Shock Waves

pp 1–11 | Cite as

Sonic boom generated by a slender body aerodynamically shaded by a disk spike

  • A. V. Potapkin
  • D. Yu. Moskvichev
Original Article


The sonic boom generated by a slender body of revolution aerodynamically shaded by another body is numerically investigated. The aerodynamic shadow is created by a disk placed upstream of the slender body across a supersonic free-stream flow. The disk size and its position upstream of the body are chosen in such a way that the aerodynamically shaded flow is quasi-stationary. A combined method of phantom bodies is used for sonic boom calculations. The method is tested by calculating the sonic boom generated by a blunted body and comparing the results with experimental investigations of the sonic boom generated by spheres of various diameters in ballistic ranges and wind tunnels. The test calculations show that the method of phantom bodies is applicable for calculating far-field parameters of shock waves generated by both slender and blunted bodies. A possibility of reducing the shock wave intensity in the far field by means of the formation of the aerodynamic shadow behind the disk placed upstream of the body is estimated. The calculations are performed for the incoming flow with the Mach number equal to 2. The effect of the disk size on the sonic boom level is calculated.


Shock waves Slender body Blunted body Method of phantom bodies Sonic boom 

List of symbols

\({\Delta } p\)

Excess pressure


Free-stream Mach number

\(\rho _{0}\)

Free-stream density of the gas


Free-stream static temperature


Free-stream static pressure


Free-stream velocity of sound

\(\gamma \)

Ratio of specific heats


Reynolds number

\(Cx^{{\varSigma }}\)

Total drag coefficient of a slender body with an attached disk

\(Cx_{0}^{{\varSigma }}\)

Total drag coefficient of a slender body with no disk

\(Cx^{\mathrm {p}}\)

Drag coefficient induced by pressure


Drag coefficient induced by viscous stresses


Body diameter


Distance from the flight trajectory to the reflecting surface

\(\{ x,r \}\)

Cylindrical coordinate system in two-dimensional calculations with axial symmetry


Distance along the axis of symmetry (flight trajectory)


Radial distance from the flight trajectory

\(\{ x,y,z \}\)

Cartesian coordinate system in three-dimensional calculations


Distance along the flight trajectory


Vertical distance from the flight trajectory


Lateral distance from the flight trajectory

h / d

Normalized distance between the flight trajectory and reflecting surface

r / d

Normalized radial distance from the flight trajectory

\(r_\mathrm {w}/d\)

Normalized radial distance between the front of the bow shock wave and the flight trajectory

x / d

Normalized distance along the flight trajectory


Length of the slender body of revolution

\(d_{\mathrm {b}}\)

Disk diameter

\(x_{\mathrm {b}}\)

Distance between the disk and the slender body of revolution


\({\mathrm {*}}\)

Dimensionless parameter

\({\mathrm {n}}\)

Near field



Free-stream condition


Number of the point on the body or pressure profile

\({\mathrm {m}}\)

Scale notification


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.ITAM SB RASNovosibirskRussia

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