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Merry Christmas and Happy New Year, guys.
Hoerner also had a lift book, in addition to his drag book. Same self-published thing. Probably obtainable from Amazon, although I have never looked for them there. I have both in my library.
There's way more in them than most of y'all would ever need. It's arranged a little backwards, as Hoerner was a German. Sort of reverse, like the grammar. Fun to look at, though.
Look in the supersonic section for projectile drag. pretty close to just about any launch rocket drag. His plots go up as far as M6. Most rockets leave the sensible air at about M2 to 3. Good enough.
The real trick is getting the "transonic drag rise" modeled - that's part of the max Q worry we've heard about for decades. Biggest CD at near-M1 just before the density starts tailing off fast as you rise up past 30-40,000 feet. Biggest forces on the structures.
GW
I have two big points to make about the costs of spaceflight, manned or unmanned.
One is the impact of a small supporting logistical tail, vs the traditional gigantic one. ULA supporting the shuttle at a billion dollars (or maybe more) for 25 metric tons max per flight is the wrong approach. Spacex at $2500/lb on Falcon-9 is more like it. Atlas-5 is similar, but watch that cost rise if something happens to Spacex! That gigantic entity of Boeing plus Lockmart requires a lot of cash to feed it. Too big is just plain bloated.
The 53 metric ton Falcon-Heavy is supposed to fly next year for the first time, priced at something around $800-1000/lb. With that coming to the market, why do we need a NASA SLS at billion-dollar shuttle prices and only 100-150 tons? We know how to dock and assemble in orbit now.
The other big point is the type of lead agency and contractors that can support such endeavors without exploding overruns. We don’t have that, and it kinda shows. What we have done for half a century since Sputnik is the wrong way to do it. It’s not about flag-and-footprints, it’s about real exploration.
I gave a paper on that very topic at last August’s Mars Society convention in Dallas, Texas. You can find that paper online at the Mars Society’s site, in its electronic archive. Or you can read a version of it on my blog site http://exrocketman.blogspot.com. Scroll down to the paper at date 7-25-11 titled “Going to Mars (or anywhere else nearby)”, and see also my second thoughts about the backup scheme, in the article dated 9-6-11 titled “Mars Mission Second Thoughts Illustrated”.
The gist of the exploration definition is getting the answer to two deceptively-simple questions: (1) what all is there? and (2) where exactly is it?
That wording is not Texas slang, I meant it exactly as written, word for word.
It means you land and you dig deep and you drill very deep. Drilling kilometers down, perhaps. You have to do this in a lot of sites, too. A real planetary survey. We never even did that on the moon, so we still don’t know what is really there, even today. And none of 4 decades’ worth of robot landers has actually answered those questions for Mars.
The gist of the “right team to do it” question is that the NASA we need is not the NASA we have, and the contractor base we need is not the contractor base we have. If we had the right team, we could go to Mars at any time for under $50B, and make dozens of landings in one trip. The right contractors would look more like a Spacex, an XCOR, or a Scaled Composites. I still don’t see any credible agency or entity to lead it, not in the US, nor in Europe or Japan. Japan may come the closest, but still misses the boat by a wide margin.
It would take too long to justify all these assertions here. I suggest you look at my convention paper, or at the two cited blog site articles.
There is a third idea in the conversation thread here: reusability. Implementing reusability in one form or another is a lot less effective than reducing logistical tails, toward reducing spaceflight costs. It’s also a very tough technological nut to crack, but it can be done, at least for lower stages.
There’s a third article on my blog site, dated 12-14-11 and titled “Reusability in Launch Rockets” that addresses what might be most fruitful things to attempt.
GW
Then again, you have to consider where the exposure standards came from: best guesses based on folks exposed. Linear dose rate models do not work. The low-exposure limits are very, very crude best-guesses based on aging Japanese A-bomb survivors, and troops exposed in tests in Nevada in the 50's.
Most old guys like me were exposed to a lot more radiation than 1 rem a year just from watching early-model TV's with unshielded Klystron tubes in them. Momma always said don't sit too close, but never knew why. Now we know: a lifetime's X-ray in a week to a month, sitting within 6 feet. I'm still here. Most of us this age still are (for a little while yet).
So, I don't really see much problem with 25-50 rem /year exposure "for a while". The career limits are more doubtful. I honestly don't know. The original WW2 standards were 25 rem a year, no career limit. A lot of those guys had problems, a lot didn't. Hard to know why and how.
I guess my point is that the low-dose standards are really guesses, not such hard science after all. The harder science is the high-dose standards. Things like 25-50 rem in a week, that's going to kill some percentage of those exposed, and within days. It's a certain thing. We've seen it and measured it, directly.
GW
Josh:
Use the simple jiggered rocket equation analysis technique to help you pick the problems to run with your trajectory code. dVo = Vex ln(MR), where Vex = Isp*gc is a useful approximation, and fprop = (MR-1)/MR, for which 1 = frop + fpay + finert. Actual dV = dVo/factor, to model gravity and drag losses. For lower stages flying in air and nearly vertically, I use factor = 1.10. For upper stages flying in vacuum and more horizontally, factor = 1.05. This kind of thing will get you started by landing you in the right ballpark.
Trajectory analysis takes more effort, but is more reliable. Usually, weight statements are no problem. Real thrust vs flowrate and real backpressure effects require some real knowledge of rocket engines and nozzles. The toughest nut to crack is realistic air drag. The best source of actual drag data that I know is Sighard F. Hoerner's "Fluid Dynamic Drag", which his widow published from her home until she died. I doubt it's available anymore, except in a library. Hoerner was one of the aerodynamics guys on the ME-109 before WW2. He had all kinds of stuff in his book, including hypersonics.
GW
For annual cosmic radiation exposure limits used for NASA astronauts, see Table 1 from http://srag.jsc.nasa.gov/Publications/T … chmemo.htm for the 50 rem that I have been using. You can glean from other sites that cosmic radiation fluxes in near-Earth space are modulated by the strength of the solar wind to between 60 rem and around 30 rem.
Most of the 22-year solar cycle, in-space exposures are within the 50 rem limit. On the surface, remember that exposure is cut in half, because the planet beneath your feet is a shield against half the sky. Shielding might not be true for small bodies like asteroids.
The problem is Table 2, the career exposure limits to cosmic radiation, which limit you to around 2 or 3 years in space. Remember, there really isn't a practical shielding technique for radiation this energetic, because of the secondary showers it creates.
For an exploration mission to Mars, a 2 year voyage is OK, but don't ask them to fly again, under these rules. With thick roofs or underground habitations on the moon and Mars, exposure should be tolerable, but will likely violate career limits after 5 years or so, due to secondary shower effects. The only real thing a meter or 10 of regolith can protect you from is solar flare radiation, not cosmic rays.
Shoot, we get hit with cosmic rays right here on Earth, some primary, some secondary shower coming down from our own atmosphere, the mass of which is the real shield. Our magnetic field turns solar flare particles, not cosmic rays.
BTW, average Earth natural background radiation (of all types) is around 0.3 rem annually, the top third of which is radioactive emissions from coal plants. This value varies widely around the planet by a factor of 10 or more. It's pretty variable.
GW
Like I said before, I hope the guy is right. We could use some clean fusion power.
This E-cat stuff would be outside the realm of "accepted science", if it is true, not a fraud. That doesn't bother me a bit. When the universe doesn't conform to our precious theories, it's time for some new theories, I always say.
But then, I'm an engineer.
GW
Cosmic radiation is not the bugaboo that everyone thinks. The max radiation exposure occurs during solar minimum, and is just a tad beyond the yearly dose we now allow astronauts to receive anyway. At solar maximum, this exposure is cut in half by the solar wind, so that for most of the 22-year sunspot cycle, cosmic ray doses are under what is already allowed.
The real radiation danger is not cosmic rays, it is solar coronal mass ejections. Those, not cosmic rays, are what our magnetic field shields us against. Mars has none. Fortunately, these are brief events, a few hours to a day or so. About a meter of water or dirt works pretty good as a shield. Nothing special there.
GW
Josh:
That's exactly what I did writing codes like that long ago. It'll work. Going to multiple stages is not very hard, once you get the basic algorithm working. You just shift weight statement and drag, plus any thrust controls, at staging. It'll take some idiotic fractional time step to exactly hit the stagepoint. That's the hardest part, and it's not that bad.
GW
I'm thinking some sort of steel-making plant is one of the first things a permanent base will need. Shipping the plant once (whatever it really is) is cheaper over the life of the base (decades+) than shipping steel stocks from Earth, almost no matter what the cost to LEO is.
The other is some sort of plastics-making plant. Not everything should be made of steel. Aluminum can come later. If you've got plastics and steel, you can pretty well cope for a while.
On Mars, concrete is going to be a bit of a problem, as limestone does not seem to be available, although water is. There has to be some equivalent with the minerals widely available there. It may take a while experimenting before we find it. But find it we must, concrete is just too useful to do without it. An ice-regolith composite reinforced by steel bars might serve in some applications, as long as material temperatures do not exceed 0 C.
GW
I assume you are writing a finite-difference solution to the equations of motion, presumably in 2-D. It won't matter much if you do it 2-D Cartesian or round-Earth. The easiest version is a 2 degree-of-freedom flying particle in 2-D Cartesian, I'd start there.
If at any given time step, you compute all the force vectors (magnitude and direction) acting on the vehicle (thrust, weight, air drag), their sum and the current particle mass gives you the acceleration vector direction and magnitude. This force sum includes the weight force, which then automatically accounts for the "gravity loss" as you "integrate" the trajectory. Acceleration times time step is the delta-vee vector increment to the next step. This delta-vee times time step is the displacement to the next step. The velocity change and position change take place in the direction of the acceleration vector, so you do components to figure the new 2-D vector position. It is easier and more useful to keep track of velocity magnitude tangent to the current path, as that is how drag is figured. This gives you the position and velocity at the next time step, where you do it all over again.
You will need to build a "model" of your vehicle with many facets. First is a good thrust model. That can be a large topic, even for a rocket, as delivered thrust and impulse are functions of backpressure and exit area, even at constant propellant flow rate. Second is a good weight statement, such as I had been calculating for Falcon-9 and the reusability trades I just did. Third is a good drag model, which requires coefficient vs at least Mach, and a suitable reference area, for each shape the vehicle takes on as it stages. The coefficients are most definitely not constants. You can pretty well zero the drag forces above around 200,000 feet, no matter how fast you are flying, as the density is becoming too low. But, you will need a model atmosphere, so you can figure speed of sound from ambient temperature, to calculate Mach for looking up the drag.
You have to keep the time step very small. Make no more than a 10% change in any physical condition such as velocity, weight, or thrust, in any given step. 1% would be more accurate. It is possible to use this to program an adaptive time step that is very fine near launch, but "steps out" bigger as the vehicle flies fast. You can do this in the very simple forward-stepping procedure I described above quite accurately. You don't need Runge-Kutta integration, that was for the ancient computers with kilohertz or slower processing speeds.
The hardest part is initial conditions. If you are doing an adaptive time step, it may get hung up at launch. Sometimes you have to give the vehicle a trivial upward velocity to succeed with the calculation. Maybe 30 cm/sec.
And all of that is what it takes for non-lifting gravity turn flight. Winged lifting vehicles require at least a 3-degree of freedom model that includes moment sums and pitch inertia, for just a 2-D Cartesian model. They also require pitch control as a user input, and a description of lift curve slope vs Mach, plus drag-due-to-lift vs Mach. Not for the amateur.
Hope that guidance helps.
GW
Last data I saw posted / projected for Falcon-heavy said $800-1000/lb to LEO, at 53 metric ton sizes. Of what possible attraction is an SLS at 8,000-10,000/lb? Only larger payloads? So what? We know how to rendezvous and dock.
There's very little we would want to do in the next few decades that we couldn't do with Falcon-heavy. I haven't been to Spacex's site lately, so I am not (yet) acquainted with any Falcon-super-heavy. But, Falcon-heavy is supposed to fly sometime next year out of Vandenburg AFB. I know they are building a new thrust stand here in McGregor, Texas, to accommodate an all-up Falcon-heavy test, at reduced noise.
GW
Don't worry about imperial units for me, I speak both. I just think a bit better in imperial, because that's what we used the most when I worked in the defense industry long ago. It's just practice, not a problem understanding.
Hadn't thought about methanol, might be a good idea. Not so sure about methanol-in-contact-with-N2O4 or any other oxidizer. Pre-mixed flammables and explosives are a bit scary. A lot of folks don't realize that methanol is a skin-absorption nerve poison. It is possible to absorb a lethal dose through the skin of your hands, if you keep them immersed for a few hours in a day. But, it's a very nice fuel material, solvent, etc, if you just treat it with a tad of respect. It is a bit corrosive to a lot of materials, especially polymers. Steel works OK, stainless is better. Aluminum, not so much.
GW
JoshNH4H:
I'm fast becoming a methane convert myself. Easier to make, handle, and store than hydrogen, no matter where in the solar system you are. Also usable in ramjets instead of kerosene (common fuel rocket and ramjet). I know XCOR is getting excited about methane fuel, too. Cleaner by far than any kerosene available. Far fewer injector orifice clogging problems. I kinda like all of that.
GW
Sure, but it's still deep burial for clathrates. It would be around 200 meters at 2C on Earth under a dirt overburden (that's figured at about 105 lb/cu.ft for loose dirt, vs 62.4 lb/cu.ft for fresh water). On Mars at 0.38 gee, it's almost 3 times that depth. That's a lot of digging. Building pressure tanks is probably easier.
One of the first things to import is probably a steel mill. Ha! Ha!
GW
The methane clathrate is stable on Earth in deep cold water. Most of what we know about is in the 0-2 C range, hotter comes apart. Most of what we know about is 300 meters deep or deeper. Shallower is unstable.
I rather like the plain methane myself. If we will be using chemical propulsion, it make a lot of sense in the first stage, because the volume is lower (less structure). I dunno about Mars, but on Earth, the first stage of a rocket flight is thrust-limited, not Isp-limited. Lower-Isp fuels like methane make better sense because of their higher density.
It is the second stage that is more Isp-limited, where hydrogen itself makes more sense. Methane and oxygen are easier to process and store than hydrogen, so for practicality, all-methane-LOX makes a lot of sense, even for an upper stage.
GW
JoshNH4H, you and Hop and Louis, don't desert us. This discussion is getting very interesting. Air drop launch has entered the fray, perhaps commercially.
I will keep my posts short here. Any long and technical stuff, I will post over at my "exrocketman" site. Y'all know where that is.
GW
More ice on Mars. True, but you have to get there first.
Without a space race motivated by something other than rationality (like last time to the moon), you have to bootstrap your way there, slowly. Too many with political clout dig in their heels about space travel. Gotta do this gradual to sneak it by them.
Right now, the moon is far easier to reach with the puny chemical rockets we have. The propellants for an initial trip to Mars (perhaps along with other stuff intended for use here at home) might be made robotically on the moon, instead of launched up from Earth. It's energetically very easy to ship stuff from the moon. Men might have to get involved in that shipment for safety's sake, which is a good excuse to fly beyond Earth orbit once again.
GW
Wait, I'm just trying to say that we don't know yet what Mars might have to offer economically. Whatever it is, it would have to be a very high value-added physical commodity, to justify the shipping costs. But, it might be an intellectual property, capable of being transmitted electronically. Or something else we simply haven't thought of yet. It will become clear, just give it time once folks are there.
I kind of doubt plain rocks would ever be that valuable. Lots of gold or diamonds might be, at least for a while before the market gets flooded. A supply of high-grade uranium or thorium might be worth it, if enriched and/or bred on Mars to high-grade fission fuels before transport to Earth. (Of course, that last would assume we get over our irrational fears about nuclear power, and proceed with rational solutions to the very real problems of waste disposal and plant vulnerabilities to natural disasters.) Not very likely for a while yet.
I quite agree that what I called "prospecting" would naturally occur, once manned bases get put on Mars. And having robots there working with the men at short distances, is exactly what needs to be done. I rather think we ought to do some serious exploring, based from orbit, at many landing sites, in a single first mission. Then the best 2 or 3 sites get the initial surface bases on the next mission, after we've had time to digest all the data from the first mission.
That's the most practical way to identify what actually might support a future colony. If you don't do that, the colonies never prosper: Spain's mistake 500 years ago with an extractive-mining-only model. Most of those colonies today are 3rd-world countries still.
GW
Once somebody has actually been to Mars the first time and brought some rocks back, I kind of doubt that Mars minerals will remain as valuable commodities. It's a perception thing.
The real value to be derived is as yet unknown, because the exploration is not done. You have to find out what's there and where it is (unevenly distributed, just like here), before you can spend successful time learning to live off the land and figuring out what might actually be useful for trade ("prospecting").
But it is there. Somewhere. You just have to trust that this will be true, because it always has been before, here on Earth.
And you have to get all that exploration and "prospecting" done before it is probable that any colony you plant will be long-term successful. That's history. Just because we're talking about another planet makes no difference to that history lesson. We don't want any failures like Roanoke, or very-marginal survivals like Jamestown.
GW
Hi Rune:
Glad to see you on the new forums. Hi Adaptation - I see you saw the same thing Rune and I saw.
I, too, saw the news articles about a Rutan carrier plane for a Spacex rocket. I believe the rocket is a derivative of the Falcon-5 (5-engine) design they did not originally build, instead going straight to the Falcon-9 (9-engine) design.
The wing is for dropped-rocket pull-up to the steep path angle for a non-lifting gravity turn trajectory. That’s something the carrier plane cannot do at high altitudes in the thin air, especially since it’s a subsonic airplane. 50,000 feet is just about ceiling for most practical designs (the U-2 being an exception) – there is little speed margin between stall speed and maximum speed at such thin-air conditions.
Throwaway designs would drop the wing as unnecessary right after pull-up. A reusable stage might fly to a landing on that wing, at the cost of smaller upper stage(s) and payload. The wing costs weight allowance.
This carrier plane idea is a reprise of the older Pegasus system that Orbital Sciences flew but marketed unsuccessfully about a quarter century ago. Pegasus was a throwaway winged two-stage rocket dropped from a DC-10 airliner. Pretty much the same upper stages now sit (without the wing) on top of an ex-ICBM first stage. Orbital now calls that system Taurus, which is a conventional surface-launched vertical ballistic rocket system.
If anyone can make subsonic air drop work economically, it would be Rutan’s bunch and Spacex. Both understand the need for a small logistical “tail” as the real key to inexpensive access to LEO. Rutan himself just retired, or so I heard. The altitude helps reduce the size of the rocket a little, but is the least effective of the three variables: speed, path angle, and altitude, in that order of importance. The pull-up wing helps a lot more.
Speed is the toughest to achieve: high supersonic or low hypersonic would be really advantageous in reducing the size of the rocket. But, it’s almost impossible to achieve with turbine, and none of the combined cycle development efforts have ever gone anywhere. Ramjet (high-speed designs, not the pitot inlet kind) might work if used separately-but-in-parallel with rockets. I think, based on design analysis numbers I have run, that M5-to-6 is achievable for drop, at altitudes near 50-60,000 feet, complete with carrier plane pull-up to the high path angle (using ramjet and rocket simultaneously). I know an outfit that wants to try this. I may get to help them start trying it, next year late.
GW
It only takes a few centimeters of dirt at 0.38 gee to provide the overburden pressure necessary to keep ice from subliming away in the near vacuum that is Mars's atmosphere. Water-as-ice is easily stored outdoors without a container, if you just bury it in a "shallow grave".
Methane clathrate is only stable at 2 C and 300-meter Earth ocean pressures, which is some 30+ atmospheres pressure. To store it without a container on Mars would require very deep burial indeed. A pressurized container on the surface would be the better deal, if methane clathrate is really what you want to store. Actually, plain liquid methane would be easier to deal with.
I don't think chemical energy storage has been adequately explored, for application here or on Mars. There's more in this world than just batteries and water electrolysis into H2 and O2. What, I dunno.
GW
Scanning through the final page of this conversation, I noticed two things: (1) the huge difference between exploration and colonization efforts is becoming recognized, and (2) there is a need to explore further at Mars, because we don't really know what resources are really available there, not yet.
The paper I gave at the recent August convention of the Mars Society in Dallas deals with those issues, plus the "prospecting" phase that fits between exploration and colonization. Exploration can be done with the tinkertoys we have right now, although it would be easier to do effectively if we were to resurrect the old solid core nuclear thermal rocket technology that did everything but fly 4 decades ago. Exploration seems to me best based from orbit, from which you can do science while you watch over the team on the surface.
"Prospecting" seems to me to be best done with a few surface bases where we learn how to live off the land and to produce some sort of commodity (as yet unknown) that would make a trading colony viable. The same existing spaceflight tinkertoys could be used for this as well as exploration.
Exploration answers two deceptively-simple questions: (1) what all is there? and (2) where exactly is it? And I do mean those questions exactly as worded, that is not slang or dialect. Answering these requires (as one of many parts) the drilling of samples deep under the surface: kilometers, not centimeters. I'd recommend making a bunch of widely-separated landings all in one trip, effecting what amounts to a planetary survey, based from orbit. This concept is way far more than an Apollo-style flag-and-footprints mission. Yet it can be done with chemical or nuclear thermal ships built in LEO massing a few hundred tons, not some ridiculous "Battlestar Galactica". Depending upon who leads it and who does the work, such a mission could be done for 10's of $B (billions), not $T's (trillions). But it cannot be done Apollo style, not for that price. NASA's underestimate for an Apollo-like mission is $450B, last I heard.
Colonization comes later, and actually requires really big ships to be affordable. We don't have anything like that yet. In the absence of any better candidate technologies, I'd suggest the old nuclear pulse propulsion idea, perhaps updated a bit. Half a dozen vessels like that could enable colonies all over the solar system, spread over a century or so. The place to build and test stuff like that safely is the moon.
Just some out-of-the-usual-path ideas for your discussions.
GW
Here's an odd idea. Water seems to be ubiquitously available on a variety of celestial objects, although some purification may be needed. Why not store it and ship it as ice, which requires only the mildest pressure to prevent sublimation into space, and has considerable structural strength in and of itself. If you ship it robotically to your destination months ahead of time, then you can robotically use small-power-level solar or nuclear power to electrolyze it into hydrogen and oxygen.
The fact that electrolysis is inefficient is no problem if the power is essentially free, as with solar or nuclear. The fact that electrolysis production rates are very low is no problem if you have months to get the job done before men ever arrive.
For example, mine ice from the south pole of the weak-gravity moon, and send it with an electrolysis plant to Mars orbit robotically. Do it with a min-energy Hohmann transfer. Have a supply of LH2 and LOX waiting on you when you arrive. Use that supply to support landings and the return trip. Once Phobos has been explored, you may (or may not) have a supply of ice in situ in Mars orbit. But either way, you have the first manned Mars mission covered.
Electrolysis creates H2 and O2 at 2:1 molar, which is 8:1 oxygen:fuel by mass. Even LH2-LOX engines do not use it stoichiometric, they run rich on H2, so there is always excess oxygen to breathe available. Breathing oxygen is really abundant if your engines are nuclear thermal, which typically use only the hydrogen.
GW
I cleaned up my reusability study and illustrated it, and posted it over at http://exrocketman.blogspot.com a few minutes ago. It was based on parachute-slowed ocean impact recovery.
I, too, saw some stuff on Spacex's website about landing the first stage of Falcon-9 on its tail. It was a bit unclear to me exactly how they propose to do this, but I had the impression of parachute-slowed fall to a last-second rocket-braked landing on landing legs. The landing legs and the extra propellant would have the same effect as increased inert weights for ocean impact. Both scenarios have some sort of chute system.
Falcon-Heavy is supposed to fly for the first time out of their new pad at Vandenburg AFB next year, last I heard. It will use the Merlin 1-D, which then retrofits onto Falcon-9 and Falcon-1 later. It's the 1-D that got them to 53 metric tons to LEO, instead of 34 tons.
GW
I re-ran the design trade study I did on the two-stage Falcon-9 with constant payload instead of constant launch weight. I used better estimating models for re-scaling the interstage ring and the payload shroud, which did not affect a payload-constant calculation. What I got differed from the original reusability study for increasingly-heavy stage 1 hardware differed only in the second decimal place.
Stg1 inert fraction payload/launch
4.082% 3.136% (baseline Falcon-9)
8.163% 2.516% (vs 2.512 before)
12.245% 1.898% (vs 1.888 before)
With launch costs proportional to launch weight (all else being equal), a drop in payload fraction is a big increase in cost per unit mass of payload delivered. On the other hand, first stage reusability is very difficult to obtain because of (1) the challenges of reentry at M11.8, and (2) the challenges of ocean chute impact, thermal shock, and saltwater corrosion.
The shuttle SRM’s were sometimes reusable, sometimes not, at inert fractions around 10% for a solid motor pressure vessel case. I rather doubt that Falcon-9 first stage reusability is obtainable much below inert fraction 10%, which would be pretty close to a payload fraction of 2% vs the “stock” 3.1% value. That’s about a factor 1.5 hike in cost per unit mass to LEO, all else being equal. Somehow I don’t see routine reusability of a first stage offsetting that, since hardware and propellant costs pale into insignificance beside logistical costs.
So, I looked at the 3-stage option, based on throwaway second and third stages, and baselining a throwaway first stage for direct comparison to Falcon-9. I would then double and triple the first stage inert fraction to see what effect that had on payload fraction overall. I used payload shroud weight = 15.2% of the payload weight inside, same as Falcon-9. I used interstage ring weight = 0.815% of the weight supported upon it, same as Falcon-9, but both places in a 3-stage vehicle.
I started with mass ratios of 5 and Isp = 304 sec in the third and second stages, similar to the Falcon-9 second stage. I used a mass ratio of 4 and Isp = 289.5 sec in the first stage, similar to the Falcon-9 first stage. For the first stage I used the same 1.10 knockdown for gravity and drag as for Falcon-9 first stage. For the third stage I used the same knockdown of 1.05 as the Falcon-9 second stage. For my second stage, I used an intermediate knockdown of 1.07, being drag-free but more vertical. These gave me an estimated delivered delta-vee of 41,400 ft/sec vs the 26,900 required, so I knocked down all three stages’s delta-vees by 1.506, and recomputed required mass ratios. They are 2.45935 first stage, and 2.84251 in both the second and third stages. Stage 1 dropoff is 7620 ft/sec vs 11,820 for Falcon-9, stage 2 dropoff is at 17,170 ft/sec, and stage 3 burnout is 26,900 ft/sec, same as stage 2 burnout with Facon-9.
Stage propellant fraction is (MR-1)/MR, for 59.339% in the first stag and 64.820% in stages 2 and 3. The remainders must be split between inert fraction and stage “payload” fraction. I figured things as constant payload, top-down. It was easier to cope with the interstage ring weights that way. I used 4.2% inert (one engine) in the third stage, similar to Falcon-9’s second stage, for a stage payload fraction of 30.980%. I used 5% inert in the first stage, similar to the multi-engine Falcon-9 first stage, for a payload allowance of 35.661%. For the second stage, I used an intermediate inert fraction of 4.6%, reflecting multi-engine, but only a few. That stage payload is 30.580%.
The variation was to double and triple first stage inerts (5,10, and 15%), for stage payload fractions of 35.661, 30.661, and 25.661%. I assumed the shroud and first-second interstage ring drop off with the first stage, and the second-third interstage ring drops off with the second stage. Third and second stage weight statements are therefore identical for all three configurations:
Payload 23050 lb
Stg3 dry 3125 lb
Stg3 prop. 48,228 lb
Stg3 ign 74,403 lb
2-3 ring 606 lb
Stg2 payload 75,009 lb
Stg2 dry 11,283 lb
Stg2 prop. 158,996 lb
Stg2 ign 245,288 lb
1-2 ring 1999 lb
Shroud 3500 lb
Stg1 payload 245,288 lb
Stg1 dry at 5% 35,163 at 10% 81,794 at 15% 146,596 lb
Stg1 prop 417,303 485,354 579,925 lb
Stg1 ign = WL 703,253 817,935 977,308 lb
Payload/WL 3.278% 2.188% 2.359%
If you graph the two trends, it is clear the 3-stage option is more tolerant of higher inert weights in the first stage. Combine this with a lower first stage fall-back speed, and reusability seems more certain at 10% inerts, and with a higher payload fraction (nearly 3% 3-stage vs a bit over 2% 2-stage). My conclusion is that 3 stages is a better option than 2, if the first stage is to be reused. The drop from 2-stage non-reusable payload fraction is actually quite small (3.1% to about 2.8%). This is because the all-throwaway 3-stage vehicle actually has a better payload fraction than the 2-stage (3.3% vs 3.1%).
This does raise the question of whether 4 stages might allow first stage reusability at even better payload fraction, or the same payload fraction with both first and second-stage reusability. I leave that for others to investigate.
The main lesson here is you have to do something different to get a different result. Reusability will require a greater inert weight fraction to cover recovery gear, and confer the strength to survive better. It just ain’t gonna happen in the 4-8% inert range. This study sort-of points toward 10% inerts, at least. The more inerts you have to cover, the more stages you need to use, to be tolerant of lowered mass ratio in each stage.
But at least we know the job really can be done, and one well-proven way to do it.
GW