Headline:Protecting the Ship Against Interstellar Material
Date:Wednesday, March 04, 2020
Posted By:Plaid Hatter Games

NOTE: While there is some good science, the conclusion of this blog ended up being wrong. See IS Mea Culpa. The balance of this article remains as it was originally presented.


While I was patting myself on the back after Interstellar Medium can be such a drag...(or is it?), my friend Ron the Physicist asked "what about ablative loss?"

While the deceleration of drag against the Interstellar Medium is negligible, the molecules we do run into, as well as the occasional mote of dust, or heaven forbid something larger is smacking into the skin of the vessel at 0.9c. These high speed collisions are going to not just bounce off the paint. They are going to create the same sorts of atom smashing impacts as one would see in a particle accellerator.

I've dug through a pile of papers on Nasa's website, and let me tell you that the math describe an object travelling hypersonically through a gas is involved. Adding in special relativity ... is really, really, really involved.

I don't want to get the math wrong, but I also don't want to just handwave away the effect. I am putting on my science fiction writer hat, and invoking magic. What I am about to describe is plausible, but not supported by science.

Let us assume that one molecule of Intersteller material colliding with the vessel equals at least one molecule of vessel that is compromised. The nature of that compromise is randomly one of the following: ionization, chipping, or nuclear reaction. Ionization causes an atom to flash into a plasma, flinging electrons all over the place, and causing exotic chemistry to happen. Chipping causes a piece of material to flake off the vessel. Nuclear reactions cause an atom to change into a different element.

Step one, we need to estimate how many molecules of Interstellar Medium the ship will rub up against. To do that we figure out the volume of space through which the vessel will be travelling. That volume is the cross sectional area of the ship (in m^2), multiplied by the length of the voyage (in meters).

The length of the voyage is easy: 45.7 light years is 4.324E+17 meters. The cross sectional area of the ship we calculated earlier.

set length  4.324E+17 ; # 45.7 ly in meters
set area    1.54E+06  ; # circle 700m in radius
set volume [expr {$length*$area}]
set density   1e12 ; # 1e6 molecules ^ cc -> m^3
set ism_molecules [expr {$volume*$density}]

With those figures we can estimate the ship will travel through 6.659e+23 cubic meters of space, and bump up against 6.659e+35 molecules in the process. I am considering the entire length of the voyage partly because the accelleration and deceleration phases are short compared to the coasting phase, and because we really don't know the critical speed when exotic reactions will start happening.

So now that we know how many molecules, let us take a look at some likely materials we would use to stop them. And then make a hypothetical set of shield plates. Here is the math for each row:

  set kg [expr $ism_molecules*$atomic_mass/6.02214076e23/$atoms]
  set volume [expr $kg/$density]
  set thickness [expr {$volume/$area}]

Material Atomic Mass Atoms Density Shield Mass Shield Avg Thickness
per molecule kg/m^3 kg m
Lithium 6.941 1 534 7.675e+12 9332.88
Lithium Hydride 7.94894 2 780 4.395e+12 3658.64
Ice 18.01528 3 1000 6.640e+12 4311.76
Crown Glass 60.0838 3 2400 2.215e+13 5991.83
Iron 55.845 1 7874 6.175e+13 5092.41
Uranium 238.028 1 19100 2.632e+14 8948.07

Before you say "What about Aerogel?", remember that Aerogel is essentially porous glass. As are those nifty re-entry tiles from the space shuttle. We need actual molecules to stop the Interstellar Medium. Using Aerogel or Space shuttle tiles would simply mean we have to make the plates even thicker.

Now one approach could be to only lay down a few meters of shield at a time, and then replace sections during the flight. The same mass of shield would be needed, but you could reduce the amount of tile that is protruding out in front of the vessel. It's not a very good approach. Whatever you send out to do this maintenance is going to need to either be expendable or heavily shielded itself.

Another approach would be to find some way to re-use that shield material. There is nothing in the physics right now that demands our shield be something structural. Note the performance of the Ice in the table above. The only material that requires less mass in shielding is the Lithium Hydride. (And we wouldn't use Lithium Hydride for a number a reasons). And... we already have a problem of having to store an awful lot of ice that we need to be a Reaction Mass for deceleration.

The Iliad is already storing 4.889E+11 kg of ice. But we don't need that ice to be anything even vaguely structural. It just needs to be a mass, and something we can easily grind up. If it is laced with extra helium and heavy hydrogen isotopes we won't care. It is already laced with helium and heavy hydrogen isotopes because the comet we scooped up has been bombarded by cosmic rays for billions of years.

Let us not use a sphere to store our fuel, and instead use a cylinder. And let's not put a top on this tank. Instead we leave about 50 meters of wall surrounding our tank, and leave the top of the ice exposed to space.

When Interstellar Material collides with the surface of the ice, a few molecules at a time will ionize into hydrogen and oxygen. Some ice will sublimate to water vapor. Any of those gas molecules will take off in a random direction. Sideways motion of the gas is stopped by the tank walls. Any gas trying to leave out of top the tank will have to be travelling faster than the ship itself (at 0.9c). And we know from our propulsion math, that's requires a lot of energy. So on average the bulk of the gas will actually remain in the tank.

That gas floating around is yet another thing for the Intersteller Medium to smack into before it reaches the surface of the ice. The more gas the builds up, the less ice the ice ionized. If the pressure starts building up on the gas, Oxygen and Hydrogen will find each other, make sweet, sweet, chemistry, and form water. Water vapor will condense into water. Water, on contact with the walls or surface of the ice, will solidify.

Will that be how ships actually protect against Interstellar Mass? No idea. But I'm just a writer of a story, and this explanation is what works for me.

What about the deceleration leg?

When the vessel is in the final year of the journey, it will be turned 180 degrees around, with the engines facing toward the direction of travel. The question then becomes, what will shield the vessel during this phase?

The answer is actually the reaction mass from the ship's engines. While the engines are in operation they throw out thousands of tons of material, at a very high rate of speed. That plume of exhaust is going to collide with the Interstellar Medium. So long as the ship is flying through its own engine exhaust, it will be safe.

When the vessel drops down to a non-relativistic speed, normal paint and metal structure is plenty to fend off the occasional spec of dust or ionized hydrogen. Water tanks in the skin of the habitat spheres protect the living things on-board against cosmic rays.

How much of the Interstellar Medium is captured by the shield?

The big problem with these energetic collisions between our shield and the Interstellar medium is that ISM material basically lodges itself into the ship. Well wait a minute. Assuming that extra matter is now trapped with the sublimated and ionized gas from the top layer of the shield, how much mass will the ship pick up?

Let's say that 90% of the atoms that collide with the shield remain either lodged in the shield, contribute to forming exotic new isotopes, or join the cloud of gas and ions in our gas cloud. We actually have an idea of how many molecules there are, we just need to convert that into mass.

Going back to our sources on Interstellar Medium, it is composed of:

  • 91% Hydrogen
  • 8.9% Helium
  • 0.1% Other

We are estimating, so for the moment we are just going to ignore "other" Assuming isotopes of Hydrogen and Helium are in similar ratios to the Hydrogen and Helium we know at home, that's a total mass of:

set H_mass [expr {0.91 * $ism_molecules * 1.008 / 6.02214076e23}]
set HE_mass [expr {0.09 * $ism_molecules * 4.002602 / 6.02214076e23}]
set total_mass [expr {$H_mass+$HE_mass}]

1.413e+12kg of material. That's not factoring in any losses.

For reference, our ship (empty) has a mass of 1.46E+11 kg. The reaction mass for deceleration is 3.36* the ship's empty weight, or 4.889E+11 kg. This is enough material to slow our ship down 2.9 fold.

In fact, if we can collect enough mass to eventually slow down, we reduce the amount of reaction mass we require to speed up. In our original calculations for Revised Propulsion Concept we built our equations assuming that the ship would have to carry all if its reaction mass with it. Eliminate the deceleration mass, and the reaction mass our ship needs to reach 0.9c is 3.3 times the ship's empty mass, not 38 times.

We can also collect reaction mass during accelleration. It takes our craft 1.25 light years to get to our cruising speed.

set length  1.187E+16 ; # 1.25 ly in meters
set area    1.54E+06  ; # circle 700m in radius
set volume [expr {$length*$area}]
set density   1e12 ; # 1e6 molecules ^ cc -> m^3
set ism_molecules [expr {$volume*$density}]
set H_mass [expr {0.91 * $ism_molecules * 1.008 / 6.02214076e23}]
set HE_mass [expr {0.09 * $ism_molecules * 4.002602 / 6.02214076e23}]
set total_mass [expr {$H_mass+$HE_mass}]

This collected mass 3.878e+10 is mass we don't need to collect, and then spend energy to accelerate to light speed, saving on reaction mass, etc.

If we broaden our horizons slightly, if we accelerate at 7.84 m/s^2 (0.8g) instead of 9.8 m/s^2, we increase the distance over which we are accelerating from 1.187E+16 meters (1.25 ly) to 1.484E+16 meters (1.57 ly). This would allow our vessel to potentially gather 4.848e+10 kg.

Slowing acceleration down to 4.9 m/s^2 (0.5g) we could gather 7.756e+10 kg over 2.51 light years.

Another approach could be to make the collection area larger. Let's stick with 0.8g for the moment, but double the radius of our shield:

We gather 1.939e+11 kg. That is more mass than the ship itself. (1.28E+11 kg empty mass). We may actually eliminate the need for massive tanks of inert material. The ship will need some reaction mass to get started, no doubt.

I fiddled around with this in a spreadsheet and I calculated that we always end up needing SOME reaction mass to start with (obviously). Assuming we accelerate at 0.8g, there is a break-even point at 0.43c. Below that point and we don't cover enough distance to gather the fuel to reach that speed. Above that point, and the ship actually collects enough reaction mass.

Essentially, the ships will only need to carry enough reaction mass to reach 0.43c. A one-way acceleration to 0.43c requires a reaction mass that is 58% of the vessel's empty mass. After 0.43c, there is enough intersteller medium being collected (assuming 1e12 molecules per meter) to accelerate the vessel through to 0.98c.

The concept begins to approach something Alan Bond described in his paper as a Ram Augmented Interstellar_Rocket. We aren't trying to be a complete Bussard Ramjet. But then again, you never go complete Bussard Ramjet.