From: gcowan@eagle.ca   
      
   Dre wrote:   
   >   
   > I was thinking recently what would be requirements of an ideal   
   > interplanetary spacecraft capable of carrying humans around the solar system   
   > within reasonable times (ie 1 week to 2 years) ignoring the costs of   
   > development. I thought the following would be necessary:   
   >   
   > Radiation protection   
   >   
   > Artificial-gravity generation   
   >   
   > Fuel/Food supplies/generation for up to 4 years   
   >   
   > Adequate living space   
   >   
   > Ship velocities of up 100km/s   
   >   
   > 100km/s Debris Impact Shield   
   >   
   > In focusing on the velocity aspect and propulsion requirements I chose   
   > 100km/s because if you take a solar system map or NASA's solar system   
   > simulator you can see at 100km/s you can get almost anywhere within the   
   > times shown above and still have enough delta-V to break orbit from some of   
   > the largest gas giants. I also concluded that in order for the ship achieve   
   > these travel times it should achieve 100km/s within 1 day (24hrs).   
   >   
   > This means for a ship of mass, 1000 tons, a force of 1160kN would be   
   > required to produce an acceleration of 1.16m/s^2 at 0.12 gees. Is this   
   > right?   
   >   
   > Also what kind of propulsion system could achieve this? Thermo-nuclear?   
   > Vasimr? Fusion?   
      
      
   The really difficult thing is the radiator.   
   Heat engines need to get rid of heat.   
      
   Some fundamental relations for a simplified model follow --   
   not quite as simplified as "Assume constant acceleration", though.   
      
   I think if you try them out,   
   you'll find there are better acceleration schedules to follow   
   than your "achieve 100km/s within 1 day".   
   You have the fission reactor and the ultra-high-performance   
   radiator; why not use them for most of the trip?   
   (If you have a fusion reactor, it hardly matters.   
   The radiator is the limiting factor.)   
      
   These rules take into account how an ion rocket's acceleration varies   
   as its constant thrust acts on its diminishing mass.   
      
   Imagine a ruler of length 'D', negligible mass,   
   sitting in vacuum, free fall,   
   and assign a fraction 'f' of its length that a rocketship   
   flying along the edge will traverse with its motor on --   
   either forward or braking acceleration.   
      
   [1] PoweredFlightTime = sqrt (2fDJ/Z) + fD/J   
   [2] MassRatio = 1 + PoweredFlightTime*Z/(0.5*J^2)   
   [3] T = PoweredFlightTime + (1-f)*D/(J/2 * ln (MassRatio))   
   [4] FinalAcceleration = 2Z/J   
   [5] InitialAcceleration = 2Z/(J*MassRatio).   
      
   'Z' is the ratio of kinetic power in the departing propellant stream   
   to nonpropellant mass. 'J' is how fast the propellant is thrown.   
      
   I don't know what values of 'Z' are seriously proposed;   
   1 kilowatt per kilogram sounds difficult, but conceivable.   
   So a vessel with mass 30 tonnes, plus propellant --   
   the stuff that will be thrown aft as ions --   
   will have 'Z' = 1 kW/kg if it can put 30 MW into the jet.   
      
   That can probably be done with a 300-thermal-megawatt reactor   
   and a 270-thermal-MW radiator;   
   conceivably just 150 MW, with 120 MW dumped.   
      
   Putting 'J', the ion expulsion speed, to 37,000 m/s,   
   we get that if Mars and Earth were motionless   
   with respect to each other, 63 million km apart,   
   and the ship crossed between them with its ion rocket working   
   through 0.4 of the distance ('f'=0.4),   
   and their gravity could be ignored --   
   as might be fairly close to true   
   if the trip were between space stations   
   in high orbit around each planet --   
   a trip between them could take a little over 40 days.   
      
   PV panels could provide much lower values of 'Z' at Earth,   
   lower still at Mars; that variability cannot be handled   
   by the simple functions of 'D', 'Z', 'f', and 'J'   
   except maybe very crudely, by putting in an average.   
   Try it.   
      
   Interestingly, larger values of 'f', such as   
   thrusting all the way, 'f' = 1.0, mean you arrive later.   
   So of course do much smaller values.   
      
      
   --- Graham Cowan   
   http://www.eagle.ca/~gcowan/Paper_for_11th_CHC.doc --   
   How individual mobility gains nuclear cachet.   
   Link if you want it to happen.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)