Standard_Departure ..."From The ATC Side"
No need to belabor the technical parameters of TCAS, because when an RA is commanded it's because ATC already has failed in its traffic separation duties.
Because of the delayed descent of one airplane, and therefore because of obvious questionable vertical separation, as "extra insurance," the controller's duty should have included vectors for lateral separation.
Just four words to each airplane would have insured positive separation and would have saved the day.
DHL, IMMEDIATE LEFT TURN
BASHKIRIAN, IMMEDIATE RIGHT TURN
