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Part of the book series: Archimedes ((ARIM,volume 3))

Abstract

If you have looked out the window of an airplane lately, you may have noticed that jet engines are gradually getting shorter and fatter. You will see 737s, the most common airliner in service, with two types of engines of distinctly different shapes. The older models have long, stovepipe-shaped engines under the wings, where the newer ones (or older ones which have been retrofitted with new engines) have rounder, shorter powerplants, with a large shell or nacelle around the outside and a smaller cylinder protruding from the rear. Boeing’s latest, the 777, has relatively short but immense engines — each with diameter equivalent to the fuselage of the 737. This change represents the maturing of the turbofan engine, which in the early 1960s superseded the older turbojet engine. Strictly speaking, for the past thirty-five years we have been living in the fan age more than the jet age.

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Notes

  1. “Aero Engines 1967,” Flight Magazine,# 2531, v. 72, 26 July 57, pp. 107–110.

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  2. Otis E. Lancaster, “Aviation,” Journal of Engineering for Power, American Society of Mechanical Engineers, vol. 81, ser. A, no. 3, July, 1959, p. 269.

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  4. Edward Constant, The Origins of the Turbojet Revolution (Baltimore: Johns Hopkins University Press, 1981).

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  5. For a detailed discussion of data regarding the economics of aircraft engines in different flight regimes over time, see D. J. Jordan and H. S. Crim, “Evolution of Modern Air-Transport Powerplants,” Journal of Aircraft, v. 1, no. 5, 1964, pp. 225–229.

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  6. Walter Vincenti, What Engineers Know and How They Know It: Analytical Studies from Aeronautical History (Baltimore: Johns Hopkins Press, 1990).

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  7. L. C. Wright and R. A. Novak, “Aerodynamic Design and Development of the General Electric CJ80523 Aft Fan Component,” ASME Paper 60-WA-270, The American Society of Mechanical Engineers, 1960.

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  8. Some highly swept, many-bladed propellors of more recent vintage are efficient up to flight speeds as high as Mach 0.8. None of these have gone into production, however, because the additional gain at today’s fuel prices does not justify the development cost. While Figure 3 is still qualitatively correct, today’s component technology has shifted the peaks of all three curves to the right. (We thank Arthur J. Wennerstrom for this point.)

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  9. Vincenti, op. cit., pp. 7–12; Constant, op. cit., Ch. 1, pp. 1–32. Constant’s schema, of course, reflects Thomas Kuhn’s distinction between normal and extraordinary science in The Structure of Scientific Revolution (Chicago: University of Chicago Press, 1970).

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  10. Frank Whittle, British Patent no. 471, 368, “Improvements Relating to the Propulsion of Aircraft,” September 3, 1937. See also Whittle, “A Brief Summary of Power Jets’ Work on Turbofans,” Technical Appendix 6 in John Golley and Frank Whittle, Whittle: The True Story, (Washington, DC: Smithsonian Institution Press, 1987), 263–4.

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  11. Frank Whittle, British Patent nos. 583,111; 583,112; 593,403; 588,085; 588,918. When Whittle’s company, Power Jets, broke apart in 1945 and his engineering team disbanded, it had a bypass engine at some stage of completion, but the project ended at that point.

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  12. See Geoffrey L. Wilde, “Engineering the High-Bypass Ratio Turbofan at Rolls-Royce,” R. Tom Sawyer 1995 Award Lecture, The American Society of Mechanical Engineers, Houston, 1995; and Edward W. Constant II, The Origins of the Turbojet Revolution (Baltimore: Johns Hopkins University Press, 1980), p.214.

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  13. These engines are mentioned in passing in G. Geoffrey Smith, Gas Turbines and Jet Propulsion, Revised and Enlarged by F. C. Sheffield, 6th ed. (London: Iliffe & Sons, 1955), pp. 66–67.

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  14. Higher specific-power also calls for higher turbine inlet temperatures. Turbine technology had to go through advances paralleling those in compressor technology described in the text in order for the modern turbofan to emerge. Because the advances in turbine design during the period in question were less dramatic than those in compressor design, and because their effects were more indirect, we are ignoring them here.

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  15. David Gordon Wilson, The Design of High-Efficiency Turbomachinery and Gas Turbines (Cambridge: MIT Press, 1984), p. 281. The aerodynamics in a compressor blade row is enormously more complicated than across a wing. This is not just because compressor blade rows, unlike wings, are expected to produce a pressure rise from leading edge to trailing edge. The tip and the hub of a rotor blade, rotating at the same rpm, are moving at different speeds, implying different flow incidence velocities; this is why compressor blades are twisted and their airfoil profiles change from hub to tip. Although the force doing the work in a rotor blade arises from the pressure difference across the blade profile, entirely akin to the lifting force on a wing, the flow in a cascade is not flow across an isolated airfoil, but flow in a channel defined by the suction surface of one blade and the pressure surface of the adjacent blade. The boundary layers developing on the blade surfaces alter the shape of the free-stream channel, and the boundary layers developing along the casing and hub similarly reduce the flow area in the blade passage. More importantly, the rear half of the blade channel acts as a diffuser, decelerating the flow and thereby converting velocity into pressure. The turning of the flow within the blade passage, along with the gap between the rotor blade and the casing at the tip, produce three-dimensional effects, including so-called secondary flows causing the flow near the surfaces to migrate within the passage. On top of all this, alternating rotating and stationary blade rows make the flow in a compressor inherently unsteady. Reasonably realistic calculations of the flow in a compressor blade row became possible only in the late 1980s, and even these calculations employ approximate engineering models of turbulence rather than solving the equations of motion for turbulent flows. Worse, before the advent of laser velocimetry in the late 1970s, flow measurements could be made only upstream and downstream of blade rows, not within them. Throughout most of the maturation period of axial compressor technology, designers were forced to treat the blade rows themselves as “black-boxes”, formed out of standard two-dimensional airfoils with outlet flow conditions defined by empirically determined functions of inlet conditions.

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  16. See A. R. Howell, “Fluid Dynamics of Axial Compressors,” and “Design of Axial Compressors,” War Emergency Issue No. 12, published by Institute of Mechanical Engineers (London), 153, 1945, reprinted in Transactions of the American Society of Mechanical Engineers, January 1947, pp. 441–462.

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  17. A further goal, or at least hope, of some of those engaged in compressor research was to find a way of increasing the airflow per unit engine-frontal-area in order to limit the drag associated with the engine. The effort NACA put into transonic stages, discussed below, was as much motivated by this goal as by the goal of achieving higher pressure-ratios per stage.

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  18. See, for example, Frederick Ehrich, “From the Whittle Jet to the Ultra-High Bypass Fan — Technological Development of the Aircraft Gas Turbine Engine,” a talk given at the International Gas Turbine Institute’s Aircraft Committee Theme Session in Houston, Texas, 6 Jun 1995; notes from this talk are available from the IGTI.

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  19. Jane’s All the World’s Aircraft, 1960–61 (New York: McGraw Hill, 1960), p. 559.

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  20. Paul H. Wilkinson, Aircraft Engines of the World,1959/60 (Washington D.C.: Paul H. Wilkinson, 1960), pp. 108–115.

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  21. GE did not originate the idea of variable stator vanes. NACA, for example, had explored this approach both analytically and experimentally in 1944; see John T. Sinnette and William J. Voss, Extension of Useful Operating Range of Axial-Flow Compressors by Use of Adjustable Stator Vanes, NACA Report RM 915, 1948.

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  22. Ibid., p. 303ff.

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  23. Ibid., p. 88f.

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  24. T. A. Heppenheimer, Turbulent Skies: The History of Commercial Aviation (New York: Wiley, 1995), p. 162ff.

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  25. The turbine inlet temperatures of the commercial versions were downgraded a little to provide longer times between overhauls, some material substitutions were made for lower cost and increased safety margins, and thrust-reversers and exhaust noise suppressors were added to them.

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  26. Bill Gunston, Rolls-Royce Aero Engines (London: Thorson Pub. Group, 1989), pp. 136–140.

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  27. Specifically, 69 of the 1519 Boeing 707s and 720s were powered by the Conway.

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  28. See Gunston, op. cit., p. 143, and ‘By-Pass Assessment: A Plain Man’s Guide to the RR Conway,“ Flight Magazine, # 2507, v. 71, 8 Feb 1957, pp. 183–186.

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  29. Centrifugal compressors were limited to a pressure-ratio around 4 to 1 and an adiabatic efficiency below 85 percent, and they required a comparatively large engine frontal area, increasing the drag of the engine; the cross-over ducting needed if multiple stages of centrifugal compressors were used exacerbated the frontal area shortcoming. By contrast, stages can be added to an axial compressor without increasing frontal area, and axial compressors in principle can achieve efficiencies around 90 percent.

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  30. Note 12 above cites the articles defining this base point. See J. H. Horlock, Axial Flow Compressors (London: Butterworth, 1958) for an assessment of it.

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  31. By ‘cascade’ here is meant a sequence of identical airfoil profiles at a uniform stagger angle, defining two-dimensional flow passages between them, as shown in Figure 6. Figure 8 exhibits flow conditions in a cascade during a test at much higher Mach numbers than those in the tests referred to here.

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  32. NACA Memorandums E56B03, E56B03a, and E56B03b. This work was declassified in 1958 and reissued in 1965 under the title, Aerodynamic Design of Axial-Flow Compressors, ed. I. A. Johnsen and R. O. Bullock, NASA SP-36.

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  33. This is not to say that NACA took no notice at all of turbofan engines. In the mid-1950s, the Air Force carried out analytical studies of the potential advantages of turbofan engines for the supersonic flight regime, and NACA conducted at least one (classified) analytical study in parallel with these efforts: James F. Dugan, Investigation of Rotating-Stall Limits in a Supersonic Turbofan Engine, NACA RM57G26a, 1957. The hypothetical configuration was a low (1 to 1) bypass ratio engine in which the outer flow of the first two stages of the single-spool 8-stage compressor was ducted around the core engine, in the manner of the Conway. The announced reason for the bypass was to unload the back stages of the compressor by diverting flow away from them, again like the Conway. The compressor used in the study was the NACA 8-stage compressor, mentioned below, in which the first two stages were transonic. The hypothetical engine was for flight up to Mach 2.95. The question addressed in the study was whether splitting the flow behind the first two stages of this compressor — i.e. the fan — would induce rotating stall, compromising the mechanical integrity of the blading. The report was completed in August 1957, one month before the fan for GE’s CJ805–23 went on test. This hypothetical engine was thus unrelated to GE’s first successful turbofan. As will be evident below, however, it can be viewed as an intermediate step between Rolls-Royce’s Conway and P&W’s first turbofan engine, the JT3D.

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  34. Joseph L. Herrig, James C. Emery, and John R. Erwin, Systematic Two-Dimensional Cascade Tests of NACA 65-Series Compressor Blades at Low Speeds, NACA RM L51G31, 1951. This report, and other related ones, was subsequently superseded by a NACA Report of the same title, Report 1368 by James C. Emery, L. Joseph Herrig, John R. Erwin, and A. Richard Felix, 1958.

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  35. The most prominent alternative parameter, still in use today, is the static pressure-rise coefficient: the ratio of the static pressure rise across a blade row to the inlet dynamic head — i.e. the fluid density times the inlet relative velocity squared divided by 2. This parameter suggests that a higher pressure rise can be obtained by increasing the relative inlet velocity, with the blade loading, as measured by the parameter, remaining the same. As the velocity was pushed higher, however, keeping the pressure-rise coefficient the same, a point was encountered where losses would abruptly increase.

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  36. Seymour Lieblein, Francis C. Schwenk, and Robert L. Broderick, Diffusion Factor for Estimating Losses and Limiting Blade Loadings in Axial-Flow-Compressor Blade Elements,NACA RM E53D01, 1953.

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  37. Seymour Lieblein, Review of High-Performance Axial-Flow-Compressor Blade-Element Theory, NACA RM E53L22, 1953; and “Loss and Stall Analysis of Compressor Cascades,” Journal of Basic Engineering, American Society of Mechanical Engineers, September, 1959, pp. 387–400.

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  38. A. J. Wennerstrom, “Highly Loaded Axial Flow Compressors: History and Current Developments,” Papers from the Ninth International Symposium on Air Breathing Engines, ed. F. S. Billig, Vol. 2, ISABE 89–7002 (Washington: AIAA, 1989), pp. 21–34.

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  39. Seymour Lieblein, George W. Lewis, and Donald M. Sandercock, Experimental Investigation of an Axial-Flow Compressor Inlet Stage Operating at Transonic Relative Inlet Mach Numbers: I - Over-All Performance of Stage with Transonic Rotor and Subsonic Stators up to Rotor Relative Inlet Mach Number of 1.1, NACA RM E52A24, 1952.

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  40. The NACA 5-stage compressor was originally reported in three Research Memoranda: Experimental Investigation of a Five-Stage Axial-Flow Research Compressor with Transonic Rotors in All Stages: I - Compressor Design, by Donald M. Sandercock, Karl Kovach, and Seymour Lieblein, Rlvt E54F24, 1954; Experimental Investigation of a Five-Stage Axial-Flow Research Compressor with Transonic Rotors in All Stages: II - Compressor Over-All Performance, by Kovach and Sandercock, RM54G01, 1954; and Experimental Investigation of a Five-Stage Axial-Flow Research Compressor with Transonic Rotors in All Stages: III - Interstage Data and Individual Stage Performance Characteristics, by Sandercock and Kovach, RM E56G24, 1956. A more readily accessible discussion can be found in Karl Kovach and D. M. Sandercock, “Aerodynamic Design and Performance of Five-Stage Transonic Axial-Flow Compressor, Journal of Engineering for Power, American Society of Mechanical Engineers, Vol. 83 No. 3, July 1961, pp. 303–321. Reviews of the transonic compressor research at NACA can be found in two articles in this same issue of Journal of Engineering for Power: Seymour Lieblein and I. A. Johnsen, ”Résumé of Transonic-Compressor Research at NACA Lewis Laboratory,“ pp. 219–234, and M. Savage, E. Boxer, and J. R. Erwin, ”Résumé of Compressor Research at NACA Lewis Laboratory,“ pp. 269–285. Other articles in this issue discuss details of this research and parallel research on transonic and supersonic compressors conducted in industry.

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  41. NACA demonstrated this application of transonic stages in an 8-stage compressor in which the first two stages were transonic. This compressor is described in a sequence of NACA Research Memorandums by various authors (principally C. H. Voit, R. P. Geye, and R. M. Standahar), under the general title, Investigation of a High-Pressure-Ratio Eight-Stage Axial-Flow Research Compressor with Two Transonic Inlet Stages: NACA RM E53124, 1953; RM E53J06, 1953; RM E54H17, 1954; RM E55B28, 1955; RM E55A03, 1955; NACA RM E55I13, 1955; and RM E56L1Ia, 1957. Research continued on this configuration after 1956, including replacing the blades on the first two stages with long-chord transonic stages, the results for which began to demonstrate the advantages of long-chord blading; see NACA RM E57H14, 1958 and A. J. Wennerstrom, “Low Aspect Ratio Axial Compressors, Why and What it Means,” Society of Automotive Engineeers, Special Publication No. 683, 1986.

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  42. For an overview of this and parallel research on supersonic compressors, see J. F. Klapproth, “A Review of Supersonic Compressor Development,” Journal of Engineering for Power, American Society of Mechanical Engineers, Vol. 83 No. 3, July 1961, pp. 258–268.

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  43. John Klapproth, John J. Jacklitch, Jr, and Edward Tysl, Design and Performance of a 1400-FootperSecond Tip-Speed Supersonic Compressor Rotor, NACA RM E55A27, 1955, p. 1.

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  44. Ibid., p. 17.

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  45. At least one new design was based on the results of Klapproth et al. before NACA curtailed compressor research. Linwood Wright and Ward Wilcox designed a quite promising 1260 ft/sec tip-speed transonic stage, corresponding to 90 percent speed of the Klapproth design. This stage, which was intended to be the first stage of a two-stage counter-rotating compressor, had a hub-to-tip radius ratio of 0.5, compared with 0.7 in the Klapproth design. For details, see Investigation of Two-Stage Counterrotating Compressor, I - Design and Over-All Performance of Transonic First Stage, by Ward W. Wilcox and Linwood C. Wright, NACA RM E56C15, 1956; and II - First-Rotor Blade Element Performance, by Wright and Wilcox, NACA RM E56G09, 1956.

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  46. Virginia R. Dawson, Engines and Innovation: Lewis Laboratory and American Propulsion Technology, (Washington, D.C., National Aeronautics and Space Administration, 1991), p. 147 n.50.

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  47. Kovach worked on the transonic stages of the compressor for the J-93, the engine for the Mach 3.5 B70 and the never-to-fly F-108. Klapproth had gone to GE specifically because they had agreed to continue his work on the “comprex,” a rotating series of passages around the periphery of a cylinder in which unsteady wave phenomena were utilized for compression. In later years, Klapproth, who remained at GE until his retirement, made major contributions to the design of advanced high-bypass-ratio turbofans. [Communication from L. C. Wright, October 23, 1997]

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  48. Golley and Whittle, op. cit., Appendix.

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  49. John Blanton, personal communication, in an interview with the author (Smith) on October 24, 1996; notes and tapes in author’s possession.

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  50. Frank Whittle, British Patent # 583,112, 10 Dec 1946, and # 588,918, 6 Jun 1947.

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  51. “Principles and Applications of By-Pass Turbojet Engines,” presented at the SAE Golden Anniversary Aeronautic Meeting, New York, 18–21 April 1955.

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  52. Eight Decades of Progress: A Heritage of Aircraft Turbine Technology (Cincinnati: General Electric Company, 1990), p. 123.

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  53. Personal communication, John Blanton and Lin Wright, 24 October 1996. For references on this design, see note 45.

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  54. Ibid.

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  55. See note 45 for references. The principal shortcoming of Wright’s 1260 ft/sec rotor for purposes of GE’s fan design was a blade exit velocity that, while appropriate for a counter-rotating design, implied excessive Mach numbers at the stator inlet in a conventional design (Wright and Novak, op. cit., p. 4).

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  56. Wright and Novak, op. cit.,p. 4.

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  57. A streamline is the path followed by a fluid particle. When the flow is treated as axisymmetric — i.e., circumferentially uniform — as in the GE program, the streamline in effect defines a stream-surface (of revolution). The GE program was developed under the direction of Leroy H. Smith, Jr., who had just joined GE after a period of post-doctoral research with Wislicenus at Penn State.

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  58. When used for calculating off-design performance, the blade rows are modelled by “black-box” functions relating (circumferentially average) flow conditions at the exit of the row to conditions at its inlet.

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  59. This paragraph is based on George Smith’s work in developing and applying computer programs while at General Electric, Evendale, in the late 1950s, and in numerous conversations over the years he had with the late R. A. Novak. The importance of the streamline-curvature method is discussed in W. R. Hawthorne and R. A. Novak, “The Aerodynamics of Turbo-Machinery,” Annual Review of Fluid Mechanics, Vol. 1, ed. W. R. Sears and M. Van Dyke (Palo Alto: Annual Reviews Inc., 1969), pp. 341–366.

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  60. Wright and Novak, op. cit., p. 6. The authors add, “The procedure is, of course, theoretically inexact in some respects which could be important for some designs. The Crocco equation as used does not include a body-force term. This is justifiable only if the blades are radial or nearly so. Furthermore, for some types of designs, an additional term expressing the rate of change of energy input along a stream surface would be necessary. The magnitude of these neglected terms can be checked with the completion of any design pass described in the foregoing. In the case of the CJ805–23 fan, it is justifiable to neglect them.”

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  61. Ibid., p. 5.

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  62. In a paper a few years later, after he had moved from GE to AiResearch, Wright discussed the place arbitrary blade contours have, versus the much wider use of standard profiles, in modern axial-flow compressor design. See his “Blade Selection for a Modern Axial-Flow Compressor,” Fluid Mechanics,Acoustics, and Design of Turbomachinery, Part II, ed. B. Lakshminarayana et al., NASA SP-304, 1974, pp. 603–626.

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  63. The method does allow the blockage from the blades to be augmented to include the additional blockage from the blade profile boundary layers. Whether such an allowance was made in the design of the CJ805–23 fan is unclear.

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  64. C.-H. Wu, A General Through-Flow Theory of Fluid Flow With Subsonic or Supersonic Velocity in Turbomachines of Arbitrary Hub and Casing Shapes, NACA TN 2302, 1951, and C.-H. Wu and C. A. Brown, “A Theory of Direct and Inverse Problems of Compressible Flow Past Cascades of Arbitrary Airfoils,” Journal of Aeronautical Science, v. 19, 1952, pp. 183–196.

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  65. The method that Wright and Novak devised for the CJ805–23 involved two elements: the so-called through-blade analysis of the stream-surface flow within the blade rows and the indirect approach of specifying work and loss distributions along the stream-surfaces and inferring the blade shapes. The through-blade analysis was a significant advance over anything that had been done before. As Arthur Wennerstrom remarked in 1989, even though Wright and Novak introduced this method into the literature in 1960, “it did not come into widespread use by the rest of the industry until after 1970. As a result, most of the earlier supersonic stages designed did not have the benefit of this level of sophistication in their design. Considering how sensitive the performance of high Mach number blading is to the blade configuration, the widespread adoption of through-blade design methods during the 1970’s can be considered a major advancement in the ability to deal with higher Mach numbers successfully.” (A. J. Wennerstrom, “Highly Loaded Axial Compressors: History and Current Developments,” cited in note 38.)

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  66. Wright and Novak, op. cit., p. 13.

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  67. L. C. Wright, personal communication, 24 October 1996.

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  68. Paul H. Wilkinson, Aircraft Engines of the World, 1961/62 (Washington, D.C.: Paul H. Wilkinson, 1961), p. 69.

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  69. Paul H. Wilkinson, Aircraft Engines of the World, 1959/60,p. 169.

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  70. Rolls-Royce responded to GE’s CJ805–23 with an aft fan Avon for the Caravelle according to Gunston, op. cit., p. 142.

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  71. This section of the paper is based in part on Smith’s years at P&W, 1962–1964, where he headed the group charged with the development of advanced computer methods. In this capacity he supervised the development of experimental computer codes used in designing the high-Mach-number fan for the STF200, the prototype engine that became the JT9D. The authors have been unable to locate and interview those who were directly involved in the design of the JT3D.

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  72. T. A Heppenheimer reports that Boeing’s Maynard Pennell, who headed the 707 program, informed P&WA in January 1958 that, “unless Pratt & Whitney could come up with a fanjet as well, Boeing would shift to the GE aft-fan.” (Turbulent Skies: The History of Commercial Aviation (New York: Wiley, 1995), p. 190.

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  73. The Eisenhower administration had envisaged a nuclear powered turbojet engine as a powerplant for strategic bombers that could be kept in the air indefinitely, providing an airborne nuclear deterrent comparable to the underwater deterrent provided by nuclear submarines. GE and P&W were conducting parallel design and development programs. The termination of these programs was one of the first actions taken by the Kennedy administration.

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  74. Wilkinson, 1959/60, p. 117.

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  75. GE had not used inlet guide vanes in the CJ805–23 fan for fear that the added noise they would generate would more than offset the noise gain from the reduced exhaust velocity (see Wright and Novak, op. cit., p. 13). P&W argued that the inlet guide vanes on their front fan had the further virtue of adding durability by shielding the fan blades from foreign object damage. Nevertheless, they abandoned the use of inlet guide vanes in the JT-9, the high-bypass fan engine designed for the Boeing 747.

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  76. Wilkinson, 1959/60, p. 117.

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  77. Wilkinson, 1959/60, p. 119.

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  78. Ibid. See also Jordan and Crim, op. cit., p. 227. In later versions of the JT3D the fan was made of titanium too.

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  79. Wilkinson, 1959/60, pp. 117–119.

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  80. See “Turbofans: A Survey of Current Airline Powerplants,” Flight Magazine, 30 Oct 1959, pp. 455459, which compares P&W’s JT3D and GE’s CJ805–23, as then announced, with Rolls-Royce’s Conway; also “Aero Engines 1959,” Flight Magazine, 20 Mar 1959, p. 408.

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  81. We owe this last suggestion to Lin Wright, who joined P&W in the 1970s; personal communication, 24 October 1996.

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  82. Eight Decades of Progress, pp. 132f.

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  83. Ibid.

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  84. Ibid., p. 125.

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  85. The high-bypass fan was not a simple, incremental evolution, combining the higher tip Mach number of GE’s low-bypass fan with P&W’s front fan configuration. The front fan configuration dominates because of the need to use titanium or some other low-weight material in the long fan blades. The tip Mach numbers of these blades are around 1.5, far above the 1.25 of GE’s CJ805–23; Mach numbers this high require careful design for locating and controlling the effects of shocks.

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  86. Vincenti, op. cit., p. 140ff.

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  87. See Genevieve R. Miller, George W. Lewis, Jr., and Melvin J. Hartmann, “Shock Losses in Transonic Compressor Blade Rows,” Journal of Engineering for Power, American Society of Mechanical Engineers, Vol. 83 No. 3, July 1961, pp. 235–242.

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  88. Vincenti, op. cit., p. 45.

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  89. Ibid., p. 167.

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  90. The key contribution made by C.-H. Wu at NACA in the work cited in note 64 above, was not so much the analytical procedure he put forward as the judgment he exercised in deciding which features of the flow did and did not require accurate calculation. This is the aspect of Wu’s method that has remained central ever since.

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  91. George K. Serovy, “Axial Flow Aerodynamics,” in The Aerothermodynamics of Aircraft Gas Turbine Engines, ed. Gordon C. Oates, AFAPL TR 78–52, Air Force Aeropropulsion Laboratory, 1978, p. 17–21.

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Smith, G.E., Mindell, D.A. (2000). The Emergence of the Turbofan Engine. In: Galison, P., Roland, A. (eds) Atmospheric Flight in the Twentieth Century. Archimedes, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4379-0_4

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