Well, I think arguments based on mass ratio and “average” Isp are too crude to get you anything useful for ramjet (or any other airbreather). You need a real cycle analysis, which should be a subroutine in a real trajectory code, or which you can use for point performance calculations over a flight envelope for empirical correlation. I’ve done both, they’re both effective approaches to first order. Fixed averages are not. Sorry, that’s a simple fact-of-life.
You do need to understand thrust and drag accounting, because if you don’t, it is really easy to leave out some very important drag forces in your force balance. I’m not talking about basic ram drag here (the “airbreather’s burden”), I’m talking about things like additive drag, spillage drag, diverter drag, and bleed drag. These are quite important, both at takeover, and at very high flight speeds. These are neither trivial to understand, nor trivial in their effects. You need some training in propulsion aerodynamics for these. This isn’t basic physics textbook stuff, and never will be.
All this stuff will be in my ramjet book, which is not yet ready for publication. Its intended audience is engineers working in ramjet propulsion, whether for missiles, or for launch vehicle work. I’m still trying to “rough-write”-down all the topics, but I think I have most of them documented in rough form, just not all of them. All this stuff is currently very rough first-draft stuff, and will need extensive re-organization and re-write, before it is book-ready. But, I really am working on it.There are two speed ranges for ramjet design, “low” and “high”. Low speed range designs have simple pitot (normal-shock) inlets, convergent-only nozzles, and can be ignited at subsonic speeds. They will show nacelle thrust greater than drag down to very low speeds, but will have specific impulse lower than composite solid rocket, below about half a Mach number. Peak specific impulse potential is at about Mach 1.1 or so, at about half or 2/3 the max Isp potential of supersonic designs. Max useful speed is about Mach 2, or maybe Mach 2.5 at the very outside. With hydrocarbon fuels of almost all types, about the biggest nozzle throat/combustor area ratio is 0.65, limited by flame-holding considerations. Performance at lower area ratios is inherently lower.
High speed-range designs feature external compression features like ramps or spikes that protrude ahead of the inlet cowl lip. They also have almost-zero thrust potential below about Mach 1.6 to 2. But, they work just fine to about Mach 5-or-6, depending far more on vehicle drag characteristics, than anything about the ramjet engine design. With kerosene fuels, peak Isp potential is around 1200-1300 sec at about Mach 2.5-ish, lower slower, and lower faster. Nozzles are C-D, but exit “bell” area ratios are closer to 1.5-max, than anything to do with the expansion ratios one sees in rockets. With hydrocarbon fuels of almost all types, about the biggest nozzle throat/combustor area ratio is 0.65, limited by flame-holding considerations. Performance at lower area ratios is inherently lower.These things can be very lightweight, depending upon whether it has to be re-usable or not. The “best” designs have been one-shot missile designs, with an ablative combustor liner, for missile speeds up to about Mach 4. External heat protection is also an issue, from about Mach 3 on up for reusable designs, even with steel construction. There are air-cooled perforated liner designs from the 1940’s and 1950’s that would actually work to Mach 6 on a transient, exclusive of external heat protection problems. There are ablatives that would work externally to Mach 6 on a transient, but these have replacement issues. Missiles generally always use ablatives inside, and maybe outside, if needed.
There is my oddball ceramic-ceramic composite combustor liner material, which offers considerable potential for a re-usable combustor. It might also serve as external heat protection, for a fully-re-usable design. This is still an experimental material, though. (See also the 3-18-13 posting "Low Density Non-Ablative Ceramic Heat Shields" below).
Ramjets require boosters to reach takeover speed: about Mach 0.5 to 0.8 for “low speed” designs, and about Mach 1.6-to-2 for “high speed” designs. For one-shot missile applications, the best choice has proven to be the “integral rocket-ramjet”, wherein a solid rocket booster is cast or loaded within the ramjet combustor. This requires an appropriate ejectable booster nozzle nested within the ramjet nozzle, and some sort of inlet duct obturator, usually ejectable or frangible port covers. Re-usable launch applications might well be “best” with parallel-burn rocket and ramjet engines in the same airframe. It really helps if the rocket and the ramjet use a common fuel.
From a flame-holding standpoint, I think the dump combustor has “way-to-hell-and-gone” more potential than the V-gutter, or can, or “colander” (or any other type of obstruction-type) flameholder. Dump combustors have very little sensitivity to dump plane speeds, compared to any of the blockage-element types. Variable speeds at the dump are inherent with launch accelerators, whether vertical-launch or horizontal takeoff. Almost no textbooks describe dump combustors. My book will.Ramjet liquid fuels can be any kerosene (or kerosene-like synthetic), or any liquifiable hydrocarbon. The early engines with subsonic ignition used mainly low-grade gasoline. Today, in supersonic-inlet designs, JP-4, JP-5, JP-7, Jet-A, Jet-B, Jet-A1, RP-1, K-1 kerosene, a synthetic variously known as RJ-5 or Shelldyne-H, and even liquefied methane, are all very attractive candidates.
I have even used propane, but it and LPG are not all that attractive, for their inherently-heavy fuel storage considerations. LCH4 will require extra care to insure full vaporization, and extra care with flame-holding issues. RJ-5 is a synthetic that resembles kerosene, except that its density is substantially higher. It was used in ASALM-PTV, with one test that reached Mach 6.
I hope the book might be available in a year or two. It’ll be the ramjet analog to the famous (or infamous) “drag bible” written long ago by Hoerner.
The "high speed range" ramjet designs would be most applicable to a horizontal-takeoff (HTO) two-stage design featuring a winged airplane as its first stage. The most important consideration for selecting the best staging point seems to be as fast as possible. The upper speed limit for the ramjet airbreather is about Mach 5 to 6.
This is limited more by the vehicle drag, than anything to do with the ramjet design, although the minimalist variable inlet geometry of constant shock-on-lip seems to be the best enhancement one could try. Max specific impulse (Isp) potential with hydrocarbon fuels is about 1300 sec near Mach 2-to-2.5, and about half that, at the upper and lower ends of the speed range.
Scramjet (supersonic combustion ramjet) might fly much faster, but has a far higher takeover velocity (Mach 4, 1.2 km/s), and (worst of all) is simply not technologically-ready for application. The inlet, combustor, and nozzle geometries for scramjet are completely incompatible with those of the ramjet. If included at all, it would have to be yet-a-third engine type carried on the first stage. That tends to increase both stage inert weights and vehicle drag. Heat protection is also an extreme problem above Mach 6, especially for shock-impingement zones.
As a second-most important consideration, this ramjet staging point is deeper in the atmosphere than most people would assume: only about 60,000 feet (18.3 km). The frontal thrust density of the ramjet depends very strongly upon ambient air pressure, and it simply takes too long to accelerate if the air is any thinner than that. As it is, there is no thrust margin-over-drag at max speed to support a climb, without serious and sudden deceleration. That means rocket thrust from somewhere must be added, to support a short pull-up maneuver transient at staging.
(As an aside, scramjet suffers from almost exactly the very same thin-air altitude limitations.)
The third-most important consideration at ramjet staging is the pull-up trajectory path angle. Something around 40 degrees above horizontal seems to be about right. This relieves the second stage of any lift (or major thrust vector) capability required to pull up. It may simply fly a ballistic gravity turn trajectory from staging. This is a serious consideration, since the delta-vee (mass ratio) required of the second stage is quite significant. That's because Mach 5 to 6 at 60,000 feet (18.3 km) is only about 1.5 to 1.8 km/s velocities. A total of 7.7 km/s plus gravity and drag losses is required to orbit.
This leads one to a combined rocket/ramjet winged HTO aircraft as the first stage. It could carry either a rocket pod or a rocket airplane as the second stage. The characteristics of this first stage aircraft, if a truly reusable design, would resemble more a supersonic bomber, than any of the prior space launch vehicles we have ever flown, including the shuttle. There is a practical size limit, which makes this (most likely) a small payload niche application, probably around 5 tons max.
It would take off in rocket power, accelerate on rocket to takeover speed, then climb on ramjet. Once at altitude, it would pull over level and accelerate in ramjet to stage speed. With some rocket help, the vehicle pulls up sharply for second stage release. Then it cuts off rockets and throttles-back its ramjets, and returns to launch site in ramjet thrust at low supersonic speed (for best range). It's a dead-stick glider for landing, except for enough rocket propellant reserve to support a "go-around".
Update 9-12-13: new concept I hadn't considered before. One could pull up in parallel burn, but not stage yet. Transition back to all-rocket, and climb to staging at a little bit a higher speed and altitude. The first stage airplane is a bit bigger because it has to contain more rocket propellants. But, the faster and higher the stage point (at steep path angle), the lower the velocity requirement imposed on the second stage, and the bigger the payload it can carry to orbit. It'll be some sort of tradeoff of payload vs first stage size, probably constraint-limited by the square-cube law scaling "landing gear" problem at launch weight.
I don't yet know whether ramjet-assist to a vertical-takeoff (VTO) launch rocket would actually be worthwhile. But for the VTO rockets we are accustomed to designing, the vehicle leaves the sensible atmosphere (max 80,000 feet, 24.3 km) at speeds near Mach 2 (only about 0.6 km/s). So, I am sure the "low speed range" ramjet design is best suited, and should be staged off for recovery at that thin-air point, long before the first stage rocket core burns out (typically well outside the atmosphere at about 3 km/s).
This kind of ramjet provides useful subsonic thrust from about 0.7 Mach (about 0.2 km/s) up to the low supersonic speed at staging. (Mach 2 is about the max useful speed anyway.) Max Isp potential of this kind of design is about half to 2/3 that of the supersonic types, near Mach 1.1-to-1.2, and half or less of that, at the slow and fast limits. I rather doubt that such ramjet strap-on pods would ever exceed about 25% of the thrust at low altitudes, far less as the staging point is approached, but I could be wrong, as I have not yet fully researched that kind of design.
But, if this is actually attractive, the way to make it reusable is very definitely the strap-on pod approach. Even with ballistic fall-back, recovery will be very near the launch site. I rather suspect that some kind of folding wings and fins would turn the strap-on into a big remote control aircraft, that could be runway-landed, on land adjacent to the launch site. The logistics of that offer very low recovery and refurbishment costs.
VTO rockets are always short on takeoff thrust. The integral booster approach, one-shot as it is, might well actually be very attractive, as a takeoff thrust enhancement available from the ramjet strap-on pod. This does put some limits upon the internal combustor heat protection scheme, since solid rocket pressures are quite high. Ablatives may be the only practical answer.
For such strap-on pod designs, it would be well to separate the combustor/booster case from the tankage and inlet hardware. These cases might (or might not) be refurbished and reused, while the rest of the hardware definitely could be easily reused.
Update 9-12-13: Another thought for the two stage airplane scenario would be to solve the square-cube law "landing gear" problem by going to vertical launch, then bending over to the same flattish ramjet acceleration to Mach 6, before pulling up again to stage. That's a thrust-enhanced turn deep in the atmosphere: gravity and drag losses are simply enormous. Plus, to get the far larger takeoff thrust, it'll drive you toward integral solid rocket boosters inside the ramjet engines, a major limitation on designing for reusability. So I don't recommend going that way, for technical reasons, not to mention the psychology.
The psychology has to do with traditional rocket launch-type thinking versus traditional aircraft-type dispatch thinking. Vertical rocket launch, especially with one-shot components like integral boosters in the ramjets, leads to designs that have enormous logistical support tails. In contrast, thinking like an airplane leads one toward very low logistical support, and thus very much lower costs. This "high-cost rocket launch logistics thing" has been true of government designs since the end of WW2. SpaceX and ULA commercial launch rockets with reduced logistics that reduce cost are the recent exceptions that actually prove the rule.
Better to look like an airplane so you think like an airplane. You're far more likely to get to a lower launch cost that way.