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

*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:

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

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.

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

================================

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:

From the first formula the critical buckling load without the pressurization effect is: σ

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

Bob Clark

_{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*10^{9}= 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 m^{2}. 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