The Coming SSTO's: multi-Vulcain Ariane.

Copyright 2013 Robert Clark

 The option the ESA decided on for the planned Ariane 6 was the version using a solid propellant first stage:

CNES, ASI Favor Solid-Rocket Design For Ariane 6.

By Amy Svitak

Source: Aviation Week & Space Technology

October 15, 2010

https://web.archive.org/web/20130419155317/http://www.aviationweek.com/Article.aspx?id=/article-xml/AW_10_15_2012_p26-505016.xml&p=1

 However,  one of the other options discussed for the Ariane 6 would also allow manned European flight capability. This would be the two Vulcain core version.

CNES is evaluating these three launch vehicle concepts for a next-generation Ariane 6: two based on solid-rocket-motor technology plus an all-liquid-fueled launcher with optional solid-motor boosters. (Credit: CNES)

 To estimate the payload capability for the twin Vulcain core I'll use John Schillings launch performance calculator:

Launch Vehicle Performance Calculator.
http://www.silverbirdastronautics.com/LVperform.html

 In the calculations for this multi-Vulcain Ariane core stage, I used this page for the specifications on the Ariane:

Space Launch Report:  Ariane 5 Data Sheet.
http://www.spacelaunchreport.com/ariane5.html#config

 For the Vulcain 2 specifications, I've seen different numbers in different sources, though close to each other. I'll use this source:

Vulcain 2.
http://www.astronautix.com/engines/vulcain2.htm

 I'll also use the earlier Ariane 5 "G" version that is lighter than the current "E" version to be lofted by two Vulcains without side boosters. According to the SpaceLaunchReport page it had a 170 mT gross mass for the core at a 158 mT propellant load, giving a 12 mT dry mass.
 According to the Astronautix page, Vulcain 2 has a 434 s vacuum Isp and 1350 kN vacuum thrust. So two will have a 2700 kN vacuum thrust. The Vulcain's mass is listed as 1,800 kg. So adding another will bring the stage dry mass to 13,800 kg.
Now input this data into Schilling's calculator. Select again default residuals and select "No" for the "Restartable Upper Stage?" option. Select the Kourou launch site for this Ariane 5 core rocket. For the orbital inclination, I input 5.2 degrees. I gather Schilling uses this for Kourou's latitude since deviating from this decreases the payload. I chose also direct ascent for the trajectory.

Then the result I got was 7,456 kg(!) to orbit:

================================
Mission Performance:
Launch Vehicle:     User-Defined Launch Vehicle
Launch Site:     Guiana Space Center (Kourou)
Destination Orbit:      185 x 185 km, 5 deg
Estimated Payload:      7456 kg
95% Confidence Interval:      4528 - 10898 kg
================================

 We should be able to remove a component on the Ariane 5 core to lighten the weight for this application. Ed Kyle on his Spacelaunchreport.com page discusses the Liberty rocket that had been planned to use a SRB first stage and an Ariane 5 core second stage. For the Liberty application, a forward skirt on the core called the JAVE ("Jupe AVant Equipée") that transmits the forces of the two solid boosters to the core would be removed. This will also be removed for our application without solid boosters.
 The JAVE massed 1,700 kg. So our payload could be increased to 9,156 kg. However, Kyle also discusses on his page on the Liberty rocket that the increased thrust from the SRB first stage would require thicker walls on the Ariane core now used as an upper stage.
 The thicker walls on the Ariane 5 core for the Liberty rocket are indicated in this video:

 The 5-segment SRB to be used on the Liberty rocket has 12 times the thrust of the Vulcain engine. Yet as seen in the video the increased thickness to handle the increased axial load is only 50%. Then only doubling the thrust by adding a second Vulcain quite likely will require a much smaller increase in thickness. I'm informed that the 158 mT propellant mass tank has a dry weight in the range of 4,400 kg. So even increasing the thickness 50% increases the weight by ca. 2,200 kg, and the payload would still be approx. 7,000 kg.  A problem with this estimate though, aside from the unknown accuracy of the video, is that it is based on the larger Evolution "E" version of the Ariane 5 core, which might not require as much strengthening to handle the higher thrust loads as the smaller "G" version.  So we'll use a formula for calculating the thickness of a propellant tank based on the axial load as given on this lecture page: Launch Vehicle Design: Configurations and Structures. Space System Design, MAE 342, Princeton University Robert Stengel http://www.princeton.edu/~stengel/MAE342Lecture4.pdf  on page 9:

  From the first formula the critical buckling load without the pressurization effect is:   σ_{c,w/o pressure} = [9(t/R)^1.6 + 0.16(t/L)^1.3]*E.   Multiplying out the second formula for critical buckling with the pressurization effect you see it's:   σ_{c,w/ pressure} = σ_{c,w/o pressure} + 0.191p(R/t).   Now use the formula on p. 8 that relates the tensile strength of the material to the thickness required of a pressurized tank:

   _{You see that}  σ_hoop = p(R/t)  so that the formula above becomes:     σ_{c,w/ pressure} = σ_{c,w/o pressure} + 0.191σ_{hoop .   Now use values for the tensile strength of aluminum alloy. The aluminum alloy used on the Ariane 5 core tanks, Al 2219, happens to get stronger at cryogenic temperatures:}

 Table taken from Properties of Aluminum Alloys: Tensile, Creep, and Fatigue Data at High and Low Temperatures, page 86. The table gives the aluminum alloy strength at liquid hydrogen temperatures as 685 MPa and elasticity modulus, E, as 85 GPa.  For the Ariane 5 core "G" version, the hydrogen tank walls are only 1.3 mm thick, while the oxygen's, 4.7 mm. The diameter of the tanks is 5.4 m. Because of its extreme wall thinness it's the _{hydrogen tank whose stress has to be limited. It's length is about 18 m. Then the formula for the critical buckling load without pressurization gives:} σ_{c,w/o pressure} = [9(t/R)^1.6 + 0.16(t/L)^1.3]*E = [9(0.0013/2.7)^1.6 + 0.16(0.0013/18)^1.3]*85*10⁹ = 3,800,000 Pa.  And the additional buckling strength due to pressurization is 0.191σ_hoop = 0.191*685,000,000 = 130,800,000 Pa, for a total critical buckling load of 134,600,000 Pa.  The maximum thrust of two Vulcain 2's will be 2,700,000 N. The cross-sectional area of the hydrogen tank walls is 2*π*R*t = 2(3.14)(2.7)(0.0013) = 0.022 m² . Then the maximum axial pressure is 2,700,000/0.022 = 123,000,000 Pa.  This is indeed less than the critical buckling load of 134.6 MPa. However, for a manned launcher a safety factor of 1.4 is usually included. This will require the maximum axial pressure to be less than 96 MPa. This requires a wall thickness of 1.6 mm, about a 25% increase. This still only increases the tank weight by 1,000 kg, so the payload becomes now ca. 8,000 kg, still quite high for a SSTO. Remember also switching to aluminum-lithium alloy can save as much as 25% off the dry weight which would bring us again to the 9,000 kg payload range.


   Bob Clark