With Blue Origin’s successful launches and recoveries of New Shepard starting just about six months ago, there have been many people questioning how relevant it is to future orbital launch vehicles. Some of this seems to be honest curiosity about how much more Blue Origin needs to learn before it can join SpaceX, ULA, and OrbitalATK in having an orbit-capable launch vehicle, and some quite frankly seems to be unsportsmanlike attempts by SpaceX fans trying to downplay Blue Origin’s reusable launch accomplishments1. Regardless of the motives of the question though, it’s still a legitimate and interesting technical question, and one worth discussing. A lot of what I’m about to discuss is a rehash of an article I wrote almost a decade ago2 about sRLV performance requirements that seems to have been forgotten by many of those discussing these issues.
How Much Delta-V does an Existing New Shepard Produce?
A lot of the discussion I’ve seen about the question of New Shepard’s relevance to orbital launch is based on what I think are erroneous assumptions about the Delta-V capability of the New Shephard vehicle, based on naive analysis. You’ve probably read at least one article where someone stated something along the lines of “While their New Shepard landing was really neat, orbital launch requires X times more energy than suborbital launch”, where X is usually a large number between 25 and 81. The problem is that most of this math is really, really naive.
Most people who haven’t worked with rockets, but who know physics, will use kinetic energy vs. potential energy to solve for the required rocket velocity to reach 100km. 1/2mv^2 = mgh, m’s cancel out, and you solve for v and get ~1400m/s. If you compare this to the velocity needed for orbit (~7800m/s horizontal velocity), that works out to 5.5x more velocity and 31x more energy to reach orbit. The problem is that 1400m/s isn’t the delta-V capacity of New Shepard, and in fact if the New Shepard only had 1400m/s of delta-V capacity, it would have a hard time getting to 25km altitude, let alone 100km.
Why is that? Landing propulsion, drag losses, and gravity losses3. These are due to earth having an atmosphere, propulsion systems having non-infinite thrust to weight ratio, and needing to slow down so your rocket doesn’t go splat.
So let’s take a look at each of these in turn (in order of ease of estimating them):
- Gravity Losses: This is the easiest term to calculate, because New Shepard flies vertically. Every second that the engine is firing straight down, you’re losing 9.807m/s of delta-V to gravity losses. According to Wikipedia, the ascent burn is ~110s, and based on the video of the most recent landing, I counted approximately 17s of landing burn, yielding a total gravity loss of ~1245m/s.
- Landing Losses: The next easiest to estimate is the landing losses. I’m just going to go off of a comment Blue Origin made that if the engine ignition at 3600ft had failed, that six seconds later, the stage would’ve hit the ground. I’m going to assume that 3600ft is engine start altitude, and that startup takes 2 seconds, so that the landing velocity that has to be killed is 3600ft/8s converted to metric (~137m/s). I’m sure you could get a higher fidelity number by some other means, but this is just an estimate.
- Drag Losses: The hardest to estimate is the drag losses. Usually to do this right, you’d want to create a numerical simulation of the whole flight with drag force varying by velocity and altitude, engine thrust and Isp varying with altitude, and the vehicle mass changing as propellant is consumed. You can do a reasonable hack at a 1DOF flight analysis using Excel, if you have enough information, but a lot of the information is guesswork anyway, so I took a shortcut hack. I found an online reference to drag estimates for historical launch vehicles. I took the two vehicles from the list without strapons (Atlas I and Saturn V), and extrapolated the drag loss delta-V by assuming it scaled linearly with frontal area and inversely with liftoff mass. This should make sense because the drag force is linearly proportional to frontal area4, and the drag acceleration is inversely proportional to the mass5. The drag loss delta-V is really just the integral of the drag acceleration with respect to time. Using a 3.66m frontal diameter for New Shepard, and a ~80klb takeoff weight, I’m getting ~528m/s of drag losses. That number is probably only accurate to with in +/- 25% due to all the simplifying assumptions we made, but without doing a full-blown trajectory analysis that’s about the best we can do at the moment. Note this is 4-5x the drag losses of a typical orbital launch in large part due to the very low ballistic coefficient6 of New Shepard compared to an orbital vehicle7. New Shepard has almost the same frontal area of a Falcon 9/Dragon launch while having a takeoff mass almost 15x lower.
If you take those numbers and add them to the ~1400m/s we had just to provide the required potential energy increase, you get a total New Shepard stage delta-V of ~3300m/s8. And that 3300m/s is with a 8000lb capsule as the payload on top. Compared to the ~9000m/s a typical launch vehicle needs to make orbit heading due east, once you’ve included gravity and drag losses, and that doesn’t sound quite so shabby anymore. For orbit you still need 7.4x more energy, but that doesn’t sound anywhere near as cool as 25-81x.
New Shepard Derived Upper Stage
Two other considerations are important when thinking about developing an expendable upper stage based on the New Shepard vehicle: New Shepard does not use a vacuum optimized engine, and New Shepard carries a lot of mass in its reuse hardware.
Because New Shepard is a single-engine vehicle that does powered landing, the engine has to be able to stably throttle down to ~20% of it’s liftoff thrust. This implies that the engine has a very low expansion ratio compared to an upper stage. My best estimates I’ve seen for BE-3 performance is actually only a bit better than the RD-180 Isp-wise: 310s SL and 360s Vac. Which interesting is really similar to the performance of the RL-10A-5 engines that were made for the DC-X, which also had to do low-altitude hover and land. The BE-3U upper stage engine that you would use on an expendable orbital upper stage however, will have a much higher expansion ratio, because you don’t need to do low-altitude, low-thrust operations. I haven’t seen great estimates for the BE-3U engine performance yet, but my guess is probably in the 440s range, possibly higher. Lower than RL-10 because of not being a closed-cycle engine, but dramatically better than the vacuum and mission-averaged Isp you’d see on BE-3 used suborbitally. If you assume that the dry mass of the New Shepard stage is ~30klb plus the 8klb payload9, swapping in the BE-3U for the BE-3, and operating purely in vacuum gets the stage up to ~4100m/s delta-V, which would require a first stage staging Mach Number of ~10.8, which IIRC is only a bit higher than the staging velocity used by F9R with barge landings.
If you assume the reuse hardware (the steering fins on top and bottom, the landing legs and hydraulics, etc) are 30% of the stage dry mass, getting rid of those and going with the BE-3U upper stage engine gets the stage up to ~4840m/s, which would require the first stage to stage at around Mach 8.6. If you assume the reuse hardware is 40% of the stage dry weight, you get ~5160m/s, requiring a Mach 7.7 staging velocity. Both of which are right around the high end of the range for what you could achieve with a ground boost-back recovered first stage.
And all of that is without stretching the tanks any to take advantage of the much higher vacuum thrust of a BE-3U, or the much lower needed T/W ratio for an upper stage (this stage would have a 2:1 T/W ratio instead of the ~1:3 T/W ratio on the last Centaur flight).
Long-story short, it looks like New Shepard is very relevant for becoming the expendable upper stage of a TSTO RLV, just like Blue Origin has been saying.
[Update 1: I ran the numbers, and with the same pmf as the existing New Shepard sans reuse equipment (80%), and same 8000lb payload, but with tanks scaled up to have the stage T/W ratio close to 1:1, the upper stage would have ~5200-5600m/s of delta-V, requiring a staging velocity of only Mach 6.4-7.6, which is just above the sweet spot for a boostback RTLS first stage.]
[Update 2: Chris pointed out that my description of gravity losses was a bit of an oversimplification that overcounts the gravity loss effects a bit, and that the landing dV (~300m/s including gravity losses) was with just the stage and not the capsule, thus knocking ~80m/s off of my estimate. Also, the numbers from the FAA Experimental permit were a little different from what was reported in the first version of this post–I thought the 30klb dry mass included the capsule, but it didn’t include it. I’ve updated the numbers throughout to reflect that. Now those FAA numbers are conservative numbers from their filing almost 2yrs before the first flight, but it does give us bounding numbers to work with. With those more conservative numbers, a New Shepard stage minus reuse hardware and with a BE-3U is still right in the range needed for an expendable upper stage for an 8000lb payload. Could they still improve their mass fraction or stretch their tanks to better take advantage of the higher thrust of the BE-3U? Of course, and I expect they will, but my point was that they’ve already demonstrated good-enough-for-orbital-launch performance.]
Jonathan Goff
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- Though admittedly there were some barbs traded between Bezos and Musk after the first New Shepard flight or two, so it’s not like the snark didn’t go both ways
- The Myth of 25X
- In increasing order of importance
- Fd=1/2rho*Cd*A*V^2
- a=Fd/m
- Beta=Cd*A/m
- Which as I pointed out in my previous article is due to both the square-cube law not being your friend in this case and the shorter aspect ratio of typical VTVL stages
- Which compares pretty favorably to my previous estimate of 3000-3500m/s needed for a 100km capable vehicle
- Based on the FAA Experimental Permit information mentioned to in the previous link, updated from the ~22klb number I erroneously used earlier
Isn’t a new BE4 vehicle more likely? The BE3 seems like a stepping stone (an important one.)
You count a ton of gravity losses for landing, but that’s WITHOUT a capsule. Additionally, your discussion of launch losses is slightly naive. For instance, suppose I launch with about 50m/s initial velocity at super high T/W, then keep the engine on the whole time ascending 10km at 50m/s (taking 200 seconds) until I cut the throttle then float up a bit and come back down. The naive assumption would be that the ENTIRE delta-v other than that initial 50m/s is gravity loss, but clearly that isn’t true because when the burn ENDS (and you’re still going up at 50m/s), you have expended 2000m/s of delta-v but your height equivalent delta-v is about 450m/s (in addition to that 50m/s). So you’re counting pure gravity losses something which ISN’T, but instead is a conversion of delta-v to potential energy.
I’ve seen this assumption before, where “gravity loss” actually incorporates non-losses for some reason. Just because the burn doesn’t show up as velocity does not mean it’s an actual loss. This is something like double-counting.
The amount of time the engine is on is not pure loss. Only if you’re hovering is that true.
Ken,
The current plan, at least as far as I’ve heard from their public statements, is that the orbital vehicle will use a BE-4 powered first stage with a BE-3U powered upper stage.
Chris,
Yes, the ~300m/s landing delta-V and gravity loss are with the 8000lb capsule gone. Since the dry mass of the rest of the stage is ~22klb, that only makes a ~80m/s difference overall. And you’re right that I simplified gravity losses a little bit, in a way that could lower things a little. But if you run the delta-V numbers based on the assumed Isp (310s SL/360s Vac) and the dry and wet mass numbers (30klb dry including capsule, 60klb prop) from their FAA document you get ~3500m/s raw delta-V, so my numbers can’t be off by that much. Which, since we don’t know how much prop they have leftover at the end of the flight, and we don’t know if they’re always topping the tanks off all the way, still seems pretty accurate.
My main point though was that the delta-V capacity of this stage is over twice what many detractors seem to be assuming.
~Jon
For fun, calculate the delta-v for an expendable Falcon 9 v1.2 first stage without reuse hardware and with the same 8000lb payload…
I think New Shepard is good at what it is, and does indeed test out the tech needed for a RTLS first stage. But it is not a very good design for an expendable upper stage, which wants about twice the propellant and none of the (very extensive) reus hardware. The only major thing you’d want to keep is the engine, maybe some of its plumbing…
Chris,
As per my last update, yes for an expendable upper stage, you don’t need anywhere near as high of a T/W ratio, so yeah you would stretch the tanks. But my point was that the performance level they’ve demonstrated with their suborbital vehicle is sufficient for a decent orbital launch vehicle. Can you do better? Of course you can. Centaur is dramatically higher pmf for instance. But is it good enough to get the job done without requiring bleeding-edge performance from the first stage? Yes.
~Jon
Pingback: How Relevant is New Shepard to Orbital Launch?
It’d probably be good enough for reaching LEO, but not really anything else.
Ultimately, the idea of a stripped NS as an expendable upper stage just seem like fan-wanking to me. It could reach LEO (like a Falcon 1 first stage serving as a Falcon 9 upper stage), but in reality they’d significantly redo it even for expendable.
(BTW, note that ORIGINALLY this was a discussion of NS as a /reusable/ upper stage… Something which is clearly not feasible without a very, very different design.)
Chris,
They’re not going to stop with their first orbital vehicle, my point was just that they are probably a lot closer to being able to do an orbital vehicle than many of their detractors give them credit for.
~Jon
Are BO intending on moving quickly to an orbital vehicle, with this suborbital system being just a test rig from which they’ll move on once they have the larger first stage, or are they intending on continuing development of this suborbital system as manned suborbital launcher for “space tourism”, independently from any future orbital development?
The latter originally seemed to be the plan, but since they started test flights it feels like the former.
(And that seems to be everyone’s assumption now. It was “VG & Blue Origin” as competitors, now it’s “SpaceX & Blue Origin”.)
Paul,
It’s really both–they intend to both refine the existing NS design for suborbital launch, while simultaneously taking lessons learned and hardware from it to develop the reusable first stage and expendable upper stage for their orbital vehicle.
As for who their competitors are, once again it’s both VG for their suborbital side and SpaceX for their orbital side. They’re going after both markets. At least as far as I can tell.
~Jon
Jon, Chris. Thanks for the thoughtful analysis – love the back and forth, here and on Twitter! Not sure there are many topics that support it, but I’d love to read long form rebuttals. Point-counterpoint blogging instead of sifting through comments/Twitter threads. Just a thought.
I was noodling this question last night: How relevant is New Shepard to *suborbital* launch? Virgin has already flown humans. Armadillo as been issued a launch license. Blue hasn’t done either of those things. I figure Blue has less than that 10 flights to their credit, arguably making them the *least flown* suborbital space launch company. Virgin, Exos, Masten, and XCOR all have more sRLV flights. XCOR, Virgin, and Masten all have cryogenic, pump fed rockets. When it comes to rapid resuability, Masten and XCOR are handsdown leading race.
Food for thought.
Pug,
Thanks. Chris and I tend to disagree a lot, which was why I invited him to be a coblogger. 🙂 Keeps things more interesting.
Regarding your other question…
1- VG has only flown people on some relatively low altitude SS2 test flights, one of which resulted in a fatal accident. Scaled flew people past the von Karman line a decade ago, but mostly as a stunt to win the X-Prize. Blue Origin is probably closer to having a vehicle that can do regular passenger flights to 100km than anyone else in the suborbital industry.
2- Armadillo has been out of business for 3 or 4 years now. Did they actually get a launch license, or just an experimental permit? Blue Origin is actively working their launch license for New Shepard (I think they’ve submitted their materials already in fact), and should have one soon.
3- They don’t have as many flights under their belt as Masten or XCOR, if you count low altitude vehicles that aren’t capable of reaching 100km, but I’m pretty sure they have more powered flights than Virgin at this point, and I don’t think exos has flown at all yet. Of vehicles with the performance to make it past even 50km, they have more flight experience than anyone other than maybe Scaled Composites.
I wouldn’t blow them off–they’re probably going to be the first sRLV operator in regular operating service, for both manned and unmanned flights. So I’d say they’re pretty relevant.
~Jon
With your analysis of the specifications of the New Shepard, could you do an analysis of a smaller-sized version of the New Shepard as an upper stage with the New Shepard itself used as the first stage?
What would the payload be?
Bob Clark
Check the archives for 24 January when he did that one already.
This may be a stupid question, but what does TSTO stand for?
“Long-story short, it looks like New Shepard is very relevant for becoming the expendable upper stage of a TSTO RLV, just like Blue Origin has been saying.”
(I know RLV is Reusable Launch Vehicle.)
Nolan,
No worries, TSTO = Twp Stage To Orbit. It’s just some launch vehicle jargon to identify a rocket that only has two main stages to reach orbit. In this case saying that a NS-derived upper stage could be put on a suitably sized first stage and produce a reasonable two-stage orbital launch vehicle.
Clear as mud?
~Jon
Clear as water, thanks!
In many forums I’ve seen exactly what you describe: comparing the difference in potential energy between altitudes to the kinetic energy needed for orbit. More recently an obligatory XKCD comic is tossed in along with this naive comparison. My typical response was to mention gravity loss. Which generally fell on deaf ears.
But with the examples of SpaceX Falcon rockets it has dawned on some that the booster is significant fraction of launch expense. I don’t hear “it’s just a sounding rocket” as much these days.
I’m happy to see Bezos in the game.
Since the early days of usenet Simberg, Spencer and others have been pushing R&D in possibly doable technologies:
Reusable boosters
Tougher and less massive thermal protection
New composites giving more strength with less mass
Economies of scale with mass manufacture
ISRU
There are a number of approaches to further the goal of less expensive access to space. And the more players in the game, the more likely some of these approaches will pay off.