Re: rocket motion

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

Barlow can speak for himself, but let me give another bystander's
viewpoint. I interpreted his remark "the rocket throws out mass
linearly" to mean that the fuel flow rate was constant and so the
mass decrease of the rocket+fuel is linear, and therefore the thrust
is constant. His conclusion is that it will accelerate as long as
there is fuel--not a surprise, but that does imply that there is no
speed limit of the nature "the rocket can't go faster than its
exhaust." The only speed limit is given by the fact that the fuel
supply cannot be more that the value of his parameter m (i.e., 100%
of the initial mass).

I didn't try to rederive his equation, but the consequences of it
seem reasonable. One conclusion is that if the fraction of the
initial rocket mass, m, that is fuel is less than 0.637 (1-1/e) then
the rocket will run out of fuel before its speed is greater than the
speed of the exhaust, v. If the fraction is greater than that then
the final speed of the rocket can be greater than v. Of course all
this assumes that the only force on the rocket is that of the fuel
exhaust (which is constant), and that the rocket starts from rest (or
at least that the rocket speed is measured WRT an inertial reference
frame in which it was originally at rest). It strikes me as
interesting that this factor is independent of the value of m. I
probably wouldn't have guessed that in advance, but since the mass
frequently drops out of equations where the mass appears on both
sides of F=ma, I suppose it isn't too surprising.

Hugh

> I'm sure I must be misunderstanding Barlow's rocket model.
> Barlow draws a limited conclusion concerning
> a model of rocket propulsion of a rather unusual kind
> i.e with continually increasing thrust) - the conclusion
> being that in this case the rocket accelerates.
> (His last sentence, starting, "Apparently...")
>
> To which I respond...."and a rocket with constant
> or diminishing thrust also accelerates!"
>
> I would appreciate a further clarification of
>  Barlow's position.
>
> Brian
>
> At 10:24 12/16/99 EST5EDT, you wrote:
>  >Gang:
>  >
>  >Do you like solving already solved problems?  Sometimes
>  >they are fun.  I made two assumptions about rocket
>  >motion;  (a) the rocket throws out mass linearly; and (b)
>  >the relative velocity of the rocket with respect to the
>  >exhaust is constant.   If we let v be the relative velocity
>  >of the rocket with respect to the exhaust,  m be the
>  >initial mass of the rocket and fuel, and a be the rate at
>  >which the mass of rocket and fuel decreases; then we can
>  >calculate the distance the rocket has moved with reference
>  >to some origin in outer space with respect to a time
>  >parameter.
>  >
>  >My result is:
>  >
>  >        x(t) = (mv/a){(1 - at/m)ln(1 - at/m) + at/m}
>  >
>  >Apparently, its speed continues to increase as long as the
>  >rocket motors will continue throwing out the mass so that
>  >the relative velocity is constant and the decrease of the
>  >mass of the rocket-fuel part of the system is linear. WBN
>  >Barlow Newbolt
>  >Department of Physics and Engineering
>  >Washington and Lee University
>  >Lexington, VA 24450
>  >
>  >Young man if I could remember the names of all of
>  >these particles I would have become a botanist
>  >                        Enrico Fermi
>  >Telephone and Phone Mail:  540-463-8881
>  >Fax: 540-463-8884
>  >e-mail: NewboltW@madison.acad.wlu.edu
>  >
>  >
> brian whatcott <inet@intellisys.net>
> Altus OK


Hugh Haskell
<mailto://hhaskell@mindspring.com>

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