  Hypersonic waveriders are special shapes with leading edges coincident with
the body's shock wave, yielding high lift-to-drag ratios. The waverider
geometry results from streamline tracing using the solutions of a basic flow
field such as the wedge or the cone for specified shock and base curves. The
base and shock curves can be independently prescribed in the osculating cone
method enabling a larger design space. Generally, low values of the conical
shock angle (9-15 degrees) are used. The lack of any method to limit the
maximum cone angle for osculating cone waverider motivates this study.
Mathematical expressions are derived for geometrical conditions that result in
successful osculating cone waverider generation. A power law curve and a Bezier
curve are analyzed. Closed-form expressions for the maximum cone shock angle
are obtained for the power law curve. A numerical procedure to solve the same
for the Bezier curve is developed. The results, for a typical Mach number of
6.0, evidently show that the maximum cone shock angle for successful waverider
generation is significantly lower than the maximum angle for attached shock
solutions. The limiting conditions developed will be essential in constraining
the waverider sample space for automated multiobjective optimization routines.
