# starship-design: My two cents

```Ken Wharton writes:
> Steve and Timothy have had this argument before.  I think the misunderstanding
> is stemming from what they mean by minimizing "Energy".
>
> If you try to minimize TOTAL ship-energy = Kinetic Energy + Rest Mass Energy
> then Steve is right; photons are best.
>
> If you try to minimize the Kinetic Energy you need (i.e. assume that mass is
> "free"), then Timothy is right: there is an optimum exhaust speed.
>
> So which is correct?  That depends on the technology.  If it's "easy" to
> turn mass into energy, then they're basically equivalent, and Steve is right.
>
> If it's very difficult to turn mass into energy, then rest mass is much
> easier to come by than the kinetic energy, so you try to minimize Kinetic
> Energy alone, and Timothy is right.
>
> So, as I understand it, right now Timothy is right about there being an
> "optimum" exhaust speed because it's tough to turn mass into energy.  But
> given that antimatter might make this easy in the future, Steve's slant
> could very well be correct by the time we build the spaceship.

As far as I know my analysis is correct both for high-conversion and
low-conversion cases; the nice thing about relativistic mechanics is
that both total energy and momentum are completely conserved, unlike
Newtonian mechanics where only momentum is conserved and kinetic energy
is not.

The final velocity of a self-contained starship, after burning its fuel,
is a function of the total energy extracted from the fuel, the
fuel-to-payload ratio, and the rate at which the fuel is burnt.
Essentially, the derivations I did showed that you could maximize the
final speed of the starship by any of converting more of the fuel to
energy, having a higher fuel-to-payload ratio, or burning the fuel
faster.  On the other hand, for a manned spacecraft you do have
important limits on the reaction rate of the fuel (required to keep the
shipboard acceleration around 1 g or so), so you then either have to
have a higher fuel-to-payload ratio or have a higher conversion
efficiency for the fuel to reach a given speed.

```