FEBA
Sometimes very simple questions are the devil to answer without writing a book, but here goes. It is all about the basics of thrust. Thrust comes from good old M x V. M is the mass of air taken in by the system and V is the speed that is imparted to the air. A Sea King’s rotor in the hover takes in a huge M and gives it a modest v while a Sea Harrier’s Pegasus takes in a modest m and gives it a relatively big V. They both weigh the same in a heavy hover, so both are using the same thrust (MxV) but the nature of that thrust (downwash) is quite different.
To fly supersonically you need an engine system that delivers air with a very big V and we only know how to do that by making said air pretty hot. Any fighter using reheat on takeoff makes that point.
Standing such a fighter vertically on its tail a few feet off the ground and letting it do a VTO is not on. It is not that the amount of thrust is wrong it is that the type of thrust (hot and fast) is not usable with rubber tyres underneath you and a solid ground surface of normal materials.
So the Pegasus could not have used PCB during VTO or VL. And the cold non PCB thrust was not enough to hover (and so VL) an aeroplane that was big enough to carry all the fuel needed to use the PCB for a sensible period of time during the sortie. Catch 22.
The Lockheed and Boeing JSF teams had to use the same basic F-119 engine. They could modify it as they saw fit for STOVL. Boeing added nozzles like a Harriers under the CG and shut down the rear exhaust for the hover. If you saw the Channel 4 progs you may have seen the dull red glow inside the Boeing nozzles. This hot air must not find its way into the intake or the engine will likely surge or worse. Boeing used a ‘jet- screen’ of coldish air tapped off before the combustion chambers and exhausted down in front of the hovering nozzles in an attempt to build a barrier between the really hot main exhaust and the nose intake. It proved somewhat marginal.
Lockheed decide to turn the engine into a sort of turbo prop on the downwind leg by using a shaft to drive a lift fan behind the cockpit. Complicated mechanically, but very efficient when it came to generating lift. Taking 26,000 shaft HP out from the engine reduced the thrust at the back by 6000lb. But that same SHP produced 16,000 lb of thrust when driving the fan. A gain of 10,000lb of hover capability over a pure jet. Rather more than an edge in a competition?
Finally, the Lockheed way enabled the huge column of cool fan air to robustly blow back the hot air from the rear when it tried to migrate forward. The IR film showing the way the cold column turns back the hot column as it tries to move forward under the aircraft is the stuff old Harrier guys can only dream about.
Regards