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The science of pressure chambers have also advanced, we could just pump whatever material, like liquid air into a pressure tank and then load it into the rocket. No mixing or pumping needed just open the valve and let the pressure out and you will have a very cheap and simple rocket.

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This is absolutely not true - injector design is the most important aspect of designing a thrust chamber. Poor mixing of propellants leads to severe combustion instability, which often leads to explosions. Even the earliest space programs did significant testing on propellant choices and injector designs (see Ignition! by John D. Clark)

Also, pressure fed rockets have always been a fairly terrible design. Pressure feeding requires heavy tanks, and incurs a big mass fraction (dry mass / wet mass) penalty. Outside of rare cases, it's only used for ground testing.

just drop the tank when the weight/thrust ratio is too low. Thanks for the book suggestion! (have not read it yet)

The rocket equation would like to have a word with you. The wall thicknesses required to create rockets with enough thrust to get to orbit on pressure-fed would render the rocket physically impossible.

There is also a lot of control that goes into flying a rocket, and pressure-fed rockets are kind of hard to control.

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