Getting from here to there

My previous post dealt with business jets. It was discouraging in that for a lot of money, you purchase the opportunity to use a lot of fuel on very expensive trips. I didn't get into so-called "direct operating costs" which include such items as engine inspection/overhaul reserve, maintenance, pilot costs (for a professional), etc. not to mention hangaring, insurance, and more, but suffice it to say that these aren't trivial for a "bizjet."



So who flies on a bizjet and why? And, for the matter of that, how should I decide how to get from here to there? I determined to apply logic and spreadsheets to the questions. I decided that the relevant factors are: speed; convenience; cost; and fuel (carbon). I subdivided convenience into: location near departure point and destination; security check hassles; schedule convenience; schedule reliability; and baggage limitations. I rated five methods of getting from here to there: airlines; my Land Rover LR3 HSE; the Phenom 100 of the previous post; my Saratoga; and an intercity bus. Sadly, having investigated intercity rail for a couple of trips, for most purposes that mode is completely impractical. There are exceptions of course, for example, downtown Los Angeles to downtown San Diego.



For each analyzed mode I used various numbers - some objective (e.g., speed, fuel economy) and some subjective (e.g., convenience) and scaled the rating for each transportation method in each category with the best rated in the category as "1." Then I assigned weights to each factor and summed them to determine a "merit index" for each mode of transport. I then played with the weights to see what considerations would result in which mode being the preferred choice.



For me, on an intermediate length business trip (say, Long Beach to Salt Lake City), I figured the weighting factors to be: speed - 0.4; convenience - 0.25; cost - 0.25; fuel burn (carbon emitted) - 0.1. Using these, the airline trip has the highest merit index, followed by the LR3, the Phenom 100, the bus, and finally the Saratoga. This is most interesting, in that I made just such a trip a few weeks ago and took the Saratoga.



So what weights result in choosing the Saratoga? If the biggest factor is convenience followed by speed as about half as important, cost of little importance and fuel of trivial importance, the Saratoga wins. Similarly, if speed and convenience are the only factors and speed is half again as important as convenience, the Phenom 100 is the way to go. Note that this literally means "money and fuel are no object, get me there fast and easily."



Looking for a combination resulting in driving being the choice, convenience dominates with everything else relatively minor. I'm in no hurry, not too concerned about cost and fuel. Finally, what would motivate me to take the bus? If my main concern is fuel burn and minimizing carbon footprint, with convenience and speed not among my considerations (not to mention how I smell when I arrive) then the bus is my choice.



It's clear that this analysis is of limited practical applicability - I certainly wouldn't take a bus or drive to New York City, nor take my Saratoga to Glendale, CA. And to call the methodology simplistic would be an insult to simpletons. Furthermore, it leaves out the "because I wanted to" factor that motivates the Saratoga trips. I'm suspicious that such a factor may also be operative in many bizjet flights. It's built around a typical business trip for my company, say, to Phoenix, Sacramento, Salt Lake City, etc. But even at that, it provides a valid comparison for bizjet vs. airline to New York or Saratoga vs. driving to Las Vegas.



The biggest revelation coming from this exercise is the wide range of considerations that lead to the airline being the preferred choice. Obviously nothing earth shattering, but it has helped me to crystallize my thoughts and to understand how I'd have to rationalize... er... justify... ummm that is, what considerations would have to be most important for me to make the purchase of a bizjet something I "couldn't afford not to do."

Just how bad are business jets?

As regular readers will know, I'm a pilot and the owner of a Piper Saratoga. That's a single engine propeller driven aircraft. In it, I get on the order of 11 statute miles per gallon and cruise at around 190 miles per hour. With no headwind, I can fly from my base in Long Beach, CA to Colorado Springs to see my brother and his family without a fuel stop, though I can rarely fly back non-stop. Like most pilots ("most" meaning, I would guess, greater than 95%) I wouldn't mind flying something faster, quieter, and with greater range. I'll also add more comfort (pressurization) and more all-weather capability (fully deiced) to the wish list.



In the current economic situation, traveling in business jets has become a very guilty pleasure indeed - witness the opprobrium heaped upon the GM and Chrysler executives who took their corporate jets to Washington to plead for bail out money. Suitably chastened by the Congressional panelists - who never waste taxpayer money - they drove hybrids to their next Congressional begging session. In the end, however, both companies entered and exited bankruptcy. I'm sure the executive jets were the proximate cause. So, are private jets really so bad?



Yesterday I had a chance to catch a ride in an Embraer Phenom 100, a so-called "very light jet." It's certificated for single pilot operation, and operates up to 41,000 feet, above almost all weather, at about 415 miles per hour. At that speed its two Pratt & Whitney PW617F-E turbofans burn about 704 pounds of Jet A fuel per hour, delivering a fuel economy of about 4 miles per gallon. Its full fuel range (with full fuel you'll be able to carry about 580 pounds of passengers and baggage not including the pilot) is about 1,400 statute miles in no-wind conditions.



The Phenom 100 cabin is quite comfortable; a passenger could sleep, work, converse comfortably with associates, or listen to Sirius satellite radio. It treats its passengers as those who get around in business jets expect to be treated (or, not being such a person, so it seems to me). Admittedly, it lacks the quiche heater and bidet one finds in higher end jets, but the interior was designed by BMW Group DesignworksUSA so you won't need to apologize for it. It has six seats - two in the cockpit and four in the cabin, plus a potty that can be used as a seventh seat. Assuming that the pilot is a professional, the five remaining seats mean that the aircraft can deliver something like 20 passenger seat miles per gallon. If I'm the pilot and I have five passengers, the figure is 24 seat miles per gallon. You'll have to queue up to purchase yours for about $3.6M.



Now, were my blog to catch on, the ad revenues to flow like water, and my bank account to swell like a balloon, I've always felt that the best, fastest, longest range airplane FLYABLE BY A SINGLE PILOT would be my ultimate ride. It's a short list of candidates and the Phenom 100 would be on it. Just how bad is this in terms of fuel consumption? In 2008, it's estimated that U.S. air carriers delivered about 58 seat miles per gallon. The Boeing 737-800 gets about 80 seat miles per gallon. If I look at my Land Rover LR3 as a five seat vehicle, I'm currently getting about 105 seat miles per gallon, though for 95% of the miles, I'm getting 21 passenger miles per gallon. Were I to use the Phenom 100 as I use my Saratoga it also would have a single occupant for the vast majority of its flight hours, thus providing four passenger miles per gallon.



I have to concede that this is a depressing post. It's difficult for me to enumerate these facts and then desire to purchase a jet. By no means am I financially able to contemplate such a purchase at this point anyway, but it had been nice to dream.

Powerkuff

In May, I attended the Cleantech conference in Houston, TX. While at one of the sessions, a presenter made a passing remark (and held his example up for us to see) about the "Powerkuff." This simple device wraps around the electrical service to my house at the service panel and wirelessly sends a continuous stream of data on power use. Added to information on price, it allows me to see just how much electricity is being used and how much money is being spent.



The device is fairly foolproof, and the output can be read on a small box and sent to a proprietary program through a USB port to a graphical display on the computer, showing power as a function of time. It comes complete and shipped for about $109, and the software to upload usage data to my computer is a free download on the Powerkuff web site. And Chuck Wagner is very helpful and accessible. The software is quite rudimentary, data cannot be stored or output to Excel. But it's still quite interesting.



For example, my "base power" right now (no A/C, no pool pump, electric stove and oven off, etc.) appears to be about 2.1 kilowatts. That's right, the refrigerator plus the various "phantom loads" (Direct TV boxes, DVD players, PS3, televisions, clocks, etc.) are sucking electrical energy and turning it into heat and light and coldness at the rate of 2100 joules/second (2.1 kilowatts). Yikes! In a year, this will amount to over $2,000 just to have food cold and entertainment "ready to go." This needs some rethinking.



With the A/C and pool pump on in the daytime, we're looking at about 7.5 kilowatts. Wow! I've mentioned in a previous post that I estimate my family's use of energy to be equivalent to about 40 kilowatts. This includes vehicles, food, "stuff," electricity at home and work, etc. I had estimated my average continuous use of electrical energy in the house at about 2.8 kilowatts. Now, I'm not so sure. The pool pump goes year around (though not continuously - about six hours per day). Obviously the A/C doesn't but still, I think I may have underestimated.



I live in Anaheim, CA where electricity is provided by Anaheim Public Utilities at relatively reasonable rates and yet I must be spending at least $3,000/year on electricity. It's clearly time to start the same process for my house that I've engaged in with my car. This will certainly be a more difficult undertaking, but the payoff in savings and in CO2 reduction dictates that I undertake it forthwith. I could have gotten the information above by checking the meter and the bill, but like the ScanGauge II I use in my car, the Powerkuff makes it easy and fun to monitor home electrical energy use.



Update: A somewhat frustrating aspect of the Powerkuff is that one must remove the cover of the sensor with a screwdriver to change the three AA batteries. Further, the only way to turn the sensor off is to remove the batteries (or at least a battery). And if you monitor for extended periods, you will be doing a LOT of battery changing. Admittedly, there's a transformer and AC power input so that the unit can be plugged in. But I suspect that, like me, most people don't have an electrical outlet near their service panel.



One could go through a set of batteries every day at a cost of, say, $5. Needless to say, the Powerkuff won't help you save electricity at a rate such as to justify this. I tried using rechargeable batteries (1.2 V NiMH) but they're good for only a few hours, or even less.



The sensor unit needs a switch so that it can easily be turned on when information is being sought and turned off when attention isn't being paid. As I mentioned above, the data can't be stored anyway. Better still would be the ability to turn it off remotely, either from the display unit or the computer. Should I decide that the Powerkuff is something I need to keep, (which is up in the air due to this issue) I'll probably have the power supply wired into the unit from the service panel.

The low hanging fruit

I've been driving to maximize fuel economy (minimize fuel consumption) and keeping detailed records of the effort for almost four years. I've been blogging about this and related topics for over three years. I've done all this while driving what would be considered "gas guzzlers." Some may scoff at such efforts, and the following is not meant to encourage people to trade in their fuel sippers for SUV's with big engines.



But I'm driving a vehicle (the Land Rover LR3 HSE) that is EPA estimated to achieve 16 m.p.g. combined. This is pretty close too, in the early days of driving it when I gave up on hypermiling attempts and drove it normally, that was about what I got. I now have a 10 tank and combined moving average of 21 m.p.g. A five m.p.g. difference, big deal, you say. Ah, but it is.



We discuss m.p.g., but the key here is g.p.m., the inverse. In a typical 10,000 mile year, at 16 m.p.g., a vehicle would use 625 gallons of fuel. At 21 m.p.g., it uses 476 gallons, 149 gallons less. If you're currently in a vehicle that gets 30 m.p.g., you'd have to drive in such a way as to achieve 54.2 m.p.g. to save a similar amount of fuel. And each of those saved gallons means about 19 pounds of carbon dioxide is not emitted.



If a driver can change his or her habits to increase mileage from 14 m.p.g. to 15 m.p.g., in a 10,000 mile year that driver will save approximately the same number of gallons as a driver who increases mileage from 25 m.p.g. to 28.4 m.p.g.



The point here is not to justify gas guzzlers, nor is it to pat myself on the back. Rather, it is to point out that there are an awful lot of gas guzzlers on the road, and they are the "low hanging fruit" for fuel savings. Unfortunately, few of the drivers of such vehicles share my craving for maximum fuel economy so the trick is in getting people on board this fruit truck.



And the same rationale that applies to individual drivers applies to car companies as well. Dramatically more fuel is saved if Ford improves the mileage of 20,000 pickup trucks from 14 m.p.g. to 17 m.p.g. than if they change the mileage of 20,000 compact cars from 32 m.p.g. to 35 m.p.g. I know that I'm not the first to come to this realization, but I think it receives far too little attention in the hypermiling and fuel economizing communities.

First order ordinary differential equations and the World Series of Poker

I play a fair amount of poker, both cash games and tournaments, both online and in "brick and mortar" casinos. Thus, of course, the World Series of Poker is of more than passing interest. That interest is shared by my CFO, and he sends me updates on the Main Event via im (internet messenger). He mentioned that, before tonight's dinner break, there were 1431 players left, and then mentioned later that there were 1071 (out of a starting field of 6494). And intuitively, the rate of elimination of players should be proportional to the number of players remaining. Sounds like a first order differential equation to me.



So, let p(t) be the number of players left at time t, then dp/dt=k*p(t) with k a negative constant. Now the time stamp from msm im for 1431 was at 18:54 PDT, and there were 1071 at 20:38 PDT. This is 104 minutes, but the dinner break is 90 minutes. This means that 360 eliminations took place in 14 minutes, absolutely not possible. This must mean that the updates are sporadic. I'll try a different method of finding two times with a known number of players and a known number of playing minutes between them. It looks like Level 13 ended with 945 players, and 90 minutes of play later, Level 14 ended with 810 players. Even this is sketchy, WSOP's own tournament update page has both 810 and 789 players as the current count. Oh well, I'm going with what I have.



Thus: dp(t)/dt-k*p(t)=0, p(0)=945, p(90)=810. This is a very simple problem and the solution is p(t)=945*exp(-0.0017127853*t). So, the tournament is won when p(t)=1, i.e., when one player is left. Now, this model has assumed that p(t) is a continuous function on the real numbers. At p(t)=945, this approximation may be reasonably accurate but when p(t) is, say, 3, it's clearly not. There are not going to be 3.43 or 2.71 players left. Nonetheless, solving the expression for t when p(t) =1 yields t of approximately 4000. That means after about 4000 more minutes of play, we should know a champion. That's about 67 hours and since they play something like 11 more days with 12 hours per day less breaks of about 3 hours, I'd guess there are actually about 100 hours left.



Various strategic considerations lead to certain times (particularly around getting "into the money" and getting to "the final table") when stalling and cautious play takes place.Thus, k, which I've assumed is a constant, is actually a function of p(t). That's a much more difficult problem though, and I'd only be guessing at the values of the relevant parameters. Possibly analyzing p(t) "piecewise" with k constant in each piece would do better. But the error is also partly attributable to the inaccurate reporting of players left at any given time. So predicting 67 hours is gratifyingly close. For a general idea, see the graph below.



This is, as the mathematically inclined will immediately see, a completely trivial problem. But for those who are not, it may be interesting to see the way a backslid mathematician looks at the world. For those whose interest is piqued by this exercise, I'd recommend "Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics" by Robert B. Banks.

GGBFS - will it save the world?

Concrete is a ubiquitous construction material, from ancient times through today. The primary expenditure of energy in concrete production is in the manufacture of cement (the gray powdery substance that binds the aggregates together after addition of water). And, as mentioned in an earlier post, with respect to CO2 emissions, its impacts extend beyond the emissions from the heat necessary to produce it since turning limestone, CaCO3, into lime, CaO, releases CO2. It's estimated that, worldwide, cement production is responsible for about 5% of CO2 emissions, and that on the order of a ton of CO2 is released in the production of a ton of cement.



It's difficult to conceive of a replacement for concrete, so efforts to mitigate the impact of concrete construction on CO2 emissions revolve around replacement of the most CO2 intensive components of the cement. As mentioned in the article linked above, one possibility is "Eco-Cement" which uses magnesium carbonate instead of calcium carbonate (limestone) to produce cement. The topic of this post is the partial replacement of cement with ground granulated blast furnace slag ("GGBFS").



GGBFS is a by-product of producing iron from ore or from producing certain types of steel. The slag typically consists of silicates, aluminosilicates, and calcium-alumina-silicates. The molten slag can be cooled slowly or quickly, but must be quenched (cooled very quickly) to prevent the formation of crystals. The slag must be "vitreous" (glassy) in order to have cementitious properties. The vitreous, granulated slag is then ground to an extremely fine powder for use as a substitute for portland cement in proportions as high as 70% in concrete.



The concrete produced using GGBFS has many desirable characteristics, including increased strength, increased density, decreased permeability and (arguably) increased resistance to sulfate attack and the dreaded alkali silica reaction. Its only significant drawbacks are increased setting time and lower early strength. These can be mitigated where necessary by the addition of appropriate admixtures. Further, the slow setting and strength gain is at least partially due to the relative large (compared to portland cement) grain size using current economically feasible technology. As grinding technology improves, this limitation will diminish. And slow setting is sometimes an advantage, for example, when long transit routes are necessary or during hot weather concreting. That slow setting is sometimes a benefit is demonstrated by the fact that there are currently marketed set retarding admixtures.



This use of what has, in the past, been a waste product of iron and steel production for an environmentally and structurally beneficial application seems to be a win for all concerned. But can it save the world? I wouldn't go that far. When utilized in concrete with equal portions of portland cement and GGBFS, the overall CO2 emission can be roughly halved. This is accomplished by both a reduced need for heating energy and by a reduction in the amount of limestone to be calcined for a given amount of cement.



So what's the potential? Using very rough figures, about 320 million metric tons of slag of suitable chemistry are produced worldwide each year. Some of this is used for other purposes, but we'll use that amount to set a cap on the replacement possible. Approximately 2.5 billion metric tons of cement are produced annually, and roughly 0.8 tons of CO2 emission are avoided for each ton of GGBFS utilized in place of portland cement. Obviously, plenty of capacity is available to use of all the slag produced if this could actually be accomplished. This would result in reduction in CO2 emissions of about 250 million metric tons or, roughly, 1% of world CO2 emissions. It won't save the world but with the G8 agreeing today to reduce emissions 80% by 2050, we have to start somewhere.

Solar hot water

Would an American building owner tolerate a roof line such as that seen here? Could an American architect stomach such an appearance? Doubtful. These are evacuated tube solar water heaters as seen on rooftops throughout the cities we visited in China. China is encouraging the use of this technology and the results are visually apparent. But are the energy savings (and consequent emissions reductions) significant?



A report by the National Renewable Energy Laboratory (NREL) concludes that solar thermal water heating has the technical potential to save about one "quad" (quadrillion, or 10^15, btu) of primary energy per year, or right at 1% of our primary energy consumption. This would result in the avoidance of the emission of between 50 and 75 million metric tons of carbon dioxide and potentially save on the order of $8 billion per year in energy expenditures. The report is dated April of 2007, so the financial considerations are likely more compelling now, with rising primary energy costs. It would seem as if China were on the right track.



The evacuated tube technology is capable of delivering hot water even when skies are cloudy and temperatures are cool. In fact, they can operate in ambient temperatures below freezing. So, are there downsides? Not many, the primary negative is the payback period. For reasons I can't clearly explain, the Chinese systems typically cost on the order of 4,500 yuan, or about $660. In the U.S. similar systems cost more like $5,000 installed. This is a major disincentive, though beneficial tax treatment may reduce the cost in some areas. And although some think they're ugly (and my %&*^%^#@^ homeowners' association would scream bloody murder), I think they're lovely.

Chinese "vehicle" traffic

While in China, we motored around on well paved roads (except for a visit to a farming village - more on that in another post) in air conditioned buses and flew from city to city on the best of Boeing's and Airbus' stable. And we were by no means alone as the only modern vehicle on China's highways. But there were a vast number of two and three wheeled vehicles, and both kinds came in motorized (internal combustion engine, electric motors) and human powered. And among the three wheeled vehicles, there was everything from large trucks hauling cargo to pedal powered carts hauling huge amounts of grain, water, children, etc. In all, it was an incredible mix of vehicle types and uses, far far beyond anything one would see in the United States.



We saw lots of these enclosed "taxis" on a three wheeled motorcycle base. Few were as pristine as this one, outside of the Forbidden City, but they were plentiful. I don't know what kind of mileage they might get, but I will hazard a guess of 40 m.p.g., based on what I've heard about various motorcycles. Certainly, that's better than an automobile taxi would get.



Then there were people doing goods transportation with muscle power. The example shown here is fairly extreme but not uniquely so. China is still a developing country and has many of the characteristics of such a status. But it's developing fast.



As I mentioned above, there were also full-size vehicles of types not seen in the U.S., both for personal transportation and for moving cargo. I haven't yet determined the benefit of the three wheeled configuration, any suggestions?



The alternative vehicles I've contemplated in this blog (here, here, and here), i.e., electric scooters, are extremely popular in China. There is some controversy over their use and the gas powered scooter purveyors, car manufacturers, etc. want them banned, but they certainly appear to have reached critical mass in China.



It's easy to tell that this is not a photograph of a U.S. street. And I'm not so sure we're doing a better job, the vehicle sizes and weights are much more appropriate to the loads they carry. As I've mentioned, my 6000 pound Land Rover LR3 HSE is a heck of a lot of metal to carry around a 185 pound man. Unfortunately, the Chinese appear to aspire to our situation rather than the reverse.



Finally, these vehicles, of which we saw many in Kunming, caused me the greatest amount of head scratching. Can it really be efficient to have a belt driven vehicle with an exposed engine? But, given the number of these that were on the road, there's undoubtedly a sound economic reason for their use. Any ideas?

Energy use in construction in China

I've been fortunate enough to have spent almost two weeks in China. I spent four days in Beijing, four days in Xi' An, three in Kunming, and most of a day in Guangzhou. I was there as part of a People to People Citizen Ambassador Program with a Public Works delegation. As such, the concentration during the professional meetings revolved around public works and we met with highway and traffic engineering groups, wastewater treatment facilities managers and engineers, and "underground" (known in the U.S. as subway) engineers.



We also had several cultural opportunities and were fortunate enough to visit many of the premier Chinese cultural sites, such as Tian An Men Square, the Forbidden City, the Great Wall, and the Terracotta Warriors. I felt privileged to visit these amazing sites, but the most compelling memories I'll keep are related to the openness of the people. We talked about politics, about Chairman Mao (60% good, 40% bad according to one of the people I spoke with in depth), the Cultural Revolution, local, regional, national, and global politics. I believe I got at least a rudimentary understanding of how the Chinese people (though certainly not the Government) feel about their place in the world, both historically and currently.



But one of the very most stunning things was the construction activity in China. In every city we visited, there were literally hundreds of tower cranes erecting massive structures. The vast majority of the structures were concrete, and I got curious about the consequent energy usage and greenhouse gas emissions. Per Wikipedia (and consequently unarguably) it takes anywhere from three to six gigajoules of energy to produce a tonne of cement. I think, based on my observations, that China would be at the high end of this range, so I'll go with six. This is is about 2.72*10^6 joules per pound. A sack of cement contains 94 pounds, and a garden variety concrete mix might use about 6.7 sacks of cement per cubic yard. So, just the cement in a cubic yard of concrete requires 6.7*94*2.72*10^6 or 1.71*10^9 joules of energy to produce. This is the total heat energy available in about 14 gallons of gasoline. It takes no account of the aggregate, the sand, the water, and the admixtures, nor of the other construction materials utilized.



Further, the production of cement is a "double whammy" with respect to carbon dioxide emissions. Not only is it extremely energy intensive, but the fundamental process of cement production is to "calcine" limestone, that is, to take limestone (calcium carbonate, CaCO3) and use heat to turn this limestone to lime (CaO), releasing CO2 in the process. One of the goals of my China adventure is to find a way to work with the Chinese to produce cementitious materials with a reduced cement content and thus reduce the CO2 impact of concrete construction.



In any case, the graphic above (courtesy of Prof. Goose at The Oil Drum) shows Chinese cement production in 2007 at 1.3*10^9 metric tonnes (1.3 "gigatonnes"). Using the energy input estimate from above, this would involve about 7.8*10^18 joules. This amount of energy in a year is an average power (easily found using WolframAlpha) of 2.47*10^11 watts.



This is a staggering rate of energy use. Typing "7.8*10^18 joules/year in watts" into WolframAlpha yields not only the above number for power but shows that this about 1.9% of the rate of global power consumption. And this is just to make cement, not the power required from limestone quarrying through placing concrete into a structure, let alone all of the other components comprising a completed structure.



Using a variety of approximations and estimates for the amount of "space" this quantity of cement could be used to produce, and the embedded energy in building construction (see here), I estimate that overall energy use in concrete framed construction in China in 2007 was on the order of 3.8*10^19 joules. This is getting to be a very significant portion of world energy usage, on the order of 9%. It's also over 40% of China's total energy usage. This would seem to be the real "Great Leap Forward," but how long can it last?