Headline: | Interstellar Medium can be such a drag...(or is it?) |
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Date: | Tuesday, March 03, 2020 |

Posted By: | Plaid Hatter Games |

NOTE: In the process of writing IS Mea Culpa I discovered that my original estimate for the density of the portion of the Intersteller Medium the Iliad would be travelling through was wrong. While the conclusion for this article is unchanged, drag is an order of magnetude less. The balance of this article is the original posting.

Well if you remember from my earlier post Revised Propulsion Concept,
I had a casual Science Fiction line of *We then let it coast, perhaps losing a little speed due to drag. (There are still trace
bits of gas and dust in interstellar space.)*.

So, of course I got a question about it. From a physicist. And now I feel compelled to answer exactly what that force would be and whether the ship can ignore the drag, have to mitigate the drag, or even exploit that drag.

First, let us introduce the drag equation:

- Fd is the force of drag (what we are solving for)
- Rho is the density of the fluid
- u is the flow velocity
- Cd is a fudge factor for the shape of the object
- A is the total frontal area of the object

What should immediately scare me is the u and A terms. The ship is traveling very fast (0.9c) and the frontal area is immense. But in the back of my mind, I also know that the Rho term, the density, is extremely tiny.

How tiny? There really isn't much out there to bump into. According to Interstellar Medium, material is really rarefied. Assuming a cold part of space, in the midst of a cloud, there could potentially be 1e6 molecules of matter per cubic centimeter of space. Thats 1 with six zeros. 100000. A million.

While a million molecules per cubic centimeter sounds like a huge number, it is actually not. 1e6 molecules/cc astonishingly small. The Earth's atmosphere at Sea level has a 1e19 molecules/cc. The inside of a working vacuum chamber in a laboratory has 1e10 molecules/cc.

At the same time, the molecules we will be bumping into are going to be extremely light. By molecule count: 91% hydrogen, 8.9% helium, and trace amounts of heavier elements. By mass: 70% hydrogen, 28% helium, and 1.5% something else. Our atmosphere is far more dense being comprised of 80% nitrogen and 19% oxygen. Much, much heavier molecules.

Interstellar Medium (ISM) is not half of a laboratory vacuum. Not a percent of a laboratory vacuum. 10e6 seconds is 115.6 days. 1e10 seconds is 3180 years. 1e19 seconds is 3,177,421,093,195 years.

We need a number for Rho, and because we are solving for force in Newtons, I need Rho to be expressed in Kg/m^3. We'll assume roughly the same isotope densities for ISM as here on Earth (which is a mistake) but it's at least an initial estimate. Hydrogen has an atomic weight of 1.008. Helium has an atomic weight of 4.002. For our trace element, we'll call use Carbon atomic weight 12.011.

If you remember from chemistry, the atomic number tells you how much a mole of that substance will make. To calculate our density:

(1.008*0.91+4.002*.089+12.001*(1-0.91-0.089))* (1e6 molecules/cc) / {Avagado's number} * {1000 kg/m^3} / {1 g/cm^3}

Which equals 2.134554803681946e-15

But of course, we only keep the significant figures: 2.135e-15 kg/m^3. Air, by comparison is 1.225 kg/m^3. Fresh water is 1000 kg/m^3. So this is not very dense stuff.

Plugging into our equations assuming u=2.70E+08 m/s (0.9 c). Let's assume there is a cap or tank over the frontal area of the ship that is roughly spherical and 1400 meters in diameter. That gives us a surface area of 3.08E+06 meters. But... for aerodynamics we only care about the frontal area. And for a sphere that size it is 1.54E+06. A half-sphere has a Drag Coefficient of 0.42.

set rho 2.135e-15 set vel 2.70E+08 set drag 0.42 set area 1.54E+06 set force [expr {0.5*$rho*($vel**2)*$drag*$area}]

Our total force of drag in Newtons: 5.033e+07.

Oh my. To put that into perspective, that is 11315640 pounds for force. That force, left unchecked, would decelerate the ship. By how much? Lets go back to Newton (the scientist not the unit of measure). Force=mass*acceleration. An a=F/m. The mass of our ship has a mass of 1.46E+11 kg. It's reaction mass for deceleration is: 3.36x the mass of the payload. This gives us a total mass of 6.365600e+11.

Our ship is slowed down by 1.581e-04 meters/s^2. The entire coast phase at 0.9c will last for 1.447E+08 second, in map time. The cloud mass is assumed to be as near as makes no difference to at rest relative to the same framework we measure Earth against. Thus gives us a total deceleration of 2.288e+04 meters/second. Expressed as a fraction of the ship's total speed, that loss is 1:8.475411e-05. 18 percent. Of a percent. Of a percent.

So, in the end, no. Drag is not much of factor in space. Even at tremendous speed.

But while we are out of the woods as far as drag goes, we have another problem with Protecting the Ship Against Interstellar Material