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.
Much of the mass that needs to be lifted into orbit consists of propulsion fluids, and the the majority of the fluid is the oxidizer. The total cost of operating in space could be reduced if there was a ready supply of liquid oxygen already in orbit. One application would be to refuel space tugs. The idea is that instead of blasting oxygen into space using rockets, gradually gather oxygen by skimming the extreme upper atmosphere. This idea goes back to work by Serge T. Demetriades, and it was published in the Journal of the British Interplanetary Society (Serge T. Demetriades, “A Novel System for Space Flight Using a Propulsive Fluid Accumulator”, J. British Interplanetary Society, 17 (1959) pp. 114-119.). The original idea was to gather gas, liquefy, and separate the oxygen from nitrogen. The nitrogen could then be used as a propulsive reaction mass using an MHD device. There are some nice cartoons of the device here. The whole thing would be powered by a nuclear reactor. Solar power would be impractical because of the added drag of the panels. A space tug would periodically dock with the device to transfer the liquid oxygen.The concept has come to known by the name PROFAC.
The concept has been reworked more recently by a team at Worcester Polytechnic Institute. From what I can gather, Paul Klinkman began reconsider PROFAC in about 2005. In particular, he found it beneficial to raise the collection altitude to 150-200 km where there is a higher concentration of oxygen, and he has proposed methods for collection. The most complete technical reference I’ve been able to find is an internal document by a WPI undergraduate. There’s also some information in this report, but the report focuses mostly on team dynamics. There is also AIAA Paper 2009-6759, but I have been motivated to purchase a copy. What originally intrigued me about the WPI work is the idea of using an electrodynamic tether for propulsion. This a particularly good application for tether propulsion because the system stays near the earth where the earth’s magnetic field is strong. And a long cable could raise solar panels far enough above the atmosphere to reduce the total drag. But mostly I liked the idea because I have a bunch of notes from 1983 that explore this combination of tethers and PROFAC (no claim of precedence; only publishing counts, and I didn’t publish anything, plus I don’t care). It appears that Klinkman has now moved away from tethers as the preferred propulsion for PROFAC, but I’d like continue to do some studies. As an aside, everyone assumes that nitrogen is a byproduct, but I think that any mass at orbital velocity is valuable in an integrated space transportation system. Below is my cartoon of what the system might look like.
Mass accumulator with electrodynamic tether propulsion
The most recent website update is a page on atmosphere harvesting, and the one study included to date is a solution for the shape a tether takes when used to drag a collector through the atmosphere. I was curious about the relation between the tidal forces that tend to keep the tether vertical and the drag at one end that will tend to bend the tether horizontally. The equations come from my 1983 notes, but at the time I didn’t have a handy way to solve the resulting coupled differential equations. The current Mathematica NDSolve function has no problem at all. There’s some heavy calculus involved, so I don’t particularly recommend the study as casual reading unless you need to do a similar calculation. I plan to use the results in a more complete system study, which should make for more interesting reading.
First off, I’m back from an extended trip. Thus, my excuse for not doing any space work for about 4 weeks.
Previously, I had worked out solutions for the orbital mechanics of a gun assisted launch in which we simply took the initial condition as the projectile velocity vector at the top of the atmosphere. That way, aerodynamic losses did not have to included. Then in a separate study, I looked at the aerodynamic losses associated with a given desired velocity at the edge of the atmosphere. Doing the two bits separately might have been convenient because of the different solution methods, but it made seeing the whole picture difficult. Therefore, I blended the two solutions. Using numerical search methods, we can now find the gun exit velocity for a given desired orbit accounting for aerodynamic drag and lift. We still use the closed-form elliptical orbit solution beyond the atmosphere, and a numerical integration within the atmosphere. I also established that the numerical integration could be used by itself to give the same result, but the closed-form solutions have advantages when combined with the numerical search for the gun initial condition. The results are at http://alnaspaceprogram.org/gun.html#gunstudy5.
Honest, I’m going to get off the topic of guns for a while.
(Only Mathematica nerds need read further) I’m still experimenting with publication methods. Earlier, in order to create a summary document I had been using copy and paste to place results into a fresh notebook. Although that seems to be common practice in the Mathematica world, it felt redundant. For this study I simply added text to my full calculation notebook, then closed the Mathematica input cells to hide the details. The formatting is sometimes a little off, but it seems to be a more efficient approach. The only problem is that there is a lot of text in the way the next time I want to play with the calculations. Also, it made sense to include function definitions from previous studies as external packages. I’ve included these in a zip file. The packages are made by turning the function definitions into initialization cells and then saving in package format.
I finally added some words to an existing study on rotovators (a rotating tether system) and posted the study on the main web site (see “Circular orbits from a rotating tether using variable release angles”). I wanted to consider some of the operational aspects of a rotovator. In particular, could one take advantage of different release points to achieve a range of circular orbit heights. The answer is definitely yes. A single rotating tether can be used to send payloads anywhere from near-earth orbit to geosynchronous by picking the release point. I focused on a configuration in which the lifter rocket that docks with the tether has to reach 50% of the orbital velocity at the tether docking altitude. This balance between what the rocket provides and what the tether adds allows for the tether to be built with existing materials without an excessive mass ratio. After release, the lifter must apply an additional rocket burn to circularize the orbit. An efficiency metric would be the total lifter delta V; the sum of the burn needed to catch up with the tether, plus the burn needed to circularize the orbit. For the 50% tether tip velocity selected, the total deltaV to orbit is less then 60% of the pure rocket deltaV for a wide range of orbit heights.
Posting stuff is partially slowed down by me still discovering the details of using Mathematica to create CDF and html pages. For html, I discovered that some sloppy style formatting prevents images from being converted to gif files. For CDF, I’ve been discovering all sorts of ways to break an interactive manipulate window when there are complicated packages and functions involved. Basically, the manipulate cannot reference any external packages. That causes a lot of grief in the final stages of preparing the files.
So the big question is what to write up next. I have some interesting notes on suborbital refueling that I’ve always wanted to get organized. But there may be a big break while I get ready for a summer trip.
I’ve been spending a fair amount of time just getting the initial version of the website designed and organized. There’s a balance between making things interesting and accessible, and not going overboard. This is not meant to be a grand undertaking, just a record of a hobby that my be interesting or possibly even useful to other people.
On-deck are a couple of notebooks on tethers. One shows the derivation of minimum masses for various types of tethers (non-synchronous skyhook and rotovator). The other goes through the mechanics of using a rotovator (a spinning tether) to put mass into orbit. The slightly novel bit is to study releasing the mass at an arbitrary position as the tether spins in order to get a variety of orbits.
The Alna Space Program presents some of the results from my spaceflight engineering hobby. For many years, I’ve been interested in methods of reaching space that either do not involve rockets, or assist in rocket flight. Most of the concepts have already been described in some form, but my interest is in pursuing the detailed calculations and simulations needed to flesh out the engineering. As such, I’m only interested in concepts with some degree of near-term feasibility. Exotic propulsion schemes that involve poorly defined physics or unattainable materials are germane to this site.
The ultimate goal of non-rocket propulsion is to reduce the cost of transporting material into space. One reason that spaceflight is so expensive is that chemical rockets are at the edge of their performance capabilities when accelerating to orbital velocities. The result is that payloads are a tiny fraction of the initial rocket mass, and the whole rocket has to be extremely weight efficient. The non-rocket methods have the potential for dramatically increasing payload fraction. This should reduce the cost enough that serious space industry and large projects could be pursued.
The blog is a supplement to a website that I am slowly building. The website is meant to be a more stable reference location for results, organized by topics. The blog is meant to be chronological, and is intended to describe what projects are in progress, and less formal musings. If anyone is interested, I’d welcome comments and suggestions from other space nuts that would like to play along.
I’m also experimenting with different methods for publishing engineering work. As a serious amateur not relying on publication to further a career, I’m not very interested in the detailed preparation needed for traditional scientific papers. At the same time, I always found papers on engineering analysis frustrating because of the work needed to reproduce someone else’s mathematics. In response, the website features the notebooks written using Wolfram’s Mathematica. These notebooks allow anyone else with a Mathematica license to check, reproduce, or modify my work. I’m also using Wolfram’s CDF (computational document file) format that can be viewed using a free viewer available from Wolfram. As I said, this is all an experiment and may evolve over time.
Finally, the name “Alna Space Program” is firmly tongue-in-check. Alna is a tiny town in coastal Maine where I came to live after retirement. Once at a party I admitted to someone my interest in spaceflight. They remarked that it would be cool to have an Alna space program. So here it is.
About comments: I’d love to get feedback and discussion going on the blog. However, as a naive blogger, I’ve recently discovered blog spam. From now on, comments must give some clue that you’ve actually read the post in order to be approved.