Interplanetary Express

I was thinking recently what would be requirements of an ideal
interplanetary spacecraft capable of carrying humans around the solar system
within reasonable times (ie 1 week to 2 years) ignoring the costs of
development. I thought the following would be necessary:

Radiation protection

Artificial-gravity generation

Fuel/Food supplies/generation for up to 4 years

Adequate living space

Ship velocities of up 100km/s

100km/s Debris Impact Shield

In focusing on the velocity aspect and propulsion requirements I chose
100km/s because if you take a solar system map or NASA's solar system
simulator you can see at 100km/s you can get almost anywhere within the
times shown above and still have enough delta-V to break orbit from some of
the largest gas giants. I also concluded that in order for the ship achieve
these travel times it should achieve 100km/s within 1 day (24hrs).

This means for a ship of mass, 1000 tons, a force of 1160kN would be
required to produce an acceleration of 1.16m/s^2 at 0.12 gees. Is this
right?

Also what kind of propulsion system could achieve this? Thermo-nuclear?
Vasimr? Fusion?

Dre wrote:

I was thinking recently what would be requirements of an ideal
interplanetary spacecraft capable of carrying humans around the solar system
within reasonable times (ie 1 week to 2 years) ignoring the costs of
development. I thought the following would be necessary:

Radiation protection

Artificial-gravity generation

Fuel/Food supplies/generation for up to 4 years

Adequate living space

Ship velocities of up 100km/s

100km/s Debris Impact Shield

In focusing on the velocity aspect and propulsion requirements I chose
100km/s because if you take a solar system map or NASA's solar system
simulator you can see at 100km/s you can get almost anywhere within the
times shown above and still have enough delta-V to break orbit from some of
the largest gas giants. I also concluded that in order for the ship achieve
these travel times it should achieve 100km/s within 1 day (24hrs).

This means for a ship of mass, 1000 tons, a force of 1160kN would be
required to produce an acceleration of 1.16m/s^2 at 0.12 gees. Is this
right?

Also what kind of propulsion system could achieve this? Thermo-nuclear?
Vasimr? Fusion?


The really difficult thing is the radiator.
Heat engines need to get rid of heat.

Some fundamental relations for a simplified model follow --
not quite as simplified as "Assume constant acceleration", though.

I think if you try them out,
you'll find there are better acceleration schedules to follow
than your "achieve 100km/s within 1 day".
You have the fission reactor and the ultra-high-performance
radiator; why not use them for most of the trip?
(If you have a fusion reactor, it hardly matters.
The radiator is the limiting factor.)

These rules take into account how an ion rocket's acceleration varies
as its constant thrust acts on its diminishing mass.

Imagine a ruler of length 'D', negligible mass,
sitting in vacuum, free fall,
and assign a fraction 'f' of its length that a rocketship
flying along the edge will traverse with its motor on --
either forward or braking acceleration.

[1] PoweredFlightTime = sqrt (2fDJ/Z) + fD/J
[2] MassRatio = 1 + PoweredFlightTime*Z/(0.5*J^2)
[3] T = PoweredFlightTime + (1-f)*D/(J/2 * ln (MassRatio))
[4] FinalAcceleration = 2Z/J
[5] InitialAcceleration = 2Z/(J*MassRatio).

'Z' is the ratio of kinetic power in the departing propellant stream
to nonpropellant mass. 'J' is how fast the propellant is thrown.

I don't know what values of 'Z' are seriously proposed;
1 kilowatt per kilogram sounds difficult, but conceivable.
So a vessel with mass 30 tonnes, plus propellant --
the stuff that will be thrown aft as ions --
will have 'Z' = 1 kW/kg if it can put 30 MW into the jet.

That can probably be done with a 300-thermal-megawatt reactor
and a 270-thermal-MW radiator;
conceivably just 150 MW, with 120 MW dumped.

Putting 'J', the ion expulsion speed, to 37,000 m/s,
we get that if Mars and Earth were motionless
with respect to each other, 63 million km apart,
and the ship crossed between them with its ion rocket working
through 0.4 of the distance ('f'=0.4),
and their gravity could be ignored --
as might be fairly close to true
if the trip were between space stations
in high orbit around each planet --
a trip between them could take a little over 40 days.

PV panels could provide much lower values of 'Z' at Earth,
lower still at Mars; that variability cannot be handled
by the simple functions of 'D', 'Z', 'f', and 'J'
except maybe very crudely, by putting in an average.
Try it.

Interestingly, larger values of 'f', such as
thrusting all the way, 'f' = 1.0, mean you arrive later.
So of course do much smaller values.


--- Graham Cowan
http://www.eagle.ca/~gcowan/Paper_for_11th_CHC.doc --
How individual mobility gains nuclear cachet.
Link if you want it to happen.