SSME based SSTO’s. UPDATED, 6/28/2021 - Extension to the Delta IV Heavy

 Copyright 2021 Robert Clark

 The SSME makes possible *practical* SSTO’s, that is, with significant payloads. Need to use known lightweight materials, such as carbon fiber. As discussed in the blog post,

DARPA's Spaceplane: an X-33 version, Page 2

https://exoscientist.blogspot.com/2018/06/darpas-spaceplane-x-33-version-page-2.html , 

some ultra high strength metals would also work:

 The standard aluminum the Delta IV used for its propellant tanks had about a 25 to 1 propellant to tank mass ratio. At 200 ton propellant mass, this gives a tank mass of 8 tons. So using light weight materials we can get this down to 4 tons.

 To estimate payload possible we need the required delta-v to low Earth orbit(LEO). Various estimates are given for this depending on altitude and orbital inclination. I’ll use the estimate give in this report of 9,000 m/s:

Towards Reusable Launchers - A Widening Perspective.

https://www.esa.int/esapub/bulletin/bullet87/pfeffe87.htm

 The Delta IV launch vehicle used the low cost, RS-68, an engine designed for low cost, but only at mid level performance. But for an SSTO you need both high performance engines and weight optimized structures. So we’ll replace the RS-68 with two SSME’s. The two SSME’s will have about the same mass as the RS-68 with slightly more thrust. But most importantly they have a much better vacuum Isp at 452.3 s compared to 412 s.

 The dry mass of the Delta IV first stage is about 26 tons. By light weighting the tank, we cut 4 tons from the tank mass to bring the dry mass to 22 tons. Then we can get a payload of 8 tons to orbit. By the rocket equation:

452.3*9.81ln(1 + 200/(22 + 8.2)) = 9,012 m/s.

 The Delta-IV TSTO, with no side boosters, has about the same payload to LEO using a Centaur upper stage:

https://en.m.wikipedia.org/wiki/Delta_IV#RS-68A_booster_engine_upgrade

The higher Isp of the SSME’s explains why the SSTO can match the performance of the TSTO to LEO.

 It is true that most launches now are for satellites actually to go to GEO, geosynchronous orbit. For this you can use the current Centaur upper stage. But firstly the use of the Centaur would allow higher payload to LEO than the current TSTO. The Centaur has about a 21 ton propellant load and 2 ton dry mass for a 23 ton gross mass with an Isp of 462 s. Then the TSTO could now get 21 tons to LEO:

452.3*9.81ln(1 + 200/(22 + 23 + 21.5)) + 462*9.81ln(1 + 21/(2 + 21.5)) = 9,050 m/s. 

 This is well above the 8 tons or so of the current TSTO version and is close to the payload of the Falcon 9 full thrust version.

 This TSTO does get more than the SSTO, but in point of fact you don’t need the maximal payload for most launches, so why use the upper stage if it is unneeded? 

 The additional delta-v required to GEO is about 3,800 m/s. Then a total of 12,800 m/s would be required to get the payload to GEO. This TSTO version could get 6 tons to GEO:

452.3*9.81ln(1 + 200/(22 + 23 + 6)) + 462*9.81ln(1 + 21/(2 + 6)) = 12,900 m/s. 

 This is multiple times higher than the current version:

http://spacelaunchreport.com/delta4.html#config

However, the SSME’s are expensive engines. To get the full usefulness of an SSTO you really need reusability. In point of fact by using lightweight thermal protection and landing legs, and lightweight wings or propellant storage for final approach, the additional mass for reusability can be less than 10% of the landed mass. So the SSTO would still get significant mass to LEO.

 Reusables do get their most usefulness at high launch rates. Then to serve various markets we would also want a smaller vehicle than this SSTO. We could get this by cutting down the tank size and using a single SSME: 

 We’ll cut down the propellant size to 150 tons, 3/4ths the usual size, and again we’ll use light-weighting on the tank of the Delta IV first stage. Subtracting off the 8 tons for the standard tank the dry mass is 18 tons. The tank mass at 3/4ths size would be 6 tons. But we’re lightweighting it so it’ll be 3 tons. That brings the dry mass to 21 tons.

 But the SSME at 3.2 tons is also a lighter engine than the RS-68, at 6.6 tons. So we’ll subtract off an additional 3.4 tons from the dry mass to bring it to 17.6 tons. There will be additional reductions in the dry mass due to smaller thrust structure for the lower thrust of the single SSME, and smaller insulation and wiring for the smaller vehicle, but not as large as the other reductions. 

 So for the first estimate take the dry mass as 17.6 tons. Then we can get 5 tons to LEO with this smaller SSTO:

452.3*9.81ln(1 + 150/(17.6 + 5)) = 9,020 m/s.

 Since less than 10% would be needed for reusability we can still get ca. 3 tons to LEO as a reusable SSTO.

  

   Robert Clark

UPDATED, 6/28/2021.

 The advantage of using high performance engines and lightweight tanks is not just for getting a SSTO. As mentioned above using this, the two-stage-to-orbit(TSTO) Delta IV can double its LEO payload to ca. 20 tons to match that of the Falcon 9 Full Thrust. Its payload capacity to the lucrative GEO satellite market would also match that of the Falcon 9 FT.

 ULA could then be competitive with SpaceX for the largest current market for commercial launches. Note that ULA could also match SpaceX in it's partially reusable approach of returning only the first stage. ULA head Tory Bruno has said the SpaceX approach of boosting back the first stage to the launch site requires too much fuel, and loses too much payload.

 Instead what ULA has proposed doing is returning the engine package only, catching it in midair on return by parachute. The rest of the first stage would be thrown away. This is a kludge, an inelegant solution just to get by. A kludge never provides a long lasting solution. The Space Shuttle was a kludge, which explains why it never reached its goal of fast and low cost reusability. However, by increasing the Delta IV's payload capacity in the described manner, ULA can also boost back to the launch site and match SpaceX in reusable payload capacity.

 The startling increase in payload would also apply to the Delta IV Heavy, with the addition of cross-feed fueling. This is where for a parallel staged vehicle the fuel for the central core is taking from the side boosters during the parallel burn portion of the flight. This allows the central core to be fully fueled when the side boosters are jettisoned.

55th International Astronautical Congress 2004 - Vancouver, Canada 

1 IAC-04-V.4.03 

DELTA IV LAUNCH VEHICLE GROWTH OPTIONS TO SUPPORT NASA’S SPACE EXPLORATION VISION

https://www.ulalaunch.com/docs/default-source/evolution/delta-iv-launch-vehicle-growth-options-to-support-nasas-space-exploration-vision.pdf

 We'll use the rocket equation to again estimate the payload possible for the Delta IV Heavy. Because of how cross-feed fueling works, the calculation works as if the it were a three stage vehicle with the fuel only being from the side-boosters during the "first stage":

452.3*9.81ln(1 + 400/(44 + 220 + 23 + 68)) + 452.3*9.81ln(1 + 200/(22 + 23 + 68)) +462*9.81ln(1 + 21/(2 + 68)) = 9,060 m/s.

 This payload of 68 tons nearly triples the payload of the current version of the Delta IV Heavy, and now matches the payload of the Falcon Heavy.

 This is still using the expensive SSME's however. But the point of the matter is this is doable for the current engine RS-68 used on the Delta IV as well if given altitude compensating nozzles.

 There are various means of adding altitude compensating nozzles to existing engines. They could be like the RL-10B with extendible nozzles, or flexible, expandable nozzles, or mechanically moving "petal" arrangements as with variable area nozzles on jet engines, or several other ways. 

 This last is interesting in that this method of achieving variable area nozzles has been in existence since the 70's. As a total WAG it might improve the performance for jets by, say, 10%. But for rockets using variable nozzles could improve performance by 100% or more and it still has not been used for rockets. 

 In such a way, a midlevel performance engine such as the RS-68 could be upgraded to achieve comparable performance of the high performance SSME's. I won't offer a calculation here using the rocket equation for this case. The reason is while such estimates frequently take the vacuum Isp for a fixed nozzle engine, this may or not be accurate for the case of an altitude compensating nozzle. On the one hand you can give the RS-68 a higher vacuum Isp than SSME, even at 470+ s, but the higher chamber pressure of the SSME, suggests it should have better performance at ground level than the RS-68 given alt.comp.  

 The calculation of the delta-v possible through altitude compensation is one that should be made by the launch companies.

Regular Manned Lunar Flights.

 The use of the higher performance engines gives us the capability of SSTO's with the Delta IV and also heavy lift with the Delta IV Heavy, with payload comparable to the first planned version of the SLS at ca. 70 tons. With this we have the possibility of routine manned flights to the Moon and beyond. Robert Zubrin has written a proposal for a low cost architecture for setting up a Moon base with regular flights to the Moon. Remarkable all it would need beyond the current capability is a reusable lunar lander.

 In the Zubrin proposal it would take only 3 flights of the Falcon Heavy and one flight of a manned Falcon 9 to set up the manned lunar base:

Op-ed | Moon Direct: How to build a moonbase in four years.

by Robert Zubrin — March 30, 2018

https://spacenews.com/op-ed-moon-direct-how-to-build-a-moonbase-in-four-years/

 But with the extra capabilities of the Delta IV Heavy, the three Falcon Heavy launches could be replaced by three launches of the Delta IV Heavy.

 Recall I said Zubrins plan only needed a lunar lander. ULA is planning the upper stage of its upcoming Vulcan lander, the Centaur V, to have in-space reusability. Then this upper stage could also be used as a reusable lunar lander. See discussion here:

Robust Lunar Exploration Using an Efficient Lunar

Lander Derived from Existing Upper Stages

AIAA 2009-6566

Bernard F. Kutter et al.

https://www.ulalaunch.com/docs/default-source/exploration/dual-thrust-axis-lander-(dtal)-2009.pdf

 In regards to adapting the Centaur V or a currently in use Centaur to a horizontal landing lunar lander, I advise the landing rockets be just pressure-fed thrusters fueled from the regular tanks of the hydrolox tanks of the Centaur.

Case proven: SSTO's are better than two-stage launchers.

Copyright 2019 Robert Clark

I remember thinking when reading of the debate about reusable vehicles between proponents of horizontal winged and vertical propulsive landing that all this debate was about a measly 100 m/s delta-v. The reason is whether you use wings or not almost all the speed of orbital velocity is going to be killed off aerodynamically on return. For even for vertical landing, the stage entering broadside will be slowed to terminal velocity, ca. 100 m/s. This is only about 1.3% that of orbital velocity of 7,800 m/s.

This was confirmed by a graphic just released by SpaceX about the BFR’s Starship upper stage reentry:

As discussed for example in this article:

http://www.parabolicarc.com/2019/08/03/nasa-releases-draft-environmental-assessment-for-spacex-starship-super-heavy-at-ksc/

 Here is Elon also discussing how the Starship will land on Earth, including the low terminal velocity, and low final landing burn:

How SpaceX's BFR Rocket Will Land - Elon Musk Explains.

 This shows for the Starship it only has to fire the engines at about Mach 0.25, 80 m/s. So it only has to kill off 80 m/s propulsively. But with the Starship just needing to kill off a 80 m/s velocity with a 3,300 m/s Raptor sea level exhaust velocity, about 330s Isp, by the rocket equation the mass ratio to do this is e[80/3300] = 1.025. Subtracting 1 from this is the ratio of the propellant required to the dry mass. The tanker version of the BFR upper stage, i.e., without the passenger quarters, will have a dry mass of ca. 50 tons (compared to the 85 tons of the Mars Colonial Starship version.) This means you only lose 1.25 tons for the landing.

But a rocket equation estimate using a 356 s vacuum Isp for the sea level raptors gives a ca. 40 ton payload for the tanker version as an SSTO.

See for example here:

SpaceX BFR tanker as an SSTO.

Then the 1.25 tons lost due to propellant kept on reserve loses ca. 3% of the payload due just to the reserve propellant required. You also lose a proportion due to thermal protection system and landing legs but that’s also true for the TSTO.

However, because of the huge amount that needs to be kept on reserve for a first stage booster of a TSTO for slowing the booster down for reentry and for boost back to the launch site as well as for final landing approach, you can lose 40% of the payload for full reusability as indicated by the Falcon 9. Actually, for the BFR for full reusability Elon has said it will lose 50% payload off the expendable version.

Because of this huge loss for reusability for the TSTO, on a percentage of the rocket size basis, and therefore also on a cost basis, the SSTO is more cost effective.

The advantage of the SSTO becomes even greater when you add altitude compensation nozzles. Used on a TSTO this can improve the payload ca. 25%. But on a SSTO it can improve the payload 100% or even more.

 Bob Clark

Half-size Ariane core stage for a reusable launcher.

Copyright 2018 Robert Clark

 Long-time space advocates will recall back in the late 90's there was a push for large numbers of communication satellites for the purposes of cell-phone communication. This led to the creation of several private launch companies then to serve what was expected to be hundreds to thousands of required launches.

 However, it turned out the great majority of cell-phone communications could be served by terrestrial cell towers. The large satellite constellation plans were then abandoned, and those private launch companies then collapsed.

 But now once again there are renewed plans for satellite megaconstellations containing hundreds to thousands of satellites, such as OneWeb or SpaceX's StarLink. This time it is primarily for high speed internet service. This time there is billion dollar backing for the projects and there have been preliminary launches to test the idea.

 It's very likely now that the projects will take place. For space advocates, an important result of the large numbers of launches required is that it provides a clear advantage for low cost reusable launchers.

 SpaceX always believed reusable launchers could be financially feasible. But other space launch providers were skeptical. They didn't think the number of launches under the current market would pay for reusability.

 But now with the advent of the new megaconstellation plans even previously skeptical Arianespace plans to transition to reusability. See for example the articles here:

https://satelliteobservation.net/2018/05/21/ariane-6-and-beyond/

https://satelliteobservation.net/2018/06/02/cnes-director-of-launchers-talks-reusable-rockets/

 One project Arianspace is planning is called Callisto. It is to be a small sized hydrolox test vehicle to test reusable, vertical landing boosters. It is to be analogous to the SpaceX Grasshopper tests.

 However, unlike the SpaceX Grasshopper that used the original Merlin engines and the same F9 propellant tanks, though perhaps only partially filled, the Callisto plan is to use an entirely newly designed and built stage.

 I see a problem with this. For the money spent on Callisto, it will not be an actual operational vehicle. This mirrors a problem with the X-33 test vehicle that was supposed to test the technologies for an operational SSTO vehicle. But for all the money spent on the X-33, it itself would not have been an operational vehicle.

 I believe this was a mistake. It would have been better if the X-33 itself was to be used as an operational vehicle. It could have been used as a reusable first stage booster to cut costs for a two-stage to orbit system, a la the SpaceX plan:

DARPA's Spaceplane: an X-33 version.

https://exoscientist.blogspot.com/2013/10/darpas-spaceplane-x-33-version.html

 Then my recommendation is not to repeat the mistake of the X-33 program by instead actually using operational stages to test reusability and vertical landing.

 This could be done with two existing Arianespace stages. The Ariane 5 core stage and the Ariane H10-3 cryogenic upper stage. In both cases you would use partially filled tanks, approx. half-filled so that the stage could lift-off on their single engines.

 For the operational versions, you would make the tanks themselves half-size, instead of half-filling a full-sized tank, to save dry mass, at least for the Ariane 5 core. For the Ariane H10-3 for the upper stage use it might be able to carry its full propellant load dependent on the propellant load on the Ariane 5 core to be able to lift off on its single Vulcain engine.

 Another advantage of this approach is that it would finally provide Europe with an independent manned spaceflight capability.

 There is a key problem that would need to be solved. Discussion on on a space forum was that the Vulcain II is not throttleable. The HM7-B engine used on the Ariane H10-3 upper stage is also not throttleable. Then both engines would need to be upgraded to be throttleable. As support for the idea this should be feasible, it should be noted the original versions of the SpaceX Merlin engines prior to the Merlin 1D were not throttleable. SpaceX has also shown with its "hoverslam" approach to vertical landing, it would not have to have a high degree of throttleability. Probably the degree of throttleability common to liquid fuel engines in the range of 60% would be sufficient.

See discussion here:

A half-size Ariane for manned spaceflight.

https://exoscientist.blogspot.com/2014/11/a-half-size-ariane-for-manned.html

 Bob Clark

UPDATE: 6/10/2018

 In the discussion above I forgot a key point. The most important factor in
regards to cost is not the development cost.
The key cost factor is what they would charge per flight for a reusable
launcher. Robert Zubrin made this point insightfully in one of his books. He
recounts that he made the argument for reusable launchers in his former job
with one of the big launch companies.

 He argued that they could cut the cost of launch by an order of magnitude.
The company execs responded: why would we do that? Their view was their
revenue would then be slashed by a factor of ten. They were assuming the
market would still be the same but they would be getting one-tenth the
revenue.

 So the OldSpace companies were acting quite rationally in a business sense
in discounting reusability. They were saying the market was not enough to
make it advantageous to them.

 But if there were a large market then they would make more money making more launchers at the lower price. That is, the price would be reduced by a factor of ten but the number of launches would be increased by more than a factor of ten.

 Also, the importance of the large market and lowered prices for satellite
launches extends beyond that of just the satellite market. By making
launches at such reduced prices, that increases the possible market for
passenger flights to space. So the impending megaconstellation launches may
also bring to fruition the long desired routine passenger flights to space.

New Shepard as a booster for an orbital launcher.

Copyright 2016 Robert Clark

 Blue Origin scored another first by successfully relaunching their vertical landing New Shepard suborbital rocket:

 In the blog post "Triple Cored New Shepard as an orbital vehicle", I suggested using three cores of the New Shepard rocket with a small upper stage could form an orbital launcher. However Jonathan Goff on his blog page SelenianBoondocks raised the possibility a single New Shepard could serve as the first stage booster of an orbital rocket:

Random Thoughts: New Shepard for Pop-Up TSTO NanoSat Launch.
http://selenianboondocks.com/2016/01/random-thoughts-new-shepard-for-pop-up-tsto-nanosat-launch/

  I think it should be doable using a similar small cryogenic upper stage as for the triple-cored case. The stage I suggested there was the cryogenic upper stage of the Ariane 4, the Ariane H10-3, or one developed by Blue Origin similar to it. It had a dry mass of 1,240 kg and a propellant mass of 11,860 kg. The Isp was 445 s with a vacuum thrust of 64.8 kN. However, simply using a nozzle extension as on the RL-10B-2 can give it likewise an Isp of 462 s and vacuum thrust of 110 kN. So we'll use these values.

 To make the estimate of the payload we need the vacuum values for the Isp and thrust of the BE-3 engine. In the "Triple Cored New Shepard as an orbital vehicle" blog post I estimated these to be 360 s and 568.8 kN respectively.

 However, to loft the vehicle with the additional weight of the upper stage we'll need to increase the BE-3 thrust slightly. This should doable. For instance the SSME’s could operate at 109% of their originally rated thrust, and the Merlin 1D had a 15% thrust upgrade. So say the BE-3 vacuum thrust is increased 9% to 620 kN, keeping the same Isp.

 Now use Dr. John Schilling's payload estimator program. For the "Restartable upper stage" option check "No", otherwise the payload will be reduced. Select Cape Canaveral as the launch site and enter 28.5 for the launch inclination in degrees to match the latitude of the launch site. Then the calculator gives the result:

Mission Performance:

Launch Vehicle:	User-Defined Launch Vehicle
Launch Site:	Cape Canaveral / KSC
Destination Orbit:	185 x 185 km, 28 deg
Estimated Payload:	1690 kg
95% Confidence Interval:	1298 - 2153 kg

"Payload" refers to complete payload system weight, including any necessary payload attachment fittings or multiple payload adapters

This is an estimate based on the best publicly-available engineering and performance data, and should not be used for detailed mission planning. Operational constraints may reduce performance or preclude this mission.

 Altitude Compensation to Increase Payload.
  As I discussed in the "Triple Cored New Shepard as an orbital vehicle" blog post, altitude compensation provides a simple, low cost method of improving payload.  For instance by attaching a nozzle extension the vacuum Isp of the BE-3 can be increased to the 462 s range of the RL-10B-2 engine. The vacuum thrust will then be increased proportionally to (462/360)*620 = 796 kN.

 Then the Schilling calculator gives the result:

Mission Performance:

Launch Vehicle:	User-Defined Launch Vehicle
Launch Site:	Cape Canaveral / KSC
Destination Orbit:	185 x 185 km, 28 deg
Estimated Payload:	2324 kg
95% Confidence Interval:	1841 - 2895 kg

"Payload" refers to complete payload system weight, including any necessary payload attachment fittings or multiple payload adapters

This is an estimate based on the best publicly-available engineering and performance data, and should not be used for detailed mission planning. Operational constraints may reduce performance or preclude this mission.



  Bob Clark

UPDATE, Feb. 28, 2016:

 This considered an Ariane hydrolox upper stage as the upper stage for this New Shepard launcher. This would be problematical since it would be a direct competitor to Arianespace's Vega rocket at a much lower cost than the Vega's $35 million.

 Blue Origin very likely could develop a hydrolox upper stage that would be cheaper than the Ariane one. But that would take time and significant development cost. Instead of that, Blue Origin could produce a New Shepard derived launcher for cubesats at minimal extra development cost since the required small upper stages already exist.

 Existing upper stages that could work would be the large Star solid rocket upper stages such as the Star 63F:

Star 63F:
http://www.astronautix.com/engines/star63f.htm

 Using this for the upper stage, Schillings launch performance calculator gives:

Mission Performance:

Launch Vehicle:	User-Defined Launch Vehicle
Launch Site:	Cape Canaveral / KSC
Destination Orbit:	185 x 185 km, 28 deg
Estimated Payload:	293 kg
95% Confidence Interval:	174 - 443 kg

 This is in the range being considered for the cubesat launchers that NASA has already awarded million dollar contracts to:

Firefly, Rocket Lab and Virgin Galactic Win CubeSat Launch Contracts from NASA.
By Caleb Henry | October 15, 2015 | Feature, Government, Launch, North America, Regional, Satellite TODAY News Feed
http://www.satellitetoday.com/launch/2015/10/15/firefly-rocket-lab-and-virgin-galactic-win-cubesat-launch-contracts-from-nasa/

 Considering the quoted prices there, this New Shepard based launcher very likely could beat these prices especially using the reusable New Shepard.

 And since the upper stage already exists, it very likely would also beat to launch these other systems still in development.

 About the quick route to operational status of this orbital rocket, I think it is significant that Blue Origin was able to beat SpaceX on a relaunch of its returned booster. The argument has been made that New Shepard is not an orbital launcher. But if Blue Origin developed this orbital launcher from New Shepard then they would be able to beat SpaceX at reusing a booster for a true orbital launcher as well.

 My opinion is SpaceX will have difficulty with getting their booster to land in reliable fashion as long as it does not have hovering ability. And because the New Shepard does have hovering ability it will be more reliable as a reusable booster.

 BTW, as Blue Origin develops its large high performance dense propellant engines, it will have the same problem as SpaceX it getting its booster to be able to hover, resulting in the same problem of reduced reliability on landing. For this reason I think Blue Origin should investigate methods of giving its large planned boosters hovering ability such as discussed here:

Hovering capability for the reusable Falcon 9, page 3: hovering ability can increase the payload of a RLV.
http://exoscientist.blogspot.com/2015/12/hovering-capability-for-reusable-falcon.html

 Surprisingly, it turns out that hovering ability when properly implemented can actually improve the the payload for a reusable rocket.

Triple Cored New Shepard as an orbital vehicle.

Copyright 2016 Robert Clark

 Blue Origin made a significant achievement in successfully landing their New Shepard rocket after a suborbital spaceflight:

 As their next development Blue Origin intends to make a several million pound thrust rocket capable of sending 25 metric tons to LEO. This would be a very large and expensive development for their first orbital rocket, comparable in size to the largest orbital rockets available now, larger for example than the Falcon 9.

 I suggest an intermediate development for their first orbital rocket. Running the numbers, their New Shepard suborbital rocket could be used to make an orbital rocket using three cores with a smaller upper stage, a la the Delta IV Heavy.

 It would have a payload to LEO in the range of 3,000 kg, about the size of the Arianespace Vega rocket. The Vega costs in the range of $35 million. Considering the small size of the New Shepard, even at three cores, Blue Origin should be able to beat this price.

 Moreover, this version would have the capability to be reusable. SpaceX is planning to make the three cores of the Falcon Heavy reusable by returning the two side cores to the launch site and recovering the central core by a barge landing out at sea. Quite likely this would work for a 3-cored New Shepard launcher as well.

Specifications of the New Shepard BE-3 engine.

 Here's a formula for calculating the sea level thrust from the vacuum thrust and back pressure:

F = q × Ve + (Pe - Pa) × Ae
where F = Thrust
q = Propellant mass flow rate
Ve = Velocity of exhaust gases
Pe = Pressure at nozzle exit
Pa = Ambient pressure
Ae = Area of nozzle exit
http://www.braeunig.us/space/sup1.htm

 Estimating the nozzle exit diameter as 1 meter, the exit plane area would be: π*0.5^2 = .7854. Then the back pressure to be subtracted off would be 101,000Pa*.7854 = 79,325 N. 
Blue Origin has given the sea level thrust as 110,000 lb, 110,000*4.45 = 489,500 N. So the vacuum thrust is 489,500N + 79,325N = 568,825 N. 

 We also need to calculate the Isp. One other piece of information will allow us to calculate this. This Blue Origin page gives the horsepower of the BE-3 as over 1,000,000 hp:

https://www.blueorigin.com/technology

 The power of a jet or rocket engine is (1/2)*(thrust)*(exhaust velocity). The 1,000,000 hp at sea level is 1,000,000*746 = 746,000,000 watts. Then using the formula the exhaust velocity at sea level is 3,048 m/s, and the Isp is 310 s.

 Since (thrust) = (exhaust velocity)*(propellant flow rate), we also get the propellant flow rate as 489,500/3,048 = 160.6 kg/s. Now we can get the exhaust velocity and Isp at vacuum. From the 568,825 N vacuum thrust, we get the vacuum exhaust velocity as 568,825 N/160.6 = 3,540 m/s, and the vacuum Isp as 360 s.

  It is interesting that the diameter and sea level and vacuum Isp's are close to those of the RL-10A5,  the sea level version of the RL-10 used on the DC-X:

http://www.astronautix.com/engines/rl10a5.htm

Size Specifications for the New Shepard.
 The Blue Origin environmental impact statement:

Final Supplemental Environmental Assessment for the Blue Origin West Texas Launch Site.
February 2014
https://www.faa.gov/about/office_org/headquarters_offices/ast/media/Blue_Origin_Supplemental_EA_and_FONSI.pdf

on p. 4 lists the max dry mass as 30,000 pounds (13,600 kg) and max propellant load as 60,000 pounds (27,300 kg). This corresponds to estimates made of the New Shepard gross mass based on its dimensions.

 We need also a small upper stage. The cryogenic upper stage of the Ariane 4 will suit the purpose, the Ariane H10-3. It had a dry mass of 1,240 kg and a propellant mass of 11,860 kg. The Isp was 445 s with a vacuum thrust of 64.8 kN. However, simply using a nozzle extension as on the RL-10B-2 can give it likewise an Isp of 462 s and vacuum thrust of 110 kN. So we'll use these values.

 Use now Dr. John Schilling's Launch Performance Calculator to estimate the payload. We'll also use cross-feed fueling to increase the payload. Cross-feed fueling is not an unknown technology having been used on jet aircraft such as the Concorde for decades and also on the Space Shuttle's OMS engines.

 To emulate cross-feed fueling with the Schilling calculator for two side boosters, enter in 2/3rds of the actual propellant load into the propellant field for the side boosters. And for the central core enter in (1 + 2/3) times the propellant load in the field for the first stage. (See  discussion here for explanation of how the Schilling calculator emulates cross-feed fueling.)

 So in the dry mass fields for the side boosters and first stage enter 13,600 kg. And in the propellant field for the side boosters enter 18,200 kg and 45,500 kg for the first stage. For the second stage enter 11,860 kg for the propellant and 1,240 kg for the dry mass.

 In the thrust fields and Isp fields enter in the vacuum values. So for the side boosters and first stage enter 568.8 for the thrust in kilonewtons and 110 for the second stage. In the Isp fields enter 360 for the side boosters and first stage Isp in seconds and 462 for the second stage. 

 For the "Restartable upper stage" option check "No", otherwise the payload will be reduced. Select Cape Canaveral as the launch site and enter 28.5 for the launch inclination in degrees to match the latitude of the launch site.

 The calculator gives:

Mission Performance:

Launch Vehicle:	User-Defined Launch Vehicle
Launch Site:	Cape Canaveral / KSC
Destination Orbit:	185 x 185 km, 28 deg
Estimated Payload:	3420 kg
95% Confidence Interval:	2766 - 4205 kg

"Payload" refers to complete payload system weight, including any necessary payload attachment fittings or multiple payload adapters

This is an estimate based on the best publicly-available engineering and performance data, and should not be used for detailed mission planning. Operational constraints may reduce performance or preclude this mission.


  This would be using an Arianespace upper stage. But this would be a competitor to their Vega launcher so that is problematical. Blue Origin could use instead the Rl-10B2 engine and their own constructed upper stage. The RL-10 though is a rather expensive engine. Another possibility is the 25,000 lb thrust hydrolox engine being developed by XCOR.

Altitude Compensation Increases Payload Even for Multistage Vehicles.
 It is unfortunate that SSTO's have (incorrectly) been deemed unviable. Since altitude compensation has only been thought of in terms of improving the payload of SSTO's, little research has gone into such methods, with SSTO's not being considered worthwhile.

 However, in point of fact altitude compensation improves the payload even for multistage rockets. As with the RL-10B-2 we can get a vacuum Isp of 462 s on the New Shepard hydrolox engine simply by the addition of a nozzle extension. Other methods of accomplishing it are discussed in the blog post "Altitude compensation attachments for standard rocket engines, and applications."

 Increasing the Isp will also increase the thrust proportionally. So at a 462 s Isp for the BE-3, the thrust becomes 568.8*(462/360) = 730 kN. Entering these values into the thrust and Isp fields for the side boosters and first stage gives the result:

Mission Performance:

Launch Vehicle:	User-Defined Launch Vehicle
Launch Site:	Cape Canaveral / KSC
Destination Orbit:	185 x 185 km, 28 deg
Estimated Payload:	5302 kg
95% Confidence Interval:	4359 - 6438 kg

"Payload" refers to complete payload system weight, including any necessary payload attachment fittings or multiple payload adapters

This is an estimate based on the best publicly-available engineering and performance data, and should not be used for detailed mission planning. Operational constraints may reduce performance or preclude this mission.


 This now is a serious payload capability. Note for example NASA awarded Orbital Sciences with a billion dollar contract to deliver payload to the ISS with their Antares rocket with a 5,000 kg payload to LEO capacity.


 Bob Clark

UPDATE, February, 3, 2016:

 Jonathan Goff on his SelenianBoondocks.com blog raised the possibility that a single New Shepard could serve as a booster for an orbital rocket. I confirmed it could at the 1 to 2 metric ton payload range by using the same type of hydrolox upper stage as discussed above in the triple-cored case:

New Shepard as a booster for an orbital launcher.
http://exoscientist.blogspot.com/2016/01/new-shepard-as-booster-for-orbital.html

 It could also serve as a booster for a smaller launcher by using instead one of the Star solid rocket upper stages, giving a few hundred kilos payload. This would have the advantage that little extra development would be required.

 Plus, it may allow Blue Origin to beat SpaceX at reusing a booster for an orbital launcher.

Hovering capability for the reusable Falcon 9, page 3: hovering ability can increase the payload of a RLV.

Copyright 2015 Robert Clark

 Blue Origin successfully landed their New Shepard rocket after reaching suborbital space:

 Observing the last portion of the video showing the landing, deviations from the vertical are visible but the ability to hover allowed it sufficient time to correct.

 Comparing this to the SpaceX Falcon 9 failed attempts at landing it is apparent the inability to hover for the F9 did not allow it sufficient time to make the needed corrections.

 SpaceX has said they want their next test landing to be on land at the launch site. My opinion, they might succeed on the next test or two but they will always have failures without hovering ability.

Merlins in a pressure-fed mode.
 Achieving hovering is not even difficult. In the blog post "Hovering capability for the reusable Falcon 9, page 2: Merlin engines in a pressure-fed mode?" I suggested giving the Merlin the ability to run in a pressure-fed mode. The question was whether this was technically feasible. I found in fact that this process of giving a turbopump powered engine a pressure-fed mode, called an idle mode, had been successfully tested during the Apollo days on the J-2 upper stage engine.

 In giving the J-2 an idle mode though, it was changed from the gas generator cycle that is used by the Merlin 1D to a tap-off cycle:

Rocketdyne J-2.
https://en.wikipedia.org/wiki/Rocketdyne_J-2#J-2S

 However, there is an engine that uses the gas generator cycle and has an idle mode, the LE-5 upper stage engine of the Japanese space agency:

Development of the LE-X engine.
https://www.mhi-global.com/company/technology/review/abstracte-48-4-36.html

 In this idle mode though the thrust is significantly less than at full thrust, only 3% in the LE-5 case. If it is a similar low percentage for the Merlin's then all 9 engines would have to be used in this idle mode to allow it to hover on landing.

 The idle mode has an additional advantage since it does not use the turbopumps. It could be used to burn both residual liquid propellant and gases in the tanks. This would mean much less residual fluid would be left in the tank. This then reduces the amount of propellant that needs to be kept on reserve for the landing.

 Elon Musk has also recently said in his Twitter account that the F9 first stage has single-stage-to-orbit (SSTO) capability. For an SSTO the residuals in a first stage can subtract a significant amount from the payload it can deliver to orbit. Then the ability to run in an idle mode with minimal residuals left over can significantly increase the payload for an SSTO. So this would be a further advantage of giving the Merlins an idle mode.

Hovering by use of flexible nozzle extensions.
 In the blog post "Altitude compensation attachments for standard rocket engines, and applications", I discussed another method of achieving hovering capability, attaching nozzle extensions to the bottom of the engines that would allow restriction of the thrust. The flexible high temperature materials already exist in the reentry materials used in NASA's Inflatable Re-entry Vehicle Experiment (IRVE). This has the advantage that the nozzle extension would have to only be applied to the one central engine to reduce its thrust on landing.

 However, the extendable nozzle attachments also have an advantage to the SSTO case. By using an extension that can be retracted at launch and fully extended at high altitude, you can get engines usable at sea level that can reach the high vacuum Isp's usually reserved for upper stage engines. In this way the 311 s vacuum Isp of the Merlin 1D can be raised to the same level of 340 s as the Merlin Vacuum. An increase in the vacuum Isp to this extent can as much as double the payload of a SSTO.

 Note that both of these techniques, idle mode or flexible nozzle extensions, would mean hovering capability can actually increase the payload rather than reduce it.

    Bob Clark