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April 15, 2004

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 (m_d), the exit velocity of the propellant (v_x), the surface area of the trailing surface (A_t) , the mass of the payload (m_p), and the total velocity imparted to the payload (v_p). 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 m_d necessary to accelerate m_p 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 m_d / m_p required for an in-system transit at 1g with midpoint turnaround.

7. Determine the time and m_d / m_p required for a 4ly transit at 1g with midpoint turnaround.
   

Posted by Chris at April 15, 2004 03:01 PM

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