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 accomplishments. 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 ago 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 losses. 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 area, and the drag acceleration is inversely proportional to the mass. 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 coefficient of New Shepard compared to an orbital vehicle. 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/s. 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 payload, 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.]