From: sylvia@email.invalid   
      
   On 31-May-21 2:46 pm, Sylvia Else wrote:   
   > On 31-May-21 1:30 pm, JF Mezei wrote:   
   >> On 2021-05-30 20:06, Sylvia Else wrote:   
   >>   
   >>> The moon bus never made sense to me, with suborbital transits seeming   
   >>> more practical.   
   >>   
   >> If gravity becomes low enough, is there a point where small vertical   
   >> trusters to maintain low altitude over ground become feasable?   
   >   
   > If it was so low that ion thrusters were sufficient, then I suppose.   
   > Otherwise I don't see it happening.   
   >   
   >>   
   >> If you are doing a survey or search and rescue, you don't want to be   
   >> going too fast or too high.   
   >>   
   >> I take it moon gravity at 1/6s of earth is still too much for such   
   >> horizontal travel above ground ?   
   >>   
   >   
      
   OK, let's try that again, this time, shaking out the aging-brain   
   cobwebs, and using the equation for change in velocity rather than   
   distance travelled.   
      
   > Consider that the rockets supporting the moon-bus have to provide thrust   
   > that would, in free space, impart an acceleration of 1/6g.   
   >   
   > So in free space, the delta-v would be   
   >   
   >      g/6 * t   
   >   
   > where t is the duration in seconds.   
   >   
   > Applying the Tsiolkovsky rocket equation to this gives   
   >   
   >      g/6 * t = Isp * g * ln(m0/mf)   
   >   
   > where Isp is the specific impulse, m0 is the initial mass (full   
   > fuelled), and mf is final mass (all fuel gone).   
   >   
   > Rearranging, and cancelling the g's gives,   
   >   
   >      ln(m0/mf) = 1/6 * t / Isp.   
   >   
   > Pull a reasonably typical Isp of 300 out of the air, and try for a 30   
   > minute (1800 second) mission, gives   
   >   
   >      ln(m0/mf) = 1/6 * 1800 / 300   
   >   
   The right side happens to come to 1. And, presumably again for aging   
   brain reasons, I made a second mistake here in the interpretation.   
      
   Anyway, that means that m0/mf is about 2.7, meaning the vehicle is   
   initially 63% fuel.   
      
   Assuming that I've got this right this time, it's still a lot of fuel to   
   be obtained from somewhere, but not as bad as I previously thought.   
   Perhaps the documentary wasn't so far wrong.   
      
   Note though that things get progressively worse for longer missions. The   
   natural log (ln) on the left means that the fuel fraction goes up   
   exponentially with mission length, and if there's no fuel at the   
   destination, the mission length is the round-trip time.   
      
   Sylvia.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)