Medieval windmills to wind turbines: a history of theory and experiment

Abstract

Windmills were developed to a high degree between their initial European use in the twelfth century and the twentieth century when mathematical analysis was first applied to optimise the design of their sails. It led immediately to the concept of twisted sails in which the weather angle decreased with radius. Various theories were tested experimentally by Smeaton, who found twisted sails to be better than common sails but less good than the Dutch sails then normally used. A century passed before Rankine applied Newton’s laws of motion to derive their power and efficiency (power coefficient). Annular windmills were developed in both Britain and the United States where they were extensively tested by Perry, who found them as efficient as Smeaton’s sails. In the twentieth century, Lanchester, Betz, and Joukowski independently derived an upper limit for windmill power coefficient and this, combined with aerodynamic theory and streamlined aerofoils led to the development of the modern wind turbine.

keywords:

• Parent
• Maclaurin
• Bouguer
• Smeaton
• Rankine
• Perry
• Betz
• momentum theory
• blade element theory

Notes

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2 S. Freese, Windmills and Millwrighting (Cambridge University Press, 1957).

3 R. Wailes, The English Windmill (London: Routledge & Kegan Paul, 1954).

4 R. I. Hills, Power from the Wind (Cambridge University Press, 1994).

5 R. Wailes, ‘Windmills of Eastern Long Island,’ Transactions of the Newcomen Society, 15 (1934–5), 117–52; R. Wailes, ‘Norfolk Windmills: Part 1, Corn Mills,’ Transactions of the Newcomen Society, 26 (1947–49), 231–58.

6 A. Titley and H. D. Haines, ‘A Warwickshire Windmill and Some Notes on Early Millwrighting,’ Transactions of the Newcomen Society, 28 (1951–52), 239–44.

7 A. Jesperson, ‘Danish Windmills,’ Transactions of the Newcomen Society, 31 (1957–58), 301–11.

8 Trans. 1^st International Symposium on Molinology, Portugal, September 9, 1965; Trans. 2^nd International Symposium on Molinology, Denmark, May 1969.

9 Hero, Pneumatics, 1.43.

10 R. J. Forbes, Studies in Ancient History (Leiden: E.J.Brill, 1955), vol. 2, p. 114.

11 H. P. Vowles, ‘An Inquiry into the Origins of Windmills,’ Transactions of the Newcomen Society, 11 (1930–31), 1–14.

12 Hills, op.cit., 1994, p. 37.

13 Jocelyn of Brakeland, Chronicle of the Abbey of Bury St Edmunds, trans. by D. Greenaway and D. Sayers (Oxford University Press, 1989), p. 9.

14 R. B. Pugh and E. Crittall, eds., Court Rolls of the Wiltshire Manors of Adam de Stratton (Devizes: Wiltshire Record Society, 1970), XXIV.

15 A. Ramelli, The Various and Ingenious Machines of Agostino Ramelli, trans. by M. T. Gnudi (New York: Dover Publications, 1994), pp. 334–5. Originally published 1588.

16 Ramelli, op. cit., pp. 332–3, pp. 206–7.

17 S. Freese, Windmills and Millwrighting (Cambridge University Press, 1957), p. 15.

18 Hills, op.cit., p. 107.

19 Bennett and Elton, vol. 1–3, p. 258.

20 Ibid.

21 Bennett and Elton, op.cit., p 262.

22 A. Parent, Recherches de Mathématiques et de Physique (Paris, 1713).

23 C. Maclaurin, An Account of Sir Isaac Newton’s Philosophy (1748), published by subscription by Peter Murdock.

24 J. Harland and M. Mayers, Seamanship in the Age of Sail (London: Conway Maritime Press, 1984), p. 62.

25 Ibid.

26 J. Smeaton, Experimental Enquiry Concerning the Natural Powers of Wind and Water to Turn Mills and Other Machines Depending on Circular Motion (Royal Society, 1759), pp. 38–69.

27 W. J. M. Rankine, Manual on Steam Engines and Other Prime Movers (Charles Griffin & Co, 1859), pp. 214–21.

28 J. K. Major, The Windmills of John Wallis Titt (The International Molinological Society, 1977).

29 T. O. Perry, Experiments with Windmills (Washington: United States Geological Survey, 1899).

30 F. W. Lanchester, Aerodynamics (London: Archibald Constable & Co Ltd, 1906), p. 335.

31 Dines, ‘On Wind Pressure upon Inclined Surfaces,’ Proceedings of the Royal Society of London, XLVIII (1890).

32 W. M. Kutta, ‘Lifting Forces in Flowing Fluids,’ Illust. Aeronaut. Mitt., 1902.

33 N. E. Joukowski, ‘Uber die Kriftnturen der Tragflächen der Drachenflieger’ [About the Contours of the Wings of the Hang-Glider], Zeitschrift fűr Flugtechnik und Motorluftschiffaht, 1, pp. 281–4, and (1912), vol. 3, pp. 91–86.

34 D. J. Acheson, Elementary Fluid Dynamics (Oxford: Clarendon Press, 1990), pp. 137–303.

35 B. H. Wick, ‘Study of Sub-sonic Forces and Moments on an Inclined Platee of Infinite Span,’ NACA Technical Note 3221, 1954.

36 A. M. van Kuik Gijs, ‘The Lanchester-Betz-Joukowski Limit,’ Wind Energy, 10 (2007), pp. 289–91.

37 A. Betz, Wind Energy and Its Utilisation through Windmills (Gőttingen: Vandenhoeck & Ruprecht, 1926), reprint Öko-Buchverlag, Kassel, 1982.

38 J. F. Maxwell, I. G. McGowan and A. L. Rogers, Wind Energy Explained (Chichester, UK: John Wiley & Sons, Ltd.), p. 22.

39 W. J. M. Rankine, A Manual of the Steam Engine and Other Prime Movers, 1859, available on books.google.co.uk

40 G. Schmitz, ‘Theory and Design of Windwheels with an Optimum Performance,’ Wiss.Zeitschrift der Universität Rostock, 5, Jahrgang, 1955/56.

41 Maxwell, McGowan and Rogers, op. cit., pp. 113–32.

42 R. E. Wilson, P. B. S. Lissaman and S. N. Walker, ‘Aerodynamic Performance of Wind Turbines,’ Energy Research and Development Administration, ERDA/NSF/04014-76/1.

43 www.ge.com.

44 www.carbonbrief.com.

45 Daily Telegraph, October 6, 2020, p. 1.

46 www.morayeast.com; www.seagreenwindenergy.com.

Additional information

Notes on contributors

Bryan Lawton

Dr Lawton retired from his post as Reader in Thermal Power at Cranfield University (Shrivenham) fifteen years ago and has since published papers on the history of canals, technology, early gas engines, tunnelling in the 18th century, and on the R101 airship disaster. He was one of the organisers of the “Piston Engine Revolution” and the “Swords into Ploughshares” conferences. He has published a two volume work on the early history of mechanical engineering, “Various and Ingenious Machines”, for which he was given the American Society of Mechanical Engineers “Engineer-Historian” Award, and subsequently published an introduction.

Correspondence to: Bryan Lawton. Email: [email protected].