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Next: The Procedure for Calculating Up: Upstream Mach number, M1, Previous: Upstream Mach number, M1,   Index

#### The simple procedure

For example, in Figure (13.4) and (13.5), the imaginary angle is shown. The flow is far away from the object and does not see' the object. For example, for, the maximum deflection angle is calculated when . This can be done by evaluating the terms , , and for .

With these values the coefficients and are

and

Solving equation (13.28) after substituting these values of and provides series of roots from which only one root is possible. This root, in the case , is just above (note that the maximum is also a function of the heat ratio, ).

While the above procedure provides the general solution for the three roots, there is simplified transformation that provides solution for the strong and and weak solution. It must be noted that in doing this transformation the first solution is lost'' supposedly because it is negative.'' In reality the first solution is not negative but rather some value between zero and the weak angle. Several researchers13.15 suggested that instead Thompson's equation should be expressed by equation (13.18) by and is transformed into

The solution to this equation (13.31) for the weak angle is