Originally Posted by tdracer
"...An air breathing launch vehicle that could carry an orbiter to ~120,000 ft./Mach 7 (or better) would mean the orbiter wouldn't need to be huge to carry the fuel to get into orbit.""
Originally Posted by joema
"...because of the v^2 term. Mach 7 is only 7.8% of orbital kinetic energy..."
Originally Posted by tdracer
"Wrong, quite wrong. Rockets engines are effectively constant thrust devices, not constant power. Discounting aerodynamic drag, it takes exactly the same amount of thrust to accelerate a given mass from zero to 10,000 ft./sec. as it does to accelerate from 10,000 to 20,000 ft./sec."
As I stated, because KE=1/2*m*v^2, it takes tremendous kinetic energy to reach orbit. A Mach 7 reusable booster is easier to design but it makes the orbiter much heavier. This is because the remaining delta-V is a squared term, hence energy required falls disproportionately on the orbiter.
Since the development cost of similar aerospace vehicles tends to scale upward with gross mass, It is conceivable a TSTO design with a Mach 7 booster would cost more than one with a Mach 12 booster. This can be non-intuitive, but some relevant data and research are in this graph, taken from "Propulsion and Staging Considerations for an Orbital Sortie Vehicle (Stengel, 1987):
https://joema.smugmug.com/Aerospace/...6t/i-nKLmZSR/O
Original paper (PDF):
http://www.princeton.edu/~stengel/Prop.pdf
A reusable air-breathing first stage does seem compelling and has been discussed and studied many times. The problem is it requires a very large, very heavy, very complex hypersonic airbreathing launch vehicle, whether that is Mach 7 or Mach 12. Maybe a lower, more achievable staging velocity is the answer, providing a lighter, less expensive launcher?
E.g, assume launch vehicle is twice the gross weight of an XB-70 (about 1 million lbs), and can reach Mach 5 @ 120,000 ft. Mach 5 is a good number because it is (barely) within ramjet limits so avoids the uncertainty, development risk and extra mass of scramjets.
Assume it can carry twice the XB-70 external payload, about 100,000 lbs. Given a Mach 5 running start, could a 100,000 lb winged manned orbiter reach orbit with any useful payload?
The X-15A-2 had a mass ratio of about 0.72. We'll assume technical progress improves this to 0.8. The XLR-99 engine had an ISP of about 256 sec. Assume ISP improves to about 314 sec. Rough guess at exhaust velocity: 3000 m/sec. Using the rocket equation, this gives:
delta V = Ve * ln (full mass/dry mass)
delta V = 3000 m/sec * ln (45000 kg / 9000 kg)
delta V = 4828 m/sec (10,800 mph)
This would give a final delta V (launch ship + drop ship) of roughly 6,528 meters/sec, far short of 8,000 m/sec orbital velocity.
Thus it appears a winged, manned orbiter could not reach orbit -- even with zero payload -- if boosted to Mach 5 by a ramjet-powered XB-70 successor with double the payload capacity.
Air-breathing winged launchers and winged orbiters look cool, and have long been romanticised. However in the real world they don't work that well. This was discussed by Henry Spencer in the article "Rockets, not air-breathing planes, will be tomorrow's spaceships":
https://www.newscientist.com/blogs/s...hing-plan.html