Re: Spaceship with constant acceleration

On Jan 15, 10:57 pm, Erik Max Francis <m...@xxxxxxxxxxx> wrote:
Wayne Throop wrote:

Hm?  I don't follow.  He was optimizing for trip time, and hang the cost.
You're given a motor, and some payload, as fixed assumptions; now optimize
your trip time.  Spend all you want on fuel, rection mass, whatever.
That's it.

No, I listed various specific scenarios, where you keep one or more
factors constant, while improving one or more other factors constant.

 And the conclusion is that you'll always have a non-zero-
duration freefall segment of your trip, but it need not be very
close to what you'd call impulsive.

Right, so what's the optimal cruise phase (in terms of displacement or
duration, whatever's most useful to phrase)?

I'm not going to calculate out a general solution. I gave a specific
solution, for a specific set of circumstances.

For a wide set of potential factors, a cruise phase of 10% is
optimal if the mass ratio is 1.05. (This is a rather low mass
ratio.) My actual argument was to demonstrate that you
want a cruise phase of at least 10% if your mass ratio is
greater than 1.05.

What _I_ am interested in saying is that a significant cruise
phase is always desirable under plausible mission conditions.
So for me, the mathematical proof of this inequality is
sufficient. You want an equation, rather than an inequality.
Well, why don't you start by at least specifying the exact
thing YOU want to optimize for?

Quoting him:

| I've been making the general assumption that given a
| particular mission plan, increasing payload or decreasing
| cost is always a good thing (while keeping the trip time
| the same).

That's exactly right.

and later:

| I explicitly list propellant mass, energy, power, and
| trip time as factors which are reduced.  I explicitly
| list payload as a factor which is increased.

Exactly.

So he's not talking about the same kind of optimization problem as we
are.  That's kind of the point:  I don't know exactly which optimization
problem he's solving, and he still hasn't stated an optimal solution, so
can't guess.

I told you exactly what I was optimizing for. You even
quoted it above. I'm showing that the minimum 10%
cruise phase is best whether you're optimizing for
propellant mass, energy, power, trip time, or payload,
or any combination of the above.

You will generally have some particular multi-dimensional
function of "desirability". This will be a function of
propellant mass, energy, power, trip time, and payload.
I assume that:

Decreasing propellant mass is always neutral/desirable.
Decreasing energy is always neutral/desirable.
Decreasing power is always neutral/desirable.
Decreasing trip time is always neutral/desirable.
Increasing payload is always neutral/desirable.

No matter what desirability function you're optimizing
for, as long as this function satisfies the above assumptions,
then a cruise leg of 10% or more will be optimal for any
reasonable mass ratio (1.05 or more).

This is why I kept asking him to list explicitly what he was holding
constant, what he was allowing to vary, and what he was optimizing for.

And as I keep having to explain, my argument does not rely
upon a specific optimization function. It is valid for a wide
range of optimization functions.

  Because it makes quite a big difference.  He's kind of listing all of
them.  There surely are some regions where what he's saying is true if
you take _all these variables_ as things you want to improve, but then
again that's pretty obvious.  However, it doesn't give you a very useful
optimal solution in a specific case.

What I'm saying is true if you take any combination of those
variables, weighted to any degree.

The regions where what I'm saying is true is where the mass
ratio is greater than 1.05.

Contrary to his tone, I never even said he was wrong; I just want to
know what the optimal solution is.

If you want to know what "the" optimal solution is, you're going to
need
to specify exactly what YOU want to optimize for.

You're getting hung up on what I'm supposed to be specifically
optimizing for, when I explicitly and repeatedly explain that my
argument applies to a broad range of optimizing functions.
Why should I bother with restricting my argument to a bunch
of specific optimization functions when I have the mathematical
option to provide a general argument that encompasses them all?

Isaac Kuo
.

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