Schrollini wrote:Is that the figure for one or both SRBs?
Oh, don't I feel stupid. Yeah, that piecewise integration was each of the two SRBs, so the total work is 1.14e12 J.
I confess that I'm not sold on how you arrived at the value for total energy, though. For one thing, the exhaust velocity relative to the ground
should decrease over time as the rocket gains speed. And even then, I'm not so sure that total energy should be represented as the kinetic energy of the propellant. Wouldn't the total chemical energy be the kinetic energy of the propellant plus
the work done to the rocket?
The SRBs are jettisoned at 150,000 ft (45 km). There's essentially no air up there, so atmospheric drag losses should be minimal for the rest of the ascent.
The pressure in the stratosphere is around 1/1000th of sea level pressure, so yeah, there shouldn't be much more drag. But still some. For reference to the larger question of a lighter-than-air high-altitude launch platform, note that the highest unmanned balloon went to 173,900 feet, so it's unlikely that our launch platform would be able to go any higher than the point of typical SRB jettison. The major difference, of course, would be that our launch vehicle would have to start at this altitude from negligible velocity.
The advantage is that we don't have to spend energy on the drag from ground to (this) altitude.
The sum work pre-jettison is 1.45e12 J. At jettison, we've lifted the two empty SRBs, the orbiter, and a tank that is still around 75.6% full (a sum total of 876 tonnes) to 45 km at a velocity of 1.34 km/s. The combined KE and GPE here comes to 1.17e12 J, meaning this first stage costs 2.8e11 J in drag, or 19% of total work done up to that point.
However, note that the KE and GPE of the SRBs (182 tonnes, for a total energy of 2.44e11 J) is also wasted. All in all, this is 5.24e11 J wasted, or 36% of our work-done. Which means our actual launch vehicle can be that much lighter.
It's not currently feasible to launch a SSTO ship using a hybrid turbojet-scramjet engine as the primary stage. The efficiency is higher, but the weight of the fuel to get up to altitude/velocity is just too much. By eliminating the drag and lost energy of getting up to altitude, perhaps a hybrid turbojet-scramjet engine would be more feasible. One could envision a couple of small boost rockets (much cheaper than the SRBs) used to launch from the high-altitude platform, then a ramjet/scramjet to push up to near-orbital speeds before using a short burn from the OMS to jump into orbit. This would almost completely eliminate gravity drag, as the rockets would never be thrusting vertically except during orbital insertion.
I'm sure the shuttle is thrusting almost horizontally from here on out, so gravity drag losses should also be minimal. So the work done on the vehicle after separation should be almost equal to the energy gained between separation and MECO. This appears to be somewhat off: 1.1e13 J of work after separation and somewhat less than 5e12 J energy gained. Either there's more drag than I expect, or one of these numbers is a bit off.
One consideration: at SRB jettison, the thrust-to-weight ratio of the SSME is less than 1, and so the altitude actually declines for a bit before the mass of the system decreases enough to begin climbing. That may be the source of the discrepancy.
But for the purposes of a vacuum zeppelin launch platform, it's that first stage that we're most worried about.
Our real goal, I think, is to make the launch vehicle as small and as reusable as possible.
I'm a little suspicious that the SSMEs do 30x the work after SRB separation as before. But they are essentially release energy stored in the fuel during the first phase of liftoff, so it's not crazy.
Yeah, it seems odd, but if you're looking at the total remaining chemical energy, you have to factor in the kinetic energy of the propellant at SRB jettison. With 75.6% of its propellant remaining, that's 554 tonnes with a kinetic energy of 4.98e11 J, which is hardly shabby.
The one number I'm still suspicious of is the distance covered during the downthrottling phase. 18,600 km is nearly half the diameter of the Earth, and it's an order of magnitude more than the total displacement calculated earlier for the total launch period. But since this number goes into subtracting
from the work done by the SSMEs, it's not a major factor; even if it's seriously off, that's only adding conservatism.
So let's say we can build a floating launch platform at 150,000 feet. What then?
We could consider a turbofan-to-ramjet-to-scramjet approach, since our fuel requirements are going to be much lower, but carrying a turbofan into orbit will probably be more trouble than it's worth. I think a mini-SRB is a better bet. Can we do a disposable-solid-rocket-to-scramjet-to-OMS launch? We need to get to at least Mach 5 before a hybrid sc/ramjet will function. Thanks to the stratopause, the speed of sound at 45 km decreases significantly, so that Mach 5 is only 1.64 km/s. Limiting acceleration to 3 g
s would require a solid-rocket burn time of at least 55 seconds, at which point the boosters would break away and the scramjet engine would take over. The ship's body need only provide sufficient lift (at 1/1000th of an atmosphere) to counteract gravity during that boost phase.
How small of a launch vehicle can we realistically construct? If we want to use this to ferry either people or cargo into orbit (with the ultimate aim of dramatically reducing the cost/kg of orbital launch), what's a rule of thumb on payload size? Should we try to replicate the Shuttle's payload, or go with something more modest?