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In the Falcon 9 user guide manual it is noted that the first and second stage LOX tanks are monocoque. That means the tank is made of a single cylindrical shell. Is that possible? How can the first stage LOX tank be monocoque?

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The dictionary definition of monocoque

  • an aircraft or vehicle structure in which the chassis is integral with the body.

Based on that definition, Falcon 9 has monocoque fuel tanks. The tank wall is also the outer skin of the rocket. In your question, you specifically call out the first stage LOX tank. Both stages use similar manufacturing techniques and they are built from common materials and welding rigs.

A concept you might not be familiar with is SpaceX's use of a common bulkhead. This is an internal divider between the LOX tank and the RP-1 tank, where both propellants share a single divider.

From a similar question: What are the criteria to put the oxygen tank above or below the fuel tank for a given stage of a rocket? enter image description here

A monocoque fuel tank looks like the second example in the above image. This has a few advantages. It is the most mass-efficient design, since all tank structure is used as vehicle structure, and no additional tank walls are "doubled" by using multiple bulkheads.

However, it introduces several engineering challenges. A common bulkhead might need to separate two propellants of drastically different temperatures. Also since the propellant tanks are the physical rocket structure, adding external or internal mounting points for things like grid fins, sensors, and other mechanisms can be challenging.

In comparison, the N-1 rocket used spherical tanks with supporting structural elements. enter image description here

http://www.ninfinger.org/karld/My%20Space%20Museum/n1.htm
That's a lot more empty space in the vehicle and extra material to connect things together, which ultimately increases dry mass and reduces the delta-v of the rocket.

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