From: mjessick@verizon.net   
      
   Parallax wrote:   
   > Sorry if I am belabouring the obvious but rocketry is not my field   
   > (x-ray optics is) but was curious about solar thermal rockets so   
   > looked in my old physics book at the derivation of the rocket   
   > equation.   
   >   
   > Using M=Moexp(-v/ve)   
   > where M is payload mass, v is rocket final velocity and ve is exhaust   
   > velocity of fuel, plugging in some numbers of about 2 km/sec for ve   
   > and 8 km/sec for orbital velocity we get a mass ratio of Mo/M of 55.   
   > That is, the payload is only 1/55 of total initial mass.   
      
   all good   
      
   > Do the same for the same velocity ratio where the fuel is all burned   
   > at one time and we get a mass ratio of 1/5, a huge increase.   
      
   >   
   > Mp/Mo=r     Mf/Mo=1-r   
   >   
   > MfVf=MpVp   
   >   
   > gives (1-r)/r=4 gives r=1/5.   
      
   > This seems to imply that whenever the exhaust velocity is limited in   
   > some fashion, for a given amount of fuel, it makes more sense to   
   > expend as much fuel as fast as you can than to expend it slowly.   
      
   This is incorrect using simplistic open space assumptions   
   (zero gravity, or burning perpendicular to constant gravity),   
   where the rocket equation strictly applies. In this very simple   
   situation, the burn rate doesn't matter.   
      
   The rocket equation is independent of the amount of thrust (how fast   
   (mass flow rate) you burn), as long as there is some limit (as you   
   correctly point out). In practice, for a "rocket", there is always   
   a limit.   
      
   Your "v" is usually described as "delta V", the change in velocity.   
      
      
   So, the mass flow rate doesn't matter in open space, where the rocket   
   equation strictly applies. In an inverse square gravity field, however,   
   mass flow rate does matter because if you are expending energy raising   
   the propellant to a higher potential energy state before burning it,   
   you aren't getting all the energy out of it you otherwise could.   
      
      
   > This would seem to imply for ion engines where the fuel speed is   
   > limited by the electric field that can be applied, that capacitors be   
   > charged to ionize a lot of fuel at one time rather than run the   
   > ionization continously.  The same fuel expenditure results in far more   
   > velocity for the pulsed case than the continously emitted case.   
      
    > It also seems to imply that for something like a solar thermal engine   
    > that it might be better to charge capacitors and discharge them to   
    > heat a burst of propellant than to heat it continously.   
    >   
    > Does this make sense?   
    >   
      
   Yes, this is correct in practice. But _only_ because of the   
   second order orbital mechanics effects described above.   
   In open space, the delta-V at high mass flow rate   
   and at low rate would be the same. Value as calculated   
   by the rocket equation.   
      
   Integrate to derive the rocket equation yourself for constant mass flow   
   rate and exhaust velocity and you will see how it works. (The mass flow   
   rate drops out)   
      
      
   > Nothing more confusing than an old former physicist trying to   
   > re-understand basic stuff like this.   
      
   As I google'd for " "rocket eqution" and derivation "   
   I found people confused because their teachers had asked them a question   
   intending to get the rocket equation as an answer, but the problem   
   statements included effects that the rocket equation doesn't consider   
   (e.g.: gravity)  This kind of thing is counter productive.   
   (Kind of like the Galileo rock dropping experiment that is only   
   correct in a vacuum.)   
      
      
   So my summary is: your conclusion is correct in practice, but the   
   reasoning is faulty because it used a solution to a simpler problem   
   where the effect you seem to be interested in isn't considered.   
      
      
   Your wider question of the optimization of the mass flow rate   
   I'll leave to others. I'll just point out that adding   
   energy storage means adding mass that you have to accelerate.   
      
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    * Origin: you cannot sedate... all the things you hate (1:229/2)