An overview of the Magnus effect of projectiles and missiles is presented. The first part of the paper is devoted to the description of the physical mechanisms governing the Magnus effect. For yawing and spinning projectiles, at small incidences, the spin induces a weak asymmetry of the boundary layer profiles. At high incidences, increased spin causes the separated vortex sheets to be altered. Vortex asymmetry generates an additional lateral force which gives a vortex contribution to the total Magnus effect. For finned projectiles or missiles, the origin of the Magnus effect on fins is the main issue. There are two principal sources contributing to the Magnus effect. Firstly, the interaction between the asymmetric boundary layer-wake of the body and the fins, and secondly, the spin induced modifications of the local incidences and of the flow topology around the fins. The second part of the paper is devoted to the numerical prediction and validation of these flow phenomena. A state of the art is presented including classical CFD methods based on Reynolds-averaged Navier–Stokes (RANS) and unsteady rans (URANS) equations, and also hybrid RANS/LES approach called ZDES. This last method is a recent advance in turbulence modeling methodologies that allows to take into account the unsteadiness of the flow in the base region. For validation purposes computational results were compared with wind tunnel tests. A wide range of angles of attack, spin rates, Reynolds and Mach numbers (subsonic, transonic and supersonic) have been investigated.

References

References
1.
Newton
,
I.
, 1671, “
A Letter of Mr. Isaac Newton, of the University of Cambridge, Containing His New Theory About Light and Color
,”
Philos. Trans. R. Soc. London
,
7
, pp.
3075
3087
.
2.
Robins
,
B.
, 1742,
New Principles of Gunnery: Containing the Determination of the Force of Gun-Powder, and an Investigation of the Difference in the Resisting Power of the Air to Swift and Slow Motions
,
John Nourse
,
London, England
.
3.
Magnus
,
G.
, 1852, “
Über die Abweichung der Geschosse
,” Abhandlungen der Königlichen Akademie der Wissenschaften zu Berlin, pp.
1
23
.
4.
Magnus
,
G.
, 1853, “
Über die Abweichung der Geschosse, und: Über eine abfallende Erscheinung bei rotierenden Körpern
,”
Ann. Phys.
,
164
(
1
), pp.
1
29
.
5.
Rayleigh
,
J. W.
, 1877, “
On the Irregular Flight of a Tennis Ball
,”
Messenger of Mathematics
,
7
, p.
14
.
6.
Lafay
,
A.
, 1910, “
Sur l’Inversion du Phénomène de Magnus
,”
Compt. Rend.
,
151
.
7.
Chapman
,
D. R.
,
Wimbrow
,
W. R.
, and
Kester
,
R. H.
, 1952, “
Experimental Investigation of the Base Pressure on Blunt-Trailing-Edge Wings at Supersonic Velocities
,” Report No. NACA TN 2611.
8.
Krahn
,
E.
, 1955, “
The Laminar Boundary Layer on a Rotating Cylinder in Crossflow
,” U.S. NOL, Maryland, Report Nos. NAVORD Rep. 4022 and Aerobal. Res. Rep. 288.
9.
Martin
,
J. C.
, 1955, “
On the Magnus Effects Caused by the Boundary Layer Displacement Thickness on Bodies of Revolution at Small Angles of Attack
,”
Aberdeen Proving Ground
, Maryland, BRL, Report No. 870.
10.
Platou
,
A. S.
, 1960, “
Magnus Characteristics of Fined and Non Finned Projectiles
,”
AIAA J.
,
3
(
1
), pp.
83
90
.
11.
Jacobson
,
I. D.
, 1970, “
Magnus Characteristics of Arbitrary Rotating Bodies
,”
AGARDograph
, Report No. AG-171.
12.
Dwyer
,
H.
and
Sander
,
B. R.
, 1976, “
Magnus Forces Spinning Supersonic Cones. Part I: The Boundary Layer
,”
AIAA J.
,
14
, p.
498
.
13.
Sander
,
B. R.
and
Dwyer
,
H.
, 1976, “
Magnus Forces Spinning Supersonic Cones. Part I: The Inviscid Flow
,”
AIAA J.
,
14
, pp.
576
582
.
14.
Sturek
,
W. B.
,
Dwyer
,
H.
,
Kayser
,
L.
,
Nietubicz
,
C.
,
Reklis
,
R.
, and
Opalka
,
K.
, 1978,
“Computations of Magnus Effects for Yawed Spinning Body of Revolution
,”
AIAA J.
,
16
(
7
), pp.
687
692
.
15.
Kayser
,
L.
,
Sturek
,
W. B.
, and
Yanta
,
W.
, 1978, “
Measurements in the Turbulent Boundary Layer of Yawed Spinning Body of Revolution at Mach 3 With a Laser Velocimeter and Impact Probe
,” AIAA Paper No. 78-824.
16.
Schiff
,
L.
and
Steger
,
J. L.
, 1979, “
Numerical Simulation of Steady Supersonic Viscous Flow
,” AIAA Paper No. 79-0130.
17.
Kegelman
,
J.
,
Nelson
,
R.
, and
Mueller
,
T.
, 1980, “
Boundary Layer and Side Force Characteristics of a Spinning Axisymmetric Body
,” AIAA Paper No. 80-1584.
18.
Sturek
,
W. B.
and
Schiff
,
L.
, 1980, “
Computations of the Magnus Effect for Slender Bodies in Supersonic Flow
,” AIAA Paper No. 80-1586.
19.
Sturek
,
W. B.
,
Mylin
,
D.
, and
Yanta
,
W.
, 1980, “
Computational Study of the Aerodynamics of Spinning Slender Bodies at Supersonic Speeds
,” AIAA Paper No. 80-1885.
20.
Nietubicz
,
C.
and
Opalka
,
K.
, 1980, “
Supersonic Wind Tunnel Measurements of Static and Magnus Aerodynamic Coefficients for Projectile Shapes With Tangent and Secant Ogive Noses
,” Memorandum Report No. ARBRL-MR-02991.
21.
Sturek
,
W. B.
and
Mylin
,
D. C.
, 1981, “
Computational Parametric Study of the Magnus Effect on Boattailed Shell at Supersonic Speed
,” AIAA Paper No. 81-1900.
22.
Miller
,
M. C.
, 1983, “
Wind Tunnel Measurements of the Magnus Induced Surface Pressures on a Spinning Projectile in the Transonic Regime
,” AIAA Paper No. 83-1838.
23.
Sturek
,
W. B.
and
Nietubicz
,
C.
, 1992, “
Recent Applications of CFD to the Aerodynamics of Army Projectiles at the U.S. Army Ballistic Research Laboratory
,” AIAA Paper No. 92-4349.
24.
Netterfield
,
M. P.
, 1993, “
Modern CFD Methods Applied to Aerodynamics Predictions of Spinning Projectile
,” AIAA Paper No. 93-0500.
25.
Weinacht
,
P.
and
Sahu
,
J.
, 1994, “
Navier-Stokes Predictions of Missile Aerodynamics
,” AGARD Report No. 804.
26.
Cayzac
,
R.
,
Carette
,
E.
,
Péchier
,
M.
, and
Guillen
,
P.
, 1999, “
Navier-Stokes Computations and Validations of a Yawed Spinning Projectile
,”
18th International Symposium on Ballistics
,
San Antonio, TX1
, pp.
28
37
.
27.
Péchier
,
M.
, 1999, “
Numerical Predictions of Magnus Effects Over Ammunition Configurations
,” Ph.D. thesis (in French), Mechanical Engineering, University of Poitiers, Poitiers, France.
28.
Cayzac
,
R.
and
Carette
,
E.
, 2000, “
Intermediate Ballistics and Aeroballistics Overview
,”
European Forum on Ballistics of Projectiles
,
ISL
,
Saint Louis, France
, pp.
259
274
.
29.
Péchier
,
M.
,
Guillen
,
P.
, and
Cayzac
,
R.
, 2001, “
Magnus Effect Over Finned Projectiles
,”
AIAA, Journal of Spacecraft and Rockets
,
38
(
4
), pp.
542
549
.
30.
Cayzac
,
R.
,
Trouillot
,
C.
,
Carette
,
E.
,
Champigny
,
P.
,
Thépot
,
R.
, and
Donneaud
,
O.
, 2002, “
Recent Developments on Aeroballistics of Yawing and Spinning Projectiles: Part I, Wind Tunnel Tests
,”
20th International Symposium on Ballistics
,
Orlando
,
FL
, Vol.
1
, pp.
203
208
.
31.
Donneaud
,
O.
,
Cayzac
,
R.
,
Carette
,
E.
,
Champigny
,
P.
, and
Thépot
,
R.
, 2002, “
Recent Developments on Aeroballistics of Yawing and Spinning Projectiles: Part II, Free Flight Tests
,”
20th International Symposium on Ballistics
,
Orlando, FL
, Vol.
1
, pp.
157
164
.
32.
Cayzac
,
R.
,
Carette
,
E.
,
Champigny
,
P.
,
Thépot
,
R.
, and
Donneaud
,
O.
, 2002, “
Recent Developments on Aeroballistics of Yawing and Spinning Projectiles: Part III, Validation Results
,”
20th International Symposium on Ballistics
,
Orlando, FL
, Vol.
1
, pp.
11
19
.
33.
Cayzac
,
R.
,
Carette
,
E.
,
Champigny
,
P.
,
Thépot
,
R.
, and
Donneaud
,
O.
, 2004, “
Analysis of Static and Dynamic Stability of Spinning Projectiles
,”
21st International Symposium on Ballistics
,
Adelaide
,
Australia
, Vol.
1
, pp.
504
510
.
34.
DeSpirito
,
J.
and
Heavy
,
K. R
., (2004), “
CFD Computations of Magnus Moment and Roll Damping Moment of Spinning Projectile
,” AIAA Paper No. 2004-4713.
35.
Cayzac
,
R.
and
Carette
,
E.
, 2004, “
CFD Computations of Projectile Unsteady Aerodynamics
,”
55th Meeting of the Aeroballistics Range Association
,
Freiburg
,
Germany
.
36.
Cayzac
,
R.
,
Carette
,
E.
, and
Thepot
,
R.
, 2005, “
Recent Computations and Validations of Projectile Unsteady Aerodynamics
,”
22nd International Symposium on Ballistics
,
Vancouver
,
Canada
, Vol.
1
, pp.
29
37
.
37.
Simon
,
F.
,
Deck
,
S.
,
Guillen
,
P.
,
Cayzac
,
R.
,
Sagaut
,
P.
, and
Merlen
,
A.
, 2007, “
RANS/LES Simulations of Projectiles With and Without Rotation in the Subsonic and Transonic Regimes
,”
23rd International Symposium on Ballistics
,
Tarragona
,
Spain
, pp.
755
763
.
38.
Weinacht
,
P.
, 2007, “
Virtual Wind Tunnel Method for Projectile Aerodynamic Characterization
,”
23rd International Symposium on Ballistics
,
Tarragona
,
Spain
, pp.
631
638
.
39.
Simon
,
F.
, 2007, “
Hybrid RANS/LES Numerical Simulations of Projectile Aerodynamics
,” Ph.D. thesis (in French), Mechanical Engineering, University of Poitiers, Poitiers, France.
40.
Simon
,
F.
,
Deck
,
S.
,
Guillen
,
P.
,
Cayzac
,
R.
, and
Merlen
, 2007, “
Zonal-Detached-Eddy Simulation of Projectiles in the Subsonic and Transonic Regimes
,”
AIAA J.
,
45
(
7
), pp.
1606
1619
.
41.
Janzon
,
B.
,
Backofen
,
J.
,
Brown
,
R. E.
,
Cayzac
,
R.
,
Diederen
,
A.
,
Giraud
,
M. M.
,
Held
,
M.
,
Horst
,
A. W
.
, and
Thoma
,
K.
, 2007, “
The Future of Warheads, Armour and Ballistics
, “
23rd International Symposium on Ballistics
,
Tarragona
,
Spain
, Vol.
1
, pp.
3
27
.
42.
Sagaut
,
P.
,
Deck
,
S.
, and
Terracol
,
M.
, 2006,
Multiscale and Multiresolution Approaches in Turbulence
,
Imperial College Press
,
London, England
.
43.
Deck
,
S.
, 2005, “
Numerical Simulation of Transonic Buffet Over a Supercritical Airfoil
,”
AIAA J.
,
43
(
7
), pp.
1556
1566
.
44.
Deck
,
S.
, 2005, “
Zonal-Detached Eddy Simulation of the Flow Around a High Lift Configuration
,”
AIAA J.
,
43
(
11
), pp.
2372
2384
.
45.
Spalart
,
P. R.
,
Jou
,
W. H.
,
Strelets
,
M.
, and
Allmaras
,
S. R.
, 1997, “
Comments on the Feasibility of LES for Wings and on a Hybrid RANS/LES Approach
,”
Proceedings of the First AFSOR International Conference on DNS/LES
,
Ruston
,
USA
.
46.
Deck
,
S.
,
Garnier
,
S. E.
, and
Guillen
,
P.
, 2002, “
Turbulence Modelling Applied to Space Launcher Configurations
,”
J. Turbul.
,
3
(
57
), pp.
1
21
.
You do not currently have access to this content.