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Spaceship design

Bigelow BA-330 habitat
Bigelow Genesis habitat

The chief obstacle to spaceship design is radiation shielding. At least 3 meters of ice are required to stop cosmic rays. If you have this much ice then everything else is easy, because the ice can also be used for rocket fuel and life support.

The Bigelow BA-330 has as much room as the bridge of the Enterprise and the Bigelow Genesis has as much room as a Humvee. Bigelow habitats are lighter than NASA habitats and they have thicker walls. Thicker walls are helpful for defending against micrometeorites and radiation.

                 Volume    Mass   Wall thickness
                  (m3)    (tons)       (m)

Bigelow Genesis    11.5     1.36    .15
NASA Orion         19.6     8.91
Bigelow BA-330    330      23       .46
Space Station     837     450       .003
International Space Station
NASA Orion

Radiation in space

The Earth's atmosphere is thick enough to block cosmic rays from space and Mars' atmosphere isn't. The walls of spaceships are too thin to protect against cosmic rays.

            Atmosphere thicknes

Venus              1000
Titan                73
Earth, sea level     10
Earth, 12 km high     4.9
Mars                   .16

                                       mSieverts     Shielding thickness
                                         /year       (tons/m2)
Terrestrial radiation                    2.02        n/a
Average medical radiation                 .60        n/a
Earth surface, cosmic rays only           .39         10
Earth surface, all radiation             3.5          10
Earth 2 km altitude, cosmic rays only     .9           8
Earth 3 km altitude, cosmic rays only    1.7           7
Earth 4 km altitude, cosmic rays only    3.3           6
Earth, 12 km altitude, equator          20             2.5
Earth, 12 km altitude, poles           100             2.5
Space station, 420 km altitude         150              .01   1/8 inch aluminum walls
Space                                  600              .01
Space, 4 tons/m2 shield                  2.5           4
Mars surface                           220              .16

"Space" refers to interplanetary space between Earth and Mars.

At the space station, the Earth's magnetic field blocks 3/4 of the radiation from space.

The sun's magnetic field stops cosmic ray particles below 1 GeV.

The Earth's magnetic field deflects all but the highest-energy cosmic rays.

5 hour airplane flight incurs ~ .03 millisieverts.
A dose of 4800 millisieverts has a 50% risk of death.

Life support

Aeroponic plants
Space station life support

The space station life support system:
1 kWatt/person/day
1 liter of water/person/day
1 kg of food/person/day

         Mass fraction
         in human body

Oxygen     .65
Carbon     .18
Hydrogen   .10
Nitrogen   .03
Calcium    .014
Phosphorus .011
Potassium  .0025
Sulfur     .0025
Sodium     .0015
Chlorine   .0015
Magnesium  .0005
Iron       .00006
Air and water are the biggest challenges for life support in space. Water can be obtained from the moon and electrolysized to produce oxygen for air. Air also requires nitrogen, which cannot be found on the moon but is abundant in Mars' atmosphere.

The principal components of fertilizer are nitrogen, phosphorus, and potassium, with nitrogen being the heaviest component. Nitrogen can be obtained from Mars's atmosphere. If you want to grow crops on Mars you will have to bring phosphorus and potassium.

The most efficient way to grow plants in space is with aeroponics, where the roots are grown in open air.

Artificial gravity

If artificial gravity is generated by spinning a spaceship, then according to, the spin period has to be at least 30 seconds for the inhabitants to not get dizzy. If we assume a spin period of 30 seconds and a gravity of 1 g,

Spin period    =  T  =  2 π R / V   =  30 seconds
Spin radius    =  R  =  T2 A / (2π)2 =  228 meters
Velocity       =  V  =  2 π R / T   =  48 meters/second
Acceleration   =  A  =  V2 / R      =  10 meters/second2


Suppose we use a tether to connect a spinning spaceship. Zylon is the material with the best tensile strength to density ratio.

Tether density           =  D  =  1520 kg/m3 for Zylon
Tether tensile strength  =  P  =  F / Ar  =  5.8 GPa
Mass of spaceship        =  M
Radius of tether         =  R  =  T2 A / 4 pi2  =  V2 / A
Tether cross-section     =  Ar
Mass of tether           =  m  =  2 R Ar D
Centripetal acceleration =  A  =  10 meters/second2
Tether tension force     =  F  =  M A
Spaceship spin period    =  T  =  2 π R / V  =  30 seconds
The mass ratio of the tether to the spaceship is
m/M  =  2 T2 D A2 / P / (4 π2)  =  1.33e-6 T2  = .00119
To be safe, the tether can be given a mass 10 times larger then this. Even so, the tether weighs much less than the habitable module, and so the mass of the tether is not a factor in the spaceship design.

If the spaceship mass is M=1000 tons, the tether mass is m=12 tons. Such a tether can easily be launched from the Earth.

For extremely large tethers you can use iron from the moon.

Radiation shielding

The above data suggests that to shield against cosmic rays, you need at least 3 tons/meter2 of shielding.

Suppose a spherical spaceship is shielded with ice.

Radius of spaceship   =  r  =  3 meters
Radius of ice shield  =  R  =  6 meters
Density of ice shield =  D  =  1000 kg/meter3
Mass of ice shield    =  (4 &pi / 3) (R3-r3)  =  792 tons
The only way to get this much ice is from the moon. This is the source of the mass for the tether calculation.
Space stations

Good locations for space bases are:
Earth orbit
The moon
Moon orbit
The L2 Lagrange point
Mars orbit

Ice can be shipped from the moon to the other stations.

The L2 point stays tethered to the Earth as the Earth orbits.

The L2 point is ideal for telescopes because from there you can shield the sun, the Earth, and the moon all at the same time. The Webb telescope will go there. If we had a manned space station at L2 then we could assemble telescopes on-site and build colossal telescopes.

Radiation shielding

Cosmic rays consist mostly of high-energy protons with energies > 1000 MeV. When a proton passes through matter it loses energy from collisions with electrons and with nuclei. Electron collisions subtract a small amount of energy from the proton and nuclear collisions subtract most of the energy. This is because collisions with electrons are mediated by the electromagnetic force and collisions with nuclei are mediated by the strong force.

E = Proton energy
L = Distance the proton travels through matter (meters)
D = Density of the matter (kg/meter3)
V = Proton velocity
C = Speed of light
Proton kinetic energy is measured in MeV. 1 MeV = 1.6e-13 Joules. The rest energy of a proton is 1000 MeV.

Proton energy loss is governed by the "Bethe-Bloch" formula. For cosmic ray protons with E > 1000 MeV, the formula may be approximated as

EnergyLoss  =  200 L (D/1000) MeV
If the proton is traveling through water with a mass density of 1000 kg/meter3, the energy loss rate is 200 MeV/meter. The amount of matter required to stop a proton with E = 1000 MeV is 5 meters.

Spacecraft walls are thick enough to stop low-energy protons from the solar wind but they are of no help in stopping cosmic rays. Mars' atmosphere isn't thick enough either.

When a high-energy proton collides with a nucleus, most of the energy is lost in the collision, hence the transmission of protons through matter can be modeled as an exponential.

T  =  Initial intensity of protons
t  =  Transmitted intensity of protons passing through a distance L of matter
L  =  Distance the proton has traveled through the matter
S  =  Characteristic stopping-length of the matter
D  =  Density of the matter in kg/meter3
A  =  Atomic number of the nuclei in the matter
   =  1 for protons
   =  8 for oxygen

t = T exp(-L/S)

S  =  .35 A1/3 1000/D  meters
For oxygen, A = 8 and D=1000, hence the characteristic stopping length of protons in water is S = 0.2 meters.

Suppose you want to stop 99% of the protons.

t = .01 T

L = 4.6 S
If water is used to stop cosmic ray protons, the formula predicts you need least 1 meter of it. This translates to a column density of 1 ton/meter2.

This is an underestimate of the shielding required because when a high-energy proton hits a nucleus it creates a shower of secondary particles which must then be shielded. In practice, 4 meters of water are required. Muons are the biggest nuisance because they don't feel the strong force. Most of the cosmic radiation at the Earth's surface is from muons.

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