[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

Re: starship-design: Re: FTL travel

In a message dated 3/20/00 8:54:15 PM Pacific Standard Time, stevev@efn.org 

>  The ship carries the fuel.  Either both the ship and the fuel get more
>  massive with velocity or both the ship and the fuel stay the same mass.
>  Are you claiming that the fuel gets more massive but the ship that
>  carries it stays the same?  Either way the fuel can only provide so much
>  acceleration, and that little fission fuel can't propel a heavier
>  payload to relativistic velocities.
Hi Steve,
Taking for example the general equation MVof exhaust=MVof payload.
to accelerate a given payload mass of 5 tons twice light speed requires I 
accelerate 100 tons of exhaust to 1/10 light speed (at 1 g acceleration).
Using the equation E(kinetic)=1/2 MV we get the energy required.
using the equation E=Mc^2 we get the mass that needs to be converted 
providing the energy.

>From the laws of conservation momentum(P) we have the equation P=MV
as momentum is required by universal law to be conserved. P of exhaust= P of 
payload. this shown in the equation MV of exhaust=P=MV of payload.
it is proven mathematically with an identity proof (the strongest of math 
proofs)stating if a=b and b=c then a=c or (a=b=c).

Machines like partical accelerators that use the general instantaneous 
acceleration equation of E'=1/2 MV gamma, reguire the Energy relativistic 
equation to be used for the energy is delivered intantaneously (small 
increment of time)from the relativistic(observer or rest) frame instead of 
the frame of moving(inertial) object and is therefore limited to below light 
speed relativistic so that momentum is conserved.

The equation commonly leading to a erroneous velocity real calculation of 
like .3 or .8c was derived by Einstein and clearly labeled Velocity Rel.(for 
relativistic velocity) in the margin. Subsequent typists saw the label out 
there by itself and not knowing what it meant dropped the label and kept the 
equation. Mathematicians often tire of writing the full variable parameter of 
velocity relativistic in freehand so use V (subscript rel.) or better yet 
just v as v=Velocity Relativistic with the understanding the equations are 
under the defining label and the relativistic(observer) frame and 
distinguishable from velocity real of the ship frame of reference also 
designated as Velocity Real by label.

Just remember that regardless of what an observer on earth calculates as 
relativistic regarding the moving ship, aboard the ship all remains normal 
(real) as a basic postulate of relativity. Placing both sets of equations on 
a page can be confusing as some use prime( ' ) for relativistic and drop the 
subscript real just using the small case variable letter without prime and 
the labels and variable definitions are required to be placed at the top any 
calculations to prevent confusion.

Another common mistake with rocket equations when I give students a problem 
with constants to solve containing 1 g some invariably look through the 
unified field of equations I also give and select the first one with 1 g in 
it and attempt to solve with ISP(specific impulse calculation) and when the 
equation v=gt is the one to be used.

ISP numbers stamped on model rocket engines are determined by measurements of 
actually firings of chemical rockets so that a given payload mass attached 
can be reliably calculated with the special equation to give an accurate 
velocity predictions in a uniform gravitational field of one g (near earth's 
surface). ISP numbers and predictions of what they would be are only guess 
work (usually poor guesses at that) for atomic engines as the measurement 
database has yet to be built.  To get accurate velocity calculations the 
original general rocket equations are to used.