiency at high altitudes, and is much more flexible (in rate of rotation) than present engines.

It should also have a greater efficiency than the steam turbine, which is the most efficient prime mover at present. Greater thermal efficiency obviously means greater range for a given quantity of fuel.

The most important developments, which will take place, will follow as a result of the development of a more suitable prime mover, i.e. an air turbine.

Appendix Appendix Aims : Optimising Power Output

The Appendix is the ‘meat’ in the thesis, but one wonders if it was added after a preliminary discussion with Whittle’s supervisor, when he may have been asked (ordered?) to make a quantitative assessment of the power output. It is done by taking into account of both the positive and negative work aspects of the cycle, as represented by the respective adiabatics for the turbine and compressor sections of the ‘engine’. The equations are manipulated so as to calculate the pressure ratio at which the work is at a maximum for a given turbine inlet temperature. As mentioned earlier, this approach is now a commonplace in the design of gas turbines, but it was exceedingly perceptive of Whittle to have recognised this important relationship. It is unlikely that his supervisor would have seen the need for this type of calculation.

PAGE 43

Figure 12. PV diagram (redrawn from small sketch on Page 45) used to estimate the net work from the piston engine/compressor/gas turbine combination 75

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o The figure of 800 K is used by Whittle to estimate the ‘net work’ in the PV diagram. This is done fairly simply by subtracting the area LEDM, alongside the compression adiabatic curve, from the similar area LFGM alongside the turbine adiabatic in Figure 12.

These areas are obtained by the integration of the respective adiabatic curves which are of the form:-

The cycle shown in Figure 8 is perfect and there are no losses. Compression and expansion are isentropic, so that the minimum amount of energy is used in compression, and during expansion the turbine gives out the maximum amount of work. Engine output would be at the theoretical maximum.

It was perfectly in order for Whittle to take this approach. At that time, quantitative values for isentropic efficiencies for turbomachinery would have been hard to come by. It would require the construction of jet engines and gas turbine power plants before such measurements became commonplace.

A more sophisticated analysis would have separated what was happening to the energy usage and flows in the petrol engine, which is not really going through the normal four stroke cycle. Whittle himself passed over what might be the sequence of operations.

One surmises, soon after combustion occurs, when the pressure in the engine is high, an exhaust valve opens, releasing part of the extremely hot combustion products into the boiler, where they would mix with the compressed air. Quite quickly this valve would then close. Then, hopefully, there would be enough pressure left in the combustion chamber for the piston to keep the engine turning and drive the compressor. At the end of this actual ‘power stroke’, a second exhaust valve would open, allowing the release of the combustion products to the atmosphere, in the normal way.

Clearly, even with the fullest information on the pressure, temperature and volume changes in the petrol engine, especially during combustion, it would be a complex problem to model it thermo- dynamically. Whittle had the courage and insight to put these issues to one side, seeing that if a simplified analysis of the concept showed it not to be producing any useful power, it was unlikely that a more in depth study would prove it to be practical.

Calculation of Maximum Theoretical Work PAGE 43 and halfway down PAGE 45

By assuming a perfect cycle, some major simplifications can be made in the calculations. Because the work is calculated using Vdp, and since there is no change in pressure during the intake and combustion parts of the cycle, there is no work done during these periods, either positive or negative. It is then a fairly simple job to replace “V” in the integral Vdp with a pressure term.

This is done using the expression for isothermal expansion and compression PV = RT where R is the Gas Constant and T the absolute temperature ( note that in this commentary a capital T for temperature is used, rather than the lower case version used by Whittle).

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Accordingly, at point F, in Figure 8, where the pressure is P2, then: and γ Similarly, the equation for the adiabatic, PV for either compression or expansion also reduces to a constant term, depending on the start conditions for pressure, volume and temperature. For the adiabatic at point F, the constant term is K (i.e. capital K). Hence: γ

K = P2 V The actual value of the volume at point F depends on the pressure, not known at this stage, and the o temperature and mass of gas. However, the temperature is 800 K, and the mass of gas (later on shown to be 1 lb) are given. Since the mass of gas is fixed, this constrains the volume at the start of compression and expansion.

Substituting for volume in the adiabatic equation for expansion we have: = K Eliminating the exponent from the volume term:

therefore

But in the integral for the work output of the turbine, is fixed, hence the equation reduces to:

Similarly, the negative work ‘k’ done in driving the compressor is determined using the intake conditions to the compressor, which are sea level conditions. Whittle in the manuscript uses, somewhat confusingly, a capital ‘K’ for the turbine work and a lower case ‘k’ for the work done on the compressor. To clarify matters, in this text, the capital ‘K’ is made to be bold, and the lower case “k” is non-bold, in italics. Hence the net work is given by:

-

-

The integration of these two functions results in:

 1  p 1 2 1  p   k     1   1     p 1

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Removal of the brackets gives an equation in which the net work from the cycle can be expressed in terms of the inlet and outlet pressures. Furthermore since K and k are partly dependent on the temperature, the equation takes into account this factor. Hence:

Work =

K at this stage is unknown since it also contains P2, the turbine inlet pressure. It is given by:

Whittle uses these two equations to find the turbine inlet pressure. First he substitutes for K in the work equation, the pressure, temperature and gas constant term in the equation immediately above. He then simplifies the equation. The maximum work occurs at the point when the rate of change of work, versus the change in turbine inlet pressure, is zero. This is found by differentiating the “Work 2 2 Equation”, so as to give d W / dP

Unfortunately Whittle’s writing of the equation, where K has been substituted, is difficult to understand, but it seems to be;

Work =

It is also not clear how this has been arrived at, and how Whittle then produces the final simplified equation: 1 1 1 1 1 1 1 1 1 1       RT p2 k  p1 p2 RT k p1 1 1  It becomes somewhat more obvious by manipulation of the ‘γ’ type power functions in the equation:

Eliminating the γ from the bracketed term gives:

therefore

is then substituted for in the work equation giving:

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The initial term in the equation above has which results in them cancelling the P2 terms, so that only RT remains.

Calculation of Power Output

Whittle then moves on to calculating the theoretical power.

Whittle initially simplifies the equation, using 1.4 as the value of “γ” for air.

Hence = 0.72 and = 0.28

The equation for work at any pressure and temperature is then given by

or

Here, Whittle has made an arithmetic slip at this point in the substitution of = 0.28; the correct equation being

Fortunately, the main use of the work output equation is to derive the turbine inlet pressure, which is done by differentiating this equation and then simplifying the differential. It will then be seen that these arithmetic slips disappear from the final equation, and Whittle’s estimate of the turbine inlet pressure is unchanged.

So staying with the uncorrected version we have

Keeping the inlet pressure as a constant, since it is that of the pressure at sea level, this equation can now be differentiated to give the rate of change of work, as determined by the change in P 2, the inlet pressure to the turbine. In so doing, RT and the inlet pressure terms disappear from the differential:

When the work output is at a maximum, the rate of change of work, with respect to pressure, is zero. Hence:

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0 = +

Simplifying

Whittle then gives some figures for air at ground level, namely: k = 65,600 , R = 96

P1 = 2,120 lbs /sq ft. The Gas Constant R is required to determine ‘k’, as well being used in the maximum work calculation. This is given in the units that were common at the time, so that: R = 96 ft. lb/lb air/° C

Unfortunately, ‘T’, the temperature at ground level, is not given, but it is possible to calculate this o since k is stated to be 65,600. My calculation gives T as being close to 263 K, about minus 10° C, which is obviously too low for air temperature at sea level. I am not sure how this mistake came to be made.

But using a figure of 65,600, the optimum turbine inlet pressure for maximum work is given by:-

Work

o If the turbine inlet temperature is 800 K, that is 523° C

46  3550  151200 Then P2 = = 15,910 lbs/sq ft. 155000

The optimum pressure ratio for maximum work is therefore 7.51.

Whittle has also made a slight mistake with the value for R, the Gas Constant, using 98 rather than 96. There are also some rounding off errors.

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Using a more realistic value for k of 77,231, corresponding to an inlet temperature of 15°C, the optimum turbine inlet pressure would be about 20% lower than his estimate. Given the very modest inlet temperature to the turbine, this seems a more reasonable value.

Whittle then moves onto calculating the actual work output of the device. One wonders if the Staff Tutor had expressed concern about the rather complex work equation and suggested that, a more accessible calculation should be done using the difference between the turbine and compressor work. This is a straight forward calculation using the work curves associated with the respective adiabatics.

Accordingly, staying with Whittle’s turbine inlet pressure of 15,910 lb/ft2, this is used to derive a K value of 148,300 for the inlet air to the turbine, where the temperature is 800 degrees absolute. The respective values for K and k, of 148,300 and 65,600, and the sea level and turbine inlet pressures of 2,120 and 15,910 lb/ft2, are then substituted in the net work equation to give the output from each pound of air flow.

= (5250 x 23.3) – (2885 x 23.3) = 55000 ft. lb/ lb of airflow per second

Somewhat fortuitously, the calculations, show that if the rate of airflow into the piston engine/ compressor/turbine combination was one pound per second, this figure would equate to 100 horse power. Whittle goes on to point out that in the high stratosphere, where the air density falls to about one hundredth of that at sea level, and more importantly, the ambient temperature falls to minus 50° C, the output would rise to 118 hp per pound of air per second. No calculations are shown in support of this estimate, but one would suppose that a pressure ratio of 7.5/1 was still used. Whittle then reiterates that the turbine inlet pressure is a function of the inlet temperature. In turn this is determined by the temperature capability of the turbine materials.

A pressure ratio of 7.5/1 would have resulted in an extremely high figure for the peripheral speed, well outside of accepted limits. In this context Whittle would have seen the table that Stodola had prepared, showing stress levels versus speed, for both metric and Imperial units. Table 1 is based on this, wherein Stodola states that normal limit is 100 - 120 m/s. Later in his book Stodola acknowledges that a de Lavel type turbine with a bulged centre has run at a peripheral speed of 343 metres/sec (1,124 ft/sec), which is not too far from that based on Whittle’s pressure ratio estimate (82).

Table 1. Stresses in turbine wheels, taken from Stodola (83) Rotation Rate m/s 25 50 75 100 150 200 400 Stress kg/cm2 50 200 450 800 1800 3200 1200 Rotation Rate ft/s 82 164 246 326 492 656 1312 Stress lb/in2 711 2845 6400 11378 25602 45514 182060

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Efficiency Calculation PAGE 49

In what may have been a final add-on to the thesis, Whittle includes a section on the efficiency of his cycle. Here again there is a lack of consistency in the use of symbols for pressure, temperature and volume and no diagram is added. Hopefully, Figure 13 represents the missing PV diagram, which is based on the set of calculations using the changes of temperature that Whittle uses to estimate the efficiency. These are detailed below, with Cp being the specific heat of air at constant pressure.

Heat received = (T3-T2). C p

Heat rejected = (T4-T1). C p

Work done = (T3-T2). Cp - (T4-T1) C p From this it follows that the efficiency η is given by:

work done T 3 - T 2 + T 1 - T 4  = =

heat received T 3 - T 2

The issue is then to calculate the unknowns, T2 and T4, from the fact that T1 is the inlet temperature to the compressor, and T3 is the turbine inlet temperature. This is done using the volume- temperature formula for adiabatic compression and expansion. For some reason Whittle uses volume ratios rather than pressure ratios in calculating the cycle temperatures. It can be shown that given his pressure ratio of 7.5, the corresponding volume ratio is just under 4.3.

Figure 13. PV diagram for calculation of the efficiency of the cycle

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For compression   1    γ-1 V 1 T2 = T    T1 R 1   1    V 2 

For expansion   1    γ-1 V 4 T3 = T    T4 R 4   1    V 3 

Having determined T2 and T4 Whittle then proceeds to substitute these in the efficiency equation, to (γ-1) formulate a series of terms involving R . The equation is then simplified to show that the efficiency is solely determined by the volume ratio, and is given by: 1 Efficiency = 1- R  1

Today it more conventional to use the pressure ratio ‘P r’ as this is easier to determine. This results in an equation for the efficiency so that:  1     = 1-  1     Pr 

Either the volume ratio or the pressure ratio is optimised for the turbine inlet temperature. Whittle does not give a value for efficiency for his concept. But, of course, whether the volume or pressure ratio equations are used, the theoretical cycle efficiency comes out at about 43%. The Carnot cycle o o efficiency, using temperatures of 288 K and 800 K for the air and turbine inlet temperature, corresponds to 64%. The higher efficiency for Carnot is to be expected, since the temperature at which the exhaust emerges from the turbine has to be higher than room temperature.

The conversion from Whittle’s volumetric formula, to that of the pressure ratio, can be done using γ the adiabatic relationship where PV is a constant for each start or finish temperature. Whittle may have considered using this relationship, since he started the section on the ‘efficiency of the constant pressure cycle’ by writing:

P 1V1 = K P 1V4 = k P 2V2 = K P 2V3 = k

It will be noted that the symbols for the constant in the adiabatic term appear to be the opposite way round from those used earlier. However, not much use is actually made of these relationships and Whittle seems to have gone straight to the efficiency and temperature calculation given earlier.

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Comments by the Staff Tutor

At the very end of the thesis, the Staff Tutor wrote the following.

It would be difficult to comment without rewriting the thesis. The thesis shows much careful and original thought and also a good deal of private reading Here there is real acknowledgement that what Whittle has produced has gone far beyond what would have been expected of the average Cadet. The phrasing, however, of these sentences does indicate that given more time, the content of the thesis could have been better set out. This is especially so, given that its content requires a reader to be (a) fully cognoscente of gas engine thermodynamics, (b) a natural at mathematics, (c|) aware of recent developments in the sphere of aeronautics. Indeed, the Staff Tutor himself would have found, just as this author did, that to properly comprehend what Whittle had produced, required “a good deal of private reading”.

References

1. The Great Pacific Flight pp 437-8, Flight, 14th June 1928, London, 1928 https://www.flightglobal.com/pdfarchive/view/1928/1928%20-%200481.html?search=p. 437 2. A. W. Judge Elementary Principles of Aircraft Design and Construction Pitman and Sons, London, 1921 3. L. Bairstow Applied Aerodynamics Longman, Green and Co, London, 1920 4. The Bristol Jupiter IV in Flight 6th Dec 1928 https://www.flightglobal.com/pdfarchive/view/1928/1928%20- %201130.html?search=britol jupiter engine 6 december 5. Bill Gunston Faster than Sound -The Story of Supersonic pp 61-77, Flight Through the Barrier, Patrick Stephens, Somerset, UK, 1992 6. Bill Gunston with Peter Gilcrest Jet Bombers - From Me262 to the Stealth B2, pp 38-45, Boeing B-47 Stratojet, Osprey, Oxford, 1993 7. D. Bloor The Enigma of the Aerofoil- Rival Theories in Aerodynamics 1909-1930 University of Chicago Press, 2011 8. H. Glauert The Elements of Aerofoil and Airscrew Theory Cambridge University Press, Cambridge, 1926 (only the second edition is now easily available) 9. A. C. Kermode The Mechanics of Flight, pp 432-433, Tables showing lift and drag of an RAF 15 aerofoil, typical of that used up to about 1935, Pitman and Sons, London, 1972 10. N. Cumpsty Jet Propulsion Figure 2.2, p.14, Lift to Drag Ratio of Boeing 747, Cambridge University Press, Cambridge, 1997 11. L. Breguet Aerodynamical Efficiency and Reduction of Air Transport Costs Aeronautical Journal, pp 307-13, Vol 26, Royal Aeronautical Society, London, 1922 12. J. D. Anderson Jr Introduction to Flight pp 437-50, McGraw Hill, New York, 2005 13. ibid pp 500-501, Historical Note: Breguet and the Range Formula

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14. ibid pp 405-407, Section 6.3, Power Required for Level Unaccelerated Flight 15. J. H. Dwinell Principles of Aerodynamics pp 260-266, Section on effect of altitude on aircraft engines, McGraw Hill, New York, 1949 16. D. Japikse and N. C. Baines Introduction to Turbomachinery pp 1-6 to 1-8 especially Fig 1.7 showing effect of pressure ratio and mass flow on isentropic efficiency, Concepts ETI, Oxford and Oxford University Press, 1994 17. Wikipedia Flight Airspeed Records https://en.wikipedia.org/wiki/Flight_airspeed_record 18. P. Lewis The British Fighter Since 1912, pp 179-182, Chapter 4 The Biplane Supreme, Putnam, London, 1979 19. Oxygen Apparatus p 504, Volume 1 Handbook of Aeronautics 3rd Edition, New Era Publishing, East Grinstead, 1937 20. Wikipedia Mikoyan-Gurevich MiG-25 https://en.wikipedia.org/wiki/Mikoyan- Gurevich_MiG-25 21. Air Commodore Frank Whittle The Early History of the Whittle Jet Propulsion Gas Turbine Proc I.Mech.E., p 423-424, Jan – Dec 1945, London, 1945 22. U-2 Specifications - Lockheed Martin www.lockheedmartin.com/us/products/u2/u-2- specifications.html 23. P. W. Brooks The Modern Airliner, Chapter 2, p 49, The First Transport Aeroplanes, Putnam, London, 1961 24. Square-cube law - Wikipedia https://en.wikipedia.org/wiki/Square-cube_law 25. R. Whitford Structural Trends, p 96 in Fundamentals of Fighter Design, Airlife, Hillingdon, Middlesex, 2000 26. M. Gurav Wing Loads and Other Loads, Section 14 in Aircraft Structures Summary, 2011 http:// aerostudents.com/files/aircraftStructures/aircraftStructuresFullVersion.pdf 27. R. Whitford Aerofoil Sections and High Lift Devices, pp 26-27, Fundamentals of Fighter Design, Airlife, Hillingdon, Middlesex, 2000 28. E. P. Warner Airplane Design Performance, p 290, Chapter 10, Variable Lift Airfoil Devices, McGraw Hill, New York, 1936 29. W. R. Gregg Standard Atmosphere, NACA Technical Report 147, Washington DC, 1922 30. W. S. Diehl Standard Atmosphere -Tables and Charts, NACA Technical Report 214, Washington DC, 1924 31. J. Golley Whittle - The True Story p 23 - 24, Airlife, Hillingdon, Middlesex, 1987 32. J. D. Anderson Jr Introduction to Flight, pp 770 – 777, Appendix B, Standard Atmosphere- English Engineering Units, McGraw Hill, New York, 2005 33. A. Lumsden Bristol Piston Aero-Engines, Part 4, pp 64-66, Engine Performance Figures, Airlife, Hillingdon, Middlesex, 1994 34. J. H. Dwinnell Principles of Aerodynamics Chapter 13, pp 270-284, Propellers, McGraw Hill, New York, 1949 35. R. Miller and D. Sawers The Technical Development of Modern Aviation pp 71-79, The Variable Pitch Propeller, Routledge and Kegan Paul, London, 1968

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36. J. H. Dwinnell Principles of Aerodynamics p 373 Figure IIIa showing propulsive efficiencies for varying blade angles, McGraw Hill, New York, 1949 37. H. Booth Aeroplane Performance Calculations Chapter X, p 99, Propeller Performance Curves, Chapman and Hall, London, 1921 38. H. C. Watts The Design of Screw Propellers for Aircraft pp 62-81 Chapter V, Longman, Green and Co., London, 1920 39. D. Stinton The Design of the Aeroplane pp 298-299, Granada Publishing, 1983 40. H. Booth Aeroplane Performance Calculations pp 55-60 Section on Long Range Cruising and pp 129-137 similar section with graphs, Chapman and Hall, London, 1921 41. F. Whittle Gas Turbine Aero-Thermodynamics Section 21 Turbo Fans, pp 217-222, Pergamon, Oxford, 1981 42. J. V. Becker The High Speed Frontier NASA SP 445, Chapter 1, pp 3-12 The High Speed Airfoil Programme, Section Background and Origin, NASA, Washington DC, 1980 https://history.nasa.gov/SP-445/contents.htm 43. A. R. Michaelis History of Technology - The Twentieth Century Part 2 (ed. T. Williams) Vol VII, pp 859-865, Section The First Rocket Flights, Clarendon Press, Wotton-under- Edge, 1978 44. Propulsive efficiency - Wikipedia https://en.wikipedia.org/wiki/Propulsive_efficiency 45. N. Cumpsty Jet Propulsion Chapter 3, pp 22-26, Creation of Thrust in a Jet Engine, Cambridge University Press, Cambridge, 1997 46. F. Whittle Gas Turbine Aero-Thermodynamics Section 13, Aircraft Propulsion General, pp 145-152, Pergamon, Oxford, 1981 47. E. Buckingham Jet Propulsion for Airplanes Report No 159, US Bureau of Standards, Washington DC, 1922 48. E. W. Constant Origins of the Turbojet Revolution pp 138-144, Section Radical Alternatives: Reaction Propulsion and Turboprops, Johns Hopkins University Press, Baltimore, 1980 49. E. W. Constant Origins of the Turbojet Revolution pp 148-150, Section The Response of Normal Technology, Johns Hopkins University Press, Baltimore, 1980 50. D. A. Low Heat Engines Chapter IV, pp 88-89, Ideal Heat Engine Cycles, Longman, Green and Co., London, 1920 51. A. Stodola Steam Turbines with an Appendix on Gas Turbines and the Future of Heat Engines 2nd edition, trans Loewenstein, Van Nostrand, NewYork, and Archibald Constable, Edinburgh, 1905 52. ibid Section 2, pp 4-8, Formula of St Vénant 53. ibid Section 93, pp 417-423, Calculation of a Uniform Pressure Gas Turbine 54. J. A. Moyer Steam Turbines, 3rd edition, Chapter II, pp 10-35, Elementary Theory of Heat, Wiley, Hoboken, New Jersey, 1914

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55. R. M. Neilson The Steam Turbine, 2nd edition, Chapter V11, pp 87-101, Theoretical Consideration of Different Treatments of Steam in a Heat Engine, Longman, Green and Co., London, 1903 56. F. Whittle Gas Turbine Aero-Thermodynamics, A Note on Entropy, Pergamon, Oxford, 1981 57. ibid Section 7, pp 67-73, Gas Turbine Cycle Calculations Using Approximate Methods 58. G. F. C. Rodgers and Y. R. Mayhew Engineering Thermodynamics Work and Heat Transfer Section 12.2, pp 220-223, Simple Gas Turbine Cycle, Longman, Green and Co., London, 1957 (7th Impression 1965) 59. N. Cumpsty Jet Propulsion Chapter 4, pp 25 - 43, The Gas Turbine Cycle, Cambridge University Press, Cambridge, 1997 60. G. F. C. Rodgers and Y. R. Mayhew Gas Turbine Theory Section 3.3, Total Head Temperature and Pressure, Longman, Green and Co., London, 1951 61. ibid pp 222-223, discussion on blade temperatures 62. J. G. Kernan Elementary Theory of Gas Turbines and Jet Propulsion Chapter VIII, pp 145- 169, Impulse Turbines, Oxford University Press, Oxford, 1946 63. Turbine Temperatures Vel Vector-Euler GT; Lost internet reference from 2013 giving calculation methods for blade temperatures in uncooled impulse and reaction turbines c/o F. Starr 64. A. Stodola Steam Turbines with an Appendix on Gas Turbines and the Future of Heat Engines Section 6, pp16-17, The Ideal Impulse Turbine, 2nd edition, trans Loewenstein, Van Nostrand, New York, and Archibald Constable, Edinburgh, 1905 65. G. F. C. Rodgers and Y. R. Mayhew Gas Turbine Theory Section 19.2, pp 404-411 Axial Flow Turbines, Longman, Green and Co., London, 1951 66. N. Cumpsty Jet Propulsion Chapter 3, pp 22 - 26, The Creation of Thrust in a Jet Engine, Cambridge University Press, Cambridge, 1997 67. A. Stodola Steam Turbines with an Appendix on Gas Turbines and the Future of Heat Engines Section 36, pp155 - 157, Wheel Drums, 2nd edition, trans Loewenstein, Van Nostrand, New York, and Archibald Constable, Edinburgh, 1905 68: J. A. Moyer Steam Turbines, 3rd edition, Chapter XV, pp 313-339, Stresses in Rings, Rotors and Disc, Wiley, Hoboken, New Jersey, 1914 69 0. Lasch and W. Kieser (trans A. L. Mellanby and W. Roylands Cooper) Materials and Design in Turbo-Generator Plant Chapter IV, pp 48-68, Turbine Wheels, Oliver and Boyd, Edinburgh, 1927 70. D. G. Wilson The Thermodynamics of Gas-Turbine Power Cycles Sections 3.5 and 3.6, pp 108-115, Cycle Designation and Cycle Calculations, MIT Press, Cambridge, Massachusetts, 1984 71. A. Lumsden Bristol Piston Aero-Engines, Chapter 7, pp 33-35, Supercharging, Airlife, Hillingdon, Middlesex, 1994 72. ibid pp 201-216, Section on the Rolls Royce Merlin

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73. G. G. Smith Examination of the Mercedes Benz DB601N Flight Magazine April 16th 1942, pp 365-369 https://www.flightglobal.com/pdfarchive/search.aspx?ArchiveSearchForm%24search=s mith+mercedes&ArchiveSearchForm%24fromYear=1942&ArchiveSearchForm%24toY ear=1942&x=42&y=10 74. B. Gunston Classic WWII Aircraft Cutaways pp122-23, description and cutaway of the Lockheed Lightning, Bounty Books, Octopus Publishing Group, London, 2013 75. P. C. Ruffles The History of the Rolls-Royce RB211 Turbo Fan Engine p 107, The Rolls- Royce Heritage Trust, Derby, 2014 76. D. G. Wilson The Thermodynamics of Gas-Turbine Power Cycles pp 25-34, sections on the history of Gas Turbine Engines and The Turbojet, MIT Press, Cambridge, Massachusetts, 1984 77. D. Eckardt and P. Ruffi Advanced Gas Turbine Technology: ABB/BCC Historical Firsts ASME J. Eng. Gas Turb. Power, Vol 124, pp 542-549, July 2002 78. J. V. Becker The High Speed Frontier NASA SP 445, Chapter 1, pp 3-13 The High Speed Airfoil Programme, NASA, Washington DC, 1980 https://history.nasa.gov/SP- 445/contents.htm 79. A. Stodola Steam Turbines with an Appendix on Gas Turbines and the Future of Heat Engines pp214 - 216, the de Lavel Turbine, 2nd edition, trans Loewenstein, Van Nostrand, New York, and Archibald Constable, Edinburgh, 1905 80. A. W. Judge Modern Gas Turbines p 201 on the Goblin and a p 206 on the Derwent Jet Engines, Chapman and Hall, London, 1947 81. C. G. Smith Gas Turbines and Jet Propulsion for Aircraft p 95, table on The DH Goblin II _Performance Design Data and Dimensions, 4th Edition, Iliffe, London, 1946 82. A. Stodola Steam Turbines with an Appendix on Gas Turbines and the Future of Heat Engines p222, table of characteristics of a De Lavel Turbine, 2nd edition, trans Loewenstein, Van Nostrand, New York, and Archibald Constable, Edinburgh, 1905 83. ibid p 156, tables of stresses in wheel drums

The Author

Dr Fred Starr PhD, FIMMM, MIMechE, CEng

Fred Starr graduated as Metallurgist from Battersea College (now the University of Surrey) in 1966. He joined British Gas, London Research Station, for 25 years, where he was responsible for failure investigations of the steam reforming type. Later he initiated an in-house programme and sponsored University work to develop high temperature alloys for the manufacture of Substitute Natural Gas (SNG) using oil and coal.

When all work on SNG terminated, he came up with novel ideas for generating electricity using natural gas a fuel. Here Dr Starr made use of his deep although amateur interest in aircraft and aircraft engines. This led to the closed cycle and inverted cycle gas turbine projects. Privatisation cut money for R&D, and Dr Starr decided to leave. His most important job after leaving British Gas 88

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was with the EU’s Joint Research Centre in the Netherlands, where he did the basic design for a HYPOGEN plant making hydrogen from coal.

Formally “retiring” in 2007, he became an active member of the Newcomen Society, focusing on the Industrial History of the 20th Century. He encouraged the Society to run conferences on The Piston Engine Revolution (the development of the IC engine) and Swords into Ploughshares (how WWI transformed British Engineering). Fred has also published a three part paper in the Newcomen Journal on the development of materials for IC engine poppet valves.

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