Originally Posted by
pasta
I think what it's getting at is there are 2 factors: the different flight profile of a winged vehicle and the increased specific impulse of an air-breathing engine.
Apologies, I'm probably not going to explain this very well, but I'll have a go. Bear in mind that around 90% of the energy of an orbital vehicle is kinetic rather than potential; in other words, the real work is getting it up to speed rather than getting it up:
For a conventional rocket ascending almost vertically through the lower atmosphere (which is the most efficient profile for a non-winged vehicle) quite a lot of its thrust is "wasted" in resisting gravity. For instance, if a 10 ton rocket has engines generating 30 tons of thrust, 10 tons of thrust are required just to stop the thing accelerating downwards, so only 2/3 of that thrust actually causes the rocket to accelerate in the intended direction. Apparently this was a very significant factor for the Saturn 5, which (checking Wikipedia) weighed just under 3 million kg fully fuelled, and generated 34,000 kN of thrust (in other words, at the point of lift-off, only about 10% of the thrust was actually accelerating the vehicle). A winged vehicle is able to use the atmosphere to generate lift, which is how we are able to fly aircraft with a thrust:weight ratio of less than 1, so it's able to use a much greater proportion of that thrust to accelerate. Now combine the fact that the SABRE engine in air-breathing mode has just over 7x the specific impulse of a decent rocket engine (because no oxidiser is carried) and it's able to do so with around 1/7 the fuel burn of a rocket-powered winged vehicle.
This is only helpful for the first part of the launch, but by the time the Sabre engine is switched to internal oxidiser, my calculations have it travelling at ~1600m/s (Mach 5.5@94,000ft), which is 70% of the speed (2300m/s) that the Saturn 5 jettisoned its first stage (representing about 75% of its overall mass).
It’s also how the falcon 9 can get back to launch site with minimal fuel (plus the significantly reduced mass on the 1st stage) A lot of the fuel has been expended giving the “up” velocity vector, whereas the 2nd stage gives much more to the horizontal component, which in the case of SABRE open loop can only kick in once aerodynamic drag has a minimal effect.
Noted your point thanks on the He being completely closed loop thermodynamic cycle, hadn’t realised this, thought they were ditching it overboard to get rid of waste heat.