starship-design: The Size of the Problem

[DotarSojat@aol.com]

MEMORANDUM
TO:      The Starship Design Group
FROM:    Rex Finke
SUBJECT: The Size of the Problem

INTRODUCTION AND SUMMARY

A challenge has been identified to convey to the SD group the
size of the problem of providing the energy required for inter-
stellar flight.

Let us consider an example mission to deliver 100 tonnes to a
distance of 8 light-years at a continuous acceleration/
deceleration of 1 g, a mission for which we have some numbers.

Calculations below indicate that this mission, if powered by
antimatter, requires a mass of antimatter that represents an
investment in energy equivalent to at least 105,500 years of
the rate of production of electric energy in the entire US in
1987.

CALCULATIONS

A. ENERGY CONTENT of ANTIMATTER

The specific energy of annihilation (also creation) of 1 kg of
matter-plus-antimatter (m+am) is

      mc^2 = 1 kg x (2.9979 x 10^8 m/sec)^2
           = 8.9874 x 10^16 kg m^2/sec^2    
             .......(1 kg m^2/sec^2 = 1 joule = 10^-6 Mw-sec)
           = 8.9874 x 10^10 Mw-sec
             .......(1 yr = 3.156 x 10^7 sec)
           = 2,847.7 Mw-yr (per kg of m+am)

B. ELECTRIC ENERGY PRODUCTION in the US

My 1994 Grolier Encyclopedia says, under "power, generation and
transmission of,"
"In 1987, production of electric energy by utilities in the United
States totaled 2,570 billion kilowatt-hours."

   2,570 x 10^9 kw-hr x 3600 sec/hr / (1000 kw/Mw x
                        3.156 x 10^7 sec/yr)
      = 293,156 Mw-yr

Let us call 293,156 Mw-yr 1 "USE."  Then

   1 USE = 293,156 Mw-yr / 2,847.7 Mw-yr/kg m+am
         = 102.94 kg m+am
         =  51.47 kg am

C. ANTIMATTER MASS REQUIREMENT

In my email memo of 4/4/96 at 13:26 EST to the SD Group, "Optimum
Interstellar Rockets (Minimum Antimatter Fuel)," I gave the cal-
culated values of the ratios of the minimum antimatter mass to the
burnout mass (minMam/Mbo) and the minimum antimatter mass to the
initial mass (minMam/Mi) required for various values of the final
proper velocity (Uend) up to a Uend of 5 light-years/year.  The
assumptions in the calculations were--

     1. 100 percent conversion of annihilation energy to exhaust
        kinetic energy, and
     2. The exhaust velocity was that giving the maximum conver-
        sion of exhaust kinetic energy to vehicle kinetic energy,
        i.e., that requiring the minimum mass of matter+antimat-
        ter, for each final velocity.

For acceleration to a Uend of 5, the value of minMam/Mbo given in
the memo is 3.357 and the value given for minMam/Mi is 0.2210.
With these numbers, and recognizing that the method used there
to calculate the minimum is approximate, the mass ratio for the
acceleration phase given by minMam/Mbo divided by minMam/Mi is
about 15.2, including the exhaust mass and the matter annihilated
with the antimatter.  The overall mass ratio for acceleration plus
deceleration is (15.2)^2, or about 231.  The ratio of antimatter
mass to burnout mass is about 23.6 percent (3.357/14.2) of the
"fuel ratio" (the mass ratio minus one).  The overall ratio of
antimatter mass to burnout mass is therefore about 54.3.

A Uend of 5 lt-yr/yr is achieved at an acceleration of 1 g over a
distance of 3.97 lt-yr (see my 4/4 memo).  So, a peak proper vel-
ocity of 5 lt-yr/yr is reached halfway to a destination about 8
lt-yr away, and the antimatter requirement is about 54.3 kg of
antimatter for each kg of mass delivered to that distance.

With one more assumption--

     3. 100 percent efficiency of conversion of electric energy to
        antimatter,

the minimum energy requirement to create the antimatter to deliver
1 kg to a distance of 8 lt-yr at 1-g continuous acceleration/
deceleration becomes 

         54.3 kg am / 51.47 kg am/USE = 1.055 USE   .

So the energy requirement to deliver an example final mass of 100
tonnes (10^5 kg) to an example distance of 8 lt-yr at an accel-
eration/deceleration of 1 g is 1.055 x 10^5 USE, or 105,500 years
of the rate of electric energy production in the entire US in the
year 1987, if the efficiency of conversion of electric energy to
antimatter is 100 percent.

IMPLICATIONS

Similar considerations could be applied to relate to the USE the
fusion-powered-rocket energy requirement, the sail/beam energy
requirement, etc.  All will certainly be about as much beyond
current power-generation capabilities as antimatter creation is.
Human interstellar flight in a human lifetime is even further
beyond current physics/economics than I had imagined.  Orders of
magnitude reduction in payload and increase in transit time are
required to reduce the energy problem to a "manageable" size, to
only a few USEs, say.

What to do about the energy problem for human starflight?

A few plausible ways around the problem (requiring extensions of
physics, however) come to mind:

     1. Find some process to make antimatter which does not
        require creation energy, such as changing matter to anti-
        matter through some kind of quantum manipulation (trans-
        mutation).  On 3/27/96 at 9:06 p EST, Lee Parker quoted
        Kelly Starks (private email of 3/22 at 8:40 a EST), para-
        phrased, "So physicists are talking about the possibility
        of rotating the quantum particles to convert a particle
        of matter to antimatter."
     2. Discover some ultra-cheap source of energy (cold fusion?).
     3. Tunnel through space ("warp drive"?).

The group might think of others.