Skip to main content Accessibility help

Experimental determination of the aerodynamic coefficients of spinning bodies

  • S. Nguyen (a1), M. Corey (a1), W. Chan (a1), E.S. Greenhalgh (a1) and J.M.R. Graham (a1)...


To accurately predict the probabilities of impact damage to aircraft from runway debris, it is important to understand and quantify the aerodynamic forces that contribute to runway debris lofting. These lift and drag forces were therefore measured in experiments with various bodies spun over a range of angular velocities and Reynolds numbers. For a smooth sphere, the Magnus effect was observed for ratios of spin speed to flow speed between 0.3 and 0.4, but a negative Magnus force was observed at high Reynolds numbers as a transitional boundary layer region was approached. Similar relationships between lift and spin rate were found for both cube- and cylinder-shaped test objects, particularly with a ratio of spin speed to flow speed above 0.3, which suggested comparable separation patterns between rapidly spinning cubes and cylinders. A tumbling smooth ellipsoid had aerodynamic characteristics similar to that of a smooth sphere at a high spin rate. Surface roughness in the form of attached sandpaper increased the average lift on the cylinder by 24%, and approximately doubled the lift acting on the ellipsoid in both rolling and tumbling configurations.


Corresponding author


Hide All
1.Greenhalgh, E.S., Chichester, G.A.F., Mew, A., Slade, M. and Bowen, R. Characterisation of the realistic impact threat from runway debris, Aeronaut J, 2001, 105, pp 557570.
2.Beatty, D.N., Readdy, F., Gearhart, J.J. and Duchatellier, R. The study of foreign object damage caused by aircraft operations on unconventional and bomb-damaged airfield surfaces, BDM Corp Mclean, VA, US. Report no. ADA117587, 1981, Defense Technical Information Center (DTIC), Fort Belvoir, VA.
3.Nguyen, S.N., Greenhalgh, E.S., Olsson, R., Iannucci, L. and Curtis, P.T. Modelling the lofting of runway debris by aircraft tires, J Aircraft, 2008, 45, (5), pp 17011714.
4.Cross, R. and Lindsey, C. Measurements of drag and lift on smooth balls in flight, Europ J Phys, 2017, 38, (4), pp 112.
5.Zhang, X., Toet, W. and Zerihan, J. Ground effect aerodynamics of race cars, Appl Mech Rev, 2006, 59, (1) pp 3349.
6.Nguyen, S.N., Greenhalgh, E.S., Graham, J.M.R., Francis, A. and Olsson, R. Runway debris impact threat maps for transport aircraft, Aeronaut J, 2014, 118, (1201), pp 229266.
7.Lin, N., Holmes, J.D. and Letchford, C.W. Trajectories of wind-borne debris in horizontal winds and applications to impact testing, J Struct Engrng, 2007, 133, (2), pp 274282.
8.Hradecky, S. Incident: Aeroflot A333 at Petropavlovsk-Kamchatsky on Apr 7th 2013, foreign object damage on landing, The Aviation Herald,, accessed26/03/14, 2013.
9.Tartar, E. Fighter Aircraft: MiG-29 Part 4, Fighter Tactics Academy,, accessed 26/03/14, 2007.
10.Aguirre-Lopez, M.A., Morales-Castillo, J., Diaz-Hernandez, O., Escalera Santos, G.J. and Almaguer, F.-J. Trajectories reconstruction of spinning baseball pitches by three-point-based algorithm, Appl Math Comput, 2018, 319, pp 212.
11.Maccoll, J.W. Aerodynamics of a spinning sphere, J Royal Aeronaut Soc, 1928, 28, pp 777798.
12.Beasley, D. and Camp, T. Effects of dimple design on the aerodynamic performance of a golf ball, Sci & Golf, IV, 2012.
13.Briggs, L.J. Effect of spin and speed on the lateral deflection curve of a baseball, and the Magnus effect for smooth spheres, Am J Phys, 1959, 27, pp 589596.
14.Watts, R.G. and Ferrer, R. The lateral force on a spinning sphere: aerodynamics of a curveball, Am J Phys, 1987, 55, (1), pp 4044.
15.Kray, T., Franke, J. and Frank, W. Magnus effect on a rotating soccer ball at high Reynolds numbers, J Wind Engrng Ind Aerodyn, 2014, 124, pp 4653.
16.Jing, L., Tsubokura, M. and Tsunoda, M. Numerical investigation of the flow past a rotating golf ball and its comparison with a rotating smooth sphere, Flow Turb Combustion, 2017, 99, (3–4), pp 837864.
17.Passmore, M.A., Tuplin, S. and Stawski, A. The real-time measurement of football aerodynamic loads under spinning conditions, Proc Inst Mech Engineers, Part P (J Sports Engrng Tech), 2017, 231, (4), pp 262274.
18.Maruyama, Y. Study on the physical mechanism of the Magnus effect, Trans Japan Soc Aeronaut Space Sci, 2011, 54, (185–186), pp 173181.
19.Dobson, J., Ooi, A. and Poon, E.K.W. The flow structures of a transversely rotating sphere at high rotation rates, Computers Fluids, 2014, 102, (10), pp 170181.
20.Seifert, J. A review of the Magnus effect in aeronautics, Prog Aerospace Sci, 2012, 55, pp 1745.
21.Zheng, Z., Lei, J. and Wu, X. Numerical simulation of the negative Magnus effect of a two-dimensional spinning circular cylinder, Flow Turb Combust, 2017, 98, (1), pp 109130.
22.Swanson, W.M. The Magnus effect: A summary of investigations to date, J Basic Engrng Trans ASME, 1961, 83 (3), pp 461470.
23.Lafay, A. Experimental contribution to the aerodynamics of the cylinder and study of the Magnus effect, Mech Rev, 1912, 30, pp 417442.
24.Taneda, S. Negative Magnus effect, Res Inst Appl Mech, 1957, 5, pp 123128.
25.Kim, J., Choi, H., Park, H. and Yoo, J.Y. Inverse Magnus effect on a rotating sphere: when and why, J Fluid Mech, 2014, 754, (R2), pp 111.
26.Marzuki, O.F., Mohd Rafie, A.S., Romli, F.I. and Ahmad, K.A. Magnus wind turbine: the effect of sandpaper surface roughness on cylinder blades, Acta Mechanica, 2018, 229, (1), pp 7185.
27.Wu, Z., Cao, Y. and Ismail, M. Numerical simulation of airfoil aerodynamic penalties and mechanisms in heavy rain, Int J Aerospace Engrng, 2013, 2013, pp 13.
28.Dukkipati, R.V. and Srinivas, J. Textbook of Mechanical Vibrations, 2nd ed., Phi Learning Private Ltd, 2012, New Delhi, India.
29.American Wood Council, Beam Design Formulas with Shear and Moment Diagrams, Am Forest & Paper Assoc, Design Aid, (6), American Wood Council, Washington, DC. 2007.
30.Krüger, , Critical speed of shafts, Tech Bulletin TBN 017.0, 1998.
31.Achenbach, E. The effects of surface roughness and tunnel blockage on the flow past spheres, J Fluid Mech, 1974, 65, (1) pp 113125.
32.Coleman, H.W. and Steele, W.G. Experimentation, Validation and Uncertainty Analysis for Engineers, 3rd ed., John Wiley & Sons, 2009, Hoboken, NJ.


Experimental determination of the aerodynamic coefficients of spinning bodies

  • S. Nguyen (a1), M. Corey (a1), W. Chan (a1), E.S. Greenhalgh (a1) and J.M.R. Graham (a1)...


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed