# 12.2.2.7: Maximum Value of Oblique shock

The maximum values are summarized in the following Table .

\(M_x\) | 1.1000 | 1.2000 | 1.3000 | 1.4000 | 1.5000 | 1.6000 | 1.7000 | 1.8000 | 1.9000 | 2.0000 | 2.2000 | 2.4000 | 2.6000 | 2.8000 | 3.0000 | 3.2000 | 3.4000 | 3.6000 | 3.8000 | 4.0000 | 5.0000 | 6.0000 | 7.0000 | 8.0000 | 9.0000 | 10.0000 |

\(M_y\) | 0.97131 | 0.95049 | 0.93629 | 0.92683 | 0.92165 | 0.91941 | 0.91871 | 0.91997 | 0.92224 | 0.92478 | 0.93083 | 0.93747 | 0.94387 | 0.94925 | 0.95435 | 0.95897 | 0.96335 | 0.96630 | 0.96942 | 0.97214 | 0.98183 | 0.98714 | 0.99047 | 0.99337 | 0.99440 | 0.99559 |

\(\delta_{max}\) | 1.5152 | 3.9442 | 6.6621 | 9.4272 | 12.1127 | 14.6515 | 17.0119 | 19.1833 | 21.1675 | 22.9735 | 26.1028 | 28.6814 | 30.8137 | 32.5875 | 34.0734 | 35.3275 | 36.3934 | 37.3059 | 38.0922 | 38.7739 | 41.1177 | 42.4398 | 43.2546 | 43.7908 | 44.1619 | 44.4290 |

\(\theta_{max}\) | 76.2762 | 71.9555 | 69.3645 | 67.7023 | 66.5676 | 65.7972 | 65.3066 | 64.9668 | 64.7532 | 64.6465 | 64.6074 | 64.6934 | 64.8443 | 65.0399 | 65.2309 | 65.4144 | 65.5787 | 65.7593 | 65.9087 | 66.0464 | 66.5671 | 66.9020 | 67.1196 | 67.2503 | 67.3673 | 67.4419 |

It must be noted that the calculations are for the perfect gas model. In some cases, this assumption might not be sufficient and different analysis is needed. Henderson and Menikoff suggested a procedure to calculate the maximum deflection angle for arbitrary equation of state. When the mathematical quantity \(D\) becomes positive, for large deflection angle, there isn't a physical solution to an oblique shock. Since the flow "sees'' the obstacle, the only possible reaction is by a normal shock which occurs at some distance from the body. This shock is referred to as the detach shock. The detached shock's distance from the body is a complex analysis and should be left to graduate class and researchers in this area.

### Contributors

Dr. Genick Bar-Meir. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or later or Potto license.