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I once built several 2-D trajectory codes out of the concept below, when I was young. One of them was for vertical ballistic launch, the rest were quite different problems. It matched real ballistic (nonlifting) flight performance very well. I might even still have it, but none of these modern PC's and Windows versions now supports the advanced BASIC language that I wrote it in. It was meant for a DOS machine, not Windows. The last Windows variant that still could execute it in its DOS emulator was Windows 98. (I still have a working antique like that. Every time I power it up, I wonder if it will die this time.)
Here's the concept:
Along the flight path forward acts thrust, which you can set as a user-defined set of inputs. Also, drag in the reverse direction, which varies with speed squared and density, and as an empirical coefficient as a function of Mach (different for each stage). The flight path makes an angle to the horizontal, but starts out nearly vertical, usually only about half a degree off vertical. Weight acts vertically downward, but that is related to thrust by the massflow rate, and by the stage configuration. As you climb, gravity really isn't constant, either. (What I wrote was flat-Earth 2-D, but the same stuff can be programmed into spherical-Earth coordinates.)
You can use a simple forward-stepping estimate, if you choose the time step small enough. Long ago we had to be more sophisticated (such as Runge-Kutta), but with the advent of 486 PC's that was simply no longer necessary. Just calculate thrust, drag, and weight at the current time, and ignore their change over the short interval. Keep it really short, though, like under 0.1 second.
When you talk about "gravity loss", you are really talking about the effects of that non-constant vertical weight vector, integrated over time.
GW
Oh yes, X-15 was suborbital. But it did fly in space, it was rocket-powered, and each of the 3 airframes flew lots of times with very minimal ground support. The 40% inert fraction plus its record proves it was tougher than an old boot. (Actually, that service record is because it was tougher than an old boot.) So, that's what you want out of your BDB. 40% inert is no magic number, but I am certain the "right" number (for tougher than an old boot) is one whopping lot more than 8-10%.
There is a size effect for structures: weight (loads) scale as dimension cubed, while strengths scale only as dimension squared. Thus strength / weight ratio scales inversely with size, all other things the same. Gigantic vehicles end up in the same situation as water balloons supported by nails. An easy way to get around this is to build your gigantic stage as a cluster of much smaller tankage, and recover each of them separately. Not every tank needs its own engine, either.
The current optimal throwaway designs to LEO are two-stage rockets, with each stage around 10% inerts. The first stage delivers around 10,000 ft/sec delta-vee, more thrust-limited than Isp-limited, so kero-lox has been hard to beat for decades. The second stage operates not so vertically so it delivers the other 16-17,000 ft/sec, and is more Isp-limited than thrust-limited. Second stages are also physically smaller, so you can match or reduce diameter relative to the first stage, even with a super-low density propellant. That's why LH2-lox works so well.
Built tougher with higher inert fractions may require reverting back to three stages, in order that payload doesn't shrink to zero. That doesn't really make it much more complex (the 3-stage Minuteman was pretty simple, after all, and so was the 4-stage Scout), but by reducing the delta-vee from each stage, one can tolerate existing Isp's and thrust levels, at substantially higher inerts. Higher inerts mean tougher, which can mean smaller logistical tail (not guaranteed, it's more of a cultural change). That's how you make it cheaper, if you can really pull it off.
It's the last stage that worries me the most. I think it needs to burn three times (or even more), to achieve orbit along with the payload. That's not such a dumb, utterly-simple vehicle. That way, the payload can be completely inert dead-head cargo, and, you can ensure the last stage comes down exactly where you want it (it's the lower stage or stages that come down far downrange). I just don't yet have a clear picture of how best to survive reentry with a shape like that, and still be recoverable and reusable. Reentry is really tough. Mach 10-ish hypersonics are not all that bad. Mach 25? Really tough.
GW
Joshnh4h asked about his rocket trajectory. I haven't digested all of this. Old guy, slow. Also about limited trajectory distance over which ramjet adds energy: true enough for vertical launch, that's what worries me about the attractiveness of it. For HTO staged aircraft, the range spent in the air is quite long: that's why it looks so good.
Hop said something about a turbojet/ramjet aircraft. That looks pretty good, and could very well be integrated into the same engine. It would be one step past the J-58's that powered the old SR-71. Those had a 25% of airflow bypass after stage 3 compression, straight to the afterburner duct, meaning 75% of the air still went through the turbine core. Limited to about M3.8 max because of blading temperature problems at both ends of the spool.
On the other hand, if you rigged a 100% bypass capability that you could modulate 0-100, from the inlet straight to the afterburner duct, you could shut down the core turbine (to protect it, and just run the afterburner as a ramjet. Should be capable to M5 or 6.
Depending upon the arrangement, a ramjet pod or nacelle need not be complex or expensive, and can be tough as an old boot. With some sort of recovery built onto it, items like that should be more recoverable than the rocket stages we have so much trouble reusing. I'm thinking a stowed swing wing down the side, skids and a nose wheel, and R/C controlled glideback to a runway.
A ramjet airplane for HTO would be even easier. No integrated engines, just parallel-burn with separate rockets and ramjet. It's just stick-and-rudder flying. The ramjet is your fuselage. Your fuels and propellants go in the wing, the rockets go in the wing strakes, and the pilot goes in the inlet centerbody spike. The payload goes on the back.
GW
The drilling problem must be solved somehow. They did little hand cores a few centimeters deep standing on the moon. It has to be possible. It may be an art that needs to be learned that is peculiar to Mars, I dunno.
But deep drilling is the only reliable way to learn what is really underfoot, same as here on Earth. Without it you cannot truly explore: answer the two deceptively-simple questions (1) what all is there? (2) where exactly is it? To do less than answer those is but a negligible step beyond flag-and-footprints. What's the point of that?
We never really explored the moon, because we never really even tried to answer those two questions until recently.
GW Johnson
Mechanical counterpressure really is the way to go, since mobility is crucial for real exploration/investigation capability. The thing holding it back is materials not capable of 0.33 atmosphere mechanical squeeze. Unnecessary requirement, all that is needed is 0.2 to 0.25 atmosphere, and that was first done successfully back about 1969.
GW Johnson
Whatever basic rocket idea you use, re-usable or not, the real cost is the logistical tail behind it. NASA is famous for being expensive at $1B per shuttle launch (well, until recently, anyway). Why? It took the population of a major American city to support every launch, when you count all the contractors, subcontractors, and vendors. I bet $1B/launch didn't even cover the real costs - that's a lot of people to hire!
Now think "stick-and-rudder" into the black. Maybe a ground crew of under a dozen. You can throw the entire vehicle away and still be cheaper, if you can operate like that. But you cannot put all the bells and whistles on it. Not so extreme, but the same basic idea, is exactly why Spacex is so much cheaper than the majors. Nothing too hard to understand about that.
OK, now add real reusability, which means this thing (or "things" if multi-stage) have to take the abuses of spaceflight for years or even decades. You're going to have to build it tougher than an old boot to take that kind of abuse that long, and still keep the support crew small. There's simply no way around that dilemma. It also means you have to supply enough structure to take that kind of punishment: these 8-10% inert weight fractions I see bandied about are not even in the ballpark for a cheap system.
The most reusable, inexpensive rocket vehicle in all of history was the X-15. Its inert weight fraction (exclusive of its B-52 launcher) was 40%, which is not all that far from the typical supersonic bomber's 50-odd%, and not all that far from the B-52 itself. 3 X-15 airplanes flew 199 times over 2 decades, with only 1 complete airframe rebuild, and that was after destruction in an explosion in ground test. Nice record, for a manned rocket of 1955 design vintage.
GW Johnson
I hope the E-cat guy is for real. Historically, our best, most dramatic advances took place when somebody upset the applecart of conventional wisdom. It's way past time this happened to the "fusion business".
GW Johnson
Actually, any practical system capable of a flight to an NEO is capable of going to Mars. You just add landers. It's not so much the delta-vee and flight times, it;'s actually crew survival that drives what you do. If you fly weightless, you have to fly fast: one year max is demo'd on the various space stations over the last few decades, and we do not know that Mar's 0.38 gee is enough to be therapeutic. Otherwise, go 9 months one-way, several months there, and about 9 months home, and provide just about 1 gee by spinning the ship end-over-end. There's no way anyone will stay sane cooped up in any capsule; we'll need a Skylab-like module to live in. The bigger, the better. Think orbital rendezvous and assembly here, and orbital rendezvous (like the Apollo missions) at Mars. You'd better start thinking nuclear thermal rockets, maybe even gas core. You might also start thinking about the real point of going there: is it flag-and-footprints like Apollo, or is it real exploration to find out what exactly is there, and where exactly is it?
GW Johnson
Hi gang:
This is GW Johnson the old aero engineer, and ramjet expert from long ago. I surely am glad to see the forums up and running again.
In recent news: I have picked up a consulting client for a possible ramjet launch effort. And, that client and I both think I may be just about the last living US all-around expert in ram propulsion (I seem to have outlived the rest).
I’m particularly glad to see LEO access under active discussion, especially with Josh and Hop talking about reusable vehicles, and perhaps ramjet assist. The last stuff I had is a posting over at http://exrocketman.blogspot.com, where I looked at horizontal takeoff and landing with a winged first stage using separate rocket and ramjet power. That article is dated August 22, 2010, so it’s way down the list (chronological, latest on top). There’s a navigation tool by date and title on the left, under my photo. It looked to me like a staging condition of near Mach 6 at around 60,000 feet altitude might well work out, including booster flyback. And, it looks like ramjet might really pay off in this scenario.
Josh is exactly right: the frontal thrust density of ramjet is too low to support vertical acceleration of a heavily-loaded vertical launch vehicle on ramjet alone. But parallel-burn of otherwise-separate rocket and ramjet might offload some of the thrust requirement temporarily onto the higher-Isp ramjet, thus swapping a smidge of rocket propellant for a smidge of extra payload. That kind of vehicle is moving only around M2 at 60,000 feet, so it’s a “low-speed” pitot inlet design, not the “high-speed” spike inlet that makes sense for the ramjet launch airplane. Whether this idea is actually technically and economically attractive in vertical launch, remains to be seen. I just dunno, yet.
You can think of “high-speed” systems being some sort of spike or ramp inlet, a dump combustor, and a very mild-expansion convergent-divergent nozzle. Min Mach number is around 1.5, and max is around M5 to 6, depending more on vehicle drag than the ramjet design itself. I looked at nose inlets, but side inlets also work. Peak performance is around M2 to 3, and frontal thrust density falls too low to provide effective acceleration above about 60,000 feet. It doesn’t matter a lot whether you analyze RP-1 or JP-5 kerosene, or even RJ-5/Shelldyne-H synthetic, they all come out similar in proportions and performance. I think liquid methane would look very similar to kerosene, too.
“Low speed” systems are a simple pitot (normal-shock) inlet, most likely a nose inlet, a dump combustor, and a convergent-only nozzle. Min Mach is a tad fuzzy, there being thrust greater than drag (in low-drag nacelles) down under Mach 0.5, although Isp is over kero-lox rocket levels only above around Mach 0.7-ish. Max Mach is around 2 to 3, depending more on vehicle drag than the ramjet, with max performance around M1.5 to 2. I think thrust densities fall too low to be useful for acceleration above around 60,000 feet, although this remains to be seen for sure. Again, specific fuel choice is not all that important.
Whatever I do come up with, I’ll let y’all know. This stuff is fun. I haven’t done any of it in almost 2 decades, now. I think I’ll turn my old how-to notebooks into a published book. Otherwise, the art will die with me. (It’s still mostly art, until I can get it all written down). That ain’t easy.
GW