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*To*: Steve VanDevender <stevev@efn.org>*Subject*: Re: Questions about your letter to SD*From*: T.L.G.vanderLinden@student.utwente.nl (Timothy L.G. van der Linden)*Date*: Sat, 30 Sep 1995 20:50:30 +0100

Hello Steve, >I am fond of using what relativity texts call "geometrized >units". In geometrized units time is also measured in units of >distance by multiplying conventional time by c (the speed of >light), and velocity is therefore dimensionless. In more >advanced uses even mass is measured in units of distance (using >the conversion factor G/c^2)! > >The expression in conventional units, off the top of my head, >seems like it should be: > >v / c = p * c / E > >or > >v = p * c^2 / E I had seen you use these geometrized units and understood most of them. It's a bit tricky for me since I always used the conventional notation. Unfortunately you are one of the very few that use this notation. Where I made the mistake was that I had not translated the E to E/c^2. Thank you for the explanation. > > >about a 2:1 Earth time/spacecraft time ratio. Accelerating to > > >0.866c at 1 g will take about 1.14 years of spacecraft time. > > > > I think it is 1.27 years, but it does not make much difference in the > > calculated values. > >As far as I know the formula I use is correct: > >v = tanh(a' * t') > >v = velocity (unitless, as a fraction of c) >a' = spacecraft acceleration in its local frame (units of 1/distance) >t' = spacecraft elapsed time (units of distance) > >Again, this uses geometrized units; for conventional units you'd >use the formula: > >v = c * tanh(a' * t' / c) > >Perhaps you calculated the global frame time rather than the >spacecraft local time? No, I used the same formula you did and still get 1.277 years (a=9.8 c=3E8, v=0.866c). >I believe that I discussed why I considered both fuel and exhaust >velocity, by citing the example of burning the fuel and using the >energy to accelerate a lower quantity of reaction mass to a >higher velocity. I still believe that such a case results in >much poorer behavior; at least by the analysis I've done it's >better to burn the fuel and eject all the waste products at a >lower velocity than to burn the fuel and leave most or all of the >waste products on the ship. I'm sorry, I must have missed that part when I read your letter. Dumping the waste products is obviously better than dragging them with the Asimov. >Now that you've induced me to think about it further, I'd have to >say that the efficiency of the mass-to-energy conversion from >burning the fuel is really what's more critical than either the >fuel type or the reaction exhaust velocity. Using hydrogen for >fuel and burning it with fusion means that you can't convert more >than 1/300 of the fuel mass to energy (using your figure), and >hence no more than 1/300 of the fueled spacecraft mass converted >to energy can be applied to accelerating the payload. A >self-fueled ship simply cannot reach high relativistic speeds >with a reasonable fuel-to-payload ratio without being able to >convert a large fraction of the fuel to energy. Indeed, the only feasible option for self-fueled ships would be a matter & anti-matter mixture. Do you know how efficiently energy can be transferred into anti-matter these days? Or to put the question in an other way, what are the input energies of these supercolliders and how many anti-particles can be isolated after a collision. It's hard to get accurate data, so I haven't a clue of the efficiency to create anti-matter. The energy needed for the anti-matter creation probably has to come from solar power and fusion. The reason that I followed your derivation quite thorough is that about a week ago I had finished calculations which should give the same results. My approach is completely different from yours. My main goal was to calculate the energy needed for such a trip. I had planned to send it to SD soon. I'd appreciate it very much if you would look at it before I send it to SD. It's mainly formulas and about 10Kbyte long. If you are interested I will send it to you. Greetings Timothy

**Follow-Ups**:**Re: Questions about your letter to SD***From:*Steve VanDevender <stevev@efn.org>

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