Want to read Slashdot from your mobile device? Point it at m.slashdot.org and keep reading!

 



Forgot your password?
typodupeerror
×
Power Science

The Development of Ecologically Sound Jet Fuel 210

Roland Piquepaille writes "Researchers at Princeton University are currently working on two projects to reduce jet travel's role in global warming. The first one, a major project funded by the U.S. Air Force with $7.5 million, is focused on developing computational models that accurately simulate the burning of jet fuel, a complex process not well understood today. The second one, funded by NetJets, a company providing business jets, will help to develop new jet fuels with near-zero net greenhouse gas emissions."
This discussion has been archived. No new comments can be posted.

The Development of Ecologically Sound Jet Fuel

Comments Filter:
  • global dimming (Score:4, Insightful)

    by stoolpigeon ( 454276 ) * <bittercode@gmail> on Sunday October 21, 2007 @11:28PM (#21068331) Homepage Journal
    as long as they keep creating all those contrails that help keep the temperature down. we don't want to get rid of that.
    • Re: (Score:2, Interesting)

      You're wrong. According to wikipedia [wikipedia.org], contrails have a negative effect. Anyways, the effect of the contrails is vastly outweighed by the carbon emissions. I remember hearing about a study that was saying that after the 9/11 attacks, when there was no air traffic, the temperature dropped. Of course, it's a small sample size, but you can't shut down all air traffic for a month to do a science experiment.
      • Re:global dimming (Score:5, Interesting)

        by stoolpigeon ( 454276 ) * <bittercode@gmail> on Monday October 22, 2007 @12:05AM (#21068535) Homepage Journal
        You're wrong. According to wikipedia [wikipedia.org] contrails have a positive effect. Anyways, I'm not saying that the carbon emissions are good so that is irrelevant. If all they do is switch fuels, but the engines operate under the same principles as they do now, then I imagine contrails will continue to exist as engines will continue to put out water vapor.
         
        I don't think anybody has nearly as clear a picture of how our planet's weather as we would like. It sure would be nice. I could plan my days at the beach better and we could quit guessing about what is best for the environment and maybe get a little more consensus and action, though I doubt too much more. So are contrails in and of themselves good or bad? I don't think anyone can say.
        • Is it funny that both of you used the same source but made completely opposite statements about the same phenomena?

          I mean it IS wikipedia, but still...

          At any rate, I can settle this: PBS's Nova said they have a cooling effect and the temp went up after 9/11. THAT makes it true.
          • by Mike89 ( 1006497 )

            the temp went up after 9/11
            This may sound redundant, but did they take into account the fact FIRE = HOT? I mean, two 100+ story buildings burnt.. that's gotta make some heat.
          • by mengel ( 13619 )
            And that same Nova pointed out that resarchers have now demonstrated that the affect of both CO2 and "dimming" from particulates in the air were underestimated; as both pull in opposite directions. As we shift to "cleaner" fuels, the decreased dimming will increase the "pan evaporation" rate, and raise the water vapor levels, and that will really start the whole thing churning...
        • There's lots of consensus on our guesses about climate and how it's changing. About the only resistance to the consensus is manufactured by the polluting industries, which aren't going to go along just because we know better what's happening. The more we've learned, the more they've generated complaints about what we know.

          We've also got a lot of action on climate change. But most of it is bad, like pumping pollution into the sky. Converting more of that action to conserving our balanced environment would pr
        • So are contrails in and of themselves good or bad? I don't think anyone can say.
          It's all in the name. If they were good they'd be called protrails. Also let's agree that I won't graffiti your plane if you won't graffiti my my sky.
        • Weather would be easier to predict if it weren't for all those pesky people and their unpredictable behavior. Put a crap load of heat producing engines in a big long line somewhere for say 30 minutes every morning and there's got to be a net effect on the atmosphere, not to mention the carbon and other particles in the air, changing it's density.

          I wonder if our weather prediction system could be impressively enhanced by integrating our traffic patterns into the equations.

        • Contrails are not due to the water vapor put out by the engines.

          They are actually generated in the tip of the wings and are due to the disturbance of the cold, low density, high-humidity (for that temperature) air caused by the passage of the plane.

          This is why you only see contrails at high altitude (low temperature, low pressure) and then only in some days (since the air at those heights does not always contain the same amount of water vapor).

          The source of this information is, unfortunately, offline: I bel
      • Re:global dimming (Score:5, Informative)

        by Phroggy ( 441 ) <slashdot3@@@phroggy...com> on Monday October 22, 2007 @12:08AM (#21068543) Homepage
        Actually, the difference between low temperatures and high temperatures increased by two degrees [cnn.com]. Whether the net result would be warming or cooling, we don't know for sure, because as you say it's too small a sample size.

        You should read about global dimming [wikipedia.org].
      • THAT's IT! the environmentalists carried out the 9/11 attacks! It was an internal job, but we've been looking at the wrong 'wing'!!! I knew one day greenpeace would go too far!!! (dodges attack from Bill Maher)
  • by Beer_Smurf ( 700116 ) on Sunday October 21, 2007 @11:39PM (#21068387) Homepage
    Unless this fuel meets the exact spec of existing jet fuel.
    Each aircraft type will have to be tested and certificated for use with this fuel.
    This is very, very costly and time consuming.
    • Re: (Score:3, Interesting)

      by stoolpigeon ( 454276 ) *
      If a few large corporations can really clean up on this - it wont be a problem. You'd be amazed how fast laws can change when high profits can be tied to even the impression of environmental gain.
    • by Scutter ( 18425 ) on Sunday October 21, 2007 @11:43PM (#21068413) Journal
      This is very, very costly and time consuming.

      Exactly! I agree 100%! It's hard to do, so why even try?
      • Re: (Score:3, Insightful)

        by Anonymous Coward
        If you can't justify the economics of doing so, most for-profit companies (especially the airlines, on razor-thin margins as it is) won't bother. You think any more people will fly because the jet they're traveling in makes them feel better about the environment? Think that'll offset the number who can't afford to fly anymore because their ticket price just quadrupled to afford retrofitting the entire fleet?
        • by kwerle ( 39371 )
          I think you'd be amazed how fast companies will bother as soon as just a few European or Asian (Japan) countries decide they won't supply dirty fuel.

          I have a hard time imagining a clean jet fuel, though. Maybe I will RTFA.
    • by john82 ( 68332 )
      Given that one of these research projects is funded by NetJets, which is owned by Warren Buffett [netjets.com] and includes Bill Gates [wikipedia.org] on the Board of Directors, I would expect that there's something to this. Neither Buffett or Gates are particularly known for throwing their own money away in pointless exercises.
    • by rts008 ( 812749 )
      While I have no real knowledge on jet fuels, I feel comfortable with most 'milspec' requirements. I could be very wrong (really!), but I always thought that JP4 was not much more than 'strict guidelines determined the final product' highly refined kerosene ('coal oil' to the greybeards- oh crap!....I'm turning grey....and BALD!!)

      I can see where each type will have to test and certify this, and will be costly and time consuming. I have faith in the engineers involved to consider high altitude aircraft parame
      • Yes, you are mistaken. Jet fuel is usually straight-run kero (an unadulterated, distilled fraction of a sweet crude oil), with controls for particulates and water, plus a some additives (in ppm concentrations). Sour crudes SRK fraction obviously have to be cleaned up (by catalytic hydrotreating), but the end result is pretty much the same.
        • by rts008 ( 812749 )
          Thanks for the informative reply. I am aware that 'milspec' can be very general in cases like this, but expected performance of said milspec item is usually pretty uniform. (no pun intended-it just slipped)

          "High grade kerosene' was the way JP4 was explained to me. I guess my job did not really need me to understand any more than JP4 is same-same as kerosene for anything I would use it for. (in no practical or possible scenario would I ever be involved in supporting or operating jet aircraft!)

          But the Field M
    • by ColdWetDog ( 752185 ) on Monday October 22, 2007 @12:42AM (#21068707) Homepage

      Each aircraft type will have to be tested and certificated for use with this fuel.

      Nope, each aircraft engine type will have to be tested and certified. A PITA, sure - just do it once and your done.

      • "Nope, each aircraft engine type will have to be tested and certified. A PITA, sure - just do it once and your done."

        You are quite mistaken.
        Just because an engine gets approval for use of a given fuel, does not mean you can use it in an aircraft that uses that engine.
        The approved fuels for a given airframe are spelled out for that aircraft.
        You would need to test against all the aircraft systems and get FAA approval for each model aircraft.
        The mod would also involve placarding, air crew and ground crew
      • Each aircraft type will have to be tested and certificated for use with this fuel.

        Nope, each aircraft engine type will have to be tested and certified. A PITA, sure - just do it once and your done.

        Nope, they actually test the aircraft too. Mostly because there might be effects from the fuel, such as corrosion of the fuel hoses and the fuel tanks.

        Go search for MOGAS (the Aviation term for the gas used by cars) on the Internet and read about the sorts of tests necessary for certifying a plane to legally

  • Of course, you know, this means the end of the horse-drawn zeppelin!
  • by suv4x4 ( 956391 ) on Sunday October 21, 2007 @11:48PM (#21068445)
    But of course: it's salami.

    Or in the words of Mythbuster's Jamie: "This may look like a salami, it may smell like a salami, it may even taste like a salami, but it's rocket fuel."
    • Speaking of which, one of the ingredients of Russian solid rocket fuel (for military rockets) was rice husk - a byproduct of rice production. They actually cultivated short grain rice that would have a disproportionate amounts of husk specifically for this, and grew it in Southern Russia near Krasnodar. The grain itself was edible, of course, but it was not particularly good from the culinary point of view.
  • by Sosarian ( 39969 ) on Sunday October 21, 2007 @11:50PM (#21068457) Homepage
    But haven't I read a number of stories just this week that Ocean Shipping and Cement Production are bigger CO2 emitters than airlines?
    • Well, it should also be considered that demand for air travel is growing. So while it's CO2 contribution is not so great yet, it will be more significant in the future.
    • by Sosarian ( 39969 )
      Those were all great replies, I have no idea why some of them are scored at (-1) though.
  • by wamerocity ( 1106155 ) on Sunday October 21, 2007 @11:50PM (#21068459) Journal
    It's so obvious, I don't know why they haven't done this earlier. They just need to make a HYBRID plane model! Just load it up with 5000 lbs of batteries. Silly scientists...
  • by Heir Of The Mess ( 939658 ) on Sunday October 21, 2007 @11:51PM (#21068471)

    $7.5 million is nothing to the military, especially the Airforce. They blow $100 of millions on customized database applications, billions on building single aircraft, and trillions on R&D for Airframes. $7.5 million is like some spare change they give to some college students to work on a project for 5 years that will end up being canned.

    BMW have probably invested a lot more into research into alternative fuels like hydrogen and still haven't come up with something that has us all dumping our hydrocarbon ways.

    What needs to be worked on is a more novel way of taking in air and forcing it out the back, past that you need to work out how to apply external forces to aircraft. We're looking at a lot more than $7.5 mil for that kind of physics lab experimentation.

    • 7.5MM is certainly nothing to sneeze at! In fact, that will almost get you 1/4 of an F-18!

      http://www.fighter-planes.com/info/f18.htm [fighter-planes.com]

      General Characteristics, E and F models
      Primary Function: Multi-role attack and fighter aircraft
      Contractor: McDonnell Douglas
      Unit Cost: $ 35 million
      Propulsion: Two F414-GE-400 turbofan engines
      Thrust: 22,000 pounds (9,977 kg) static thrust per engine
      Length: 60.3 feet (18.5 meters)
      Height: 16 feet (4.87 meters)
      Maximum Take Off Gross Weight: 66,000 pounds (29,932 kg)
      Wingspan: 44.9 feet (13.68 meters)
      Ceiling: 50,000+ feet
      Speed: Mach 1.8+
      Crew:
      A,C and E models: One
      B,D and F models: Two
      Armament: One 20mm M-61A1 Vulcan cannon;
      External payload: AIM 9 Sidewinder, AIM 7 Sparrow, AIM-120 AMRAAM, Harpoon, Harm, Shrike, SLAM, SLAM-ER, Walleye, Maverick missiles; Joint Stand-Off Weapon (JSOW); Joint Direct Attack Munition (JDAM); various general purpose bombs, mines and rockets.
      First Flight December 1995

  • This Is Ridiculous (Score:4, Interesting)

    by Jane Q. Public ( 1010737 ) on Sunday October 21, 2007 @11:55PM (#21068485)
    Several studies have indicated that despite the carbon emissions, the vapor trails of commercial jets actually create a net COOLING effect due to albedo. The conclusion of one research paper from a reputable institution stated that if we want to alleviate global warming due to CO2, we should actively encourage jet travel!

    Jesus, people. In our zeal to protect the environment (which I share), let's concentrate on the REAL problems please! And stop all this irrelevant noise which just distracts us from those real problems.
    • Re: (Score:3, Funny)

      by Cecil ( 37810 )
      Venus is permanently covered in cloud and has the highest albedo in the solar system. I wonder how that's working out for them... oh, that's right, it's hotter than Mercury.

      Cough up these studies, please.
      • And I suppose that the thick atmosphere of Jupiter makes it warm, too?

        I made a valid point. Don't be an ass.
      • Venus is permanently covered in cloud and has the highest albedo in the solar system. I wonder how that's working out for them... oh, that's right, it's hotter than Mercury.

        Cough up these studies, please.

        Eh? Venus has a much, much, much thicker atmosphere that's almost pure CO2, clouds made of sulfuric acid, and a surface that periodically erupts into huge masses of magma (no tectonic plates... it has to vent all that internal heat somehow).

        By contrast, you have a planet (Earth) with a Nitrogen/Oxygen atmosphere, regular heat venting via tectonics (and vulcanism), and mostly water vapor clouds with a much lighter air pressure overall.

        Methinks the albedo is the only thing keeping Venus from becoming e

    • There's much more to environmentalism than global warming.
      • Yes. But according to the post TFA was about carbon emissions and global warming. Please try to follow the topic. Thanks.
    • Re: (Score:2, Informative)

      by timmarhy ( 659436 )
      Global warming is one such distraction. you all realise C02 isn't what creates the green house effect right?

      there's various holes in the global warming C02 theory.

      1. other planets are also warming

      2. C02 lags temp. increases

      3. The hottest years on record predate industrialisation.

      The idea that jet travel is a green house problem is pure, undiluted bullcrap. infact it's reading on my bullshit meter cracked the guage.

      • I am certainly aware of this. In fact, the best evidence shows that historically, CO2 lags temperature increases by a full 800 years!

        But I was not the one making a big deal out of something that, according to their own arguments, is a net benefit, not a problem. Go figure.
      • by khallow ( 566160 )

        I'm sure some of the helpful bots around here will dump a few realclimate links for you. But here's my take:

        1. solar influx has already been taken into account by all global warming models.

        2. The CO2 lag model breaks in the present of substantial human-generated CO2, meaning we can't use it now.

        3. This just indicates the modest nature of current climate change (btw, there are no true global temperature "records" preceding industrialization). It doesn't invalidate the premise that human-generated CO2 i

    • by dbIII ( 701233 )
      It's a Roland article - the science does not have to make sense. At least it isn't perpetual motion this time.
    • Several studies have indicated that despite the carbon emissions, the vapor trails of commercial jets actually create a net COOLING effect due to albedo.

      And with a greener fuel, the net cooling effect will be bigger per plane. What's your point? In a cumulative system, a bigger minus is still a plus, if you'll forgive the choice of phrasing. It's not like the effects of the jet stop once it crosses the zero line.

      The conclusion of one research paper from a reputable institution

      Oh honestly.

      In our zeal to p

  • Maglev (Score:5, Interesting)

    by BlueParrot ( 965239 ) on Monday October 22, 2007 @12:42AM (#21068709)
    For flights that don't cross the oceans it seems to me that Maglev trains is the way to go. They can actually reach higher speeds than a commercial airliner, and if you want to be really sci-fi you could operate them inside an evacuated tube, effectively eliminating air-resistance, and thus allowing velocities far above the speed of sound. Power would of course come from nuclear reactors, because as we all know, nuclear reactors cure cancer... ( no, really ).
    • Airport Security (Score:2, Insightful)

      by Airw0lf ( 795770 )
      Some people would actively seek out the trains given how much of a hassle airport security is. Everything would of course be fine until some nutjob figured out a way to blow up a maglev train...
    • One of the articles was about a jet engine research project funded by the airforce, but after reading your comment I can see clearly that they are wasting their money looking at this flying thing. Obviously what they should be doing is researching how they can lay maglev track at Mach 2.0, and have the bombs flying down the track just behind the head of construction.

      It's genius! You send down the bombs, then you send down the troops to go in and secure what's left of the place and then you can send supplie

    • by Quadraginta ( 902985 ) on Monday October 22, 2007 @01:29AM (#21068925)
      Seems likely to me this suffers from several serious problems:

      (1) I can't easily believe it's more efficient. Granted, you use a fair amount of energy raising a jetliner to 40,000 feet, but it can't be that much, compared to what you need to use to keep it levitated and push air out of the way at 600 knots for hours and hours -- and a maglev train needs to do that, too. Indeed, air resistance is surely much higher on the maglev train, which has to operate near sea level instead of at the significantly lower air pressures in the stratosphere.

      (2) You've got an incredible infrastructure problem. Essentially, you've got to build the entire Interstate highway system over again -- only this time it can't be just smooth concrete, it's got to be ultrasmooth, ultrastraight rails kept in alignment to the nearest micrometer along thousands of miles, in rain or shine, snow or mud or hurricane or flood, and with marvelous superconducting magnet windings all along them that have to be kept in absolutely perfect working order all the time, because you can't afford one small booboo in your levitation when you're flying along near the speed of sound 1.5 inches off the ground. I can't even imagine how you're going to switch maglev trains from one track to another while they're blistering along at 600 MPH. Those are going to be some very, very expensive switches.

      Thing is, with airplanes you only need to build airports, and that's really only just laying down a big long strip of concrete and installing radar. You don't need to build much stuff between destination cities. You also don't need to lay down power along the entire route of every route they fly, because the motor goes along with the carriage.

      (3) You've got an amazing safety issue. In the stratosphere there's not much you can run into at jet speeds, fortunately. But on the ground? Say a 50 pound rock falls off a rock face and dings the marvelous superconducting track, so that when the maglev train comes along 20 minutes later it hits a "dry spot" and the carriage dips down 3 inches and hits the ground at 600 knots. BOOM. You'd have to identify the passengers by DNA analysis of tiny bone fragments.

      (4) Noise? I live next to a major rail line, and those things are noisy enough at 60-80 MPH. If they came by at 600, it wouldn't be possible to live within half a mile of the track. How does that square with the fact that most of the travel would be to and through major urban areas? Thing about airplanes is, except for within a few miles of the airport, you can't hear them because they fly two miles or more above us.
      • by tylernt ( 581794 )
        Subterranean evacuated tubes address issues 1, 3, and 4.
        • I think the Big Dig experience [publicsafety.com] kind of makes tunnels a bit more susceptible to stuff falling out of the ceiling.

          Not to mention tunnels are a bit expensive [wikipedia.org]. Like $500 million or more per mile. Tunneling from LA to New York City (2462 miles by plane) would be a minimum of $1.2 TRILLION dollars.

          And what happens if a train stalls? The whole system backs up... No thanks, I'll stick with the planes, thank you (and I fly around 200,000 miles per year).

        • Well, that they do. Also magical Star Trek transporters, which are about as likely.

          Remember the SSC [wikipedia.org] in the late 80s? That needed a mere 50 miles or so of evacuated 6-inch diameter tunnel, in a ring, with very little in the way of switching. Cost was estimated as $14 billion 1985 dollars ($25 billion 2007 dollars) before it was canceled.

          Normal interstates cost about an average of $1 million per mile to build, and we have about 55,000 miles of them. Now imagine a mere 10,000 miles, say, of evacuated tunne
      • (1) I can't easily believe it's more efficient. Granted, you use a fair amount of energy raising a jetliner to 40,000 feet, but it can't be that much, compared to what you need to use to keep it levitated and push air out of the way at 600 knots for hours and hours -- and a maglev train needs to do that, too. Indeed, air resistance is surely much higher on the maglev train, which has to operate near sea level instead of at the significantly lower air pressures in the stratosphere. I fly a relatively small
  • by Zymergy ( 803632 ) * on Monday October 22, 2007 @01:40AM (#21068977)
    Jet turbine power plants have have 2 SIGNIFICANT advantages:
    (1)They can operate with just about any type of chemically and thermally stable combustible fluid with a sufficient energy density having consistent and reliable combustion properties.
    and
    (2) They are not hampered by the well-known significant inefficiencies introduced by exhaust emissions systems such as mufflers, catalytic converters, EGR systems, etc..

    NOTE: Modern Jet fuels are hydrocarbon BLENDS. http://en.wikipedia.org/wiki/Jet_fuel [wikipedia.org]
    These blends are created as cheaply as possible to meet specific fuel properties and standards, including their energy content, and intended use: http://www.csgnetwork.com/jetfuel.html [csgnetwork.com]
    There have been many well-intentioned pushes for "replacement" Jet fuels, including a "safer" version which was intended to reduce fire balls when Jets crashed, but it was a flop as it introduced safety concerns as the 'safety' additive increased the possibility of a flame-out (it basically made the flash point of the fuel higher and reduced the flammability of jet fuel mist) and it cost way too much for little if any margin of safety it would have introduced. (Most people in jet crashes do not die from a fireball of jet fuel, but from actually hitting the mountain, crashing into the ground/ocean, or basically some form of 'Aortic Dissection' http://en.wikipedia.org/wiki/Aortic_dissection [wikipedia.org] )

    I say that this is really a SPIN and a PR campaign.

    Everyone looks good waving the environmental flag, but when compared to boats, trains, and trucking, jets are NEVER environmentally friendly. (Jets have to fight gravity continuously when moving goods and people = INEFFICIENT)
    TFA ( http://www.princeton.edu/main/news/archive/S18/96/92S56/index.xml [princeton.edu] ) is a Press Release about research into processing "Biomass" into Jet fuel And, oh ya BYW, COAL!! THAT'S RIGHT, COAL!
    We are talking about fuel from "other than" OIL Sources = SYNTHETIC FUEL (AKA SynFuel), specifically SYNTHETIC "JET" FUEL. http://www.syntroleum.com/pr_individualpressrelease.aspx?NewsID=907157 [syntroleum.com]

    This really has EVERYTHING to do with the price of oil being SKY HIGH (pun intended): http://www.peak-oil-news.info/new-synthetic-jet-fuel/ [peak-oil-news.info]
    Everyone knows that Aviation drinks fuel of any kind faster than other transportation types (when you realize the efficiency ratio of Distance traveled with quantity of cargo compared to actual fuel used per unit cargo (person, metric ton, etc..) for that given distance)
    We are talking about stirring up money to get more research into the conversion of Coal into Synthetic Jet fuel (and other fuels) and we'll get to work with biomass too.
    Oil is so expensive these days it is becoming just as cheap to chemically engineer/create (from scratch!) synthetic Jet Fuels from Coal. (which the US still has hundreds of years worth)
    Why expensively pump it out of the deep ocean, or the middle east, and then transport around the planet (BYW, they use ships for this because of their efficiency, not jet aircraft) when you can just dig up some local Coal or Bitumen Tar Sand deposit http://en.wikipedia.org/wiki/Tar_sands [wikipedia.org] and make your own synthetic fuel.
    (Now observe the pollutants released and the energy required during the "upgrading" of Coal/Bitumen into the new Synthetic Jet Fuel http://en.wikipedia.org/wiki/Upgrader [wikipedia.org] )
    FYI: The Germans made Synthetic Jet Fuel during WWII because they had Coal but not so much oil...
  • From the article:

    Coal, a relatively cheap and readily available source of energy, has an emissions profile at least as harmful as petroleum.

    ...snip...

    An "especially attractive feature" of processing coal and biomass together to make synfuels is that it requires only half the amount of biomaterial as pure biofuel production, while still making fuels with near-zero greenhouse gas emissions, Williams said.

    Right, so coal is "at least as harmful" as oil. But it's OK, because using it in a 50:50 mix with biofu

  • Princeton Professor of Mechanical and Aerospace Engineering Fred Dryer has a lofty goal: end the nation's reliance on oil for jet travel.

    No crime at Princeton will go unsolved with Hunter [imdb.com] on the job!

    Wasn't he [imdb.com] the guy that starred in the mostly-lame 80's cop show Hunter [imdb.com]? Nice change of careers from washed-up actor to Mech & Aero Engineer at Princeton.

  • I would be suprised if jet fuel makes up .01% of CO2 emissions. Heating (35%), Electricity (42%), and Car Traffic (19%) together make up 96% of green house gas emissions.[1] This is just a convienent sales tactic to make people feel about themselves without actually doing anything. [1] http://www.ytv.fi/ENG/future/climate_change/greenhouse_gas_emissions/frontpage.htm [www.ytv.fi]

Two can Live as Cheaply as One for Half as Long. -- Howard Kandel

Working...