In aerodynamics, a hypersonic speed is one that is highly supersonic (even though the origin of the words is the same: "super" is just the Latin version of the Greek "hyper"). Since the 1970s, the term has generally been assumed to refer to speeds of Mach 5 and above.
The precise Mach number at which a craft can be said to be flying at hypersonic speed varies, since individual physical changes in the airflow (like molecular dissociation and ionization) occur at different speeds; these effects collectively become important around Mach 5. The hypersonic regime is often alternatively defined as speeds where ramjets do not produce net thrust.
Read more about Hypersonic Speed: Characteristics of Flow, Classification of Mach Regimes, Similarity Parameters, Regimes
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