Relativistic Rocketry

Robert Forward suggested the production of positrons and their storage
as a means to implement advanced propulsion. In one instance,
positron/electron production of shaped gamma rays is used to make
compact aneutronic fusion a reality. This solves the problem of the
industrial access to the Solar System. The other instance is the use
of directed gamma rays themselves as a photonic rocket.

These ideas have been picked up by the National Research Council and
is available for public review in A REVIEW OF UNITED STATES AIR FORCE
AND DEPARTMENT OF DEFENSE AEROSPACE PROPULSION NEEDS

http://www.nap.edu/catalog.php?record_id=11780

The density achieved with positron storage is limited based on method
of storage.

http://www.icarusinterstellar.org/bl...antiparticles/

Arthur Clarke suggested in a private conversation that it might be
possible to create a way to cause a positron-electron to somehow bind
in a semi-neutral condenstate without annihilating, and then excite
the condensate to annihilate in the engine.

If positron/electron pairs could be stored as densely as hydrogen in
liquid hydrogen, then you'd get about 140 grams per cubic meter.

Of course creating anti-hydrogen and storing it to combine with
hydrogen attains 70 kg per cubic meter. Protons and anti-protons
though produce intermediate pions which reduce engine efficiency
somewhat with current proposed designs.

An anti-matter powered vehicle accelerate at 1/10th gee would deliver
a payload fraction of 26.92% a distance of 4.328 light years in 12.72
years ship time, 13.65 years Earth time. The ship attains 57.6% the
speed of light mid journey.

Using a solar sail for the first half of the journey and anti-matter
rockets for the second half increases payload fraction to 51.89%

Once a laser set up placed at alpha-centauri, laser light sails can be
used throughout the entire journey, and both ways to maintain commerce
between stars.

Now, a 12.72 year journey is possible with suspended animation, which
is a medical reality today.

http://www.ted.com/talks/mark_roth_s...animation.html

It turns out we've known since World War One how to do it. Truly
amazing. A whiff of 1,000 ppm of H2S can cause a person to pass out.
Reducing oxygen and temperature quickly - puts the person in suspended
animation. Raising temperature and oxygen reverses the process in
most cases.

If this could be made into a simple automated process - people could
be brought in and out of suspension quickly and reliably at low cost.
This would reduce their cost of living and increase their utility. If
you had a limited fixed income - say an annuity - you could live
better when you were animated if you spent long times suspended.

Without black holes, without anti-matter, it is possible to send
payloads to nearby stars in reasonable times using solar sails and
fusion rockets.

A laser light sail operating at 0.33 gee for 1 year accelerates a
payload to 32.8% light speed after traversing 0.17 light years. It
takes 1.02 years Earth time.

At the target star, using a fusion powered rocket with 33,000 km/sec
exhaust speed requires that 95.48% of the total mass be fusion
propellant, leaving 4.52% payload (including structure (but not
necessarily the sail)) Total trip time 13.9 years - Earth time and
13.2 years ship time including acceleration and slowing.

High temperature laser light sails operate at very high power levels
and can be quite compact.

In other posts I have postulated self-replicating machine cells that
are capable of transforming planets in days. A 1.5 kg payload with a
500 kg solar sail and 23.5 kg lithium-6 deuteride propellant - is a
model of a minimum unmanned probe.

A 1.5 metric ton payload with a 500 metric ton solar sail and 23.5
metric ton lithium 6 deuteride propellant - is a model of a minimum
piloted probe - equipped with a suspended animation capability.

525 kg system accelerating at 0.33 gee using a laser light sail
requires 254 GW of laser energy. This is collected by a 360 m
diameter satellite in an orbit 3.7 million km from the Sun.

A 525 ton system requires 1,000x more power and 1,000x more area which
is 31.6x the diameter - 11.4 km in diameter - in the same orbit around
the Sun.

Relativistic rocket calculation page has been taken down!

Here's a derivation of the relevant equations in a 1995 AIAA paper by
my friend Bob Forward;

http://www.relativitycalculator.com/...tions/AIAA.pdf

How to build an Anti-matter rocket for interstellar missions

http://www.aiaa.org/Participate/Uploads/2003-4676.pdf

Here's an overview;

http://en.wikipedia.org/wiki/Relativistic_rocket

Most spreadsheets will not do hyperbolic trig functions which are
needed to do these calculations. So, you will have to use the EXP -
exponential functions to calculate them yourself using;

http://mathworld.wolfram.com/HyperbolicTangent.html

TANH(x) --- (EXP(x)-EXP(-x))/(EXP(x)+EXP(-x))
--- (EXP(2*x)-1)/(EXP(2*x)+1)

http://mathworld.wolfram.com/HyperbolicSine.html

SINH(x) --- (EXP(x)-EXP(-x))/2

http://mathworld.wolfram.com/HyperbolicCosine.html

COSH(x) --- (EXP(x)+EXP(-x))/2

You can use this information to calculate how long it would take to
travel to the nearest stars.

There are 109 stars and 8 brown dwarf stars within 20 light years of
Earth.

http://www.atlasoftheuniverse.com/nearstar.html

From this data a whole host of early interstellar campaigns can be
developed.

From this point we can see that using laser light sails and anti-
matter rockets produce the following chart;

Year Distance Stars People People/star
AD Light Yr No. MM MM

2040 25 229 9,293.3 40.67
2065 50 1,828 12,338.0 6.75
2090 75 6,170 16,380.2 2.65
2115 100 14,625 21,746.7 1.49
2140 125 28,564 28,871.3 1.01
2165 150 49,359 38,330.1 0.78
2190 175 78,381 50,887.9 0.65
2215 200 117,000 67,559.7 0.58
2240 225 166,588 89,693.6 0.54
2265 250 228,516 119,079.1 0.52

Basically, one pair of cylinders per star system are sufficient to
house every man woman and child and maintain them at a high living
standard after 2140 AD while only 41 pairs are needed to house
everyone in 2040.

http://www.nss.org/settlement/space/oneillcylinder.htm