Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-06-17T01:07:30.558Z Has data issue: false hasContentIssue false

Sphere drag at Mach numbers from 0·3 to 2·0 at Reynolds numbers approaching 107

Published online by Cambridge University Press:  18 April 2017

Donald G. Miller
Affiliation:
Earth Sciences Division, Lawrence Livermore Laboratory, University of California, Livermore, California 94550
Allan B. Bailey
Affiliation:
Aerodynamics Projects Branch, Von Kármán Gas Dynamics Facility, Arnold Air Force Station, Tennessee 37389

Extract

Our analysis of 18th and 19th century cannon firings shows that knowledge of sphere drag can be substantially extended into the region of 0·3 ≤ M ≤ 2·0 and Re∞d up to 107. Bashforth’s chronographic measurements (1868) are of a quality comparable to modern measurements. The data of Mayevski (chronograph, 1868), Hutton (ballistic pendulum, 1787-1791), and Didion (ballistic pendulum, 1839-1840) are of lesser accuracy but in agreement with Bashforth’s. These cannon data are combined with modern data to provide the most extensive curves available of CD vs. Re∞d in this region. Interesting features of these curves for M ≤ 1·0 are briefly described.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1979

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bailey, A. B. & Hiatt, J. 1971 Free-Flight Measurements Of Sphere Drag At Subsonic, Transonic, Supersonic, And Hypersonic Speeds For Continuum, Transition, And Near-Free-Molecular Flow Conditions. Arnold Engng Development Ctr., Arnold Air Force Station, Tn, Rep. Aedc-Tr-70-291.Google Scholar
Bailey, A. B. & Starr, R. F. 1976 Sphere Drag At Transonic Speeds And High Reynolds Number. A.I.A.A. J. 14, 1631.Google Scholar
Bashforth, F. A. 1870 Reports On Experiments Made With The Bashforth Chronograph To Determine The Resistance Of Air To The Motion Of Projectiles, 1865-1870. H.M.S.O., London, Rep. IV, Pp. 55122.Google Scholar
Bashforth, F. A. 1881 Supplement To A Mathematical Treatise On The Motion Of Projectiles Founded Chiefly On The Results Of Experiments Made With The AuthorS Chronograph. London: Asher & Co. Google Scholar
Bashforth, F. A. 1890 A Revised Account Of The Experiments Made With The Bashforth Chronograph. Cambridge University Press.Google Scholar
British Textbook Of Small Arms 1929 H.M.S.O., London, Reprinted By Holland Press, London, 1961.Google Scholar
Charters, A. & Thomas, R. 1945 The Aerodynamic Performance Of Small Spheres From Subsonic To High Supersonic Velocities. J. Aeronaut. Sci. 12, 468476.CrossRefGoogle Scholar
Cranz, C. & Becker, K. 1921 Handbook Of Ballistics. Exterior Ballistics, Vol. I, Translated From The 2nd German Edition. London: H.M.S.O. Google Scholar
Didion, I S. 1857 Lois De La Resistance De L’Air Sur Les Projectiles. Paris: J . Dumaine, Librairie Militaire.Google Scholar
Didion, Le General 1860 Traiti De Balistique, Deuxieme Edition. Paris: J. Dumaine.Google Scholar
Helie, F. 1884 Traiti De Balistique Expirimentale, Tome Premier. Paris: Gauthier-Villars.Google Scholar
Hutton, Charles 1812 The Force Of Gunpowder With Applications To The Modern Practice Of Artillery. Tracts On Mathematical And Philosophical Subjects, Vols, 7 And In, London.Google Scholar
Ingalls, James M. 1886 Exterior Ballistics In The Plane Of Fire. Dept. Ballistics U.S. Artillery School. New York: D. Van Nostrand.Google Scholar
May, A. & Witt, W. R. 1953 Free-Flight Determinations Of The Drag Coefficients Of Spheres. J. Aeronaut. Sci. 20, 635638.Google Scholar
Mayevski, N. 1872 Traiti De Balistique Exterieure. Paris: Gauthier-Villars.Google Scholar
Natjmann, A. 1954 Aerodynamische Oesichtspunkte Der Windkanalentwicklung, Jahrbuch 1954. Braunschweig: Friedr. Vieweg & Sohn.Google Scholar
Robins, B. 1742 New Principles Of Gunnery, London; Reprinted By Richmond Publishing Company, London, 1972. Also, Mathematical Tracts, 2 Vols, (Includes New Principles Of Gunnery), J . Nourse, London, 1761.Google Scholar
Short, B. J. 1967 Dynamic Flight Behavior Of A Ballasted Sphere At Mach Numbers From 0-4 To 14-5. National Aeronautics And Space Administration, Washington, D.C.,Rept. N.A.S.A. Tech. Note Tnd-4198.Google Scholar
Stilp, A. 1965 Stromungsuntersuchungen An Kugeln Mit Transonischen And Supersonischen Qeschwindigkeiten In Luft Und Frigen-Luftgemischen, Ernst-Mach-Institut. Freiburg/B., Bericht Nr. 10/65.Google Scholar