An Exercise

This probably won’t make sense to anyone else, but I need to make a note reminding myself about something I thought about over lunch. (I always lose them otherwise, so maybe this will help me remember.) Read on if that kind of thing interests you.

Given: an ideal pseudoablative mass driver which uses pattern conversion to translate the trailing surface into a high-velocity sheet, imparting an acceleration to the remaining mass and exposing a self-similar surface. The mass driver is completely consumed by the process.

  1. Develop a set of equations relating the mass of the driver (md), the exit velocity of the propellant (vx), the surface area of the trailing surface (At) , the mass of the payload (mp), and the total velocity imparted to the payload (vp). Use the rocketry equation as a starting point, but use relativistic pseudovelocities in terms of multiples of c.
  2. Figure out how to wedge the instantaneous acceleration (a) in there somewhere.
  3. Re-develop the “ideal conversion” equation, which relates the md necessary to accelerate mp to a given pseudovelocity.
  4. What kind of exit particle would provide the best efficiency for the driver? A photon?
  5. Determine how close this engine comes to the “ideal conversion” developed in 2.
  6. Determine the time and md / mp required for an in-system transit at 1g with midpoint turnaround.
  7. Determine the time and md / mp required for a 4ly transit at 1g with midpoint turnaround.

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