Category Archives: Engineering

Of horses, trucks, and horsepower

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Horsepower is a unit of work production rate, about 3/4 of a kW, for those who like standard international units. It is also the pulling force of a work horse of the 1700s times its speed when pulling, perhaps 5 mph. A standard truck will develop 200 hp but only while accelerating at about 60 mph; to develop those same 200 horsepower at 1 mph it would have to pull with 200 times more force. That is impossible for a truck, both because of traction limitations and because of the nature of a gasoline engine when attached to typical gearing. At low speed, 1 mph, a truck will barely develop as much force as 4-5 horses, suggesting a work output about 1 hp. This is especially true for a truck pulling in the snow, as shown in the video below.

Here, a semi-truck (of milk) is being pulled out of the snow by a team of horses going perhaps 1 mph. The majority of work is done by the horse on the left — the others seem to be slipping. Assuming that the four horses manage to develop 1 hp each (4 hp total), the pull force is four times a truck at 1 mph, or as great as a 200 hp truck accelerating at 50 mph. That’s why the horse succeed where the truck does not.

You will find other videos on the internet showing that horses produce more force or hp than trucks or tractors. They always do so at low speeds. A horse will also beat a truck or car in acceleration to about the 1/4 mile mark. That’s because acceleration =force /mass: a = F/m.

I should mention that DC electric motors also, like horses, produce their highest force at very low speeds, but unlike horses, their efficiency is very low there. Electric engine efficiency is high only at speeds quite near the maximum and their horse-power output (force times speed) is at a maximum at about 1/2 the maximum speed.

Steam engines (I like steam engines) produce about the same force at all speeds, and more-or-less the same efficiency at all speeds. That efficiency is typically only about 20%, about that of a horse, but the feed cost and maintenance cost is far lower. A steam engine will eat coal, while a horse must eat oats.

March 4, 2016. Robert Buxbaum, an engineer, runs REB Research, and is running for water commissioner.

Alcohol and gasoline don’t mix in the cold

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One of the worst ideas to come out of the Iowa caucuses, I thought, was Ted Cruz claiming he’d allow farmers to blend as much alcohol into their gasoline as they liked. While this may have sounded good in Iowa, and while it’s consistent with his non-regulation theme, it’s horribly bad engineering.

At low temperatures ethanol and gasoline are no longer quite miscible

Ethanol and gasoline are that miscible at temperatures below freezing, 0°C. The tendency is greater if the ethanol is wet or the gasoline contains benzenes

We add alcohol to gasoline, not to save money, mostly, but so that farmers will produce excess so we’ll have secure food for wartime or famine — or so I understand it. But the government only allows 10% alcohol in the blend because alcohol and gasoline don’t mix well when it’s cold. You may notice, even with the 10% mixture we use, that your car starts poorly on the coldest winter days. The engine turns over and almost catches, but dies. A major reason is that the alcohol separates from the rest of the gasoline. The concentrated alcohol layer screws up combustion because alcohol doesn’t burn all that well. With Cruz’s higher alcohol allowance, you’d get separation more often, at temperatures as high as 13°C (55°F) for a 65 mol percent mix, see chart at right. Things get worse yet if the gasoline gets wet, or contains benzene. Gasoline blending is complex stuff: something the average joe should not do.

Solubility of dry alcohol (ethanol) in gasoline. The solubility is worse at low temperature and if the gasoline is wet or aromatic.

Solubility of alcohol (ethanol) in gasoline; an extrapolation based on the data above.

To estimate the separation temperature of our normal, 10% alcohol-gasoline mix, I extended the data from the chart above using linear regression. From thermodynamics, I extrapolated ln-concentration vs 1/T, and found that a 10% by volume mix (5% mol fraction alcohol) will separate at about -40°F. Chances are, you won’t see that temperature this winter (and if you you do, try to find a gas mix that has no alcohol. Another thought, add hydrogen or other combustible gas to get the engine going.

Robert E. Buxbaum, February 10, 2016. Two more thoughts: 1) Thermodynamics is a beautiful subject to learn, and (2) Avoid people who stick to foolish consistency. Too much regulation is bad, as is too little: it’s a common pattern: The difference between a cure and a poison is often just the dose.

How to help Flint and avoid lead here.

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As most folks know, Flint has a lead-poisoning problem that seems to have begun in April, 2014 when the city switched its water supply from Detroit-supplied, Lake Huron water to their own source, water from the Flint River. Here are some thoughts on how to help the affected population, and how to avoid a repeat in Oakland county, where I’m running for water commissioner. First observation, it is not enough to make sure that the source water does not contain lead. The people who decided on the switch had found that the Flint river water had no significant content of lead or other obvious toxins. A key problem, it seems: the river water did not contain anticorrosion phosphates, and none, it seems, were added by the Flint water folks. It also seems that insufficient levels of chlorine (hypochlorite) were added. After the switch, citizens started seeing disgusting, brown water come from their taps, and citizens with lead pipes or solder were poisoned with ppb-levels of lead. There was also an outbreak of legionaries disease that killed 12 people. It was the legionaries that alerted the CDC to the possibility of lead, since it seems the water folks were fudging the numbers there, and hiding that part of the problem.

Flint water, Sept 2015, before switching back to Lake Huron.

Flint water after 5 hours of flushing, Sept 2015, before switching back to Lake Huron.

The city began solving its problem by switching back to Detroit-supplied, Lake Huron water in October, 2015. Beginning in December, 2015, they started adding triple doses of phosphate to the wate. As a result, Flint tap-water is now back within EPA standards, but it’s still fairly unsafe, see here for more details.

There has been a fair amount of finger-pointing. At Detroit for raising the price of water so Flint had to switch, at water officials ignoring the early signs of lead and fudging their reports, at other employees for not adding phosphate or enough chlorine, and at “the system” for not providing Flint’s government with better oversight. My take is that a lot of the problem came from the ignorance of the water commission, and it’s commissioner. We elect our water commissioners to be competent overseers of complex infrastructure, but in may counties folks seem to pick them the same way they pick aldermen: for a nice smile, a great handshake, and an ability to remember names. That, anyway, seems to be the way that Oakland got its current water commissioner. When you pick your commissioner that way, it’s no surprise that he (or she) isn’t particularly up on corrosion chemistry, something that few people understand, and fewer care about until it bites them.

Flint river water contains corrosive chloride that probably helped dissolve the lead from pipes and solder. Contributing to the corrosion problem, I’m going to guess that Flint River water also contains, relatively little carbonate, but significant amounts of chelating chemicals, like EDTA, in 10s of ppb concentration. EDTA isn’t poisonous at these concentrations, but it’s common in industry and is the most commonly used antidote for lead poisoning. EDTA extracts lead and other metals from people and would tend to contribute to the process of extracting lead and iron oxide from the pipes surface into the drinking water. With EDTA in the water, a lot of phosphate or hypochlorite would be needed to avoid the lead poisoning problem and the deadly multiplication of disease.

Detroit ex-mayor Kwame Kilpatrick has claimed that both Flint water and Detroit water were known to be poisoned even a decade before the switch. I find these claims believable given the high levels of lead in kids blood even before the switch. Also, I note that there are areas of Detroit where the blood-lead levels are higher than Flint. Flint tested at the taps in a way that fudged the data during the first days of the poisoning, and I suspect many of our MI cities do this today — just to make the numbers look better. My first suggestion therefore is to test correctly, both at the pipes and at the taps; lead pipes are most-often found in the last few feet before the tap. In particular, we should test at all schools and other places where the state has direct authorization to fix the problem. A MI senate bill has been proposed to this effect, but I’m not sure where it stands in the MI house. It seems there are movements to add lots of ‘riders’ and that’s usually a bad sign.

Another thought is that citizens should be encouraged to test their private taps and helped to fix them. The state can’t come in and test or rip out your private pipes, even if they suspect lead, but the private owner has that authorization. The state could condemn a private property where they believe the water is bad, but I doubt they could evict the residents. It’s a democratic republic, as I understand; you have the right to be deadly stupid. But I’ll take my own suggestion to encourage you: If you think your water has lead, take a sample and call (517) 335-8184. Do it.

Another suggestion, perhaps the easiest and most important, is drink bottled water for now, and if you feel you’ve been poisoned, take an antidote.  As I understand things, the state is already providing bottles of imported water. The most common antidote is, as I’d mentioned, EDTA. Assuming that Flint River water had enough EDTA to significantly worsen the problem, the cheapest antidote might be Flint River water, assuming you drew it in lead-free pipes and chlorinated sufficiently to rid it of bugs. If there is EDTA it will help the poisoned. Another antidote is Succinic acid, something sold by REB Research, my company. As with EDTA it is non-toxic, even in fairly large doses, but its use would have to be doctor- approved.

Robert E. Buxbaum, January 19-31, 2016. I hope this helps. We’d have to check Flint River water for levels of EDTA, but I suspect we’d find biologically significant concentrations. If you think Oakland should have an engineer in charge of the water, elect Buxbaum for water commissioner.

The Hindenburg: mainly the skin burnt

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The 1937 Hindenburg disaster is often mentioned as proof that hydrogen is too flammable and dangerous for commercial use. Well hydrogen is flammable, and while the Hindenburg was full of hydrogen when it started burning, but a look at a color photograph of the fire ( below), or at the B+W  Newsreel film of the fire, suggests that it is not the hydrogen burning, but the skin of the zeppelin and the fuel. Note the red color of the majority flame, and note the black smoke. Hydrogen fires are typically invisible or very light blue, and hydrogen fires produce no smoke.

Closeup of the Hindenburg burning. It is the skin that burns, not the gaseous hydrogen

Closeup of the Hindenburg burning. It is the skin and gasoline that burns, not the gaseous hydrogen.

The Hindenburg was not a simple hydrogen balloon either. It was a 15 story tall airship with state-rooms, a dining room and an observation deck. It carried 95 or so passengers and crew. There was plenty of stuff to burn besides hydrogen. Nor could you say that a simple spark had set things off. The Hindenburg crossed the ocean often: every 2 1/2 days. Lightning strikes were common, as were “Saint Elmo’s fire,” and static electricity discharges. And passengers smoked onboard. Holes and leaks in the skin were also common, both on the Hindenburg and on earlier airships. The hydrogen-filled, Graf Zeppelin logged over 1 million flight miles and over 500 trips with no fires. And it’s not like helium-filled zeppelins and blimps are much safer. The photo below shows the fire and crash of a helium-filled Goodyear blimp, “Spirit of Safety”, June, 2011. Hydrogen has such a very high thermal conductivity that it is nearly as hard to light as helium. I recently made this video where I insert a lit cigar into a balloon filled with hydrogen. There is no fire, but the cigar goes out.  In technical terms, hydrogen is said to have a low upper combustion limit.

Helium-filled goodyear blimp catches fire and burns to destruction.

Helium-filled goodyear blimp “spirit of safety” catches fire and burns before crashing. It’s not the helium burning.

The particular problem with the Hindenburg seems to have been its paint, skin and fuel, the same problems as caused the fire aboard the “Spirit of Safety.” The skin of the Hindenburg was cotton, coated with a resin-dope paint that contained particles of aluminum and iron-oxide to help conduct static electricity. This combination is very flammable, essentially rocket fuel, and the German paint company went on to make rocket fuel of a similar composition for the V2 rockets. And the fuel was flammable too: gasoline. The pictures of the Hindenburg disaster suggest (to me) that it is the paint and the underlying cotton skin that burned, or perhaps the fuel. A similar cause seems to have beset the “Spirit of Safety.” For the Hindenburg’s replacement, The Graf II, the paint composition was changed to replace the aluminum powder with graphite – bronze, a far less flammable mixture, and more electrically conductive. Sorry to say, there was no reasonably alternative to gasoline. To this day, much of sport ballooning is done with hydrogen; statistically it appears no more dangerous than hot air ballooning.

It is possible that the start of the fire was a splash of gasoline when the Hindenburg made a bumpy contact with the ground. Another possibility is sabotage, the cause in a popular movie (see here), or perhaps an electric spark. According to Aviation Week, gasoline spoiled on a hot surface was the cause of the “Spirit of Safety fire,” and the Hindenburg disaster looks suspiciously similar. If that’s the case, of course, the lesson of the Hindenburg disaster is reversed. For safety, use hydrogen, and avoid gasoline.

Dr. Robert E. Buxbaum, January 8, 2016. My company, REB Research, makes hydrogen generators, and other hydrogen equipment. If you need hydrogen for weather balloons, or sport ballooning, or for fuel cells, give us a call.

Advanced windmills + 20 years = field of junk

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Everything wears out. This can be a comforting or a depressing thought, but it’s a truth. No old mistake, however egregious, lasts forever, and no bold advance avoids decay. At best, last year’s advance will pay for itself with interest, will wear out gracefully, and will be recalled fondly by aficionados after it’s replaced by something better. Water wheels, and early steamships are examples of this type of bold advance. Unfortunately, it is often the case that last years innovation turns out to be no advance at all: a technological dead end that never pays for itself, and becomes a dangerous, rotting eyesore or worse, a laughing-stock blot or a blot on the ecology. Our first two generations of advanced windmill farms seem to match this description; perhaps the next generation will be better, but here are some thoughts on lessons learned from the existing fields of rotting windmills.

The ancient design windmills of Don Quixote’s Spain (1300?) were boons. Farmers used them to grind grain or cut wood, and to to pump drinking water. Holland used similar early windmills to drain their land. So several American presidents came to believe advanced design windmills would be similar boons if used for continuous electric power generation. It didn’t work, and many of the problems could have been seen at the start. While the farmer didn’t care when his water was pumped, or when his wood is cut. When you’re generating electricity, there is a need to match the power demand exactly. Whenever the customer turns on the switch, electricity is expected to flow at the appropriate amount of Wattage; at other times any power generated is a waste or a nuisance. But electric generator-windmills do not produce power on demand, they produce power when the wind blows. The mismatch of wind and electric demand has bedeviled windmill reliability and economic return. It will likely continue to do so until we find a good way to store electric power cheaply. Until then windmills will not be able to produce electricity at competitive prices to compete with cheap coal and nuclear power.

There is also the problem of repair. The old windmills of Holland still turn a century later because they were relatively robust, and relatively easy to maintain. The modern windmills of the US stand much taller and move much faster. They are often hit, and damaged by lightning strikes, and their fast-turning gears tend to wear out fast, Once damaged, modern windmills are not readily fix, They are made of advanced fiberglass materials spun on special molds. Worse yet, they are constructed in mountainous, remote locations. Such blades can not be replaces by amateurs, and even the gears are not readily accessed to repair. More than half of the great power-windmills built in the last 35 years have worn out and are unlikely to ever get repair. Driving past, you see fields of them sitting idle; the ones still turning look like they will wear out soon. The companies that made and installed these behemoth are mostly out of the business, so there is no-one there to take them down even if there were an economic incentive to do so. Even where a company is found to fix the old windmills, no one would as there is not sufficient economic return — the electricity is worth less than the repair.

Komoa Wind Farm in Kona, Hawaii June 2010; Friends of Grand Ronde Valley.

Komoa Wind Farm in Kona, Hawaii, June 2010; A field of modern design wind-turbines already ruined by wear, wind, and lightning. — Friends of Grand Ronde Valley.

A single rusting windmill would be bad enough, but modern wind turbines were put up as wind farms with nominal power production targeted to match the output of small coal-fired generators. These wind farms require a lot of area,  covering many square miles along some of the most beautiful mountain ranges and ridges — places chosen because the wind was strong

Putting up these massive farms of windmills lead to a situation where the government had pay for construction of the project, and often where the government provided the land. This, generous spending gives the taxpayer the risk, and often a political gain — generally to a contributor. But there is very little political gain in paying for the repair or removal of the windmills. And since the electricity value is less than the repair cost, the owners (friends of the politician) generally leave the broken hulks to sit and rot. Politicians don’t like to pay to fix their past mistakes as it undermines their next boondoggle, suggesting it will someday rust apart without ever paying for itself.

So what can be done. I wish I could suggest less arrogance and political corruption, but I see no way to achieve that, as the poet wrote about Ozymandias (Ramses II) and his disastrous building projects, the leader inevitably believes: “I am Ozymandias, king of kings; look on my works ye mighty and despair.” So I’ll propose some other, less ambitious ideas. For one, smaller demonstration projects closer to the customer. First see if a single windmill pays for itself, and only then build a second. Also, electricity storage is absolutely key. I think it is worthwhile to store excess wind power as hydrogen (hydrogen storage is far cheaper than batteries), and the thermodynamics are not bad

Robert E. Buxbaum, January 3, 2016. These comments are not entirely altruistic. I own a company that makes hydrogen generators and hydrogen purifiers. If the government were to take my suggestions I would benefit.

The french engineering

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There is something wonderful about French Engineering. It is good, but different from US or German engineering. The French don’t seem to copy others, and very few others seem to copy them. Nonetheless French engineering managed to build an atom bomb, is a core of the Airbus consortium, and both builds and runs the fastest passenger trains on earth, the TGF, record speed 357 mph on the line between Paris and Luxembourg.

JULY 14, 2015 Students of the Ecole Polytechnique (the most prestigious engineering school in France march in the Paris Bastille Day military parade. commemorating the storming of the Bastille in 1789. (Photo by Thierry Chesnot/Getty Images).

JULY 14, 2015 Female engineering students of the Ecole Polytechnique, march in the Paris Bastille Day military parade. (Photo by Thierry Chesnot/Getty Images).

France was almost the only country to sell Israel weapons for the first 20 years of its existence, and as odd as the weapons they sold were, they worked. The Mirage jet was noted for short-range and maneuverability; in 1967, they handily defeated Egypt and Syria’s much larger force of Russian Migs. More recently, Argentina used French Exocet missiles to sink 3 British warships in the Argentine war, and last week, Turkey used a french missile to down a Su24, the new main Russian fighter-bomber. not bad for a country whose main engineering school marches in Napoleonic garb.

The classic of French Engineering, of course is the Eiffel Tower. It is generally unappreciated that this is not the only Eiffel structure designed this way. Eiffel designed railroad bridges, aqueducts. Here’s an Eiffel railroad bridge.

Eiffel railroad bridge, still in use

Eiffel railroad bridge, still in use. American, German, or British bridges of the era look nothing like this.

To get a sense of the engineering artistry of the Eifflel tower, consider that when the tower was built, in 1871, self-financed by Eiffel, it was more than twice as tall as the next-tallest building on earth. ff one weighed the air in a cylinder the height of the tower with a circle about its base, the air would weigh more than the steel of the tower. But here are some other random observations, while first level of the tower houses a restaurant, a normal American space-use choice,the second level housed, when the tower opened the print shop and offices of the International Herald Tribune; not a normal tenant. And, on the third level, near the very top, you will find Mr Eiffel’s apartment. The builder lived there; he owned the place. It’s still there today, but now there are now only mannequins in residence. It’s weird, but genius, like so much that is French engineering.

Eiffel's apartment atop the tower, now occupied by mannequins of Eiffel and Edison, a one-time guest.

Eiffel’s apartment atop the tower, now occupied by mannequins of Eiffel and Edison, a one-time guest.

Returning to the French airplane, The french were the first to make mono-planes. But having succeeded there, they made a decent-enough plane-like automobile, the 1932 Helicon car. It’s a three-man car with a propeller out front and rear-wheel steering. At first, you’d think this is a slow, unmanageable, deathtrap, like Buckminster Fuller’s Dymaxion,.  But you’d be wrong, the Helicon (apparently) is both speedy and safe it moves at 100 mph or more once it gets going, still passed French safety standards in 2000, and gets taken out for (semi-normal) jaunts. Don’t stand in front of the propeller (there’s a bicycle version too).

1932 Helicon; seats 3, rear staring, propeller-driven. Normal-ish. Photo by Yalon.

1932 Helicon car; 100 mph, seats 3, propeller-driven. Photo by Yalon.

The Helicon never quite took off, as it were, but an odd design motorcycle did quite well, at least in France, the Solex, front wheel motorcycle.Unlike US motorcycles, it’s just a bicycle with an engine above the front wheels. The engine runs “backwards” and drives the front wheel via a friction-cam. The only clutch action involves engaging the cam. Simple, elegant, and unlikely to be duplicated elsewhere.

A French Solex motorcycles, and an e-Solex. The e-Solex uses a battery.

A Solex motorcycle and an e-Solex, the battery-powered version. A Citroen and a Peugeot sport are in the background. Popular in France.

The reason I’m writing about French Engineering is perhaps because of the recent attacks. Or perhaps because of aesthetic. It’s important to have an engineering aesthetic — an idea you’re after — and to have pride in one’s craft too. The French stand out in how much they have of both. Some months ago I wrote about a more American engineering aesthetic, It’s a good article, but interestingly, I now note that some main examples I used were semi-French: the gunpowder factory of E. I. Dupont, the main productions facility of a Frenchman’s company in the US.

Robert Buxbaum, December 13, 2015. Some months ago, I wrote about a favorite car engine, finally being used on the Fiat 500 and Alfa Romeo. Fast, energy-efficient, light, maneuverable, and (I suspect) unreliable; the engine embodies a particularly Italian engineering aesthetic.

Chemical engineers and boilers, ‘I do anything’

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One of the problems I run into trying to hire chemical engineers is that their background is so varied that they imagine they can do anything. Combine this with a willingness to try to do anything, and the job interview can go like this.

Me: You have a great resume. I suppose you know that our company is a leader in hydrogen engineering (in my case). Tell me, what do you see yourself doing at our company?

Engineer: I don’t know. I do anything and everything.

Me: That covers a lot of ground. Is there something that you do particularly well, or that you would particularly like to do here?

Engineer.: Anything, really.

Me: Do you see yourself making coffee?

Engineer: I could do that, but was thinking of something with more … responsibility.

Me: OK. Could you design and build a 5 kW, gas-fired boiler?

Engineer: Himm. How much coffee did you say you guys drink?

Current version of our H2 generators (simplified) and the combustion-heated modification I'm working on.

Current version of our H2 generators (simplified) and the combustion-heated modification I’m working on.

Not quite where I was going with that. The relevance of this joke is that I’m finally getting around to redesigning our hydrogen generators so that they are heated by waste-gas combustion instead of electricity. That was the plan originally, and it appears in almost all of my patents. But electricity is so easy to deal with and control that all REB generators have been heated this way, even the largest.

The current and revised processes are shown in the figure at right. Our general process is to make ultra pure hydrogen from methanol and water in one step by the following reaction:

CH3OH + H2O –> CO2  + 3 H2.

done in a membrane reactor (see advantages). My current thought is to make the first combustion heated hydrogen generator have an output about 2/3 as large as our largest. That is, to produce 100 scfh, or 50 slpm, or 6 kg of H2/ day. This could be advantageous for people trying to fuel fork lifts or a hybrid, fuel cell car; a car could easily carry 12 kg of hydrogen, allowing it to go an extra 300 miles.

The generator with this output will need a methanol-water feed rate of about 2/3 gal per hour (about 80¢/worth pre hour), and will need a heat rate of 2.5 to 3 kW. A key design issue is that I have to be sure not to extract too much energy value from the feed because, if there’s not enough energy in the waste gas, the fire could go out. That is, nearly pure CO2 doesn’t burn. Alternately, if there is too much flow to the flame or too much energy content, there might be over-heating. In order to avoid the flame going out, I have a pilot flame that turns off the flow if it goes out. I also plan to provide 30% or so of the reactor heat about 800 W, by burning non-wast gas, natural gas in this iteration. My plan is to use this flow to provide most of the temperature control, but to provide secondary control by (and safety) by venting some of the off-gas if the reactor gets hotter than a set limit. Early experiments suggest it should work.

The business side of this is still unknown. Perhaps this would provide military power or cabins in the woods. Perhaps ship-board auxiliary power or balloons, or hydrogen fueling stations, or perhaps it will be used for chemical applications. With luck, it’ll sell to someone who needs hydrogen.

Robert E. Buxbaum. December 4, 2015. By the way, hydrogen isn’t as flammable as you might think.

my electric cart of the future

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Buxbaum and Sperka cart of future

Buxbaum and Sperka show off the (shopping) cart of future, Oak Park parade July 4, 2015.

A Roman chariot did quite well with only 1 horse-power, while the average US car requires 100 horses. Part of the problem is that our cars weigh more than a chariot and go faster, 80 mph vs of 25 mph. But most city applications don’t need all that weight nor all of that speed. 20-25 mph is fine for round-town errands, and should be particularly suited to use by young drivers and seniors.

To show what can be done with a light vehicle that only has to go 20 mph, I made this modified shopping cart, and fitted it with a small, 1 hp motor. I call it the cart-of the future and paraded around with it at our last 4th of July parade. It’s high off the ground for safety, reasonably wide for stability, and has the shopping cart cage and seat-belts for safety. There is also speed control. We went pretty slow in the parade, but here’s a link to a video of the cart zipping down the street at 17.5 mph.

In the 2 months since this picture was taken, I’ve modified the cart to have a chain drive and a rear-wheel differential — helpful for turning. My next modification, if I get to it, will be to switch to hydrogen power via a fuel cell. One of the main products we make is hydrogen generators, and I’m hoping to use the cart to advertise the advantages of hydrogen power.

Robert E. Buxbaum, August 28, 2015. I’m the one in the beige suit.

It’s rocket science

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Here are six or so rocket science insights, some simple, some advanced. It’s a fun area of engineering that touches many areas of science and politics. Besides, some people seem to think I’m a rocket scientist.

A basic question I get asked by kids is how a rocket goes up. My answer is it does not go up. That’s mostly an illusion. The majority of the rocket — the fuel — goes down, and only the light shell goes up. People imagine they are seeing the rocket go up. Taken as a whole, fuel and shell, they both go down at 1 G: 9.8 m/s2, 32 ft/sec2.

Because 1 G ofupward acceleration is always lost to gravity, you need more thrust from the rocket engine than the weight of rocket and fuel. This can be difficult at the beginning when the rocket is heaviest. If your engine provides less thrust than the weight of your rocket, your rocket sits on the launch pad, burning. If your thrust is merely twice the weight of the rocket, you waste half of your fuel doing nothing useful, just fighting gravity. The upward acceleration you’ll see, a = F/m -1G where F is the force of the engine, and m is the mass of the rocket shell + whatever fuel is in it. 1G = 9.8m/s is the upward acceleration lost to gravity.  For model rocketry, you want to design a rocket engine so that the upward acceleration, a, is in the range 5-10 G. This range avoids wasting lots of fuel without requiring you to build the rocket too sturdy.

For NASA moon rockets, a = 0.2G approximately at liftoff increasing as fuel was used. The Saturn V rose, rather majestically, into the sky with a rocket structure that had to be only strong enough to support 1.2 times the rocket weight. Higher initial accelerations would have required more structure and bigger engines. As it was the Saturn V was the size of a skyscraper. You want the structure to be light so that the majority of weight is fuel. What makes it tricky is that the acceleration weight has to sit on an engine that gimbals (slants) and runs really hot, about 3000°C. Most engineering projects have fewer constraints than this, and are thus “not rocket science.”

Basic force balance on a rocket going up.

Basic force balance on a rocket going up.

A space rocket has to reach very high, orbital speed if the rocket is to stay up indefinitely, or nearly orbital speed for long-range, military uses. You can calculate the orbital speed by balancing the acceleration of gravity, 9.8 m/s2, against the orbital acceleration of going around the earth, a sphere of 40,000 km in circumference (that’s how the meter was defined). Orbital acceleration, a = v2/r, and r = 40,000,000 m/2π = 6,366,000m. Thus, the speed you need to stay up indefinitely is v=√(6,366,000 x 9.8) = 7900 m/s = 17,800 mph. That’s roughly Mach 35, or 35 times the speed of sound at sea level, (343 m/s). You need some altitude too, just to keep air friction from killing you, but for most missions, the main thing you need is velocity, kinetic energy, not potential energy, as I’ll show below. If your speed exceeds 17,800 m/s, you go higher up, but the stable orbital velocity is lower. The gravity force is lower higher up, and the radius to the earth higher too, but you’re balancing this lower gravity force against v2/r, so v2 has to be reduced to stay stable high up, but higher to get there. This all makes docking space-ships tricky, as I’ll explain also. Rockets are the only way practical to reach Mach 35 or anything near it. No current cannon or gun gets close.

Kinetic energy is a lot more important than potential energy for sending an object into orbit. To get a sense of the comparison, consider a one kg mass at orbital speed, 7900 m/s, and 200 km altitude. For these conditions, the kinetic energy, 1/2mv2 is 31,205 kJ, while the potential energy, mgh, is only 1,960 kJ . The potential energy is thus only 1/16 the kinetic energy.

Not that it’s easy to reach 200 miles altitude, but you can do it with a sophisticated cannon. The Germans did it with “simple”, one stage, V2-style rockets. To reach orbit, you generally need multiple stages. As a way to see this, consider that the energy content of gasoline + oxygen is about 10.5 MJ/kg (10,500 kJ/kg); this is only 1/3 of the kinetic energy of the orbital rocket, but it’s 5 times the potential energy. A fairly efficient gasoline + oxygen powered cannon could not provide orbital kinetic energy since the bullet can move no faster than the explosive vapor. In a rocket this is not a constraint since most of the mass is ejected.

A shell fired at a 45° angle that reaches 200 km altitude would go about 800 km — the distance between North Korea and Japan, or between Iran and Israel. That would require twice as much energy as a shell fired straight up, about 4000 kJ/kg. This is still within the range for a (very large) cannon or a single-stage rocket. For Russia or China to hit the US would take much more: orbital, or near orbital rocketry. To reach the moon, you need more total energy, but less kinetic energy. Moon rockets have taken the approach of first going into orbit, and only later going on. While most of the kinetic energy isn’t lost, it’s likely not the best trajectory in terms of energy use.

The force produced by a rocket is equal to the rate of mass shot out times its velocity. F = ∆(mv). To get a lot of force for each bit of fuel, you want the gas exit velocity to be as fast as possible. A typical maximum is about 2,500 m/s. Mach 10, for a gasoline – oxygen engine. The acceleration of the rocket itself is this ∆mv force divided by the total remaining mass in the rocket (rocket shell plus remaining fuel) minus 1 (gravity). Thus, if the exhaust from a rocket leaves at 2,500 m/s, and you want the rocket to accelerate upward at an average of 10 G, you must exhaust fast enough to develop 10 G, 98 m/s2. The rate of mass exhaust is the average mass of the rocket times 98/2500 = .0392/second. That is, about 3.92% of the rocket mass must be ejected each second. Assuming that the fuel for your first stage engine is less than 80% of the total mass, the first stage will flare-out in about 20 seconds. Typically, the acceleration at the end of the 20 burn is much greater than at the beginning since the rocket gets lighter as fuel is burnt. This was the case with the Apollo missions. The Saturn V started up at 0.5G but reached a maximum of 4G by the time most of the fuel was used.

If you have a good math background, you can develop a differential equation for the relation between fuel consumption and altitude or final speed. This is readily done if you know calculous, or reasonably done if you use differential methods. By either method, it turns out that, for no air friction or gravity resistance, you will reach the same speed as the exhaust when 64% of the rocket mass is exhausted. In the real world, your rocket will have to exhaust 75 or 80% of its mass as first stage fuel to reach a final speed of 2,500 m/s. This is less than 1/3 orbital speed, and reaching it requires that the rest of your rocket mass: the engine, 2nd stage, payload, and any spare fuel to handle descent (Elon Musk’s approach) must weigh less than 20-25% of the original weight of the rocket on the launch pad. This gasoline and oxygen is expensive, but not horribly so if you can reuse the rocket; that’s the motivation for NASA’s and SpaceX’s work on reusable rockets. Most orbital rocket designs require three stages to accelerate to the 7900 m/s orbital speed calculated above. The second stage is dropped from high altitude and almost invariably lost. If you can set-up and solve the differential equation above, a career in science may be for you.

Now, you might wonder about the exhaust speed I’ve been using, 2500 m/s. You’ll typically want a speed at lest this high as it’s associated with a high value of thrust-seconds per weight of fuel. Thrust seconds pre weight is called specific impulse, SI, SI = lb-seconds of thrust/lb of fuel. This approximately equals speed of exhaust (m/s) divided by 9.8 m/s2. For a high molecular weight burn it’s not easy to reach gas speed much above 2500, or values of SI much above 250, but you can get high thrust since thrust is related to momentum transfer. High thrust is why US and Russian engines typically use gasoline + oxygen. The heat of combustion of gasoline is 42 MJ/kg, but burning a kg of gasoline requires roughly 2.5 kg of oxygen. Thus, for a rocket fueled by gasoline + oxygen, the heat of combustion per kg is 42/3.5 = 12,000,000 J/kg. A typical rocket engine is 30% efficient (V2 efficiency was lower, Saturn V higher). Per corrected unit of fuel+oxygen mass, 1/2 v2 = .3 x 12,000,000; v =√7,200,000 = 2680 m/s. Adding some mass for the engine and fuel tanks, the specific impulse for this engine will be, about 250 s. This is fairly typical. Higher exhaust speeds have been achieved with hydrogen fuel, it has a higher combustion energy per weight. It is also possible to increase the engine efficiency; the Saturn V, stage 2 efficiency was nearly 50%, but the thrust was low. The sources of inefficiency include inefficiencies in compression, incomplete combustion, friction flows in the engine, and back-pressure of the atmosphere. If you can make a reliable, high efficiency engine with good lift, a career in engineering may be for you. A yet bigger challenge is doing this at a reasonable cost.

At an average acceleration of 5G = 49 m/s2 and a first stage that reaches 2500 m/s, you’ll find that the first stage burns out after 51 seconds. If the rocket were going straight up (bad idea), you’d find you are at an altitude of about 63.7 km. A better idea would be an average trajectory of 30°, leaving you at an altitude of 32 km or so. At that altitude you can expect to have far less air friction, and you can expect the second stage engine to be more efficient. It seems to me, you may want to wait another 10 seconds before firing the second stage: you’ll be 12 km higher up and it seems to me that the benefit of this will be significant. I notice that space launches wait a few seconds before firing their second stage.

As a final bit, I’d mentioned that docking a rocket with a space station is difficult, in part, because docking requires an increase in angular speed, w, but this generally goes along with a decrease in altitude; a counter-intuitive outcome. Setting the acceleration due to gravity equal to the angular acceleration, we find GM/r2 = w2r, where G is the gravitational constant, and M is the mass or the earth. Rearranging, we find that w2  = GM/r3. For high angular speed, you need small r: a low altitude. When we first went to dock a space-ship, in the early 60s, we had not realized this. When the astronauts fired the engines to dock, they found that they’d accelerate in velocity, but not in angular speed: v = wr. The faster they went, the higher up they went, but the lower the angular speed got: the fewer the orbits per day. Eventually they realized that, to dock with another ship or a space-station that is in front of you, you do not accelerate, but decelerate. When you decelerate you lose altitude and gain angular speed: you catch up with the station, but at a lower altitude. Your next step is to angle your ship near-radially to the earth, and accelerate by firing engines to the side till you dock. Like much of orbital rocketry, it’s simple, but not intuitive or easy.

Robert Buxbaum, August 12, 2015. A cannon that could reach from North Korea to Japan, say, would have to be on the order of 10 km long, running along the slope of a mountain. Even at that length, the shell would have to fire at 450 G, or so, and reach a speed about 3000 m/s, or 1/3 orbital.

The mass of a car and its mpg.

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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.

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.