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.