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The deflection angle, delta, for a given wave angle, theta, and a given Mach number M is governed by

$$\mathrm{cot}\delta =\mathrm{tan}\theta [\frac{(\gamma +1){M}^{2}}{2({M}^{2}\mathrm{sin}{}^{2}\theta -1)}-1]$$This is Eq. 138 of NACA report 1135 and is illustrated in the following chart.

For a given upstream Mach number, there is a maximum value of deflection angle and you can read the value on the y-axis. If you are writing a computer code and you need a function that returns the maximum deflection angle for a given Mach number, what equation do you use? If you want a fast routine that gives you this result, simply use BrentMin on Eq. 138. BrentMin is one of the members of the library of Computer Methods for Mathematical Computation downloadable from this site. You are looking for a maximum of deflection angle, delta, and BrentMin finds a minimum. But, you are in luck, because Eq. 138 returns cot(delta) and a minimum of cot(delta) is a maximum of delta. Cool. If you want to go thru the details, see the numerics page. The results are summarized below.

Mach | delta,deg |
---|---|

1.05 | 0.56 |

1.10 | 1.52 |

1.20 | 3.94 |

1.30 | 6.66 |

1.40 | 9.43 |

1.60 | 14.65 |

1.80 | 19.18 |

2.00 | 22.97 |

2.50 | 29.80 |

3.00 | 34.07 |

4.00 | 38.77 |

5.00 | 41.12 |

6.00 | 42.44 |

8.00 | 43.79 |

10.00 | 44.43 |