In the previous post, I introduced the concept of an atmospheric harvester that skims the exosphere to gather propulsion fluid mass for use by space tugs. I felt that an electrodynamic tether was a promising way to propel the device and make up for the drag losses. I did a fair amount of work over the last couple of weeks to prove to myself that the atmospheric harvester was practical, at least from the viewpoint of propulsion and power. I had a model for the tether equilibrium, but it didn’t include tether aerodynamic drag because I didn’t have a handy atmosphere density model that went high enough. So first I had to create a better atmosphere density function in Mathematica. This was a bit of a cheat; I found a well established Fortran code, J77sri, which embodies a 1977 model by Jacchia. The code is pretty old-fashioned Fortran, so converting directly to Mathematica would have taken too much time. Instead, I just compiled and ran the Fortran, put the tabulated results into Mathematica, and interpolated the results. Good enough. Then it was a small matter to modify the tether model to include the drag terms.
The next step was to actually size some of the elements of a harvester system. The idea was to arbitrarily pick a mass collection rate and then calculate the total system mass. For the study, I used a collection goal of 1000 kg/day of oxygen plus nitrogen (I like to think big). Unfortunately, I have no information yet on the actual collection mechanism and it’s mass. So to proceed, I simply assigned 5000 kg to the collection device. Aluminum seems like a good material for the tether. We are looking for a low density material with good electrical conductivity. It turns out that strength is secondary to conductivity. The maximum working temperature of aluminum then sets the collection altitude. I found that 125km worked with 100% aluminum. I also tried adding 30% steel strands to the cable to increase the strength at elevated temperature. This allows one to operate down to 115km. In the mass trades, the higher altitude system came out much lighter. I also looked at a range of tether lengths. Seventy five kilometers seemed to work out well. That particular combination gave a system mass of about 12,000 kg. That seems like a pretty good deal for collecting 1000 kg/day of fluids, assuming I’m anywhere near the ballpark on the collector mechanism mass. Other information derived during the design cycle:
Cable Length 75 Kilo Meter
Cable Dia 0.4 Centi Meter
Cable Drag 20.814 Newton
Collector Drag 89.8506 Newton
Power to Overcome Drag 859100. Watt
Drive Voltage Drop 18897.9 Volt
Resistance Voltage Drop 7054.31 Volt
Current 45.46 Amp
Total Power 2.30069*10^6 Watt
Cable Mass 2544.69 Gram Kilo
Powerplant Mass 3403.39 Gram Kilo
Bottom Node Mass 5000 Gram Kilo
Top Node Mass 4506.28 Gram Kilo
Total System Mass 12051. Gram Kilo
Strength F.O.S 2.46726
Top Mass Check True
Cable Max. Temp 145.454
The summary document gives the basic assumptions and a series of these tables for different starting conditions. The actual steps to computing all the parameters and the iteration process are contained as a big function in the full Mathematica notebook (don’t bother downloading the notebook unless you’ve installed the free viewer from Wolfram, or have a copy of Mathematica). I get a little lazy and I don’t feel like explaining in words all the steps of the algorithm. Hopefully the code is self explanatory. I’ve tried to spell things out pretty carefully.
These types of system studies are the fun part of this little hobby. I enjoy trying to learn the physics of all the different pieces, not just my specialty (structural engineering). However, that means I also run the risk to getting something wrong. I took some big leaps on the electrical side. So please, if anyone sees a problem let me know. That’s part of why I throw this stuff out there.
By the way, you’ll notice I freely interchange “tether” and “cable”. The literature has settled on “tether”. But the definition of a tether is something that anchors something movable to something fixed. So I tend to call it a “cable”. Personal quirk.