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.

Altitude compensation attachments for standard rocket engines, and applications, Page 2: impulse pressurization methods.

Copyright 2016 Robert Clark

Usefulness of Altitude Compensation for All Rockets.

 I have argued altitude compensation has importance not just for SSTO's but for all launchers. For SSTO's it can double the payload possible. This leads to the unexpected conclusion that for both expendable and reusable rockets SSTO's with altitude compensation can be more cost efficient than two-stage rockets:

The Coming SSTO's: Falcon 9 v1.1 first stage as SSTO, Page 2.

http://exoscientist.blogspot.com/2013/11/the-coming-sstos-falcon-9-v11-first.html

 But in that blog post, it is also shown that even for two-stage rockets such as the Falcon 9 altitude compensation can improve the payload 25%.

 Another important application of it is that it makes it possible for low cost pressure-fed rockets, using multiple cores, to be able to do orbital launches. This brings orbital rockets within the range of even university aerospace departments and amateur rocket developers. Or as I like to say it:

Orbital rockets are now easy.

http://exoscientist.blogspot.com/2015/08/orbital-rockets-are-now-easy.html

  Also multi-cored rockets such as the Delta IV Heavy and Falcon Heavy can double their payload by using cross-feed fueling in conjunction with altitude compensation:

Altitude Compensation Improves Payload for All Launchers.

http://exoscientist.blogspot.com/2016/01/altitude-compensation-improves-payload.html

 This is important because by doubling the Falcon Heavy payload to ca. 100 metric tons, this brings it in the range to do a manned lunar landing mission with a single launch. Also key is that it brings it close to the $1,000/kg price range space advocates have argued is necessary to allow high launch rates and additional cost reductions by volume.

 For these reasons it is important to investigate altitude compensation techniques whether or not you believe in the value of SSTO's. Ironically, though once these techniques are applied to existing rockets, it will become apparent how valuable SSTO's are.

 Altitude Compensation by "Impulse Pressure".

  There are numerous low cost methods to achieve altitude compensation with existing engines:

Altitude compensation attachments for standard rocket engines, and applications.

http://exoscientist.blogspot.com/2014/10/altitude-compensation-attachments-for.html

 In fact part of the point I'm making is the number of ways of accomplishing it at low cost. I'll describe two others here.

 The term "impulse pressure" or "impulse pressurization" is hardly standard. What I mean to say by it is illuminated by this image showing nozzles not optimized to altitude:

Nozzles can be (top to bottom):
underexpanded,
ambient,
overexpanded,
grossly overexpanded.
If a nozzle is under- or overexpanded, then loss of efficiency occurs relative to an ideal nozzle. Grossly overexpanded nozzles have improved efficiency relative to an overexpanded nozzle (though are still less efficient than a nozzle with the ideal expansion ratio), however the exhaust jet is unstable.^[7]

https://en.wikipedia.org/wiki/Rocket_engine_nozzle

  Rocket engines achieve their best efficiency at vacuum conditions with a large nozzle that allows the exhaust to expand out to near vacuum ambient pressure. However, having a large nozzle at sea level can cause unstable flow that can even tear apart an engine. It's referred to as "flow separation" and is illustrated in the bottom image. 

 Then the idea behind the "impulse pressurization" is to use a large nozzle at sea level but direct a portion of the exhaust flow out towards the sides of the nozzle to counteract this flow separation. That is, use the momentum, the impulse, of the flow to provide outwards pressure against the walls.

 There are two ways this outwards impulse can be provided: you could have the exhaust be swirled by vanes within the nozzle to cause an outwards momentum to the flow or you could have the exhaust be deflected outwards by a shelf within the nozzle that is at an angle to direct the portion of the exhaust near the walls, outwards to impinge against the nozzle walls.

  

 Note that for both of these methods you don't want most of the flow to be swirled or directed outwards but only the portion of the flow near the walls. Note also the swirl vanes or deflecting shelf can be rather far down towards the bottom of the nozzle since the degree of flow separation usually is far down towards the bottom of the nozzle. So for both of these methods most of the thrust attained at vacuum will be maintained at sea level.

 Additionally,  as the rocket increases in altitude the ambient pressure decreases and there is reduced need for this outward pressure. So the portion of the exhaust that is directed outwards will be reduced as the rocket gains altitude, to the point that the full exhaust will be allowed to flow directly downwards when the rocket reaches near vacuum. This can be done in either method by changing the angle of the swirl vanes or deflecting shelf to gradually decrease to null as the rocket achieves altitude.

(Patent pending.) 

An Earlier Patent?

 I have found one patent that attempts altitude compensation by a swirling exhaust flow, but not the deflecting shelf method:

                3,443,384

  SWIRLING FLOW NOZZLE.

James _E. Webb, Administrator of the National Aero
nautlcs and Space Administration with respect to an
invention by Frank X. McKevitt, Palos Verdes Penin
sula, Calif.
Filed May 17, 1967, Ser. No. 640,787
Int. Cl. F02k 1/02, 9/00; B05b 3/00
U.S. Cl. 60--263 4 Claims
ABSTRACT OF THE DISCLOSURE
This disclosure relates generally to rocket engines. It
teaches a method and construction for increasing the effi
ciency of a rocket engine by matching its exhaust gas
pressure with changing ambient pressure. Essentially, a
gas is introduced tangential‘ly into the engine so as to form
a vortex within the nozzle. The size of the vortex can be
used to vary the effective throat area of the nozzle. The
size of the vortex can be changed by varying the relative
amounts of axial and/or tangential flow of gases to the
nozzle.

https://www.google.com/patents/US3443384

 There are some differences. This attempts to swirl the combustion gases right within the combustion chamber and thus induce a swirl within the entire exhaust flow inside the nozzle. In contrast, my method will attempt to maintain a large proportion of the vacuum thrust and Isp by only inducing the swirl near the bottom of the nozzle and only for the outer portions of the exhaust flow.

 But a key distinction is that my proposal could be attached to the nozzle of existing engines. That is important to maintaining the idea that altitude compensation is simple and low cost to accomplish.

 Orbital Technologies Corp (ORBITEC) is investigating swirling, vortex motion within the combustion chamber of their engines:

ORBITEC Expands Vortex Rocket Engine Family with Successful Demonstration of New Propellants.
MADISON, Wis. (Nov.  10, 2015) - Sierra Nevada Corporation’s (SNC) wholly-owned subsidiary Orbital Technologies Corporation (ORBITEC) recently completed successful testing and demonstration of three different propellant combinations for its existing 30,000-pound thrust vortex rocket engine. Completing this advancement in less than a year, ORBITEC is rapidly progressing its offering of engines for orbital maneuvering, upper-stage engines that ignite at high altitude, and small-to-medium-scale air and ground launch stage engines.
http://www.sncspace.com/AboutUs/NewsDetails/2243

  Their purpose however is for cooling techniques on the combustion chamber walls not altitude compensation. However, since it uses the same method as the prior patent it may work for altitude compensation as well.


  Bob Clark

UPDATE, January 18, 2016:
  I used the term "impulse pressurization" to describe the pressure provided by a portion of the exhaust flow directed to impinge on the nozzle walls.
 Actually, there is a term in common use for this concept, called "dynamic pressure". For instance during rocket launch, rockets have to be throttled down during the period called "Max Q" where the sum of the ambient pressure at altitude and the force pressure due to the air flow at high speed is at a maximum.

 So I could have called this idea "dynamic pressurization".

Altitude Compensation Improves Payload for All Launchers.

Copyright 2016 Robert Clark

 It is unfortunate that SSTO's have been, incorrectly, deemed unviable. Since altitude compensation has only been thought of in terms of improving the payload of SSTO's, little research has gone into these methods, as SSTO's were not considered worthwhile.

  However, in point of fact altitude compensation improves the payload even for multistage rockets. In the blog post "The Coming SSTO's: Falcon 9 v1.1 first stage as SSTO, Page 2", I showed using the payload estimator by Dr. John Schilling altitude compensation improved the payload of the two-stage Falcon 9 by 25%. 

 Interestingly, the increase for the case of a rocket with side boosters can be as high as 40%. This is the case for the Delta IV Heavy. 

 According to this page the payload to LEO of the Delta IV Heavy is 25,980 kg:

Delta IV Heavy – RS-68A Upgrade.

http://spaceflight101.com/spacerockets/delta-iv-heavy-rs-68a/

 Using the specifications from this page and inputting the vacuum values for the thrust and Isp, since the Schilling calculator requires inputting the vacuum values as it takes into account the diminution at sea level, the calculator appears as:

 And the results are:

Mission Performance:

Launch Vehicle:	User-Defined Launch Vehicle
Launch Site:	Cape Canaveral / KSC
Destination Orbit:	185 x 185 km, 28 deg
Estimated Payload:	23979 kg
95% Confidence Interval:	19412 - 29682 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.

 A rather close approximation to the actual payload. 

 Now we'll consider the result when altitude compensating nozzles are used. First, note that there are numerous low cost methods of accomplishing altitude compensation. For instance the RL-10 engine increases its vacuum Isp to ca. 464 s simply by attaching a nozzle extension. Other low cost methods are discussed in "Altitude compensation attachments for standard rocket engines, and applications."

  Increasing the vacuum Isp to 464 s increases the thrust proportionally to (464/414)*3560 = 3,990 N. Then the inputs to the calculator now appear as:

 This 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:	33410 kg
95% Confidence Interval:	27137 - 41212 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.

 About 40% higher than the case without altitude compensation. The reason why it should be expected the increase is higher than in the standard two-stage case is the center core stage in a triple-core launcher spends more of the time at high altitude where the vacuum Isp would obtain.

Altitude Compensation plus Cross-feed Fueling.

 This effect should be even more pronounced with cross-feed fueling. Cross-feed means the center core stage would have its full propellant load after the side boosters are jettisoned so it spends even more time at vacuum conditions.

 The Schilling calculator emulates cross-feed by inputting 2/3rds of the actual propellant load in the field for the side boosters, but increases the value input for the center core propellant to (1 +2/3) times the actual value (See discussion here for an explanation of how the calculator emulates cross-feed.)

 The results are:

Mission Performance:

Launch Vehicle:	User-Defined Launch Vehicle
Launch Site:	Cape Canaveral / KSC
Destination Orbit:	185 x 185 km, 28 deg
Estimated Payload:	48961 kg
95% Confidence Interval:	41112 - 58206 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 is double the initial payload capability without cross-feed and altitude compensation. Note also 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.

And For the Falcon Heavy? 
 This payload for the upgraded Delta IV Heavy would rival the announced 53 metric tons(mT) LEO payload of the Falcon Heavy with cross-feed fueling and exceed that of the FH without it. But the increase in thrust of the Merlin 1D and increase of propellant load should increase the LEO payload of the Falcon 9 and Falcon Heavy. If the payload to geostationary for the F9 is increased by 30% as announced by SpaceX, then we expect the payload to LEO for the F9 and Falcon Heavy also to be increased a similar amount.  

 Then the current upgraded Falcon Heavy with cross-feed may now be in the 70 mT range. And if altitude compensation also gives this triple-cored launcher a 40% increase in payload that would bring it to the 100 mT range. This is important because this is the range estimated to be required for a manned lunar lander mission by a single launcher, and would be one in a cost range of only $120 million.

  Bob Clark

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.