Sunday, June 19, 2011

Looking more at rockets

First, I dug out my spreadsheet of acceleration and potential energy that drove the rules for jump from earlier posts, and found that the radius I had set for Sol earlier was 1.5e15 meters (10 AUs) so just outside Saturn's orbit.  Lets use that, and the average chord of a sphere of that radius is (4/3)r or 2e12m. as the transit distance.

That gives our revised time vs acceleration table, with delta-v added:


g deta-v time (days)
0.1 2.73E+06                  32.74
0.2 4.00E+06                  23.15
0.3 4.90E+06                  18.90
0.4 5.66E+06                  16.37
0.5 6.32E+06                  14.64
0.6 6.93E+06                  13.36
0.7 7.48E+06                  12.37
0.8 8.00E+06                  11.57
0.9 8.49E+06                  10.91
1.0 8.94E+06                  10.35
2.0 1.26E+07                    7.32
3.1 1.55E+07                    5.98
4.1 1.79E+07                    5.18
5.1 2.00E+07                    4.63

Rolling out the Tsiolkovsky equation  we can work out the engine exhaust velocities we need for a range of mass ratios (that is, mass at the start of the transit over mass at the end)


m0/m1   0.1 g    1.0 g 
                 2 4.0E+06 1.3E+07
                 3 2.5E+06 8.1E+06
                 4 2.0E+06 6.5E+06
                 5 1.7E+06 5.6E+06

These are high. but not inconceivable, velocities.  Basically, we have to master some pretty fancy fusion technologies to make it work.  I'll have to do a detailed wok-through to see if I am on the right track, but so far the only outright impossibility I am talking here is still FTL.

2 comments:

  1. I'm math stupid, so I have to ask this: does your computations take into account breaking to achieve relative stopping by your destination?

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  2. This assumes a pass through, having 0 velocity at start and end, but ignoring final rendezvous. Given the delta-v we are talking, capacity to match say an earth orbit is not hard although the details of the maneuvering will be interesting.

    Once I have the map database set up, I want to develop more exact code for this. It's pretty clear, though, that reaction mass resupply is going to be a vital concern.

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