Reusable Rockets to Orbit

Hop · 2011-12-12 10:51:47

JoshNH4H wrote:

Wow, lots of posts to respond to. First, a quick question to Hop that would clear things up for me a lot:
Rune says that Gravity Drag is a function of the time it takes to get to orbit. You'll see no argument on this one from me.

Good.

JoshNH4H wrote:

You say that you have to consider orbital velocity when calculating gravity drag.

My objection was your use of potential energy alone for energy between altitudes. A vehicle acquires kinetic energy along the way so it is wrong to say the difference between altitudes is 2.81 MJkg.

Also as a vehicle picks up horizontal velocity it acquires so called centrifugal force. This centrifugal lessens the gravity pull. This has an effect on gravity loss over time.

JoshNH4H wrote:

Is your argument that because the velocity required to be in orbit is the strongest determining factor, you have to take into account the velocity required to get into orbit when calculating gravity drag?

No.

JoshNH4H wrote:

A calculator for the delta-V required to get to orbit sounds extremely useful, though.

Here's such a calculator.

If your choice of launch vehicle is user defined vehicle, you'll note Schilling asks for thrust as well as ISP.

Hop · 2011-12-12 11:15:37

Rune wrote:

How much more fuel and propellant would be required for a direct shot, in percentage terms, compared with a "sling shot approach" (is it at "opposition"?).
"Brute force" trajectories would take about as much delta-v as is the difference between the orbital speeds of mars and earth, so about 29.8km/s (for earth) - 24km/s (for mars) = 5.8km/s, without taking into account entering and leaving either planet's orbit (whichever orbit you choose to park in, the delta-v requirements vary).

This sounds like a Hohmann orbit. For injection into a Earth to Mars Hohman orbit, Vinfinity is about 3 km/s. At the end of the transfer path the hyperbola with regard to Mars has about 2.6 km/s.

Total V infinity for a Hohmann is about 5.6 km/s.

If the transfer orbit intersects Mars' or Earth's orbit at a healthy angle, the Vinfinity speeds could be a lot higher.

Rune wrote:

For comparison, the "standard" minimum energy Hohmann is about 1.5km/s, again without the departure and capture taken into account.

That is about the Hohmann delta V if your departure and arrival orbits are just under parabolic -- highly eccentric elliptical capture orbits.

But if you're departing from LEO? Then Trans Mars Injection is about 3.6 km/s for a Hohmann transfer.

Last edited by Hop (2011-12-12 11:19:42)

Rune · 2011-12-12 15:55:15

Which is why I gave the speed from C3 (earth escape) and showed him a map of the delta-v's that would get you there from anywhere, not just LEO. Of course, maybe I should have explained better, but introducing several new terms like C3 to louis before even getting into his own problem didn't seem like a good idea at the time. Would have taken longer to write too... ^^'

And 5.8km/s faster than C3 speed? That would puts you at Mars orbital speed. Anything above that divided by two, multiplied by the distance at that given time gives you travel time, on very (VERY) broad terms. At least I think it does, but it's another "gut feeling" derived from general physics. I really won't get into something requiring paper and pencil (I'm old fashioned that way and work my equations like they make me do in exams), like specific orbits from conjunction to opposition, to answer a quick post. Especially if I can give a rough answer that more or less answers the specific question, since I doubt louis is using this info for anything really crucial where he needs precision.

Rune. Pay me if you want a perfectly correct answer, and define the parameters of the work you want done... then I can say I've already had my first job!

louis · 2011-12-12 18:18:29

Rune/Hop,

I was particularly interested in what the add on was as a percentage for fuel/propellant if you go with a direct shot.

GW Johnson · 2011-12-12 19:51:24

Spacex’s Falcon-9 is a 2-stage rocket with kerosene-oxygen engines in both stages. It features an interstage ring and a payload shroud (on the satellite version) that I assume both get jettisoned at staging. The same engines are used in both stages, except that the one in the second stage has a longer bell than the nine in the first stage. I looked up most of the basic data from Spacex’s website, and reverse-engineered the rest. Here it is:

Delivered LEO payload       23,050 lb    15.648% of stage 2 ignition
Second stage dry weight          6,250 lb    4.243% of stage 2 ignition (structural inert)
Second stage propellants    118,000 lb 80.109% of stage 2 ignition
Stage 2 ignition weight    147,300 lb    100% of stage 2 ignition

Payload shroud    3,500 lb
Interstage ring    1,200 lb
Dropped at staging    4,700 lb

Stage 2 ign + dropped-at-staging 152,000 lb 20.680% of stage 1 ignition (“payload”)
First stage dry weight 30,000 lb 4.082% of stage 1 ignition (structural inert)
First stage propellants 553,000 lb 75.238% of stage 1 ignition
Stage 1 ignition weight 735,000 lb 100% of stage 1 ignition

Nine first stage kerolox engines (135 sec min burn time) average Isp is average of sea level 275 sec and vacuum 304 sec: 289.5 sec, for estimated Vex = 9314.4 ft/sec.
One second stage kerolox engine (260 sec min burn time) average Isp is vacuum Isp: 304 sec. Estimated Vex = 9780.9 ft/sec.

Use gravity & drag loss factors of 1.1 first stage (near-vertical with air drag), 1.05 second stage (more horizontal and essentially drag-free).

Stage mass ratio ideal delta-V actual delta-V
1 4.03846 13,002 ft/sec 11,820 ft/sec
2 5.02730 15,795 ft/sec 15,043 ft/sec
Overall ---- ---------- 26,863 ft/sec = 8.187 km/sec

The orbital velocity requirement for LEO is commonly said to be 8.1 km/sec. My reverse-engineering results for the Falcon-9 come remarkably close to that value at its rated satellite payload to LEO. That payload is 3.136% of launch weight. And staging does indeed occur way outside the sensible atmosphere: somewhere in the vicinity of 100-150 miles up.

They are having no success yet, re-using any of the first stage tankage or engines, after recovery at sea. There is no attempt to recover and reuse the second stage, the payload shroud, or the interstage ring. Given the 4.082% structural inert mass fraction for that stage, I am unsurprised by that outcome. I doubt they ever will reuse much first stage hardware, as long as it remains that fragile. And as long as it remains that lightweight, it will remain that fragile.

I will turn this same analysis around and see what payload reduction results in a two-stage design at higher first stage inerts, and if I can fly the same payload fraction 3-stage at higher inerts. Haven't done it yet. But when I have, y'all will have a sort of "baseline" on which to hang all these arguments.

GW

Hop · 2011-12-12 22:18:31

Rune wrote:

And 5.8km/s faster than C3 speed? That would puts you at Mars orbital speed.

Let's see. Assuming already traveling 10.9 km/s at a 300 km altitude, then doing a 5.8 km/s burn... That gives you about 12 km/s Vinf.

There are a multitude of possible directions and therefore a multitude of possible orbits.

Depending on direction, that could take you to a perihelion inside Mercury's orbit. Or it could take you out past Pluto.

Rune wrote:

Pay me if you want a perfectly correct answer

You have been paid what your answer's worth.

GW Johnson · 2011-12-12 22:28:53

I could do the two-stage launcher with tougher first stage for reusability pretty easy. Remember, these plot as a smooth curve, but thrust levels, engine size and count, common engine considerations, and vehicle acceleration levels will constrain you to specific points, not anywhere along the curve. This is based on Spacex Falcon-9, again.

What I calculated was same launch weight, same 1st stage mass ratio (for same delta-vee), same interstage ring weight (same size 1st stage), reduce the 2nd stage ignition weight plus shroud weight by the added 1st stage inert weight, scale the shroud and 2nd stage weight statements by the factor of current 2nd stage ignition weight-plus-shroud weight to its original value (knowing some of this really doesn’t quite scale that way). Thus 2nd stage mass ratio and delta-vee are the same as original. Then recompute delivered payload weight to launch weight.

Configuration original “double”    “triple”
Del ivered payload, lb 23050 18464    13879
Stage 2 dry weight, lb 6250    5007    3763
Stage 2 propellant, lb 118000 94525    71050
Stage 2 ignition, lb 147300 117996 88693

Stage 2 ign + shroud, lb 150800 120800 90800
Scale factor 1.0000 .801061008 .6021220159

Shroud weight, lb    3500    2804    2107
Interstage weight, lb    1200    1200    1200
Dropped at staging, lb    4700       4004    3307

Stage 1 “payload” (2-ig+dropped), lb 152000 122000 92000
Stage 1 dry weight, lb    30000 60000 90000
Stage 1 propellant, lb    553000 553000 553000
Stage 1 ign = launch, lb    735000 735000 735000

Stg 1 str inert fraction 4.082% 8.163% 12.245%
Overall payload fraction 3.136% 2.515% 1.888%

For comparison, I think the Shuttle boosters were somewhere near inert fraction 10%, and a lot of these segments were too dinged-up hitting the sea to reuse. So, an 8% inert fraction (configuration “double”) may well be far too fragile for effective reuse. The “triple” configuration at 12% inert may be more realistic. Or it may still be too fragile.
At any rate, once the tankage gets about as tough as a solid propellant motor, one might as well do pressure feed and eliminate the turbopump machinery. That could save some inerts, and perhaps increase reliability at very low logistical “tail”. It certainly needs to be considered as a viable option.

GW

JoshNH4H · 2011-12-13 00:32:51

First: Mod Action (I might not have actual mod powers at the moment but I have been informed that I am still a mod)

Hop wrote:

You have been paid what your answer's worth.

Hop, this is unnecessary and unmerited, and I would advise you to keep a cooler head while posting. If you think that someone is wrong or think that their post was irrelevant (which I'm not saying Rune's was, actually, though we seem to have gone off topic, that is clearly not the issue here), you can say so in a respectful manner. In the future, if you feel the need to make such a comment, I would advise thinking again.

[/mod]

_____

GW- I would say there actually has to be something wrong with your figures. The delta-V required to get into orbit for pretty much any rocket is at least 9 km/s, usuall in the range of 9.2 km/s for a big rocket like the Saturn V and somewhat higher for smaller rockets.

Hop- You're simply not correct. You're conflating gravity drag, the time derivative of which is equal to the net gravitational force, and the pure velocity required to reach a higher altitude. They are quite different. Consider the free body diagram of a rocket flying straight up in a location where there is no atmosphere:

Rocket Free Body Diagram

In this picture, the green arrow is the force from the rocket's engine, and the red arrow is the force due to gravity. You want to integrate the green arrow with respect to time (or at least its vertical component, when the rocket is not flying straight up, and ignoring air drag). It is not correct to do this because gravity drag refers to something different. Gravity drag is the time integral of the red arrow, where the red arrow is the drag due to the effective force of gravity. (If you want to get technical, it's the negative integral because the force of the rocket's engine goes the other way, but we're just looking for magnitudes here). Gravity drag is essentially rocket thrust in the vertical direction that does not add to the energy of the rocket and does not go towards overcoming air drag. The ⌂V I'm talking about as being used to increase the rocket's potential energy is in the following diagram:

The blue arrow is the length of the Green arrow minus the Red arrow. The integral of this arrow with respect to time from launch until orbit is going to be equal to 2,370 m/s for a 300 km orbit. 2,370 m/s is 2.81 MJ/kg expressed as a velocity. If you separate the two different vertical ⌂V components in this manner, the methods you would have to use to calculate both become much clearer.

This thread has gone badly off topic. If I had actual mod powers at the moment I would split it, but alas I do not. I'm going to do another post soon on revised fuel choice and then talk probably about atmospheric reentry.

Last edited by JoshNH4H (2011-12-16 13:39:16)

Rune · 2011-12-13 16:16:21

Here's something truly on topic... and it's actually news, I read it like 5 minutes ago and haven't heard a peep about it before:

Microsoft Co-Founder Paul Allen Unveils Giant Plane for Private Space Launches

Microsoft co-founder Paul Allen announced today (Dec. 13) that he is teaming up again with aerospace design mogul Burt Rutan to develop what the pair is calling a revolutionary approach to private space travel for people, cargo or satellites.
The billionaire investor and philanthropist unveiled the new company Stratolaunch Systems, which aims to create airport-like operations for space travel. The company, headquartered in Huntsville, Ala., will use a giant twin-boom aircraft to launch a rocket and space capsule from the air to carry commercial and government payloads, and eventually paying passengers, into orbit. The first flight is expected to occur within five years.

My take? Gosh, they are actually going forward with the spaceship one approach. I hope the air launch end ups giving them more than it costs... and if it does, I see it performing more because of range availability than anything else. Something which, by the way, I don't doubt is a big improvement, cost-wise. I just doubt if it is a worthwhile improvement.

Rune. And Paul Allen... there's more geeks with money every day, right? That's a good thing.

louis · 2011-12-13 16:32:11

Josh NH4H,

You may be a mod but can you please refrain from interfering with my free communication with others here. I asked a perfectly sane, polite question about use of fuel/propellant. You should not presume knowledge or ability in others and you should not attempt to stop people answering the question. I do not wish to be referred to that link again thanks.

JoshNH4H · 2011-12-13 18:03:34

Louis- I was being very clear that I cannot and would not prevent anyone from answering your question. My suggestion to not answer your question was merely as a fellow forum user and nothing more. If you feel that this did not come off clearly in my post, I will change it to better reflect that.

I do not presume any ability in anyone other than that which has already been demonstrated. The use of a calculator does not require ability beyond that which you have already demonstrated with the english language (and I suppose the ability to operate a computer in the most basic sense, which by posting on this forum you have already more than demonstrated.

Of course, the most important thing anyone should glean from this post is that I can't tell anyone what they can or can't say, so long as they follow the forum rules.

Edit: I changed the offending post to make it clear that people do not have to listen to that if they choose not to.

Last edited by JoshNH4H (2011-12-13 18:10:08)

JoshNH4H · 2011-12-13 18:11:55

Rune- Thats an interesting concept. I'm really glad to see that theres money going into space launch development.

Hop · 2011-12-13 22:27:43

JoshNH4H wrote:

With regards to the question at hand, I would advise that people not do the calculations for Louis (though of course I advise this as a fellow forumgoer as opposed to a moderator) given that he should be perfectly capable of plugging into the calculator which I have linked to previously.

Yes, Louis has been given the rocket equation many times.

By the same token, you and Rune have been shown how to figure the velocity of a hyperbola. Many, many times.

So perhaps you can understand my frustration when Rune gives Louis this spectacularly bad information. And you watch Rune dispense this misinformation, evidently clueless how wrong it is. Then Rune goes on to say there's no math behind it, just a gut feeling. And why should he invest time and effort doing math? After all, it's Hop and Louis he's talking to.

Know this:

You and Rune are no better than Louis.

Your smug arrogance and condescension towards him are completely unwarranted.

JoshNH4H wrote:

... you can say so in a respectful manner. In the future, if you feel the need to make such a comment, I would advise thinking again.
[/mod]

Thou hypocrite, pull the beam from thine own eye first.

I am not going to waste any more time here.

JoshNH4H · 2011-12-14 00:27:53

Smug and condescending? I believe not. I try to maintain a minimum level of politeness. For example, in the text you quoted or anywhere else in that post, or for that matter this entire thread, I hazard that you cannot point to any comment which I made that was rude or nasty.

Rune gave louis an approximation of the travel time. Nobody claimed that it was exact or precise. It is just an approximation.

I don't quite understand what you're trying to accomplish in that post but if you are not interested in the topic of discussion (and interestingly enough, I don't recall even ine post of yours in this thread on reusable rockets, rather you were critiquing a model that was mentioned as support of a point that has since been mostly vindicated) then further input will not be necessary.

Terraformer · 2011-12-14 02:50:11

Just wait till the post-2008 posts come back... they'll make a sharp constrast in tone.

What I'd like to know is, can Nyrath be trusted when it comes to approximating gravity drag?

Rune · 2011-12-14 08:27:13

So, instead of replying to a post that is basically just personal attacks, I'll just ask to find your own constructive contributions to this thread, Hop. See what you can find. Just one little detail: I know how to figure out hyperbolas since I was 17. Doing that wouldn't have answered louis' question, since he gave no specific departure point or date, and a hyperbola isn't a transfer orbit. I wouldn't have lost the time even if it did.

JoshNH4H wrote:

Rune gave louis an approximation of the travel time. Nobody claimed that it was exact or precise. It is just an approximation.

Actually, it was a very crude approximation of delta-v, probably just within the same order of magnitude of a real trajectory, but no matter. I am starting to see I really shouldn't have bothered.

Tell you what, Louis. Not in this thread ('cause we are cluttering it up), but give me two delta-v's (in km/s, please, I am a metric guy) and a fuel in a PM and I promise to work out the rocket equation for you and translate the mass ratios to percentages. Just to see which step is the one that turns you away... I promise no disrespect of any kind is intended, or whatever. Just honest curiosity.

Now to the real point of this post. Yes, there is one, otherwise I wouldn't have bothered replying. The news I gave yesterday? Turns out it is more interesting that I thought at first glance:
-The "multi-stage rocket" mentioned is actually a Falcon V, resurrected for the occasion (it is a rocket with 5 Merlins in the first stage built by spaceX... in my book that's a Falcon V).
-Among the people involved, the entire management crew of the Ares I, starting with Cook. Yes, I thought the same.
-Griffin does another of his "commercial is only good when I sign it" twists. He's in the board promising to "revolutionize the future of space launch" or something like that.
-The plane is mostly a couple of 747's with a new wing and structure by scaled composites. Engines, landing gear, avionics and all the rest are going to be ripped from a couple of used birds. So this is a one-off prototype, I hope they don't break anything in the qualification flights.
-Not a peep over whether the rocket is going to be reused, even partially. One would think it's easier to recover the first stage this way, right?
-Even though the video shows a Dragon as the cargo, the thing is just 13.500lb to LEO. That's an empty dragon at most, isn't it?

BTW, GW, that's a great Falcon 9 breakdown. I'll keep it as a semi-official source. I wish your country had abandoned imperial units a long time ago, though... ^^' Pounds confuse me.

I think SpaceX actually dropped pressure feeding the engines on isp grounds, I seem to recall Musk saying that in an interview. It saved weight on the overall design apparently, and the specs of the Merlin as it is are quite impressive. The current thinking seems to go in the direction of making it land so smoothly on a pad it doesn't need to survive an ocean splashdown. The big problem right now is it doesn't survive reentry into the atmosphere, either. Musk has stated that they believe they have found a way to slow it down before the atmosphere that closes the case. I'll believe him when I see a first stage landing, something which I hope comes soon.

Rune. Maybe this stuff merits it's own thread? You have my permission to cut my posts on the subject and put them somewhere else, whomever gets mod powers.

GW Johnson · 2011-12-14 10:18:00

I posted two things, a breakdown of Falcon-9 based on their website, and a design study looking at increasing the metal flown in the first stage vs lost payload fraction. The idea is that extra metal is stronger and more likely to survive ocean parachute impact for reusability.

You can do such things either by a real trajectory code, or by "jigger factors" and the simple rocket equation. I don't know of anything in-between that is reliable. I used a trajectory code at LTV Aerospace 40+ years ago doing work on the Scout launcher. I used the rocket equation and "jigger factors" to set up those studies. Really, one uses both tools.

I've been using a nominal 26,000 feet/sec (7.9 km/sec) for LEO orbital velocity. Sorry about the imperial units, just divide by 39.37/12 and by 1000. There's 2.205 pounds in a kg, BTW. The mass ratios and ideal velocity increments I got for Falcon-9 are good to under a percent, limited by the approximation of multiplying Isp by the standard gravity constant to estimate exhaust velocity. Not technically correct, but pretty close.

My jigger factors are experiential guesses. That's the 1.10 and 1.05 knockdown factors for actual; delivered first and second stage velocity increments. These are the penalties for air and gravity drag, lumped. Doing it this way got me quite close into the ballpark: 8.1 km/sec vs 7.9 required. Not bad for a guess. That was my first post on Falcon-9. Close enough to run a design study realistic enough to trust.

The second study looked at the effects on payload fraction overall of adding more metal to the first stage to make it stronger and thus more survivable and reusable. By the time I tripled inert weight, I'd pretty much cut payload by 3. Since launch costs are more proportional to launch weight than anything to do with payload, this means the reusability has to save factor 3 over non-reusable costs, just to keep the same cost per payload mass, at triple the first stage inert weight. Whether this can be achieved, I dunno, but I doubt it.

At triple the inert weight, the inert fraction starts to look like the solid SRM's of the shuttle, which were reusable, sort-of. Not always. At that level, you become pressure-vessel capable, and could do pressure-feed. History says that is uneconomic for throwaway vehicles, except for some tactical missiles. But it might be economic if you are driven to that much metal by other considerations, such as survivability / reusability.

Reusability is one tough nut to crack. Reentry above M10-12 is really tough, and ocean parachute impact, thermal shock, and corrosion are all far tougher than anyone wants to believe until they've actually tried it.

Spacex has the lowest payload costs in the industry without reusability so far. That's because they have a vehicle that is reliable with a village supporting it, not a major city like all the other contractors or NASA. I think that's the real way to go. If reusability can be achieved too, well then that's gravy. But it's not the driving factor.

I'm still looking at 3 stages vs 2, nothing to conclude yet. But I bet it's logistics, not reusability, that can be achieved with rockets like this. Airplanes, well, that's quite different. Pods assisting rockets that stage off well below M5, that's different, too. But I think we're already seeing the most effective answer with plain chemical rockets.

GW

Rxke · 2011-12-14 11:32:57

Oh Great,

we have 5 active users and already managed to alienate one.

Nice show.

And me thinking this place would be a breath of fresh air...

louis · 2011-12-14 12:30:19

Hop -

LOL - I don't know whether I should take that as a compliment, being no worse than Rune and Josh NH4H!

It would be a shame to lose your technical knowledge and ability to communicate it, Hop so I hope you do reconsider.

As regards the rocket equation, I think the problem I had was more to do with definitions. I will take a look at it again. I am not frightened of figures per se and often my ball park estimates are accurate enough. But that was what I was trying to get with the propellant/fuel required for a direct shot - a ball park estimate.

GW Johnson · 2011-12-14 15:09:18

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

Rune · 2011-12-14 17:36:56

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.

Have you seen the last video SpaceX released? In case you haven't, here you go, some eye candy. I understand completely your points, I even agree to most of them, the only problem I can see being now you are still not reusing two stages. And, as you said, ocean recovery doesn't go too well with reusing a stage quickly or for a great number of flights (Elon Musk has suggested thousands, as an ultimate goal, which I agree, sounds crazy). But they are not planning to recover on the ocean! Instead, the stage lands on rocket power on a pad, in the cape right next to the processing building if you believe the video. Never mind the horizontal distance traveled before staging.

So yeah, supposedly the video is not 100% accurate, in the words of Musk himself. And somehow making it back a few hundred miles on rocket power doesn't sounds like something easy (I hear they are looking for another launch site, which could be related). And they are talking about making it survive atmospheric reentry by slowing it down after staging. And the second stage is supposed to have a full heatshield, and a retractable engine bell (that was the thing that left me the most O_O). Oh, and Dragon has somehow acquired an active docking system besides the fancy launch escape that lands it on the same launchpad on the cape. At least one chute is kept in the Dragon for backup. As I said, eye candy.

But if you take anything from the video, or the conference that followed it (and I can't seem to find on youtube), it's the vertical landing under rocket power from terminal velocity with no chutes involved. That's really revolutionary, if realizable, and given it only has to land 4,082% of the fully fueled, stacked vehicle propulsively... Of course it won't be just that, they are talking about beefing up the stage also, but you get the idea it's an argument agaisnt increasing the dry vehicle mass stage. In other words, a trade is involved. Go figure. Seems their engineers are betting that trade goes in favor of more fuel left in the tanks, and lighter tanks. Me, I wish them most of luck in their endeavour and hope their calculations prove accurate.

As to how are they going to manage to modify the stages so much maintaining the payload, I am divided over if it's sheer magical thinking, or the performance increase of the Merlins is really going to permit VERY stretched tanks. In case you also haven't heard about that, the new and improved version of Merlin, the 1D, expected to go into service some undefined time in the future, is claimed to have 168% the thrust of the 1C that has already flown. That is an enlarged first stage with potentially up to 60% more fuel on it. Or a good deal of increased structural integrity. Or a heavier second stage that is almost a shuttle. Or a combination of the above that actually works as advertised, and then it's all business and glory to them.

Rune. The press conference after the video was an informational gold mine. And very... persuading? Musk almost made a SpaceX fanboy out me.

GW Johnson · 2011-12-14 21:26:55

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

Adaptation · 2011-12-15 00:55:09

From what I here SpaceX is now working on everything at once.

Re-entry was too hard on even there first stage because it was moving way too fast, for a near term fix they will save a bit of fuel and reignite it to slow the rocket down before parachute splashdown recovery of the first stage.

There is also the grasshopper version of the Falcon9 that has landing legs that pop out for a propulsive pad landing on all three stages (first second and dragon), heat shielding will be added where needed.

http://www.youtube.com/watch?v=mQC72UZxZlQ

Burt Rutan is building the largest plane in the world to air drop a falcon 9 modified with a small delta wing.

http://www.youtube.com/watch?&v=sh29Pm1Rrc0
http://www.stratolaunch.com

The delta wing is interesting addition on the air drop version, I am curious if perhaps they could use it for a horizontal landing on a dry lake bead or very long runway landing at a high speed and using drag chutes to slow it down.

GW Johnson · 2011-12-15 13:20:26

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

louis · 2011-12-15 14:52:29

Space X are very credible on all fronts and the great thing if their leader wants to go to Mars as quickly as possible. In my view he's only been rather quiet on the ultimate goal out of deference to his major client NASA (not wishing to humiliate them completely).

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#51 2011-12-12 10:51:47

Re: Reusable Rockets to Orbit

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Re: Reusable Rockets to Orbit

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Re: Reusable Rockets to Orbit

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Re: Reusable Rockets to Orbit

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Re: Reusable Rockets to Orbit

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Re: Reusable Rockets to Orbit

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Re: Reusable Rockets to Orbit

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Re: Reusable Rockets to Orbit

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Re: Reusable Rockets to Orbit

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Re: Reusable Rockets to Orbit

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Re: Reusable Rockets to Orbit

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Re: Reusable Rockets to Orbit

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Re: Reusable Rockets to Orbit

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Re: Reusable Rockets to Orbit

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Re: Reusable Rockets to Orbit

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Re: Reusable Rockets to Orbit

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