# The mass of a car and its mpg.

Back when I was an assistant professor at Michigan State University, MSU, they had a mileage olympics between the various engineering schools. Michigan State’s car got over 800 mpg, and lost soundly. By contrast, my current car, a Saab 9,2 gets about 30 miles per gallon on the highway, about average for US cars, and 22 to 23 mpg in the city in the summer. That’s about 1/40th the gas mileage of the Michigan State car, or about 2/3 the mileage of the 1978 VW rabbit I drove as a young professor, or the same as a Model A Ford. Why so low? My basic answer: the current car weighs a lot more.

As a first step to analyzing the energy drain of my car, or MSU’s, the energy content of gasoline is about 123 MJ/gallon. Thus, if my engine was 27% efficient (reasonably likely) and I got 22.5 mpg (36 km/gallon) driving around town, that would mean I was using about .922 MJ/km of gasoline energy. Now all I need to know is where is this energy going (the MSU car got double this efficiency, but went 40 times further).

The first energy sink I considered was rolling drag. To measure this without the fancy equipment we had at MSU, I put my car in neutral on a flat surface at 22 mph and measured how long it took for the speed to drop to 19.5 mph. From this time, 14.5 sec, and the speed drop, I calculated that the car had a rolling drag of 1.4% of its weight (if you had college physics you should be able to repeat this calculation). Since I and the car weigh about 1700 kg, or 3790 lb, the drag is 53 lb or 233 Nt (the MSU car had far less, perhaps 8 lb). For any friction, the loss per km is F•x, or 233 kJ/km for my vehicle in the summer, independent of speed. This is significant, but clearly there are other energy sinks involved. In winter, the rolling drag is about 50% higher: the effect of gooey grease, I guess.

The next energy sink is air resistance. This is calculated by multiplying the frontal area of the car by the density of air, times 1/2 the speed squared (the kinetic energy imparted to the air). There is also a form factor, measured on a wind tunnel. For my car this factor was 0.28, similar to the MSU car. That is, for both cars, the equivalent of only 28% of the air in front of the car is accelerated to the car’s speed. Based on this and the density of air in the summer, I calculate that, at 20 mph, air drag was about 5.3 lbs for my car. At 40 mph it’s 21 lbs (95 Nt), and it’s 65 lbs (295 Nt) at 70 mph. Given that my city driving is mostly at <40 mph, I expect that only 95 kJ/km is used to fight air friction in the city. That is, less than 10% of my gas energy in the city or about 30% on the highway. (The MSU car had less because of a smaller front area, and because it drove at about 25 mph)

The next energy sink was the energy used to speed up from a stop — or, if you like, the energy lost to the brakes when I slow down. This energy is proportional to the mass of the car, and to velocity squared or kinetic energy. It’s also inversely proportional to the distance between stops. For a 1700 kg car+ driver who travels at 38 mph on city streets (17 m/s) and stops, or slows every 500m, I calculate that the start-stop energy per km is 2 (1/2 m v2 ) = 1700•(17)2  = 491 kJ/km. This is more than the other two losses combined and would seem to explain the majority cause of my low gas mileage in the city.

The sum of the above losses is 0.819 MJ/km, and I’m willing to accept that the rest of the energy loss (100 kJ/km or so) is due to engine idling (the efficiency is zero then); to air conditioning and headlights; and to times when I have a passenger or lots of stuff in the car. It all adds up. When I go for long drives on the highway, this start-stop loss is no longer relevant. Though the air drag is greater, the net result is a mileage improvement. Brief rides on the highway, by contrast, hardly help my mileage. Though I slow down less often, maybe every 2 km, I go faster, so the energy loss per km is the same.

I find that the two major drags on my gas mileage are proportional to the weight of the car, and that is currently half-again the weight of my VW rabbit (only 1900 lbs, 900 kg). The MSU car was far lighter still, about 200 lbs with the driver, and it never stopped till the gas ran out. My suggestion, if you want the best gas milage, buy one light cars on the road. The Mitsubishi Mirage, for example, weighs 1000 kg, gets 35 mpg in the city.

A very aerodynamic, very big car. It’s beautiful art, but likely gets lousy mileage — especially in the city.

Short of buying a lighter car, you have few good options to improve gas mileage. One thought is to use better grease or oil; synthetic oil, like Mobil 1 helps, I’m told (I’ve not checked it). Alternately, some months ago, I tried adding hydrogen and water to the engine. This helps too (5% -10%), likely by improving ignition and reducing idling vacuum loss. Another option is fancy valving, as on the Fiat 500. If you’re willing to buy a new car, and not just a new engine, a good option is a hybrid or battery car with regenerative breaking to recover the energy normally lost to the breaks. Alternately, a car powered with hydrogen fuel cells, — an option with advantages over batteries, or with a gasoline-powered fuel cell

Robert E. Buxbaum; July 29, 2015 I make hydrogen generators and purifiers. Here’s a link to my company site. Here’s something I wrote about Peter Cooper, an industrialist who made the first practical steam locomotive, the Tom Thumb: the key innovation here: making it lighter by using a forced air, fire-tube boiler.

# 18 year pause in global warming

Here is an updated version of the climate change graph. It’s now 18+ years, and as was true with last year’s version, 17+ years of no climate change, I see no significant climate change. Similar to this: Global Warming takes a 15 year rest.

18+ years of Global Temperature anomaly to July 2015. The climate seems to have stopped changing.

Though the average planetary temperature has remained constant, there is local variation. It’s been warm in California for the past 2+ years, but cold in Michigan. Before that, it was warm in Michigan and California was cold. The Antarctic ice is at record high levels while the arctic ice has shrunk enough that we should make a Northwest passage.

Climate vs weather, from the blog of Steven Goddard. It’s funny because…

Theory suggests we should see global warming because of increased CO2 trapping of atmospheric heat 2 miles up or so. The problem with the theory is that it doesn’t include clouds. A few extra clouds, e.g. from Chinese industry, could have more cooling power than a lot of CO2 has heating power. It seems that the effects cancel, and temperature 2-3 miles up is about what you’d expect from entropy.

My biggest climate fear, BTW, is global cooling: a new ice age. They come every 110,000 years or so and we seem overdue.

Global temperatures from the antarctic ice show ice ages every 110,000 years. cyclic chaos and self-similarity.

Robert Buxbaum, July 22, 2015. You may not have noticed, but there have been relatively few hurricanes — something that could change at any minute. Here’s a link to 1/2 hour lecture by a Nobel physicist, Ivar Giaever on the subject. Like me, he notices no change, and thinks warmer is better.

# Major blunders of the American Revolution

As nice as it is to discuss the brilliant men and great battles that allowed the American colonials to win the American Revolution, there is another way to see things –perhaps less enjoyable, but just as legitimate: looking at the great dunderheads and mistakes that allowed the greatest military power on earth to be defeated by a small group of undisciplined rabble. Here follows brief essays on my three top dunderheads: two British, one French. No one realized they were dunces until much later.

Pride of place goes, I think, to King Louis 16th of France. He helped us to win the war, and lost his own empire in the process. King Louis had nothing to gain by funding the American cause. And he had quite a lot to lose in men and money. He lost his ships and men in Rhode Island, lost colonies in India and the Seychelles, and spent millions he’d need when the famine of 1789 came. Worse, by supporting America, Louis put the bug of Liberty in the French ear. Far better (for Louis) would have been if he had waited, non-committally for another 3-5 years as the Dutch and Spanish did. He could have continued to host and honor Franklin, could have continued to sell weapons (to both sides) and could have even encouraged hot-head volunteers like Lafayette to go over and fight. We might still have won (see below) but at a greater cost to us and a fraction of the cost to the French monarchy. Let us thank God for fools. Here are my thoughts on when to get involved in a foreign war.

The basic of every great dunderhead is not seeing the disaster that hides behind a small-scale victory. And that tends to be funny.

British admiral George Rodney is my second, honored dunce. He had many victories, especially after the war was lost, but his major war achievement was not-relieving Cornwallis at Yorktown, and thus losing the war. In early 1781, Rodney was defending Jamaica and other British “Sugar Islands” in the Caribbean while waiting for orders to either fight the French fleet or relieve Cornwallis. As it was, he did neither but instead attacked a Dutch-held, Caribbean island, St. Eustatius. Rodney noticed that British freighters were being hijacked by pirates and that the island was a major trading port to the American colonists. By going after these pirates, he gained booty, but left the rest of the empire under-gunned. This allowed French Admiral, de Grasse Tilly to defeat Admiral Hood in the Caribbean; allowed him to take Tobago for the French. And then, while Rodney was still protecting his St Eustatius booty, de Grasse circled back to Virginia in time to bottle up Cornwallis. British Admiral Graves tried twice to dislodge de Grasse, but without Rodney he hadn’t the firepower. Cornwallis surrounded the day Graves gave up his second, failed attempt.

Rodney’s choice was one of greed, self-interest, and glory-seeking at the expense of British national interest. It isn’t unique in the Revolution or in British military history. Clinton’s move to attack Philadelphia when he was supposed to aid Burgoyne caused the loss of Burgoyne’s army and got the French in on our side, but I judge Rodney’s screw-up bigger if only because Cornwallis’s defeat ended the war and lost America.

Finally, I give the third-place dunce cap to General Banastre Tarleton, otherwise known as “Bloody Ban,” the most hated man in America. Tarleton was the son of a noted slave trader and mayor of Liverpool. He tended to win battles, but as fictionalized in the movie, The Patriot, he rarely differentiated rebel from loyalist, burning farms and churches of both. He also became known for “Tarleton’s quarter”, killing his enemies after they had surrendered. In the long run, this sort of thing turns your friends in to your enemies, and so it did here.

The view, common in Tarlton’s regiment, was that this was at least partially a religious war. If a congregation wasn’t Anglican — a church with the king as its head — it was a “sedition shop” and needed to be eliminated. He wasn’t totally wrong, but it rarely goes down well; for example the Sunni vs Shiite, Hamas vs ISIS wars. He certainly undermined Benedict Arnold’s claims that King George was serious in granting religious freedom.

A religious dissertation: resistance to a tyrant is obedience to God.

When Tarleton was given the job of capturing Marion Francis, the Swamp Fox, his approach, with Major James Wemyss and Captain Christian Hock (or Hook), was to burn the farms, churches, and plantations of anyone in the area. In one of Wemyss memoranda, he writes he had “burnt and laid waste about 50 houses and Plantations, mostly belonging to People who have either broke their Paroles or Oaths of Allegiance, and are now in Arms against us.” Note the word, “mostly.” These methods did succeed in drawing out the Swamp Fox, but it also drew out most everyone else in the south, even those who’d given up on the revolution. The now-farmless farmers enlisted and produced enthusiastic counter-attacks at Gibson’s Meeting House, Hill’s Iron Works, Fishdam Ford (Wemyss capture), Williamson’s Plantation (Huck’s Defeat), Blackstock’s farm and Cowpens. By the end, the colonials had even figured out how to use Tarleton’s enthusiasm against him.The right way to deal with your enemy is with focus and mercy, as Grant treated Lee at Appomattox. Tarleton’s methods would have made the Revolution a centuries-long, religious war IMHO, if the French had not gotten involved on our side.

Robert Buxbaum. July 16, 2015. If you have other classics of stupidity, please tell me. I’d like to recommend two books by A. J. O’Shaughnessy: “An Empire Divided,” and “The men who lost America.” As a final note: after the war Tarleton retired to Parliament where he served until 1833 as a fierce advocate for British slavery. Britain ended their use of slave workers in the Caribbean and south Africa in 1833, but didn’t stop their use in Ceylon and areas of East India company until 1843. Most Slaves who came to the new world did so in British ships.

# Kosher sex

Last week our synagogue had a panel discussion on the topic of kosher sex. When his turn came, our rabbi got up, cleared his throat, and said, “It gives me great pleasure …”

Then he sat down. My kind of rabbi.

Robert E. Buxbaum, July 16, 2015. On a vaguely similar note: here’s a mathematical marriage counsellor and about why Einstein wore fuzzy, pink slippers.

# Say no to the dress

A popular reality TV show follows the struggles of young brides-to-be shopping for a wedding dress at a famous store, Kleinfeld’s. They’ve come to believe that this charming adornment will make their dream-wedding really perfect. There is some sort of idea that the perfect wedding is necessary (or desirable) to get you started on a perfect life. This is stated in various ways throughout the show with phrases like: “you deserve to be the princess,” or “you deserve your special day.”

Each woman brings a retinue to help her pick the gown, and to help advise her about what dress has the most pop, or looks best on her, or makes her look the most special. Often it’s someone in this retinue that will pay for the dress too, a father, uncle, or a close family member. The store caters to the retinue at lest at the beginning to get a commitment to the price, generally \$5,000 to \$10,000, but sometimes to “no limit on the price.” It then provides a dazzling variety of dresses and an old hand or two to guide the young lady to the right one. At first, the retinue chimes in, but eventually the retinue is detached, and the bride is made to embrace that it’s her special day, alone. Then, when the perfect dress is finally chosen (often at the high-end of the budget), the bride is asked: “are you ready to say yes to the dress?” She does, with tears, and everyone claps, especially the retinue. Often, there is a final shot of the beautiful bride at the beautiful wedding. It’s touching, but perhaps unnecessary. So here’s an alternate  thought: just say “no”. No to the expensive dress; no to the expensive cake (sorry, cake boss) and no to the fancy, big diamond. instead, throw a big fun wedding on the cheap, perhaps at a park in a rented gown; friends will get you through life, the big dress and big cake will not.

An expensive wedding didn’t keep John Kennedy faithful, nor did it help cement Elizabeth Taylors 7 husbands (two to Richard Burton). Just the opposite: a recent study on marriage stability showed that the higher priced the wedding, the more likely it is to end in divorce.

Marriage stability goes down as the wedding costs go up. If you dress costs \$5,000, your wedding is unlikely to come in at less than \$10k. From Francis and Mialon, “A diamond is forever and other Fairy Tales,” 2014. The average cost of a US wedding: \$30,000.

The point of the wedding is to have a long, happy marriage, not a one day party, and expensive weddings appear to be counter-productive to stability. Things are worse for those who enter poor, backing up the observation that money stresses are among the main causes of marriage failure. This is not to say that you should not have a wedding party, but that spending should be watched especially if the couple isn’t that extraordinarily rich. The average, employed US 20-something earns about \$26,000/year before taxes. That’s not bad money until you realize that the average US wedding costs over \$30,000 not including dress, ring and honeymoon. There is a far lower chance of divorce for the couple with the \$5-\$10k wedding, and even lower if the couple can keep expenses in the 0-\$5k range.

Give her a ring, but the ideal cost is between \$200 and \$2000 unless you’re super rich.

Statistics suggest that spending on the diamond doesn’t help either, unless it’s a very expensive stone — and that, perhaps, is because the very expensive stone is only bought by the very rich groom. Still, even for the 1% who can afford it, the dress or stone should be considered a sunk cost, not an investment. You’ll never be able to resell that dress at all, and though you can resell a diamond it is virtually impossible to get even half your money back. This isn’t to say that you should not give a ring — without a ring the bride will feel cheated, but most grooms will be better served giving one in the \$100-\$2000 range.

Having lots of people at the wedding is perhaps the single best thing you can do for marriage stability. On the other hand, this graph might show that the sort of person who has 200 good friends is the sort of person to remain happily married. ibid.

While your wedding should be cheap, or at least affordable, it should not be small. It turns out that having lots of friends and family in attendance correlates strongly with having a long, stable marriage. I’m not sure if this is entirely cause and effect: perhaps those with lots of friends and family are giving and stable than those without. Still, it strikes me that friendships are good for every couple, and very worth maintaining. These are people who will be there for advice, or just be there when things get rocky. Give them a good party, and don’t drive them away by sending a message that a large gift is expected. If you get married on the cheap, it’s likely your guests will feel more comfortable showing up in business clothes with simple affordable gifts. Most bridesmaids are happier if they don’t have to buy a big expensive dress.

Honeymoons help marriage stability too. ibid.

Robert E. Buxbaum, July 12, 2015. My 3 children are all entering marriageable age — and PhD age (I wrote a post comparing a wedding to a PhD.) The above are my thoughts before being hornswoggled into buying \$5,000 worth of taffeta. They are also suggestive of the sort of work to get a PhD. Another good spending investment, I think, is to go on a honeymoon. I didn’t, and though we didn’t get divorced, in retrospect it seems like a good idea. I plan to finally go on a honeymoon for our 25th anniversary. Let’s toast (with Geritol) to finding the right mate. Good luck.

# Marriage vs PhD

Marriage vs PhD, from Piled Higher and Deeper (PhD) comics.

Here’s a PhD comic comparing getting married to getting a PhD. The similarities are striking. It’s funny because …

….one does not expect so many similarities between the two endeavors. On thinking a bit further, one realizes that marriage and graduate school are the main, long-term trust relationship options for young college grads, 21-23 years old who want to move out of home and don’t want to yet enter the grind of being a single, wage slave (grease monkey, computer-code monkey, secretary, etc.)

College grads expect some self-fulfillment and, as they’ve lived away from home, mostly prefer to not move back, Entry level jobs are generally less-than fulfilling, and if you move away from home as a single, living costs can eat up all your income. One could get a same-sex room-mate, but that is a low commitment relationship, and most young grads want more: they’ve an “urge to merge.” Either PhD or marriage provides this more: you continue to live away from home, you get an environment with meals and room semi-provided (sometimes in a very cool environment) and you have some higher purpose and long-term companionship that you don’t get at home, or as a secretary with a room-mate.

I suspect that often, the choice of marriage or grad-school depends on which proffers the better offer. Some PhD programs and some marriages provide you with a stipend of spending-money. In other programs or marriages, you have to get an outside job. Even so, your spouse or advisor will typically help you get that outside job. In most communities, there’s more honor in being a scholar or a wife/ husband than there is in being a single working person. And there’s no guarantee it will be over in 7 years. A good marriage can last 30-50 years, and a good PhD may lead to an equally long stay in academia as a professor or a researcher of high standing. While not all majors are worth it financially, or emotionally, you can generally do more and make more money as a PhD than with a low-pay undergraduate degree. Or you can use your college connections to marry well.

Some people are just cut out for the grad-school life-style, and not particularly for normal jobs. Ask yourself: What type of job will make me happy? Could be it’s research or home-making? Then go find a mate or program.

Dr. Robert E. Buxbaum (married with children and a PhD), July 1,, 2015. Growing up is perhaps the most difficult and important thing anyone does; getting married or entering a PhD program is a nice step, though it doesn’t quite mean you’re an adult yet. Some months ago, I wrote an essay about an earlier stage in the process: being a 16-year-old girl. For those interested in research, here’s something on how it is done using induction, and here’s something on statistics.