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I am reading the rocket propulsion elements book by sutton and I came across the following statement: "Because the propellant tank has to fly. its mass is at a premium and the tank material is therefore highly stressed." I am just learning, and have no strong technical background, so I will appreciate the explanation! Thanks!

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    $\begingroup$ "At a premium" is a generic English expression; are you familiar with it? $\endgroup$ – chrylis Jul 11 at 23:57
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The rocket equation says that every bit of mass you carry on your rocket is very expensive, especially if that mass is not fuel. Designers of rockets are willing to spend lots of time and effort making sure that their rockets are as light as possible, hence "mass is at a premium." This inevitably means that the tanks are as thin as is feasible.

Stresses are the internal forces that are trying to tear solid objects apart. If two structures (like rocket fuel tanks) are carrying identical forces (like the pressure and weight of rocket fuel), the structure with thicker walls and bigger elements will have lower stresses because it has more area to spread the load out over. The thinner lighter structure is therefore more stressed, and closer to breaking.

Rocket structural designers have to design a structure that is just strong enough to carry the loads the rocket will see, but if they build it any stronger it will be heavier. There is a careful balancing act between safety and efficiency.

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It means, the fuel tank's mass costs fuel to move it and of course that extra fuel has mass too and that mass needs more fuel. Premium here means extra fuel.

So there is a an effort to keep the mass of the fuel tank at the absolute safe minimum, hence allowing the tank material exposed to high stresses.

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