 approxim analyt solut hyperson flow slender power-law bodi approxim analyt solut hyperson flow slender power-law bodi approxim analyt solut present two-dimension axisymmetr hyperson flow blunt-nose slender bodi shape follow power law variat bodi shape transvers bodi ordin streamwis distanc nose constant rang zero-order solut first-order small nonvanish valu solut present free-stream mach number characterist bodi streamlin slope zero-order shock shape bodi shape flow solut framework hyperson-slender-bodi theori limit case 1 correspond wedg cone flow limit case correspond constant-energi flow case includ studi appli flow zero-order shock shape rang flow field associ shock shape valu rang discuss valu 1 portion flow field riolat hyperson-slender-bodi approxim portion consist approxim 1 portion flow field consist approxim approxim solut asymptot form flow vicin bodi surfac guid write approxim express depend variabl express exactli satisfi continu energi equat arbitrari constant evalu satisfi boundari condit shock approxim solut satisfi later momentum equat shock first-order problem bodi surfac approxim solut compar numer integr equat motion valu ratio specif heat good agreement shock close bodi case suffici present evalu accuraci approxim method valu 