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Dr. James Dewar, Dr. John Jurist, Monday, 3-2-15 March 3, 2015Posted by The Space Show in Uncategorized.
Tags: B4 core, Congress, Dr. James Dewar, Dr. John Jurist, leadership, NTR (nuclear thermal rocket), NTR economic benefits, nuclear fuel, nuclear propulsion, policy, regulations, space law, Thorium, tungsten, UN Committee on the Peaceful Uses of Outer Space, Vasimr
Dr. James Dewar, Dr. John Jurist, Monday, 3-2-15
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Guests: Dr. James Dewar, Dr. John Jurist. Topics: Nuclear propulsion, nuclear policy, technology and more. Please direct all comments and questions regarding Space Show programs/guest(s) to the Space Show blog, https://thespaceshow.wordpress.com. Comments and questions should be relevant to the specific Space Show program. Written Transcripts of Space Show programs are a violation of our copyright and are not permitted without prior written consent, even if for your own use. We do not permit the commercial use of Space Show programs or any part thereof, nor do we permit editing, YouTube clips, or clips placed on other private channels & websites. Space Show programs can be quoted, but the quote must be cited or referenced using the proper citation format. Contact The Space Show for further information. In addition, please remember that your Amazon purchases can help support The Space Show/OGLF. See www.onegiantleapfoundation.org/amazon.htm. For those listening to archives using live365.com and rating the programs, please email me as to why you assign a specific rating to the show. This will help me bring better programming to the audience.
We welcomed Dr. James Dewar and Dr. John Jurist back to the show to discuss nuclear propulsion and rocket. During the first segment of our 1 hour 40 minute discussion, Both Dr. Dewar and Dr. Jurist talked about the nuclear rocket technology, fuel, cores, past experiences, and how best to modernize the nuclear rocket and move forward with new development. Most of the callers talked technology so this first segment is very technology heavy. Space attorney Michael Listner sent in emails suggesting it would never happen due to the regulatory side of things plus he provided us with the UN Committee on the Peaceful Uses of Outer Space policy on using nuclear power in space (www.unoosa.org/oosa/SpaceLaw/nps.html). Listener Kristopher spoke to our guests about core options and fuels. Check out this site that he sent us: http://www.projectrho.com/public_html/rocket/enginelist.php#ntrvapor. Toward the end of the first segment, I said that after the break the second segment would focus on what to do to make the nuclear rocket policy and to start the program and develop this form of advanced propulsion. Both Dr. Dewar and Dr. Jurist agreed.
In the second segment, we did focus on the need for leadership and organizational structure for developing the nuclear rocket and starting with nuclear propulsion. We had several callers and emails addressing how to sell a nuclear rocket program. Dr. Dewar talked about the economic benefits, jobs, opening up more of space to economic growth and access. I asked about chokepoints and both our guests suggested the biggest chokepoint was the absence of young, passionate, and competent leadership. Related issues that came included how best to get the support of congress as well as the American people, plus why a nuclear rocket was important and should be developed.
Please post your comments/questions on The Space Show blog per the above URL. You can reach either guest through me.
- 2. Andy Hill - March 9, 2015
I was wondering just how small can you make an NTR, what is the smallest core that can be made to function. Would it be possible for instance to strap a small NTR on a dreamchaser type craft and use it as a shuttle from LEO to lunar orbit. refueling when it came back to LEO each time would create a regular service for cargo or crew.
So is it possible to make one a few hundred pounds in waight and sufficiently small dimensionally that could be incorporated permanently into the body of a spacecraft? By refilling its fuel tank from an on orbit liquid hydrogen supply, such a craft could operate for years making dozens of trips.
- James A. Dewar - March 9, 2015
The first issue you raise is complex and depends on many factors, starting with core design. In NTR you have to achieve criticality, i.e., the fission process must start and continue in a controlled fashion. In theory, you have many design choices that can make this happen, but today and not fifty years from now, your choices are somewhat limited. I advocate the B-4 core design because it has been proven to work in the testing done in the 1960s. It featured a hexagonal fuel element 3/4 of an inch from flat to flat and 52-inches long and they were assembled into bundles, one in the center surrounded by six others. Many bundles then were incorporated to make up a core. The typical core dimension back then was 35-inches, but it was increased in size to 55-inches, giving a design power of 250k of thrust, and then decreased in power to 20-inches, giving a design power of 25k thrust. So the B-4 design has the flexibility to increase in size, depending on what is needed. I don't think you can go smaller than 20-inches without running into criticality problems, but one should never say never. The 20-inch core would weigh about 6000 pounds and give 25k thrust at a specific impulse of 825 seconds. However, many subsequent generations of the 20-inch core are possible, each with more thrusting power and specific impulse, so one should not get stuck here.
Now once you have a workable engine design, you can configure it to your specific mission requirements. An appropriate analogy is commercial airliners: some are for long continent to continent hauls, some for shorter city to city distances and some for smaller airports/cities. Same with NTR.
The second issue you raise was considered in the 1960s with the effort to develop the 10 hour 60 recycle fuel element (a goal that was achieved in non-nuclear testing in 1972). This transforms the space program as now you have a spaceship that can go out and come back, just like a commercial airliner. Those are not scrapped after they fly to a destination but are used over and over. So the goal of NTR back then was to make an engine that could last for 10 hours at full power with 60 starts and stops. So, yes, what you describe is possible with NTR, but very hard to achieve with chemical propulsion.
Finally, I don't think it is possible to build a NTR only several hundreds of pounds in weight. Probably couldn't achieve criticality to start up. However, you are raising the issue of a mission needing only small amounts of thrust. Here I note it is possible to "throttle down" a NTR to give a small amount of power. That was accomplished in the 1960s, they were able to take reactors with a design power of 1000MW and operate them at 25MW. For reference one MW equals 50 pounds of thrust.
I hope this helps.
- Andy Hill - March 9, 2015
A small 20″ B4 core giving 25k of thrust might be a good place to start a development project. I think starting small and giving people time to get use to it is preferable, a large project becomes a target to cut and can be plundered for funds.
Associating it with a craft gives it a purpose and another reason to exist. If the engine was developed as a stand alone item it would be open to the same type of criticism as SLS not having a mission.
- James A. Dewar - March 9, 2015
This is where I come out, start small and use the engine as a learning tool and once you have a R&D staff that feels confident, then go on to more advanced systems and more advanced missions.
This process is an adaption of what the Navy went through with the Nautilus nuclear submarine. Approved in 1948 and launched in 1954 it had no real military utility, but after it sailed submerged around the world and under the North Pole, the navy had a good feel of what it could do. Many nuclear subs followed in the 1960s with specific missions.
So I would start with a small 20″ core and after it has flown a dozen or so missions and after it has been uprated, my first formal mission would be a "free launch" program. Split the payload up into various compartments, say a meter square, then allow the private sector – i.e., private citizens – the opportunity to have a payload they build launched into LEO for free. In other words, NASA could say "if you build it, we will launch it." This is the start of a truly private sector space program, with a lot of "moms and pops." Perhaps you.
Then the program should move on to create a solar system transportation system that would operate like an airliner, train or truck, going out on a pre-determined schedule and coming back. Like an airliner, the concept is to sell "seats" or compartment space on the payload. Since even the small 20″ core should have exceptional capabilities by now, perhaps 10-15 years after the program restarted, it should be very profitable. Although this is too simplistic, when the seats were filled, the spaceship took off from LEO.
This type of NTR would have a different R&D focus than the one for reaching LEO. It's premature to speculate too much on it now.
Finally, after 10-15 years of experience with a small 20″core it is time to move on to larger systems, perhaps in 35 or 55 inch cores. These would be very powerful systems and their initial R&D should be focused on lifting massive payloads to LEO for the construction of truly large space stations. Like the 6000 ton rotating space station that von Braun conceived for the movie 2001. Big stuff, with artificial gravity, unlike the free-floating, gravity-less 440 ton space station. Now opens the door to large space stations for manufacturing, tourism, planetary defense, environmental monitoring/solar energy generation, etc.
This is where I come out and 20 years might seem like a long time, but I hold it is realistic. Look at the navy experience, starting with nothing in 1948, but having a full fledged fleet by the 1960s, including all the personnel and facilities and policies and training to handle it. About 20 years.
I hope this helps.
Jim Dewar
- 3. jimjxr - March 5, 2015
I may have heard this incorrectly, but it seems the idea here is to use NTR to launch payload to LEO? From Earth surface? I think NTR is worth consideration as in space propulsion, but using it as launch vehicle engine seems to be a very bad idea.
- James A. Dewar - March 5, 2015
That depends. If you launch a NTR from a fixed site such as the Cape, it is a bad idea. However, it is also a bad idea to launch a chemically propelled rocket from a fixed site and more than one have had to be destroyed by the range safety officer because it was veering off course and heading to populated areas.
I advocate a C5A/cargo plane launch which would start from a US controlled island in the Pacific. Or the C5A could even take off from Australia or New Zealand. The launch profile is fairly simple: the C5A would fly to an isolated ocean area and at 40,000 feet, the NTR stage would separate from the plane. Several solid rocket boosters would then fire and take the stage up to 150,000 feet whereupon the NTR would begin operation and fly the payload to LEO.
What are the benefits then? Many launch windows are available in the vast Pacific ocean, depending on where the C5A takes off and on its range. So there can be far fewer people to worry about over a fixed site and even fewer terrorists – how would they know where to go? And depending on the launch window, one could take advantage of the equatorial boost. Then the cost of maintaining a fixed site and the many people needed to operate it is eliminated and sites such as the Cape are then dedicated to fostering this expanding space program.
In other words, the cost of fixed sites adds to the cost of launching payloads. Without even running the numbers, it should be fairly intuitive that this launch profile would result in much lower payload costs, to $100/pound and then even lower as better NTRs are developed. Your basic needs are: an airport, a C5A, a flight crew, some ground personnel, several solid boosters, LH2 and a nuclear engine which could costs only several millions.
That may sound silly, but let's take a quick look. A NTR needs a pressure vessel about an inch thick and smaller than a 55 gallon drum. It needs a LH2 turbine/turbopump, 1960s vintage though updated. The same for the nozzle. The costs for some piping and valves and nuts and bolts and temperature sensors are minimal. It needs about 1000 pounds of boron/beryllium and about 500 fuel elements. In the late 1960s, these cost $1000 each, which was quite expensive, but then they had 2000 QA/QC inspections. You can make your own assumptions on what they would cost today. $5000 each? $10,000?
So what is the greater risk? To continue on with a chemical rocket space program that long ago reached its maturation point and has now stagnated or to start on a new propulsion technology that promises almost unlimited potential. The former gives you an elitest space program; the latter opens it up for the common man. It is democratic, you can participate in it and you can profit from it.
It should be obvious where my sympathies lie, but for you, what is the greater risk? (I analyze this flight profile in more detail in my second book: "The Nuclear Rocket: Making Our Planet Green, Peaceful and Prosperous." I hope you have opportunity to read it).
Jim Dewar
- jimjxr - March 5, 2015
Thank you for the detailed reply, I can see you're very passionate about this plan, but as a layman I just don't see it happening, sorry… Some thoughts:
1. You're using air launch, which has some drawbacks, for example it would be hard to scale up. I'd be interested to see how much payload you can put to LEO and GTO using C5A.
2. Past experience with air launch (i.e Pegasus) is that they're not cheap to operate.
3. Air launch would reduce some of the concerns regarding safety, but not all of them. The airplane still need to take off with nuclear material, and may have to land with it if you have an abort.
4. Regarding cost, I don't know how $100/pound is calculated, it seems this is assuming an expandable NTR rocket. I find it hard to believe that an expandable nuclear rocket would be order of magnitude cheaper to build than an expandable chemical rocket.
5. The comparison of cost should be apple to apple, i.e. if you assume cheap off the shelf components for nuclear rocket, and using air launch to reduce launch pad cost, then the same assumption needs to be made for chemical rocket's cost.
6. Of course the biggest concern is public reaction, I just don't see the public would accept lighting a nuclear engine in the atmosphere. The utilities are already closing perfectly good nuclear reactors due to public pressure, I think it's pretty much impossible to sell this idea in any country, let alone the US.
7. Regarding commercial interest, it is my impression that nuclear technology is more of a failure is not an option type of thing, this doesn't fit well with new space startup's test/fail/fix bugs/test again methodology. Case in the point, SpaceX already blow up two first stages in their testing of reusability, and they are fine with it since tests are expected to fail. I just don't see how this would work with nuclear engine.
8. Another thought about commercial interest: It is mentioned several times that the US has a nuclear navy, but what didn't get mentioned is that nobody on Earth has a nuclear cargo ship fleet. Why? I don't know, probably a combination of cost and security concerns, but if shipping company wouldn't touch the very mature navy reactors, I don't see how rocket company can be expected to be interested in nuclear rocket engine.
- James A. Dewar - March 6, 2015
Thanks for your reply, I respond via your order.
1. I don't know what is going to be scaled up. I've picked the C5A as it is the largest cargo plane we have, but I feel uneasy using a plane designed for one thing for another. It would be better, I think, to design a lift plane specifically for the NTR stage, but this might have to wait until the program gets some experience. Also, I too would like to see some hard numbers on the payload one can take to LEO/GTO. However, this is a sliding scale cause NTR can make rapid gains in thrusting power as well as specific impulse. That changes everything, making it quite fluid. I wrote a 29-page paper that projects out to 10 generations of engine improvements, each generation giving more capability to increase payload fractions and these are not limited to the engine itself. Before the program was cancelled, it had plans to use slush hydrogen, a colder form of LH2 that shrinks in volume by up to 20%. So if you had a tank weighing 10,000 pounds for X amount of LH2, now that same X amount could be contained in a tank weighing up to 8000 pounds. The 2000 pound difference can be now shifted to your payload column. I see if David Livingston can post that 29-page paper here.
2. I don't know much about Pegasus, but it seems it was limited to micro-payloads/micro-satellites. I'd like to think about this more though. The Air Force launched a Minuteman out of a C5A in the 1970s and NASA was experimenting on it in the last couple of years, but I can't think of what the space vehicle was.
3. We have transported nuclear weapons by air since 1945 and do so today. The Air Force has travelled millions of miles with them on board and out of all those miles there were only a handful of accidents and these, for the most part, were cleaned up. I view this as a non-issue.
4. I don't know what you mean by "expandable," but let's crystal ball the cost of a NTR. A metal pressure vessel smaller than a 55-gallon drum: $500,000? A nozzle, turbine/turbopump 1960s technology updated: $2 million? About 1000 pounds of boron and beryllium: $500,000? Nuts and bolts and piping and valves and temperature sensors: $500,000? The NTR core of 500 fuel elements, let's say they cost $10,000 each: $5 million. The cost so far: $8.5 million. Then you have to add the cost of the LH2 tank, several solid boosters, a C5A. Make your own guess here, but I think under $10 million would be in the ballpark since the C5A would be reusable. The total so far: $18.5 million. Now you tell me the cost of the Atlas, Delta, Ares and Space X launchers.
5. I believe 4 above also answers this.
6. Public perception and public acceptance is critical. The public accepts the nuclear navy though in the early days some cities refused to have nuclear vessels berthed in their harbors. New York city for one feared them blowing up. However, Norfolk accepted it and has had a positive revenue stream for over half a century from this nuclear presence. Nuclear power has had a checkered history, accepted for two decades starting in the 1950s, but criticized since the 1970s and much of that unfairly. But that's their problem as they have failed in their outreach efforts. Now with NTR, if you justify it on the basis of space science and manned Mars, you will have a tough sell. However, if you justify it on the basis of creating thousands of high paying jobs on earth, of solving environmental problems on earth and of creating manufacturing space stations, it will be an easier sell. Still difficult, but people will accept "risk" if there is high reward, especially if it puts money in their pocket. Just look at all the jobs that have hazardous duty pay attached to them.
7. I'm not quite certain what you mean here, but if NERVA had been built, it would have had a .997 reliability factor and those .003 would only mean it failed to operate as designed, not that it would blow up. NTR are far more rugged and reliable than chemical systems that either stop working or blow up. NTR can suffer major damage and still keep pouring out thrust. The KIWI-B1B test proved that: at 500MW, it started ejecting its core out the nozzle, but Los Alamos kept increasing its power till it reached 1000MW, its design level, all the while ejecting its core. Control was never lost. This means if a NTR suffers a core accident on a mission, it remains possible for the mission to be completed or the crew to be saved. Things do not blow up like the Challenger. Also, the KIWI-TNT reactor was purposely blown up as part of a safety program in 1965; afterwards, people went in and picked up the pieces. It wasn't a big deal and while I cannot give any data on radiation exposure of those people, because those records remain confidential, my good friend Stan Gunn said he got 10R from picking up those pieces. Stan is now 92 and still in good health.
8. If you read my 29-page paper, you will see there are two ways for a NTR company to make money. First is by launching payloads into LEO and moving them around the solar system. Here the law of supply and demand takes over: as the cost of something drops from then demand picks up. So if the cost of moving payloads to LEO drops from $5000/pound to $100/pound, you can expect an increase in demand. Second by adapting NTR technology for earth applications. Here note that NTR could operate at 3000 C and the nuclear engine company could take that technological know-how and derate it to operate at 1000 C. This is blast furnace temperatures and now gives you a steady source of process heat for many industrial applications. Smelting, chemical and petrochemical and so forth. This could revitalize key industrial sectors. Moreover, one of its biggest applications might be melting our wastes that are clogging our landfills into a liquid, then separating that into the commercial useful and true waste. Every county and city in the US has a waste problem so this possibility could be worth trillions. With that type of a profit lure, I expect NTR companies to be keenly interested.
Also, keep in mind that with the core potentially the size of a 55-gallon drum, I expect the counties/cities to be keenly interested. Small core sizes promise very low capital costs. In other words, it's possibly quite affordable to the cash-strapped.
Now you've mentioned I'm very passionate. Well, I don't know. I think disgusted might be more accurate. I see so much potential for this to be a game-changer not only for our space program but for earth as well but am frustrated that our so-called "best and brightest" are unwilling to study a flight profile they banned in 1960 for PR reasons. No technical studies, just a fear of adverse publicity. "They will never let us do that." Nonsense, come up with solid justifications and see. So we go round and round on the chemical rocket merry-go-round: ammunition (one and done) rockets, then the space shuttle, then the national aerospace plane, then the Venture Star/X-33, now SpaceX, now back to ammunition rockets in the Ares and Atlas and Delta, et.al.
I think it's time to get off the chemical rocket merry-go-round. You never answered the question I posed to you so I ask it again now: Isn't it time we got off this merry-go-round and take a serious look at NTR that has almost unlimited potential?
Jim Dewar
- jimjxr - March 7, 2015
Hi, Jim:
For #4, by "expandable", I meant whether the $100/pound cost figure assumes the NTR rocket will be reused, it looks to me you meant to use the NTR rocket once and throw it away?
Obviously we don't know the actual cost of a chemical rocket, but $18.5 million is not that far away from the listed price of SpaceX's Falcon 9 ($61.2 million). This is why I'm confused by the $100/pound number, how can it be so cheap when the NTR rocket itself is not significantly cheaper than a chemical rocket?
And to answer your question directly, I'm afraid I'm still in the chemical rocket camp. I'm a firm believer in reusable chemical rocket, and I think they should be sufficient to reduce the launch cost by an order of magnitude. I'm not an aerospace engineer, so I can only work by analogy here. When I look around at our current transportation infrastructure, I see most of them are powered by chemical energy (some are powered by electricity obviously): Cars, trains, ships, airplanes. So it's obvious to me chemical energy is sufficient for our transportation needs, and the reason launch is so expensive is not because of the chemical fuel, but because we're throwing away the launch vehicle.
- James A. Dewar - March 7, 2015
Your first two paragraphs raise issues somewhat linked to I'll respond to them together.
I envision reusing the non-nuclear components of a NTR after it returns from LEO. The fuel would not be reused since it would be "hot," but sent for recycling. The pressure vessel, turbine/turbopump, beryllium/boron, and other such components would be reused after rebuilding/recertifying. The nozzle may or may not be reusable. This essentially means the only major cost for a "new" NTR is the fuel elements, which I pegged at $10,000 each. However, one has to assume this figure can be lowered as experience is gained. This means the cost of a core will have downward pressure from $5 million ($10,000/element X 500 elements).
Now the $100/pound figure is merely a peg point on a graph. As your R&D produces ever more capable NTRs, your payload fractions increase. As they do, the cost of pounds to LEO decreases. It's that simple. I mentioned the 1968 study Rocketdyne did of replacing the third stage of the Saturn V with a first generation NERVA. It would almost double the payload to LEO, from 250k pounds to 500k. So you double the payload fraction. And that's with a first generation NTR, as you go to second, third, fourth, etc., generation systems, that payload fraction goes up. So the per pound payload cost should come down. How much and how fast are unknowns now.
Now take your Falcon 9 and find out its payload fraction – it will be around 2%. Can it be doubled, tripled, quadrupled. No. In contrast, a first generation NTR should double the payload fraction of the Falcon 9 and then get better from that. In other words, Falcon 9 and all other chemical rockets reached their maturity in the 1960s and have only marginally improved since then. Check for yourself: Google the payload fractions of the Atlas, Delta and other rockets from the 1960s and today. NTR on the other hand has an almost unlimited promise to produce better and better systems, each with larger and larger payload fractions, among other improvements. And somewhere in their future lurks the promise of the "afterburner" where the hydrogen molecule is split into two atoms. This can cause a big jump in specific impulse to where you have a rocket engine four to five times more powerful than the best chemical systems, whether solid or liquid. This would probably push the payload cost to less than $100/pound.
Your final point is a hope and dream, that the only thing holding back a chemical rocket space program is reusability. Do this, problem solved. The space shuttle, the national aerospace plane, and the Venture Star/X-33 do cast doubt on this hope and dream. Now we have the private sector funding this dream and it is premised on the belief that the government only screws things up, but the private sector can make it happen. We'll see. I doubt it, but you are firmly in the camp that it can happen.
Anyhow, I have enjoyed our exchanges and hope you have as well.
Jim Dewar
- B John - March 6, 2015
I understand that there are ideas about how a nuclear thermally propelled launch stage can be built without any radioactive exhaust. Didn't Dr. Dewar mention nuclear-powered aircraft tested in the 1950's as an example? Even if the first stage then needs to be massive, if it is reusable it may still be economically attractive.
- James A. Dewar - March 6, 2015
B John,
I am not aware of any studies that show a nuclear thermally propelled launch stage can be built without any radioactive exhaust. It seems impossible to me. You will have gamma rays and neutrons emanating from the fission process unless you have massive amounts of shielding. You will also have fission products, the radioactive elements that are formed when the U-235 atom splits in two, coming out the exhaust. The question here is how much and that is a function of your fuel element design. I think zero release is not possible, but would never say never.
That said, using NTR as a first stage seems to me a straight thrust to weight ratio type of problem. If you get enough thrust coming from a given engine weight, you can make a cement truck aerodynamic and with a nuclear rocket engine fly it to the moon. I've over stated this obviously, but Bob Bussard conceived of a nuclear SSTO and I reference it in my first book. It would use conventional jet engines to take the craft to 50k feet, then the nuclear rocket engines would fire to LEO and it is used over and over.
I also don't see any direct relevance of the aircraft nuclear propulsion program here. Their direct and indirect cycle reactors, which would power jet engines, had poor thrust to weight ratios and the technology has long since passed them by. There might be indirect relevance though in the sense of the thoughts on the direct and indirect cycles might be starting points for a new investigation.
In sum, I don't see any NTR launch stage, whether it be a nuclear rocket engine or nuclear jet engine driven, appearing at the beginning of a reconstituted program. Given 10-20 years of R&D and operational experience, who knows. And with drone technology, it could be totally unmanned for take offs and landings and that would eliminate a major design worry. So, it's definitely not impossible and may be likely once you get teams of people with positive 'we can make it happen' attitudes.
Jim Dewar
- B John - March 9, 2015
Thanks for the corrections. This is how I understand the basic dilemma:
– In-space use of NTR requires much larger missions than humans have ever conducted. NTR is too big for our probes thus far, and the Moon is too close for it to be of much use for an Apollo program. The demand would come either from for example a crewed base on Mars or an orbiter to Neptune within reasonable travel time. It would not be economical to put an NTR on a small probe like New Horizons to Pluto.
– Launching from Earth to LEO is said to be halfway to anywhere in the Solar system, in terms of delta-v. And NTR cannot be used in that role because of environmental concerns. And in a truly space faring society, launches would be so frequent that those concerns would become real.
– So you propose air launched NTR's. But how much does that really help the problem with radioactive exhausts spreading out across the atmosphere? Also, air launch adds the problems and restrictions of air launch. The C5a can take about 80 tons payload, while a launcher like Atlas V weights about 330 tons on the launch pad. I think that there is a conceptual conflict between NTR (which likes large scale missions) and air launch (which is only available for small payloads).
- James A. Dewar - March 9, 2015
B John,
Some general comments first. As you increase in specific impulse in NTRs, you increase the speed at which the rocket travels as well as the amount of payload it can carry. Or you can have a trade-off, slower speed but even more payload. That increase in speed and payload is roughly double the best chemical rocket system to start. I emphasize to start, because NTR has almost unlimited potential. Now as you increase in speed, it means you are shrinking the solar system timewise. This has its own consequences for the space program.
Now with regard to your first issue, you can build NTRs in just about any size. They are not, I repeat, they are not only for large scale missions such as manned Mars. I advocate starting with a small system, about 25k thrust (but recognizing this can be upgraded significantly both in thrusting power and specific impulse). This is more than adequate for unmanned missions to all points in the solar system. This has three important consequences. First, the speed at which missions are carried out is reduced dramatically and this would please the scientific community; they get their data back far quicker and that's the purpose of the mission in the first place. Second, the much larger payload capacity means more instruments can be loaded on board, to more either at the destination, such as Pluto, or to do things along the way. Also, ultra high-tech payloads may not be required cause there is so much more room with which to work. It might become common just to use off-the-shelf components to build the payload, thus realizing a drastic savings. Third, since NTRs can be restarted easily, it raises the possibility of a mission return so here the scientists might devise payloads with the technology to recover "stuff" from a planet or ring or some such. This is the "dead-heading" problem that so plagues the trucking, airline and shipping industries, the return to home without cargo. With NTRs, it is a problem yet to be solved.
On your second issue, there are two kinds of radioactivity emitted by NTRs. First are gamma rays and neutrons and x-rays but these would be inconsequential since the earth is already being bombarded with such from space. Space is really highly radioactivity and any further increase from a NTR would be so minor as not to be noticed. There might be a worry that the gammas and neutrons from a NTR in LEO might interfere with
other satellites, but I submit that is a problem that can be handled if it is in fact a real one. This requires further study. Second, the fission process results in the splitting of the U-235 atom into elements roughly half the the atomic number of uranium. These are called fission products and they range in radioactivity from real hot with short half-lives to not so hot but with long half lives.
In a nuclear power plant, these fission products are sealed in metal rods to keep them from wandering around and contaminating the reactor. In NTR, some fission products would escape, but the magnitude is uncertain now. It is possible to fabricate fuel elements that drastically reduce this. Also, I advocate starting a NTR above 150k feet and this would allow any fission products to disperse into an ever increasing volume around the earth's surface. Bear in mind though that neutrons from space are forming radioactive particles such as carbon 14 that then fall to earth. It is not a prestine environment. Also, bear in mind though, any release from an NTR would be quite less than that from a single, small nuclear weapon; during the period of atmospheric weapons testing, the radioactive burden ejected into the atmosphere was much larger. Many of these tests were at surface level, not 150k up. Here we are, a half a century after atmospheric testing stopped. and the earth seems to be holding its own.
On your third issue, air launch solves many problems if one launches from the Pacific. Safety issues are minimized and the possibility exists to take advantage of the equatorial boost. The C5A can lift about 300k pounds or 150 tons, but I intuitively dislike the thought of using it. You always run into problems when using something designed for one purpose for another; I'd favor designing a lift plane specifically for the NTR mission but that would probably have to wait until some experience is gained. The Atlas payload and a NTR payload are an interesting comparison. The Atlas payload is stuck and it cannot be increased in any meaningful way because its technology is mature. NTR payload capacity is a function of what generation engine you are talking about, with many generations possible. In other words, NTR has a long, long way to go. It starts off twice as good as chemicals and goes up from that.
I hope this helps.
Jim Dewar
- B John - March 9, 2015
You taking time to answer our questions here is most enlightening! It does help my understanding.
But I still worry about radioactive nuclei created and spread by an NTR launch would rain down on the surface sooner or later. I mean, we could maybe do it for a while once every few years or so without too much pollution, but it isn't the way we'll become a space faring society. And your comparison with a nuclear bomb air burst certainly won't convince many!
As for scaling, I'm most worried about the first threshold. One specific mission or program of a series of missions, needs to be in enough demand for the investment needed to mature NTR.
- James A. Dewar - March 9, 2015
B John,
I find the concern over "radioactivity in earth's environment" more illusory than real. The earth is continually being bombarded from radiation from space. Solar flares, for example, have a nice innocent sounding name, but what if we called them what they are: violent neutron-spounting volcanic eruptions many times larger than the earth. Most of the time our atmosphere protects us from them, but occasionally they overwhelm our atmosphere and they strike earth. One knocked out the power grid in Ontario, Canada in the 1980s. Space is intensely radioactive and any additional burden from a NTR is miniscule. One wag noted that God must have loved reactors since he created billions and billions of them in space.
That said, it is possible to reduce any burden NTR might add as R&D progresses. You are not stuck in one place, but can get better and better fuels that reduce the release of any fission products. How much I don't know as I don't know today's starting point. You can never get to zero, but you can certainly get lower reductions. My reference to atmospheric testing is merely to show there is an upper limit to the radioactivity injected into the atmosphere. That includes ton quantities of plutonium. If the anti-nuclear opposition claim of 7000-13,000 pounds ejected into the atmosphere is accurate and if their claim that a millionth of a gram causes cancer is also accurate, everybody should be dead or cancer-ridden now. But our population size is growing and people are living longer.
So it is good to have concern, but concern must lead to hard data to find out if it is really a concern or merely emotion. Ask yourself then: is this anti-nuclear claim on the lethality of plutonium accurate or not? Is it real or is it hype? You decide.
On your return on investment question, I have only the observation that the law of supply and demand applies. Once NTR lowers the price of moving payloads into and beyond LEO, demand for this service will pick up and that will lead to better NTRs that will, inter alia, reduce costs even more and that will lead to even greater demand. It's Econ 101.
Jim Dewar
- B John - March 14, 2015
Thanks again for your comments!
The popular argument around (I don't do the math myself, I just use secondary popular sources, like you ;-D ) about NTR not being economical for small payloads, like all interplanetary probes launched thus far, is not about chemical rockets. It is about nuclear electric propulsion (NEP). The DAWN probe is already using (solar powered) ion thrusters which gives its reaction mass, I think, about 40 times the exhaust speed compared to chemical rockets, and several to ten times higher speed than NTR achieves. And if you argue that NTR will get more efficient, well then wouldn't NEP too? The problem with NEP is, as i understand it, that it is difficult to scale up because of the problems with radiating the waste heat from generating that much electric effect. But NEP would always be better than NTR up to some payload size and speed. The tradeoff limit is likely below what's needed to get humans to Mars. NTR certainly seems to beat VASIMR carrying humans to Mars, but would it beat even solar electric power on a probe like DAWN?
I still wonder how an NTR program would fit inside a NASA budget. No new probes are planned to any of the outer planets (the proposed unnamed Europa mission for the 2030's isn't even a slideshow today) and there are no plans for any human space travel other than to the ISS, now scheduled to burn up in 9 years. Given this low ambition (which we all hate, but are stuck with), wouldn't NTR become another SLS hog which dominates the budget without having any real application in sight? I still fear that it wouldn't make current spaceflight cheaper and faster, it would only be good for larger scale spaceflight ambitions which aren't on the radar today.
- James A. Dewar - March 14, 2015
B John,
NEP has a role in a space program, but only for pushing very small, light micro payloads. It cannot push large, heavy ones though that might be possible in the future however unlikely it seems now. Now small light payloads mean very high cost ones whereas large heavy ones imply less cost and/or more instruments on it giving more data.
If the ban on using NTR to reach LEO is reversed, then I cannot see NASA funding any NTR development. As I argue in my book, The Nuclear Rocket, a private sector-government corporation would have to be formed whereby the government provided the test sites, HEU and its security, and other such, while the private sector would provide the money for the rest of the program. It also would launch the payloads via cargo planes in the Pacific. If this started small, it would be up and running within 5-7 years and by 10-15 years would be firmly entrenched, with management fully versed in the details of developing and using NTR. In other words, most but not all missions would be private and not NASA/government funded.
Gaining this experience is similar to the process the navy went through with the Nautilus nuclear sub. Approved in 1948, launched in 1954, it sailed around the world submerged and under the North Pole by 1960 and gave the navy lots of insight on how to use it. Missions in other words. These followed in the 1960s and continue to this day. I submit the same would happen with NTR if this general scheme is followed. It would take about 20 years for it to take hold and then a real space program could begin, with very large space stations and manned space missions to the various planets.
In sum, when you reverse the ban on reaching LEO with NTR you must rethink your space program totally. I have set forth a strawman argument to provoke discussion and dialogue on it. Hope this starts you thinking.
Jim Dewar
- James A. Dewar - March 4, 2015
To Daniel Kohn
Daniel Kohn provided comments separately as he was unable to give them on his blog. I will try to paraphrase his comments and then reply.
First, I thank Daniel for taking the time to listen to John and myself and I also thank Daniel for reading my two books on the nuclear rocket.
Second, Daniel holds I am accurate that the UN space principles regarding NTR are not treaty language, meaning Congress can shape any reconstituted NTR program according to its wishes. This is certainly not new or earth-shattering; treaties come into being for one set of political/economic/technical circumstances and are modified or scrapped as those circumstances change. This is International Politics 101.
Third, Daniel believes my desire to scrap "mission-itus" type thinking is wrong and that it must play an essential part in any space program. This may take some space, but let me explain my views. Since a space program based on chemical propulsion is expensive, it limits any space program to three broad categories: national security, science and commerce (mostly communications satellites). The first two are conducted by the government mostly (the national security agencies and NASA) while the latter by the private space sector. The first two follow a common path: the agency develops a mission, then gains approval of the Office of Management and Budget and then it is sent to Congress for its authorization and appropriation of funding. Obviously, this is a time-consuming process. The third can be quicker as the private sector uses its own monies and has profit as its bottom line. So if it see a profitable niche, it will develop and launch a satellite quickly.
With NTR I hold we must develop a different mind-set because the economics of taking payloads into LEO can be drastically reduced to $100/pound and below and ever more advanced NTR systems come into existence. This technology is not stagnant. Also, these large payloads can be taken elsewhere in the solar system for less money and at a greater rate of speed. When you have costs dropping dramatically, the law of supply and demand kicks in and there will be more people coming forward wanting to have their payloads launched.
Recognizing this law of supply and demand, I believe any reconstituted NTR program should start off with a small system, say around 25k thrust and just aimed at launching payloads to LEO. This keeps development costs low, but more important it helps build an infrastructure of trained people who will know how to handle the technology better as it improves and matures. I cite the Navy which started the Nautilus nuc sub in 1948 and it had no mission. When launched in 1954, it had little military utility but was a learning tool for the Navy who then built its infrastructure on a realistic basis. Then better nuc subs appeared with definite missions.
Now I have proposed two broad "categories" of missions for a small NTR. The first is a "free launch" whereby the payload is divided into smaller compartments, say a square yard each, and then these are made available to the public free of charge for a launch. "If you (the private sector) will build it, we (NASA) will launch it." This has the effect of stimulating a private sector space industry where various "moms and pops" can test out their ideas. Perhaps most would fail, but so what; the ones that succeed could turn into 21st century Apples.
Later as the small NTRs mature, I advocate the establishment of a solar system transportation system that would act like any airline, shipping or railroad company. Publish the schedule and the fee for the ticket and then launch. So now the "mission" would be determined by the private sector, e.g., if a launch to Venus was planned for 2016 and it had 50 "seats of launch compartments" that would be advertized and when the time came and "seats" were filled, then the launch went. This is highly simplistic, but I think readers will catch my drift: the solar system is being treated now as the private sector treats traveling over distances, be it land, water or air. Why should space be any different and NTR permits if not requires this type of thinking.
When you have a fully trained infrastructure, perhaps in 20 years, it is time to move on to larger and more powerful NTRs and these should be aimed at lifting large payloads into LEO (however that is defined). Here I am talking the development of large space station industries. For the reader who thinks this is just whimsy, let me say that in 1968, Rocketdyne studied replacing the third stage of the Saturn V with a first generation NERVA and found it could double the payload. From up to 250k pounds for the all chemical Saturn V to up to 500k pounds for the Saturn V-NERVA, and that was with a first generation engine. That's about 250 tons in a single launch. The entire International Space Station weighs about 440 tons.
In my book, I propose a space station similar to the one von Braun proposed back in the 1950s, one that rotates to provide gravity and weighs about 6000 tons. Now you start to have a real space program and I can see space stations coming into being for many purposes: industrial, planetary defense, tourism. To those who think the "greens" would oppose NTRs, I ask what would they say if they had the possibility of their own "green" space station; I hold that would be quite intriguing for them and their "opposition" would be tempered quite a bit.
Obviously then, this type of space program is not "mission-itus" thinking, but it will be based on the interests and desires of the private sector and it will be carried out quickly since it would not be linked to the US government budget process. I'm sure some will dismiss this as most fanciful, but it is not, it is inherent in NTR technology. But you need new thinking to make maximum use of it. That is a lesson the Nautilus taught us when it sailed submerged around the world and under the North Pole. If you had kept with diesel/electric sub thinking, the Nautilus would have surfaced every several days to recharge the batteries and air supply. That would have been absurd. New technologies demand new thinking to get the most out of them. For too long, we have applied chemical propulsion "mission-itus" thinking to NTR and it has gotten us nowhere.
Daniel, I hope I have answered your points adequately.
Jim Dewar
- 5. James A. Dewar - March 3, 2015
All highly enriched or weapons grade uranium (HEU) is owned and controlled by the Department of Energy and is located either on DOE sites or it is in the form of weapons that have been transferred to the military. When those weapons are taken out of inventory, they are returned to the DOE for disassembly and recovery of the HEU. The NRC does not have any regulatory authority over the DOE. During the Rover/NERVA program the AEC (the DOE's predecessor agency) made HEU available either to Los Alamos, a nuclear weapons laboratory, or to Westinghouse, a private contractor who was fabricating fuel elements for the NERVA. The NRC was not in existence at this time, so there was no regulatory oversight here.
Under my proposal, a government/industry corporation would be formed with the DOE providing the test areas/facilities and the HEU while the private sector would provide the money for the actual operation. Legal control of the HEU would remain with DOE at all times and during a NTR's launch into LEO and beyond, either military security would be in force or DOE security would be used, or a combination of the two. Since 1946, all security throughout the nuclear weapons complex has been performed by private contractors and it has been responsible for the movement of weapons and weapons parts throughout the US. You may have heard of the infamous "white train." The NRC has no authority and no regulatory role here. If there would be an accident involving a weapon, military and DOE cleanup crews would be involved, not the NRC.
There are many precedents for forming a government/industry corporation, so that is not new. TVA comes to mind real quickly. If this was to happen, Congress would have to hold hearings and debate the new structure and then pass legislation to bring it into being. Any regulatory role for this new structure would be determined in the course of the debate on this legislation so it is premature to even discuss it now.
The extent of any terrorist threat to this new corporation obviously would have to be considered not in the abstract but in terms of where the development sites would be, where the launch sites would be (I advocate a cargo plane launch from an island somewhere in the Pacific and this would limit any terrorist strike) and where the used nuclear engines would be recovered (also somewhere in the Pacific). I think one can construct actual scenarios whereby any terrorist threat is reduced greatly and this then shifts the justification back to what can a new NTR do for the US. I hold, if you read my second book, it can create thousands of high paying jobs initially and then as the nuclear rocket infrastructure takes root, it will turn into hundreds of thousands of high paying jobs.
I hope you have opportunity to read my second book and consider the argument more carefully. Nuclear rockets do open up the solar system for the common man, both to go there as well as to prosper from.
I hope this helps.
Jim Dewar
- Michael J. Listner (@ponder68) - March 4, 2015
I do support nuclear propulsion; however, I feel given then realities of the geopolitical world, international legal obligations and the existing terror threats that a private/government relationship where fissile material is handed over to for a private space mission will not happen. I agree there are examples of this happening in the past, including N.S. Savannah, but the vagaries of international space law and its responsibilities and liabilities, coupled with the current geopolitical environment in a post 911 world will not allow a private space mission to solely take possession of fissile material without at least a government representative or authority having on site control.
To that end, I do believe nuclear propulsion should be pursued but as a means to an end and not an end in of itself. The Apollo program was national policy and not just a stump speech, which the hardware was developed as an end. Likewise, if a future administration makes say a mission to Mars as part of the National Space Policy and makes nuclear propulsion part of that policy that would be a great means to a national policy end, which Congress could support through funding. With all the environmental and anti-nuclear lobbies exerting pressure, Congressional support would not be enough to overcome it.
Furthermore, to get the nuclear ball rolling, you need a dedicated organization similar to Naval Reactors and one strong-willed individual to run point and plow through the legal, political, technical and bureaucratic barriers that will arise.
I'm not trying to tell why it can't be done. I am trying to explain to you that the real hurdles are not technical but rather that there is a huge minefield of political and legal issues that need to recognized and navigated around if nuclear propulsion is to become a reality.
This may sound negative, but it's the realities of the current political and legal environment.
- James A. Dewar - March 4, 2015
I would encourage you to read my second book on the nuclear rocket as it would reveal that our thinking is not that far apart. To wit, I call for the creation of a government/industry corporation to develop and use nuclear rockets. For its share, the government would "contribute in kind" in the form of HEU, test facilities/sites and security while the private sector would provide the money and personnel to make it happen.(DOE has had this government/industry structure since 1946; DOE is GOCO, meaning government owned but contractor operated, so this concept is not foreign to the agency. In contrast, NASA is mostly GOGO, government owned, government operated. I can explain the reasons more for GOCO if you like). So you maintain government control over the HEU while the private sector provides the wherewithall. The latter has the benefit of avoiding the slow government funding process as well as the cumbersome and expensive government procurement process.
If the launch profile is like I set forward, the launch area is from one of our islands in the Pacific, a vast area in which terrorists would have difficulty operating and an area fairly devoid of people. That eases safety/regulatory concerns.
If this happens, then the entire program is justified by the jobs it creates on earth and here please read my thoughts on its green implications. Then as nuclear rocket propulsion develops and matures, large space stations come into the picture. This hints at the possibility of shifting our manufacturing sector there or at least parts of it.
Finally, I agree that a vigorous spokesman is needed, like a Rickover or von Braun and he or she must have an organization to reach out to other groups in the country to gain their support. This cannot be a government structure like Naval Reactors for the law forbids this. All I know is that I cannot be that spokesman. I am old, fat and slow. Perhaps you, someone younger and more vigorous.
All I can do is put a marker down, this is government slang for putting forth a first draft of a new policy, for debate and discussion purposes. It starts the ball rolling as it is something to shoot at and will not be the final product.
I hope you have a chance to read it.
Jim Dewar
- 6. Michael J. Listner (@ponder68) - March 3, 2015
Specifically, I said that use of nuclear propulsion technology is unlikely to happen because of regulatory concerns and potential acquisition of fissile material by terrorist groups. This last comment was misconstrued by the guests to mean weapons-grade fissile material, but I was speaking of non-weapons-grade fissile material.
- Michael J. Listner (@ponder68) - March 3, 2015
Edit to the above comment: Use of nuclear propulsion technology by private groups is unlikely to happen because of regulatory concerns.,,


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We are working with KeepLAMvoing as part of a broader effort to fight back against Road Diets and Traffic across the city.

subset: commoncrawl


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Jenny contacted photo-features wanting to sell her amazing true life story. After reading our website she decided that we were ideal agency to sell her story. We helped publish her real life story in The Daily Mirror.
Couple's baby joy after spending £54k on IVF treatment.
When she lost her son Jack to meningitis, just weeks before his second birthday, Jennifer Heneghan's world fell apart.
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"The consultant explained that I had developed a condition that had fused my tubes together," explains Jennifer. "I asked what they could do and he just shook his head and said nothing. I was infertile." Jennifer was only 25.
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Apparently now I had more chance of winning the lottery than having a baby."
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And now he's seven months old. "After what we went through it doesn't matter what he cost because we feel like we have won the lottery," Jennifer beams. "We never gave up on our dream and finally it came true. I can never thank Mum and Dad enough because the money they gave us bought us Tiernan."
Jennifer thinks Tiernan is the image of his big brother Jack.
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And while Jennifer admits being a mum in her 30s is much more tiring, she's loving every minute.
"I don't take anything for granted and I'm afraid to say he has me wrapped around his little finger.
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Needless to say the family had their best Christmas ever last month.
"There's only one word to describe the presents piled under our tree – shameless!" she laughs.
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"It used to be a sombre day because it's all about children and just reminded us what we couldn't have. Now Tiernan is the best gift of all."


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|Biosequences .. Software .. Molbio soft .. Network News .. FTP
Dear all, has anyone come across, and understood why all the siliques abort on some otherwise perfectly healthy looking WS2 plants? The plants can be from the same seed batch and grown in the same pot as similar-looking plants with fully developed siliques and seeds. The plants are glasshouse grown in a commercial seed raising mix with a slow release fertiliser. Thanks. Cheers, Brian ===== Brian Jones PhD PCBRC School of Botany University of Melbourne 3010 Victoria Email: bjjones at unimelb.edu.au Tel: 61 (0)3 83444008 ________________________________________________________________ Nokia 5510 looks weird sounds great. Go to http://uk.promotions.yahoo.com/nokia/ discover and win it! The competition ends 16 th of December 2001. ---


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Mankato Council Member Seeks Pardon of Dakota 38
MANKATO, Minn. (AP) — A Mankato City Council member is seeking a presidential pardon for the 38 Dakota men hanged in a mass execution at the end of the U.S.-Dakota War of 1862.
KTOE-AM reports Jack Consadine submitted a petition to the White House after he learned about the history of the hangings. His petition seeks a posthumous pardon for the "Dakota 38," plus two Dakota men who were hanged later.
Consadine says there were no defense attorneys and the trials were only three to five minutes long. He says the Dakota believed they were being invaded.
Some disagree with Consadine, and say the Dakota's war tactics were brutal.
As of Sunday, there were less than 700 signatures on the petition. A petition needs 100,000 signatures to be considered by the president.


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Look, its 2015 and everyone knows how important it is to look good online. First impressions are vital for your business and personal relationships, and you know that. So why are you using that group photo that you cropped all of your friends out of, or even worse, that selfie you took while sitting in your car at a red light, for your LinkedIn profile photo!?!!? You're embarrassing yourself. Stop it.
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Studio time: Approx. 30 min. | Final delivery: 1 retouched headshot portrait
You've got a busy schedule, I get it. Let's crank this out, so that you can get back to taking care of business.
Our goal here is to capture just one great looking headshot portrait, as quickly as possible – likely in under 30 minutes.
So how does this work? Well, you're going to arrive at my studio ready to rock – your hair is looking good, your outfit is sharp, and ladies, your makeup is perfect. We'll chat while you get settled in under the lights and let you catch your breath. We'll check out your face and find your good side – everyone has one – and then I'll start doing my thing with the camera.
I'm shooting tethered to my laptop so we're able to see the photos on the screen in real time as I'm shooting, seeing what's working and what's not. We're going to try a couple of different angles and expressions, and shoot until we find 'The One.' When we find that shot, you can take off and head back to your busy day. I'll do a bit of light retouching one your skin and stylize the edit, and then email you the photo file, ready to upload as your profile pic on Facebook, Twitter, Instagram, Tinder…wherever you need it.
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Studio time: Approx. 1 hr. 30 min. | Final delivery: 1 retouched headshot portrait + $50 each additional image
This session will be a lot like Level 1, but we're blocking out more time in the studio with the goal of creating several great images. With an hour and half in the studio, you'll have time to make a couple wardrobe changes and try out a few different looks.
When we're finished shooting, we'll take a look through the images and pick out all of the keepers along with your favorite shot. I'll get to you a retouched version of your favorite image along with a private online proofing gallery of the rest of the keepers. If you'd like to later add-on any of the additional keepers, you can do so for $50 each. Tell me which images you'd like, I'll retouch them and then send you the files.


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There's a problem that a coworker recently brought up. The problem statement can be found here.
This is a re-hash of an existing problem known as the one hundred prisoners problem. It seems impossible at first, and many naive approaches yield failing results. But, given the correct approach, it is solvable with a surprisingly high probability.
A Solution
It's really just a permutation problem. The basic idea is that the boxes are numbered 1..100 and they all contain a bill with a number 1..100. To construct a working solution, you use the bills as pointers to box numbers in the following way. You start at the box labelled with your number, and go to the box number of the bill it contains. Keep doing that, looking in the box and going to the box of the bill you find inside. Eventually, you get to the box containing the bill that points to where you started – and that's the bill you're looking for. So, the question really becomes: How often does a random permutation of degree $n$ contain a cycle having length greater than $n/2$? If you get a longer cycle, then anyone with a number in that cycle is screwed because it takes them longer than $n/2$ steps to find their bill. If there are only cycles having lengths less than $n/2$, then everyone can find their bill in the appropriate number of steps.
So, how many random permutations of degree $n=100$ contain only cycles having length less than 50? For this, we can look at approximations given by Stirling numbers of the first kind. Essentially, the number of random permutations having only cycles of length less than $n/2$ (in our case 50) as asymptotic to $log(2)$, which is around 0.3010. That's a bit surprising, because it means that the strategy above is expected to win roughly 30% of the time for large numbers of boxes.
Testing with Sage
How well does the strategy actually perform when $n=100$? We can test this out in Sage.
def max_length_orbit_random_perm(n): """ Generate a random permutation on 1..n and compute the longest orbit.""" return max([len(i) for i in Permutations(n).random_element().cycle_tuples()]) won = 0 tries = 10000 for i in range(tries): if max_length_orbit_random_perm(100) <= 50: won += 1 print "won %s out of %s" % (won, tries)
And we get the following.
won 3072 out of 10000
So, we win roughly 3 out of 10 times. If we were charged $1 to play the game, but won $100 if everyone found their dollar, then we'd be doing very well to play the game.


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Hallow's End is near an end, but not before you hear this week's show full of some extra holiday bits and info on the biggest giveaway to happen on the show yet!
For complete details on the Blizzcon Surprise contest, go to realm-maintenance.com. You have just a handful of days to enter!
Thanks to WoWhead, WoW Insider, MMO-Champion, and battle.net for their continued coverage of WoW news which was used as research for this week's show.
Podcast of the Week: Heals & Headshots
website: healsandheadshots.com
Twitter: @HHCast @noelove @podcastitute
email: email@example.com
Livestream: Every other Saturday at 9pm Eastern at http://twitch.tv/HHCast
Listen to the show on Stitcher and iTunes!
Podcast News: A Paladin's Tale, Group Quest, Extra Life Gaming Marathon on Nov. 2, Alternative Chat, Monkcraft, Monk Meditation, 30 Minute Cooldown, Hunting Party Podcast, Battle Pets, Twizzcast, Low Pop WoW, But Wait! There's Lore, Decked Out, The Starting Zone, All Things Azeroth, Dawnforge Productions Blizzcon Coverage, Legendary
Keep updated on the World of Podcasts Blizzcon gathering at worldofpodcasts.com or on Twitter @Worldofpodcasts
Realm Maintenance invites you to check the WoW podcast subreddit at http://www.reddit.com/r/wowpodcasts
Thanks to Tauren Think Tank for use of the Hallow's End intro heard on Episode 75 of their show!
Podcast Segment Spotlight: Alludra's Pets
Are you part of a WoW podcast and want your news mentioned here? Email firstname.lastname@example.com
Realm Maintenance is here to promote your show news and special events as a service to the WoW podcast community.
Follow Rho on Twitter @RhoWoW and follow the show @RealmPodcast
Leave a voicemail for the show by clicking on the "Send Voicemail" box located on the right side of realm-maintenance.com!
You can also find Rho as a co-host of All Things Azeroth every week. Find the show at allthingsazeroth.com
Questions, comments or submissions can be sent to email@example.com. All submissions received by Sunday 3pm Eastern will be read and considered for the next podcast.
Listen to the show on iTunes or Stitcher Radio!
Podcast: Play in new window | Download


text: DailyMail: Miami slugger Giancarlo Stanton has taken to Instagram to show fans how far he has come since being hit in the face by a fastball during a game last week. Stanton had doctors appointments scheduled for today after which the team will have a better idea as to whether the Marlins have any hope him returning to the team before the season ends. There will be an official statement on Wednesday, but it's doubtful he will be able to get back onto the field as he recovers from a gruesome injury. Stanton was hit in the face by an 88 mph pitch from Milwaukee Brewers starter Mike Fiers on Thursday night and sustained facial fractures and dental damage.


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Every one of you who is reading this most likely loves photography. Whether you are a professional photographer who has your own business or you just have a passion for taking photographs of anything and everything during your free time, you should check out this video.
This quick, 5-minute video by the Cooperative of Photography is all about the history of photography. See how the first digital camera was created, what the first "photoshopped" photo was and even who took the world's first selfie. Check it out and enjoy!
We hope you enjoyed this video that we originally found on FStoppers.
Did you love this? You will also enjoy reading these other fun photography articles:
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In Order to Organic Furniture.:pattern of Tree by Studio Rope-Hiroyuki Morita
Studio Rope-Hiroyuki Morita Shares The Pattern of Tree in Order to Organic Furniture
studio Rope - Hiroyuki Morita, the thinktank behind the award winning project In order to organic furniture. by studio Rope - Hiroyuki Morita illustrates, A proposition of partition that utilize conifer parts inefficiently; that is, the slender part of the trunk's upper half and the irregular shaped part of the roots. I paid attention to the organic annual rings. The overlapping organic patterns of the partition created a comfortable rhythm in an inorganic space. With the products born from this cycle of material, organic spatial-direction becomes a possibility for the consumer. Furthermore, each product's uniqueness gives them a much more higher value..
In Order to Organic Furniture.:pattern of Tree by Studio Rope-Hiroyuki Morita Images:
End of the article, click here to go back to previous page, or alternatively go back to Art and Design homepage.


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Cameron-Clegg couple gets in a muddle over war
Issued on: Modified:
Britain's ruling couple, Prime Minister David Cameron and his deputy, Nick Clegg, have ventured onto sticky military terrain, the first appearing to belittle Britain's armed forces, the second suggesting the UK had taken part in an "illegal war".
So much so, it seems, that they even time their war gaffes to match – despite the PM and his deputy being an ocean apart and talking about two very different conflicts.
Cameron was in the US this week for his first official visit to the White House.
With his trip clouded by BP's woes and new twists in the Lockerbie affair, Cameron worked hard – perhaps too hard – to appease and flatter his ally.
On Wednesday, he sought to remind the US that Britain remained "a very effective partner", if only "a junior partner".
That was simply stating the obvious. But Cameron then went on to say that "We [the British] were the junior partner in 1940 when we were fighting the Nazis," neglecting the fact that the US did not join World War II until December of the next year.
For Britain, a country priding itself in having stood alone against Nazi Germany and its allies, Japan and Italy, for over a year, the gaffe was somewhat embarrassing.
The opposition Labour Party was swift to pounce on the prime minister's remarks.
"1940 was our finest hour. Millions of Britons stood up and gave their lives to defeat fascism," said David Milliband, the shadow foreign secretary, describing Cameron's words as "a slight, not a slip".
Asked about the prime minister's remarks, a spokeswoman for No.10 Downing Street told the BBC that Cameron had emphatically not sought to belittle the efforts of British troops.
The remarks, coming from a staunch and consistent opponent of the war, would have raised few eyebrows had Clegg not become a member of government and -- more importantly -- had he not been representing the prime minister in the weekly question-and-answer session with members of parliament.
Unlike Clegg, Cameron supported the Iraq war, as did most of his Conservative party.
Perhaps more worryingly for the government, a legal expert quoted by British daily the Guardian said Clegg's remarks could be seized upon by international courts investigating the conflict.
Clegg later insisted he had spoken in his capacity as leader of the Lib Dems, while a spokesperson for Downing Street rushed to say that Clegg's words were not government policy.
"The coalition government has not expressed a view on the legality or otherwise of the Iraq conflict," he said in a statement. "But that does not mean that individual members of the government should not express their individual views."
Downing Street also said it was looking forward to receiving the conclusions of an inquiry into the run-up to the war, the so-called Chilcot inquiry.
In the meantime, it appears members of parliament will have to guess on who they will see next time Clegg stands in for Cameron, the Lib-Dem leader or the deputy prime minister.


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Other Opinions
Don't judge me for my Jesus memes
If you want to discern my faith, don't look for a cross around my neck. Look at my Facebook page. I love a good Jesus meme.
One favorite features a classic painting of villagers staring heavenward. "Jesus is coming," says the caption. "Look busy." Another fave? Jesus doing a face-palm with the caption, "Guys, I said I hate figs." These may seem like jokes from the darkest side of sacrilege, but they get a good laugh, a click of the "Like" button, and an approving prayer-hands emoji from progressive Christians like me.
In light of the anti-gay "religious freedom" bills recently signed into law in Mississippi and Tennessee, sharing a meme that substitutes "figs" for a pejorative most newspapers won't publish may not seem like much, but it's a protest nonetheless. The same with posting the meme: "Just once, the world would like to see Christians claim 'religious liberty' compelling us to feed children or curb gun violence or combat cancer or anything remotely life affirming. Instead we use it to withhold wedding cakes." It's a way of communicating that I refuse to fall for the right-wing con. "Religious liberty" legislation is not the stuff of protecting faith, but of pointing fingers.
You have to understand: I work, socialize and post in circles where the only Sunday sacrament is brunch. I move mostly in the world of "nones," otherwise known as the "spiritual-but-not-religious." Many of them don't look kindly on Christians; they don't even think they know any.
According to the Pew Research Center, "none" is "the single most common religious identity among those born between 1980 and 2000." In the United States, the study projects, Christians will decline from more than three-quarters of the population in 2010 to two-thirds in 2050, while nones will increase from 17.1 percent to 25.6 percent in the same time period.
So I sometimes feel I'm on the wrong side of history, and that makes me self-conscious about opening up a conversation on faith. But sharing posts, memes and tweets makes me feel like I can, at the very least, let the nones know that Christianity isn't what they may think it is.
The schism in Christianity these days runs far deeper than arguing over the pros and cons of accepting offerings online, or whether or not playing Christian rock during services constitutes pandering to millennials. The Ku Klux Klan, it has been reported, wants you to start thinking of it as a Christian group. A recent Washington Post/ABC poll revealed that American Christians, more than the non-religious, are likely to support torture. And then there's good old Parson Donald Trump, bungling a Corinthians reference in one breath and condemning immigrants in the next. The old hippie folk hymn paraphrasing John 13:35 says: "They'll know we are Christians by our love." Not based on my news feed.
The Christian right in America has dozens of politicians and mega-pastors broadcasting its beliefs. Meanwhile, more moderate Christians hardly make the media radar. Into that void, we're left with posting memes and retweeting comedian John Fugelsang: " Mississippi -- The poorest state w/highest unemployment, most obesity and worst education just passed a law to protect themselves from gays."
Moderate and progressive Christian activism doesn't make headlines and it's certainly not clickbait. The basic goodness in my corner of Christianity garners pretty much no mainstream media attention. Crazy gets more clicks, so the extremists get all the airplay. The progressive message needs a signal boost.
Once I started posting Jesus memes, I realized I wasn't facing anti-Christian bias on the part of my friends, but rather cluelessness. They had formulated their ideas about modern Christianity from what the media was telling them. To them, "Christian" equaled global-warming denier and homophobe. Was I one of those people, they wondered? They needed assurances that I didn't see faith and science as mutually exclusive, or even faith and common sense. It was up to me to inform them that I was down with Bill Nye, not Lou Sheldon.
Then things got interesting. They'd quiz me: Those Christian business-owners who refused, on religious grounds, to make wedding cakes or pizzas for same-sex couples, What Would Jesus Do? My answer: He'd start baking. (Could we have foreseen the culture wars being waged on a battlefield of carbs?) So, yes, social media can be a useless time suck, but it can also be a crucible for creating understanding.
I am aware of how trivial a Gospel According to Likes may seem: Too personal, as if the message were tantamount to a spiritual selfie -- lamentations from the Church of Me. I know that when I retweet UnvirtousAbbey -- "For places where it's easier to get a gun than a get a job, we pray" -- I may be merely affirming that I am not alone in my sadness about how my religion is being continually, devastatingly distorted.
If we want something to change, we start where we are, and where I am so often is online. The Bible says "Judge not lest ye be judged." It doesn't say, "Let Bible-justified cruelty, prejudice or downright nuttiness go unchallenged."
If I were to select just one social media message to communicate the outrage and sorrow I feel about the co-opting of Christianity, which hashtag, meme or emoji would I choose?
That's easy.
Lily Burana is a novelist and memoirist. She is at work on a book about her journey back to faith. She wrote this for the Los Angeles Times.