Questions about your letter to SD

[T.L.G.vanderLinden@student.utwente.nl (Timothy L.G. van der Linden)]

Hello Steve,

I'd like to ask you a few questions about your last letter to Starship
Design where you derived several formulas about what the best reaction mass
could be.

I first read "http://sunsite.unc.edu/lunar/Engineering12.html". All things
are clear to me until you write:

>The velocity of an object is its momentum divided by its total
>energy, v = p/E; hence we also have the relationships:
>
>r = Pr/Er
>
>s = Ps/Es

This seems very strange to me because:

p/E=[kg m/s]/[kg (m/s)^2]=[s/m] thus the inverse of velocity.

Please explain what is wrong. I've tried deriving the formula using now
r=Er/Pr and s=Es/Ps arrived at the formula:

f^2 = (s^2 - 1) / (r - s)^2


I also have something to ask about your last letter to SD:

>Then in the local frame of the spacecraft, every second it
>increases velocity by s, and its mass diminishes by the
>proportion f.

Do you really mean f or should it be (1-f) ?

>               Since the kind off acceleration that a human crew
>can tolerate is very low compared to the speed of light, there
>won't be much difference between treating the acceleration as
>continuous or pulsed.  Continuing the acceleration for a time t
>results in the spacecraft mass diminishing to f^t.

I'm not sure about the difference between diminish "by" or "to" since my
native language is not English. I think here it should indeed be f^t.

>about a 2:1 Earth time/spacecraft time ratio.  Accelerating to
>0.866c at 1 g will take about 1.14 years of spacecraft time.

I think it is 1.27 years, but it does not make much difference in the
calculated values.

After all this you compare different kinds of fuels. It would probably been
better if you compared exhaust velocities without mentioning the kind of
fuel. You assume that for fusion mass enough energy is released to
accelerate all the fused material. Maybe for low velocities that is true,
but I'm not sure it will work for higher velocities. It should be very easy
to calculate. The energy released in fusion "weighs" about 1/300 of the
original unfused material.

Greetings Timothy