Harrier take-off
I think you described the Harrier airshow take-off which Chief Test Pilot John Farley came up with for demonstration / show purposes, not tactical as he freely admits.
He would hover the Harrier, then use the reaction controls & move the nozzles ( all by seat of the pants, no suitable instruments ) to hover at around 40 degrees or more then apply full power & 'rocket climb' away.
My father was crew-chief when J.F. did this in a display at Farnborough in an Indian FRS51 Sea Harrier - the aircraft, half way up, was seen to stagger & level out early...
John landed uneventfully, and remarked " I always wondered what would happen if the water pump gave up at that point !"