Alright, I'll try to ask a better question on what I mean so that we figure out how one becomes weightless in a craft without having to fly steep parabolae. Other than flying parabolae or nose-down towards the Earth, you don't have to achieve first cosmic speed (orbital velocity) in order to become weightless either. The X-15, the SpaceShipOne and the SpaceShipTwo all made suborbital flights at considerably lower speeds (and lower altitudes than where more than one stable orbit would be possible). The pilots of these spaceplanes are reported to have become weightless in flights in which they reached space (both according to the U.S. definition only (50 mi, 80.47 km) or the FAI definition too (62.14 mi, 100 km). Of course these are kind of/sort of parabolae too, but that would mean that pilots of the mentioned craft would also be weightless when they don't reach outer space.
- On 30 March 1961 Joseph Walker reached 169,600 ft in the X-15 plane (thus he became the first man to reach the mesosphere and such high altitude) achieving a speed of 2760 mph and Mach 3.95.
- Two weeks earlier, Robert White in the X-15 achieved a speed of 2905 mph and Mach 4.43 and an altitude of 77,450 ft.
- On 21 April 1961 White achieved a speed of 3,074 mph and Mach 4.62 and an altitude of 105,000 ft.
- In SpaceShipOne flight 14P Mike Melvill reached an altitude of 211,400 ft (64.3 km) and Mach 2.5.
- In SpaceShipTwo flight PF03 two SS2 pilots reached an altitude of 170,800 ft (52 km) and Mach 2.47.
So while none of these above flights reached outer space according to any of the two definitions, I wonder whether they were fast and high enough for the pilots to become weightless in their planes. All of the mentioned pilots reached space in later flights and became weightless but I don't know of reports that they would feel weightless in the mentioned flights where they didn't reach space as yet.
From all of this I'm concluding the following: you need a certain speed (that doesn't have to be orbital speed) in order to achieve weightlessness in a craft. In order to achieve it, you should go to a certain altitude where the atmospheric pressure gets low enough. My question is: what speed / altitude / exterior air pressure are necessary in order to get weightless without having to fly a steep parabola and I'd appreciate if you'd tell me who first achieved weightlessness by the mentioned means (perhaps someone of those I mentioned?). Thank you.