Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-14T17:14:11.624Z Has data issue: false hasContentIssue false

Mathematical research at the Aeronautical Research Laboratories 1939–1960

Published online by Cambridge University Press:  17 February 2009

D. G. Hurley
Affiliation:
Mathematics Department, University of W.A., Nedlands, W.A.6009.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The Aeronautical Research Laboratories were established in Australia in 1939 as the CSIR Division of Aeronautics. Mathematicians were amongst the first staff employed, and their number reached a peak in the mid 1950s. They were an able group: in their subsequent careers 12 became Professors, 5 obtained higher doctorates, 6 became Fellows of the Australian Academy of Science and 6 Fellows of the Royal Society. They published over 100 papers, and these are discussed here under 11 separate headings.

The length of discussion given here to the various areas of research is not uniform. I have emphasised those with which I am familiar and those that interest me personally. Nevertheless, I believe the present paper provides an accurate picture of the mathematical research that was carried out at ARL during the period under review, and makes it clear that mathematicians at ARL made substantial contributions to many areas of theoretical aeronautics.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Batchelor, G. K., “Interference in a wind tunnel of octagonal section”, Australian Council for Aeronautics; Report ACA-1 (1944).Google Scholar
[2]Batchelor, G. K., “Interference on wings, bodies and airscrews in a closed tunnel of octagonal section”, Australian Council for Aeronautics: Report ACA-5 (1944).Google Scholar
[3]Batchelor, G. K., “Transition to turbulence within the boundary layer”, Austral. J. Sci. 6 (1944) 108112.Google Scholar
[4]Batchelor, G. K., “On the concept and properties of idealized hydrodynamic resistance”, Australian Council for Aeronautics; Report ACA-13 (1945).Google Scholar
[5]Batchelor, G. K., “Sound in wind-tunnels”, Australian Council for Aeronautics; Report ACA-18 (1945).Google Scholar
[6]Batchelor, G. K., “Power series expansion of the velocity potential in compressible flow”, Quart. Appl. Math. 2 (1945) 318328.CrossRefGoogle Scholar
[7]Batchelor, G. K., “Theory of axisymmetric turbulence”, Proc. Roy. Soc. London A 188 (1946) 480502.Google Scholar
[8]Batchelor, G. K., “Recent deductions concerning the double velocity correlation function in turbulent motion”, Nature 158 (1946) 883884.CrossRefGoogle Scholar
[9]Batchelor, G. K., “On steady laminar flow with closed stream-lines at large Reynolds number”, J. Fluid Mech. 1 (1956) 177190.CrossRefGoogle Scholar
[10]Batchelor, G. K. and Pillow, A. F., “A numerical method of determining subsonic compressible flow past an obstacle I: Circular cylinder”, A.R.L. Aero. Note No. 61 (1944).Google Scholar
[11]Batchelor, G. K. and Shaw, F. S., “A numerical method of determining subsonic compressible flow past an obstacle II: Joukowski aerofoil”, A. R. L. Aero Report A 21 and SM 28 (1944).Google Scholar
[12]Batchelor, G. K. and Shaw, F. S., “A consideration of the design of wind tunnel contractions”, Australian Council for Aeronautics; Report ACA-4 (1944).Google Scholar
[13]Batchelor, G. K. and Townsend, A. A., “Singing corner vanes”, Nature 155 (1945) 236.CrossRefGoogle Scholar
[14]Bauer, F., Garabedian, P. and Korn, D., “Supercritical wing sections”, Lecture notes in economics and mathematical systems 66 (Springer-Verlag, 1972).Google Scholar
[15]Bullen, F. P., Head, A. K. and Wood, W. A., “Structural changes during the fatigue of metals”, Proc. Roy. Soc. London A 218 (1953) 332343.Google Scholar
[16]Cherry, T. M., “Flow of a compressible fluid about a cylinder”, Proc. Roy. Soc. London A 192 (1947) 4579.Google Scholar
[17]Cherry, T. M., “Flow of a compressible fluid about a cylinder. II Flow with circulation”, Proc. Roy. Soc. London A 196 (1949) 136.Google Scholar
[18]Cherry, T. M., “A transformation of the hodograph equation and the determination of certain fluid motions”, Phil. Trans. Roy. Soc. London A 245 (1953) 583624.Google Scholar
[19]Christopherson, D. R., Fox, L., Green, J. R., Shaw, F. S. and Southwell, R. V., “Relaxation methods applied to engineering problems. VII B The elastic stability of plane frameworks and of flat plating”, Phil. Trans. Roy. Soc. London A 239 (1945) 461487.Google Scholar
[20]Clareborough, L. M., Hargraves, M. E., Head, A. K. and West, G. W., “Energy stored during fatigue of copper”, J. of Metals 7 (1955) 99.Google Scholar
[21]Collis, D. C. and Williams, M. J., “Two-dimensional convection from heated wires at low Reynolds numbers”, J. Fluid Mech. 6 (1959) 357384.CrossRefGoogle Scholar
[22]Cumming, B. L., “Review of turbulence theories”, Australian Council for Aeronautics; Report ACA-27 (1946).Google Scholar
[23]Dale, F. A. and Smith, R. C. T., “Grid sandwich panels in compression”, Australian Council for Aeronautics; Report ACA-16 (1945).Google Scholar
[24]Dalitz, R. H., “The effect of a sharp-nosed leading edge on the boundary layer of a flat plate”, A.R.L. Report A40 (1945).Google Scholar
[25]Dalitz, R. H., “Some mathematical aspects of compressible flow”, Australian Council for Aeronautics; Report ACA-20 (1946).Google Scholar
[26]Freiberger, W., “The uniform torsion of an incomplete tore”, Austral. J. Sci. Res. Ser. A 2 (1949).Google Scholar
[27]Freiberger, W., “On the solution of the equilibrium equations of elasticity in general curvilinear coordinates”, Austral. J. Sci. Rca. Ser. A 2 (1949).Google Scholar
[28]Freiberger, W., “A problem in dynamic plasticity: the enlargement of a circular hole in a flat sheet”, Proc. Camb. Phil. Soc. 48 (1952) 135148.CrossRefGoogle Scholar
[29]Freiberger, W., “The uniform torsion of a perfectly plastic circular ring”, A.R.L. Report SM213 (1953).Google Scholar
[30]Freiberger, W., Shaw, F. S., Silberstein, J. P. O. and Smith, R. C. T., “Plywood panels in end compression. Flat panels with grain at various angles to direction of loading”, Australian Council for Aeronautics; Report ACA-30 (1947).Google Scholar
[31]Freiberger, W. and Smith, R. C. T., “The uniform flexure of an incomplete tore”, Austral. J. Sci.Res. Ser. A 2 (1949).Google Scholar
[32]Gent, B. L., “Interference in a wind tunnel of regular octagonal section”, Australian Council for Aeronautics; Report ACA-2 (1944).Google Scholar
[33]Green, J. R. and Southwell, R. V., “Relaxation methods applied to engineering problems. VII. A Problems relating to large transverse displacements of thin elastic plates”, Phil. Trans. Roy. Soc. London C 1 (1944) 137176.Google Scholar
[34]Green, J. R. and Southwell, R. V., “Relaxation methods applied to engineering problems. IX High-speed flow of compressible fluid through a two-dimensional nozzle,”, Phil. Trans. Roy. Soc. London A 239 (1944) 367386.Google Scholar
[35]Guest, J., “The solution of linear simultaneous equations by matrix iteration”, Austral. J. Appl. Phys. 8 (1955).Google Scholar
[36]Guest, J., “A short note on the checking of contractants”, J. Roy. Aero. Soc. 60 (1956) 685686.CrossRefGoogle Scholar
[37]Guest, J., “The compressive buckling of a clamped parallelogram plate with a longitudinal stiffener”, Austral. J. Appl. Sci. 7 (1956) 191198.Google Scholar
[38]Guest, J., “The buckling of a clamped parallelogram plate under combined bending and compression”, Austral. J. Appl. Sci. 8 (1957) 2734.Google Scholar
[39]Head, A. K., “The mechanism of fatigue of metals”, J. Mech. Phys. Solids 1 (1953) 134141.CrossRefGoogle Scholar
[40]Head, A. K., “Edge dislocation in inhomogeneous media”, Proc. Phys. Soc. B 66 (1953) 793801.CrossRefGoogle Scholar
[41]Head, A. K., “The interaction of dislocations and boundaries”, Phil. Map. Ser. 7 44 (1953) 9294.CrossRefGoogle Scholar
[42]Head, A. K., “Fatigue”, J. Austral. Inst. Met. 1 (1956) 148154.Google Scholar
[43]Head, A. K., “The effect of frequency on the fatigue of metals”, J. Phys. Soc. of Japan 11 (1956) 468.CrossRefGoogle Scholar
[44]Head, A. K., “The propagation of fatigue cracks”, J. Appl. Mech. 23 (1956) 407.CrossRefGoogle Scholar
[45]Head, A. K., “A class of aplanatic optical systems”, Physical Soc. Proc. 71 (1958) 546551.CrossRefGoogle Scholar
[46]Head, A. K. and Hooke, F. H., “Fatigue of metals under random loads”, Nature 177 (1956) 11761177.CrossRefGoogle Scholar
[47]Head, A. K. and Louat, N. P., “The distribution of dislocations in linear arrays”, Austral. J. of Physics 8 (1955) 17.CrossRefGoogle Scholar
[48]Hoskin, B. C., “Torsional rigidity of a plastic bar of circular section under combined tension and torsion”, Austral. J. Appl. Sci. 12 (1961) 255.Google Scholar
[49]Hoskin, B. C. and Lee, E. H., “The analysis of loaded flexible surfaces over sub-grades with visco-elastic material behaviour”, Amer. Soc. Civil Eng. J. Eng. Mech.Google Scholar
[50]Hurley, D. G., “The effect of a small laminar separation bubble on the potential flow past an aerofoil”, A.R.L. Note A 148 (1955).Google Scholar
[51]Hurley, D. G., “The downstream effect of a local thickening of the laminar boundary layer”, J. Aero. Sci. 22 (1956) 383384.Google Scholar
[52]Hurley, D. C., “Note on the forces that act near the centre and the tip of a swept-back wing”, Aero. Quart. 10 (1959) 127144.CrossRefGoogle Scholar
[53]Hurley, D. G., “Mass transfer cooling in a boundary layer”, Aero. Quart. 12 (1961) 165188.CrossRefGoogle Scholar
[54]Hurley, D. G., “The use of boundary-layer control to establish free stream-line flows”, in Advances in Aeronautical Sciences 2 (ed. von K´rm´n, Th.), (Pergamon, 1959) 662708.CrossRefGoogle Scholar
[55]Hurley, D. G., “A theoretical investigation of an aerofoil equipped with a split flap”, J. Austral. Math. Soc. 2 (1961) 195205.CrossRefGoogle Scholar
[56]Hurley, D. G. and Ward, G. F., “Experiments on the effect of air jets and surface roughness on the boundary layer near the nose of an NACA 64A006 Aerofoil”, A.R.L. Note A 128 (1953).Google Scholar
[57]King, L. V., “On the convection of heat from small cylinders in a stream of fluid. Determination of convection constants of small platinum wires with application to hot-wire anemometry”, Phil. Trans. Roy. Soc. London A 214 (1914) 373432.Google Scholar
[58]Langmuir, I., “Convection and conduction of heat in gases”, Phys. Rev. 34 (1912) 401422.Google Scholar
[59]Levey, H. C., “High speed flow of a gas past an approximately elliptic cylinder”, Proc. Camb. Phil. Soc. 46 (1950) 479491.CrossRefGoogle Scholar
[60]Levey, H. C., “Exact solutions for transonic flow past cusped aerofoils”, A.R.L. Report A 87 (1954).Google Scholar
[61]Levey, H. C., “Two dimensional source flow of a viscous fluid”, Quart. AppI. Math. 12 (1954) 2548.CrossRefGoogle Scholar
[62]Levey, H. C., “The effect of a small protuberance on the potential flow past an aerofoil”, A.R.L. Note A 184 (1954).Google Scholar
[63]Levey, H. C., “A shock-free airfoil”, J. Aero. Sci. 23 (1956) 11291130.Google Scholar
[64]Levey, H. C., “Singular Perturbations: a model equation”, A.R.L. Note A 157 (1957).Google Scholar
[65]Levey, H. C., “The ‘ground’ interference of a carrier deck”, J. Roy. Aero. Soc. 61 (1957).Google Scholar
[66]Levey, H. C., “The thickness of cylindrical shocks and the P.L.K. method”, Quart. Appl. Math. 17 (1959) 7793.CrossRefGoogle Scholar
[67]Levey, H. C., “Heat transfer in slip flow at low Reynolds numbers”, J. Fluid Mech. 6 (1959) 385391.CrossRefGoogle Scholar
[68]Levey, H. C., “The back effect of a wall on a jet”, Z. Ang. Math. Phys. 11 (1960) 152157.CrossRefGoogle Scholar
[69]Love, E. R. and Silberstein, J. P. O., “Elastic vibrations of a fan”, Australian Council for Aeronautics; Report ACA-15 (1945).Google Scholar
[70]Love, E. R. and Silberstein, J. P. O., (with the assistance of Radok, J. R. M.), “Vibration of stationary and rotating propellers”, Australian Council for Aeronautics; Report ACA-86 (1947).Google Scholar
[71]Mahony, J. J., “A critique of shock-expansion theory”, J. Aero. Sci. 22 (1955) 673680.CrossRefGoogle Scholar
[72]Mahony, J. J., “Analytic treatment of two-dimensional supersonic flow, Part I Shock-free flow, Part II Flow with shock waves”, Phil. Trans. Roy. Soc. London A 248 (1956) 467515.Google Scholar
[73]Mahony, J. J., “Heat transfer at small Grashof numbers”, Proc. Roy. Soc. London A 238 (1956) 412423.Google Scholar
[74]Mahony, J. J., “The internal flow problem in axi-symmetric upersonic flow”, Phil. Trans. Roy. Soc. London A 251 (1958) 121.Google Scholar
[75]Mahony, J. J., “The large deflection of thin cantilevered plates. Part I General theory, Part II Symmetrically loaded rectangular plate”, Quart. J. Mech. Appl. Math. 14 (1961) 257282.CrossRefGoogle Scholar
[76]Mahony, J. J., “An expansion method for singular perturbation problems”, J. Austral. Math. Soc. 2 (1962) 440463.CrossRefGoogle Scholar
[77]Mann, E. H., “Theory of the Borden tube”, J. Coun. Sci. Ind. Res. (Austral.) 20, (1946) 122.Google Scholar
[78]Mann, E. H., “An elastic theory of dislocation”, Proc. Roy. Soc. London A 199 (1949) 376394.Google Scholar
[79]Miner, M. A., J. App. Mech. 12 (1945) 159.CrossRefGoogle Scholar
[80]Morawitz, C. S., “On the non-existence of continuous transonic flows past profiles”, Comm. Pure Appl. Math. 9 (1956) 4568.CrossRefGoogle Scholar
[81]Patterson, G. N., “Ducted fans: design for high efficiency”, Australian Council for Aeronautics; Report ACA-7 (1944).Google Scholar
[82]Patterson, G. N., “Ducted fans: approximate methods of design for small slipstream rotation”, Australian Council for Aeronautics; Report ACA-8 (1944).Google Scholar
[83]Patterson, G. N., “Ducted fans: effect of the straightener on overall efficiency”, Australian Council for Aeronautics; Report ACA-9 (1944).Google Scholar
[84]Patterson, G. N., “Ducted fans: high efficiency with contra-rotation”, Australian Council for Aeronautics; Report ACA-10 (1944).Google Scholar
[85]Pillow, A. F., “A review of hydrodynamic stability and its bearing on transition to turbulent flow in the boundary layer”, A.R.L. Report A 35 (1945).Google Scholar
[86]Pillow, A. F., “The formation and growth of shock waves in the one-dimensional motion of a gas”, Proc. Camb. Phil. Soc. 45 (1949) 558586.CrossRefGoogle Scholar
[87]Pillow, A. F., “The theory of heat regenerators in the unsteady state”, A.R.L. Report A 78 (1952).Google Scholar
[88]Pillow, A. F., “The free convection cell in two dimensions”, A.R.L. Report A 79 (1952).Google Scholar
[89]Radok, J. R. M., “The theory of aerofoils in unsteady motion”, Aero. Quart. 3 (1952) 297320.CrossRefGoogle Scholar
[90]Radok, J. R. M., “General instability of simply supported rectangular plates”, J. Aero. Sci. 21 (1954) 109116.CrossRefGoogle Scholar
[91]Radok, J. R. M., “The solution of eigenvalue problems of integral equations by power series”, J. of Math. and Appl. Mech. 12 (1955) 413.Google Scholar
[92]Raelok, J. R. M., “Problems of plane elasticity for reinforced boundaries”, J. Appl. Mech. 22 (1955) 249.Google Scholar
[93]Radok, J. R. M., Silberstein, J. P. O. and Wills, H. A., “A new theory for the strength of wooden box beams”, Australian Council for Aeronautics; Report ACA-40 (1948).Google Scholar
[94]Radok, J. R. M. and Stiles, L. F., “The motion and deformation of aircraft in uniform and non-uniform atmospheric disturbances”, Australian Council for Aeronautics; Report ACA-41 (1948).Google Scholar
[95]Saffman, P. G. and Tanveer, S., “Prandtl-Batchelor flow past a flat plate with a forward-facing flap”, J. Fluid Mech. 143 (1984) 351365.CrossRefGoogle Scholar
[96]Saffman, P. G. and Tanveer, S., “Vortex induced lift on two dimensional low speed wings”, Studies in Appl. Maths. 71 (1984) 6778.CrossRefGoogle Scholar
[97]Scholes, J. F. M. and Patterson, G. N., “Wind tunnel tests on ducted contra-rotating fans”, Australian Council for Aeronautics; Report ACA-14 (1945).Google Scholar
[98]Scholes, J. F. M., “Ducted fans: a monogram method of analysis”, Australian Council for Aeronautics; Report ACA-32 (1947).Google Scholar
[99]Secomb, D. A., “A wind tunnel investigation of Levey's shock-free aerofoil”, A.R.L. Note A 825 (1970).Google Scholar
[100]Shaw, F. S., “The torsion of solid and hollow prisms in the elastic and plastic range by relaxation methods”, Australian Council for Aeronautics; Report ACA-11 (1944).Google Scholar
[101]Shaw, F. S., An introduction to relaxation methods (Dover, New York, 1953).Google Scholar
[102]Shaw, F. S. and Silberstein, J. P. O., “Stress analysis of an engine mount”, Australian Council for Aeronautics; Report ACA-17 (1945).Google Scholar
[103]Silberstein, J. P. O., “Plywood panels in end compresion. Curved panels with grain at various angles to generators”, Australian Council for Aeronautics; Report ACA-31 (1949).Google Scholar
[104]Silberstein, J. P. O., “On eigenvalues and inverse singular values of compact linear operators”, Proc. Camb. Phil. Soc. 49 (1953) 201212.CrossRefGoogle Scholar
[105]Smith, R. C. T., “The buckling of flat plywood plates in compression”, Australian Council for Aeronautics; Report ACA-12 (1944).Google Scholar
[106]Smith, R. C. T., “The buckling of plywood plates in shear”, Australian Council for Aeronautics; Report ACA-29 (1946).Google Scholar
[107]Smith, R. C. T., “The approximate solution of equations in infinitely many unknowns”, Quart. J. Math. 18 (1947) 25.CrossRefGoogle Scholar
[108]Strang, W. J., “Transient source doublet and vortex solutions of the linearized equation of supersonic flow”, Proc. Roy. Soc. London A 202 (1950) 4053.Google Scholar
[109]Strang, W. J., “Transient lift of three-dimensional purely supersonic wings”, Proc. Roy. Soc. London A 202 (1950) 5480.Google Scholar
[110]Thompson, J. J. and Wittrick, W. H., “The stress in certain cylindrical swept tubes under torsion and bending”, Australian Council for Aeronautics; Report ACA-43 (1949).Google Scholar
[111]Traill-Nash, R. W., “The symmetric vibrations of aircraft”, Aero. Quart. 3 (1951) 122.CrossRefGoogle Scholar
[112]Traill-Nash, R. W., “The anti-symmetric vibrations of aircraft”, Aero. Quart. 3 (1951) 145160.CrossRefGoogle Scholar
[113]Traill-Nash, R. W., “On the excitation of pure natural modes in aircraft resonance testing”, J. Aero/Space Sci. 25 (1958) 775.CrossRefGoogle Scholar
[114]Trail-Nash, R. W. and Collar, A. R., “The effects of shear flexibility and rotary inertia on the bending vibration of beams”, Quart. J. Mech. Appl. Math. 6 (1953) 186222.CrossRefGoogle Scholar
[115]Volterra, V., Ann. École Norm. Paris Ser. S 24 (1907) 401.CrossRefGoogle Scholar
[116]Wallis, R. A., “The use of air-jets for boundary-layer control”, A.R.L. Note A 110 (1952).Google Scholar
[117]Wills, H. A., “Life of aircraft structures”, in Proc. 2nd. Intern. Aero. Conf. Inst. Aero. Sciences (1949) 361–403.Google Scholar
[118]Wills, H. A., “Structural fatigue”, Aircraft (1950) 12–14.Google Scholar
[119]Wittrick, W. H., “Stresses around reinforced elliptical holes, with application to pressure cabin windows”, Aero. Quart. 10 (1959) 373400.CrossRefGoogle Scholar
[120]Wittrick, W. H., “Some simple transformation functions for square and triangular holes with rounded corners”, Aero. Quart. 11 (1960) 195199.CrossRefGoogle Scholar
[121]Wittrick, W. H., “Preliminary analysis of a highly swept cylindrical tube under torsion and bending”, Australian Council for Aeronautics; Report ACA-39 (1948).Google Scholar
[122]Wittrick, W. H., “Torsion and bending of swept and tapered wings with rigid chordwise ribs”, Australian Council for Aeronautics; Report ACA-51 (1950).Google Scholar
[123]Wood, W. W., “Boundary layers whose streamlines are closed”, J. Fluid Mech. 1 (1957) 7787.CrossRefGoogle Scholar
[124]Wood, W. W., “The asymptotic expansion at large Reynolds numbers for steady motion between non-coaxial rotating cylinders”, J. Fluid Mech. 3 (1957) 159175.CrossRefGoogle Scholar
[125]Wood, W. W., “Properties of inviscid, recirculating flows”, J. Fluid Mech. 22 (1964) 337346.CrossRefGoogle Scholar
[126]Wood, W. W., “Tunnel interference from slotted walls”, Quart. J. Mech. Appl. Math. 17 (1964) 125140.CrossRefGoogle Scholar
[127]Wood, W. W., “Calculations for anemometry with fine hot wires”, J. Fluid Mech. 32 (1968) 919.CrossRefGoogle Scholar
[128]Wood, W. W., “Free and forced convection from hot wires”, J. Fluid Mech. 55 (1972) 419438.CrossRefGoogle Scholar