This topic has been on my mind for some time (lychee likes imagining game design, okay?), so maybe somebody can help me. In this fictional setting, we have: A rocket engine that has an exhaust velocity close to the speed of light A fuel source with incredibly high energy density that can be converted by the engine at close to 100% efficiency I’d like to calculate the following: How much delta-v can you get from a rocket engine like this? How high does the fuel energy density need to be to power this engine? —————————— Extra: The way I have this conceptualized is that the rocket engine is a particle accelerator that ejects mass (lets use hydrogen for simplicity) at velocity v where v is close to the speed of light. I’m assuming energy is converted perfectly so the energy required to accelerate mass is naively related to the kinetic energy of the ejected material (albeit my understanding of relativistic physics is poor). Let F be the fuel source with mass m that provides the energy for this engine. Let P be the propellant with mass p that is ejected by the rocket engine. Curious about what kind of mystical fuel source this engine would require, and whether this type of engine would be sufficient to drive large spaceships that you see in science fiction.