Monthly Archives: March 2018

What drives the gulf stream?

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I’m not much of a fan of todays’ kids’ science books because they don’t teach science IMHO. They have nice pictures and a few numbers; almost no equations, and lots of words. You can’t do science that way. On the odd occasion that they give the right answer to some problem, the lack of math means the kid has no way of understanding the reasoning, and no reason to believe the answer. Professional science articles on the web are bad in the opposite direction: too many numbers and for math, hey rely on supercomputers. No human can understand the outcome. I like to use my blog to offer science with insight, the type you’d get in an old “everyman science” book.

In previous posts, I gave answers to why the sky is blue, why it’s cold at the poles, why it’s cold on mountains, how tornadoes pick stuff up, and why hurricanes blow the way they do. In this post, we’ll try to figure out what drives the gulf-stream. The main argument will be deduction — disproving things that are not driving the gulf stream to leave us with one or two that could. Deduction is a classic method of science, well presented by Sherlock Holmes.

The gulf stream. The speed in the white area is ≥ 0.5 m/s (1.1 mph.).

The gulf stream. The speed in the white area is ≥ 0.5 m/s (1.1 mph.).

For those who don’t know, the Gulf stream is a massive river of water that runs within the Atlantic ocean. As shown at right, it starts roughly at the end of Florida, runs north to the Carolinas, and then turns dramatically east towards Spain. Flowing east, It’s about 150 miles wide, but only about 62 miles (100 km) when flowing along the US coast. According to some of the science books of my youth this massive flow was driven by temperature according to others, by salinity (whatever that means), and yet other books of my youth wind. My conclusion: they had no clue.

As a start to doing the science here, it’s important to fill in the numerical information that the science books left out. The Gulf stream is roughly 1000 meters deep, with a typical speed of 1 m/s (2.3 mph). The maximum speed is the surface water as the stream flows along the US coast. It is about 2.5 metres per second (5.6 mph), see map above.

From the size and the speed of the Gulf Stream, we conclude that land rivers are not driving the flow. The Mississippi is a big river with an outflow point near the head waters of the gulf stream, but the volume of flow is vastly too small. The volume of the gulf stream is roughly

Q=wdv = 100,000 x 1000 x .5 =  50 million m3/s = 1.5 billion cubic feet/s.

This is about 2000 times more flow than the volume flow of the Mississippi, 18,000 m3/s. The great difference in flow suggests the Mississippi could not be the driving force. The map of flow speeds (above) also suggest rivers do not drive the flow. The Gulf Stream does not flow at its maximum speed near the mouth of any river.  We now look for another driver.

Moving on to temperature. Temperature drives the whirl of hurricanes. The logic for temperature driving the gulf stream is as follows: it’s warm by the equator and cold at the poles; warm things expand and as water flows downhill, the polls will always be downhill from the equator. Lets put some math in here or my explanation will be lacking. First lets consider how much hight difference we might expect to see. The thermal expansivity of water is about 2x 10-4 m/m°C (.0002/°C) in the desired temperature range). To calculate the amount of expansion we multiply this by the depth of the stream, 1000m, and the temperature difference between two points, eg. the end of Florida to the Carolina coast. This is 5°C (9°F) I estimate. I calculate the temperature-induced seawater height as:

∆h (thermal) ≈ 5° x .0002/° x 1000m = 1 m (3.3 feet).

This is a fair amount of height. It’s only about 1/100 the height driving the Mississippi river, but it’s something. To see if 1 m is enough to drive the Gulf flow, I’ll compare it to the velocity-head. Velocity-head is a concept that’s useful in plumbing (I ran for water commissioner). It’s the potential energy height equivalent of any kinetic energy — typically of a fluid flow. The kinetic energy for any velocity v and mass of water, m is 1/2 mv2 . The potential energy equivalent is mgh. Combine the above and remove the mass terms, and we have:

∆h (velocity) = v2/2g.

Where g is the acceleration of gravity. Let’s consider  v = 1 m/s and g= 9.8 m/s2.≤ 0.05 m ≈ 2 inches. This is far less than the driving force calculated above. We have 5x more driving force than we need, but there is a problem: why isn’t the flow faster? Why does the Mississippi move so slowly when it has 100 times more head.

To answer the above questions, and to check if heat could really drive the Gulf Stream, we’ll check if the flow is turbulent — it is. A measure of how turbulent is based on something called the Reynolds number, Re#, it’s the ratio of kinetic energy and viscous loss in a fluid flow. Flows are turbulent if this ratio is more than 3000, or so;

Re# = vdρ/µ.

In the above, v is velocity, say 1 m/s, d is depth, 1000m, ρ = density, 1000 kg/m3 for water, and  0.00133 Pa∙s is the viscosity of water. Plug in these numbers, and we find a RE# = 750 million: this flow will be highly turbulent. Assuming a friction factor of 1/20 (.05), e find that we’d expect complete mixing 20 depths or 20 km. We find we need the above 0.05 m of velocity height to drive every 20 km of flow up the US coast. If the distance to the Carolina coast is 1000 km we need 1000*.05m/20 = 1 meter, that’s just about the velocity-head that the temperature difference would suggest. Temperature is thus a plausible driving force for 0.5 m/s, though not likely for the faster 2.5 m/s flow seen in the center of the stream. Turbulent flow is a big part of figuring the mpg of an automobile; it becomes rapidly more important at high speeds.

World sea salinity

World sea salinity. The maximum and minimum are in the wrong places.

What about salinity? For salinity to work, the salinity would have to be higher at the end of the flow. As a model of the flow, we might imagine that we freeze arctic seawater, and thus we concentrate salt in the seawater just below the ice. The heavy, saline water would flow down to the bottom of the sea, and then flow south to an area of low salinity and low pressure. Somewhere in the south, the salinity would be reduced by rains. If evaporation were to exceed the rains, the flow would go in the other direction. Sorry to say, I see no evidence of any of this. For one the end of the Gulf Stream is not that far north; there is no freezing, For two other problems: there are major rains in the Caribbean, and rains too in the North Atlantic. Finally, while the salinity head is too small. Each pen of salinity adds about 0.0001g/cc, and the salinity difference in this case is less than 1 ppm, lets say 0.5ppm.

h = .0001 x 0.5 x 1000 = 0.05m

I don’t see a case for northern-driven Gulf-stream flow caused by salinity.

Surface level winds in the Atlantic.

Surface level winds in the Atlantic. Trade winds in purple, 15-20 mph.

Now consider winds. The wind velocities are certainly enough to produce 5+ miles per hour flows, and the path of flows is appropriate. Consider, for example, the trade winds. In the southern Caribbean, they blow steadily from east to west slightly above the equator at 15 -20 mph. This could certainly drive a circulation flow of 4.5 mph north. Out of the Caribbean basin and along the eastern US coat the trade winds blow at 15-50 mph north and east. This too would easily drive a 4.5 mph flow.  I conclude that a combination of winds and temperature are the most likely drivers of the gulf stream flow. To quote Holmes, once you’ve eliminated the impossible, whatever remains, however improbable, must be the truth.

Robert E. Buxbaum, March 25, 2018. I used the thermal argument above to figure out how cold it had to be to freeze the balls off of a brass monkey.

New Chinese emperor, will famine not follow

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For most of its 2300 year history, the Chinese empire has rattled between strong leaders who brought famine, and weak leaders who brought temporary reprieve. Mao, a strong leader, killed his associates plus over 100 million by his “great leap forward” famine. Since then, 30+ years, we’ve had some weaker leaders, semi-democracy, and some personal wealth, plus the occasional massacre, e.g. at Tiananmen square, and a growing demographic problem. And now a new strongman is establishing himself with hopes of solving China’s problems. I hope for the best, but fear the repeat of the worse parts of Chinese history.

Two weeks ago, Chairman Xi amended the Chinese constitution to make himself emperor for life, essentially. He’s already in charge of the government, the party, and the military. Yesterday (Tuesday), he consolidated his power further by replacing the head of the banks. The legal system is, in theory, is the last independent part of government, but there is hardly any legal system in the sense of a balance of power. If history is any guide, “Emperor” Xi will weaken the courts further before the year is out. He will also likely remove many or all of his close associates and relatives. It is not for nothing that Nero, Stalin, and Mao killed their relatives and friends — generally for “corruption” following a show trial.

China's Imperial past is never is quite out of sight. Picture from the Economist.

China’s past is never is quite out of sight. Picture from the Economist.

Xi might be different, but he faces a looming demographic problem that makes it likely he will follow the president of the stronger emperors. China’s growth was fueled in part by a one child policy. Left behind is an aging, rural population with no children to take care of the elderly. As top-down societies do not tolerate “useless workers,” I can expect a killing famine within the next 10 years. This would shed the rural burden while providing a warning to potential critics. “Burn the chicken to scare the monkey,” is a Chinese Imperial aphorism. Besides, who needs dirt farmers when we have modern machines.

Lazy beds (feannagan) use only half the soil are for planting. The English experts were sure this was inefficient and land-wasting. Plowing was imposed on Ireland, and famine followed

“Lazy beds” of potatoes were used in Ireland for a century until experts forced their abandonment in the mid 1800s. The experts saw the beds, and the Irish as lazy, inefficient, and land-wasting. Famine followed.

Currently about 40% of the country is rural, about 560 million people spread out over a country the size of Canada or the US. The rest, 60% or 830 million, live concentrated in a few cities. The cities are rich, industrial, and young. The countryside is old, agricultural and poor, salaries are about 1/3 those of the cities. The countryside holds about 2/3 of those over 65, about 100 million elderly with no social safety net. The demographic imbalance is likely to become worse — a lot worse — within the next decade.

What is likely to happen, I fear, is that the party leaders — all of whom live in the cities — will decide that the countryside is full of non-productive, uneducated whiners. They will demand that more food should be produced, and will help them achieve this by misguided science and severe punishments. Mao’s experts, like Stalin’s and Queen Victoria’s, demanded unachievable quotas and academic-based advice that neither the leaders nor the academics had ever tried to make work. Mao’s experts told peasants to kill the birds that were stealing their grain. It worked for a while until the insects multiplied. As for the quotas, the party took grain as if the quotas were being met. If the peasants starved, they starved.

I expect that China’s experts will propose machine-based modern agriculture, perhaps imported from the US or Israel: Whatever is in style at the time. The expert attitude exists everywhere to this day, and the results are always the same. See potato famine picture above. When the famine comes, the old will request food and healthcare, but the city leaders will provide none, or just opioids as they did to ailing Elvis. When the complaining stops the doctor is happy.

China's population pyramid as of 2016. Notice the bulge of 40-55 year olds.

China’s population pyramid as of 2016. Notice the bulge of 40-55 year olds. Note too that there are millions more males (blue) than females (pink).

In single leader societies, newspapers do not report bad news. Rather, they like to show happy, well-fed peasants singing the leaders’ praise. When there’s a riot too big to ignore, rioters are presented as lazy malcontents and counter-revolutionaries. Sympathizers are sent to work in the fields. American academia will sing the praises of the autocratic leader, or will be silent. We never see the peasants, but often see the experts. And we live in a society where newspapers report only the bad, and where we only believe when there pictures. No pictures, no story. As with Stalin’s Gulags, Mao’s famine, or North Korea today, there are likely to be few pictures released to the press. Eventually, a census will reveal that tens of million aged have vanished, and we’ll have to guess where they went.

I can expect China to continue its military buildup over the next decade. The military will be necessary to put down riots, and keep young men occupied, and to protect China from foreign intervention. China will especially need to protect its ill-gotten, new oil-assets. Oil is needed if China is to replace its farmers with machines. It will be a challenge for a wise American leader to avoid being drawn into war with China, while protecting some of our interests: Taiwan, Hong Kong, etc. As with Theodore Roosevelt, he should offer support and non-biassed mediation. Is Trump up to this?  Hu Knows?

Robert Buxbaum, March 21, 2018. The above might be Xi-nephobia, Then again, this just in: Chairman Xi announces that Taiwan will face punishment if it attempts to break free. Doesn’t sound good.

Beyond oil lies … more oil + price volatility

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One of many best selling books by Kenneth Deffeyes

One of many best-selling books by Kenneth Deffeyes

While I was at Princeton, one of the most popular courses was geology 101 taught by Dr. Kenneth S. Deffeyes. It was a sort of “Rocks for Jocks,” but had an unusual bite since Dr. Deffeyes focussed particularly on the geology of oil. Deffeyes had an impressive understanding of oil and oil production, and one outcome of this impressive understanding was his certainty that US oil production had peaked in 1970, and that world oil was about to run out too. The prediction that US oil production had peaked was not original to him. It was called Hubbert’s peak after King Hubbert who correctly predicted (rationalized?) the date, but published it only in 1971. What Deffeyes added to Hubbard’s analysis was a simplified mathematical justification and a new prediction: that world oil production would peak in the 1980s, or 2000, and then run out fast. By 2005, the peak date was fixed to November 24, of the same year: Thanksgiving day 2005 ± 3 weeks.

As with any prediction of global doom, I was skeptical, but generally trusted the experts, and virtually every experts was on board to predict gloom in the near future. A British group, The Institute for Peak Oil picked 2007 for the oil to run out, and the several movies expanded the theme, e.g. Mad Max. I was convinced enough to direct my PhD research to nuclear fusion engineering. Fusion being presented as the essential salvation for our civilization to survive beyond 2050 years or so. I’m happy to report that the dire prediction of his mathematics did not come to pass, at least not yet. To quote Yogi Berra, “In theory, theory is just like reality.” Still I think it’s worthwhile to review the mathematical thinking for what went wrong, and see if some value might be retained from the rubble.

proof of peak oilDeffeyes’s Maltheisan proof went like this: take a year-by year history of the rate of production, P and divide this by the amount of oil known to be recoverable in that year, Q. Plot this P/Q data against Q, and you find the data follows a reasonably straight line: P/Q = b-mQ. This occurs between 1962 and 1983, or between 1983 and 2005. Fro whichever straight line you pick, m and b are positive. Once you find values for m and b that you trust, you can rearrange the equation to read,

P = -mQ2+ bQ

You the calculate the peak of production from this as the point where dP/dQ = 0. With a little calculus you’ll see this occurs at Q = b/2m, or at P/Q = b/2. This is the half-way point on the P/Q vs Q line. If you extrapolate the line to zero production, P=0, you predict a total possible oil production, QT = b/m. According to this model this is always double the total Q discovered by the peak. In 1983, QT was calculated to be 1 trillion barrels. By May of 2005, again predicted to be a peak year, QT had grown to two trillion barrels.

I suppose Deffayes might have suspected there was a mistake somewhere in the calculation from the way that QT had doubled, but he did not. See him lecture here in May 2005; he predicts war, famine, and pestilence, with no real chance of salvation. It’s a depressing conclusion, confidently presented by someone enamored of his own theories. In retrospect, I’d say he did not realize that he was over-enamored of his own theory, and blind to the possibility that the P/Q vs Q line might curve upward, have a positive second derivative.

Aside from his theory of peak oil, Deffayes also had a theory of oil price, one that was not all that popular. It’s not presented in the YouTube video, nor in his popular books, but it’s one that I still find valuable, and plausibly true. Deffeyes claimed the wildly varying prices of the time were the result of an inherent quay imbalance between a varying supply and an inelastic demand. If this was the cause, we’d expect the price jumps of oil up and down will match the way the wait-line at a barber shop gets longer and shorter. Assume supply varies because discoveries came in random packets, while demand rises steadily, and it all makes sense. After each new discovery, price is seen to fall. It then rises slowly till the next discovery. Price is seen as a symptom of supply unpredictability rather than a useful corrective to supply needs. This view is the opposite of Adam Smith, but I think he’s not wrong, at least in the short term with a necessary commodity like oil.

Academics accepted the peak oil prediction, I suspect, in part because it supported a Marxian remedy. If oil was running out and the market was broken, then our only recourse was government management of energy production and use. By the late 70s, Jimmy Carter told us to turn our thermostats to 65. This went with price controls, gas rationing, and a 55 mph speed limit, and a strong message of population management – birth control. We were running out of energy, we were told because we had too many people and they (we) were using too much. America’s grown days were behind us, and only the best and the brightest could be trusted to manage our decline into the abyss. I half believed these scary predictions, in part because everyone did, and in part because they made my research at Princeton particularly important. The Science fiction of the day told tales of bold energy leaders, and I was ready to step up and lead, or so I thought.

By 2009 Dr. Deffayes was being regarded as chicken little as world oil production continued to expand.

By 2009 Dr. Deffayes was being regarded as chicken little as world oil production continued to expand.

I’m happy to report that none of the dire predictions of the 70’s to 90s came to pass. Some of my colleagues became world leaders, the rest because stock brokers with their own private planes and SUVs. As of my writing in 2018, world oil production has been rising, and even King Hubbert’s original prediction of US production has been overturned. Deffayes’s reputation suffered for a few years, then politicians moved on to other dire dangers that require world-class management. Among the major dangers of today, school shootings, Ebola, and Al Gore’s claim that the ice caps will melt by 2014, flooding New York. Sooner or later, one of these predictions will come true, but the lesson I take is that it’s hard to predict change accurately.

Just when you thought US oil had beed depleted for good, production began rising. It's now higher than the 1970 peak.

Just when you thought US oil was depleted, production began rising. We now produce more than in 1970.

Much of the new oil production you’ll see on the chart above comes from tar-sands, oil the Deffeyes  considered unrecoverable, even while it was being recovered. We also  discovered new ways to extract leftover oil, and got better at using nuclear electricity and natural gas. In the long run, I expect nuclear electricity and hydrogen will replace oil. Trees have a value, as does solar. As for nuclear fusion, it has not turned out practical. See my analysis of why.

Robert Buxbaum, March 15, 2018. Happy Ides of March, a most republican holiday.

Hydrogen powered trucks and busses

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With all the attention on electric cars, I figure that we’re either at the dawn of electric propulsion or of electric propulsion hype. Elon Musk’s Tesla motor car company stock is now valued at $59 B, more than GM or Ford despite the company having massive losses and few cars. It’s a valuation that, I suspect, hangs on the future of autonomous vehicles, a future whose form is uncertain. In this space, I suspect that hydrogen-battery hybrids make more sense than batteries alone, and that the first large-impact uses will be trucks and busses — vehicles that go long distance on highways.

Factory floor, hydrogen fueling station for plug-power forklifts. Plug FCs reached their 10 millionth refueling this January.

Factory floor, hydrogen fueling station for fuel cell forklifts. This company’s fuel cells have had over 10 million refuelings so far.

Currently there are only two brands of autonomous vehicle available for sale in the US: the Cadillac CT6, a gasoline hybrid, and the Tesla, a pure battery vehicle. Neither work well except on highways because there are fewer on-highway driver-issues. Currently, the CT6 allows you to take your hands off the wheel — see review here. This, to me, is a big deal: it’s the only real point of autonomous control, and if one can only do this on the highway, that’s still great. Highway driving gets tiring after the first hundred miles or so, and any relief is welcome. With Tesla cars, you can never take your hand off the wheel or the car stops.

That battery cars compete, cost wise, I suspect, is only possible because the US government highly subsidizes the battery cost. Musk hides the true cost of the battery, I suspect, among the corporate losses. Without this subsidy, hydrogen – hybrid vehicles, I suspect, would be far cheaper than Tesla while providing better range, see my calculation here. Adding to the advantage of hybrids over our batteries, the charge time is much faster. This is very important for highway vehicles traveling any significant distance. While hydrogen fuel isn’t as cheap as gasoline, it’s becoming cheaper — now about double the price of gasoline on a per mile basis, and it’s far cheaper than batteries when the wear-and tear life of the batter is included. And unlike gasoline, hydrogen propulsion is pollution-free  and electric.

Electric propulsion seems better suited to driverless vehicles than gasoline propulsion because of how easy it is to control electricity. Gasoline vehicles can have odd acceleration issues, e.g. when the gasoline gets wet. And it’s not like there are no hydrogen fueling stations. Hydrogen, fuel-cell power has become a major competitor for fork-lifts, and has recently had its ten millionth refueling in that application. The same fueling stations that serve fork-lift users could serve the self-driving truck and bus market. For round the town use, hydrogen vehicles could use battery power along (plug-in hybrid mode). A vehicle of this sort could have very impressive performance. A Dutch company has begun to sell kits to convert Tesla model S autos to a plug-in hydrogen hybrid. The result boasts a 620 mile (1000 km) range instead of the normal 240 miles; see here. On the horizon, Hyundai has debuted the self-driving “Nexo” with a range of 370 miles. Self-driving Nexos were used to carry spectators between venues at the Pyongyang olympics. The Toyota Mirai (312 miles) and the Honda Clarity Fuel Cell (366 miles) can be expected to début with similar capabilities in the near future.

Cadillac CT6 with supercruise. An antonymous vehicle that you can buy today that allows you to take your hand off the wheel.

Cadillac CT6 with supercruise. An autonomous vehicle that you can buy today that allows you to take your hand off the wheel.

In the near-term, trucks and busses seem more suited to hydrogen than general-use cars because of the localization of hydrogen refueling, Southern California has some 36 public hydrogen refueling stations at last count, but that’s too few for most personal car users. Other states have even fewer spots; Michigan has only two where one can drive up and get hydrogen. A commercial trucking company can work around this if they go between fixed depots that may already have hydrogen dispensers, or can be fitted with dispensers. Ideally they use the same dispensers as the forklifts. If one needs extra range one can carry a “hydrogen Jerry can” or two — each jerry can providing an extra 20-30 miles of emergency range. I do not see electric vehicles working as well for trucks and busses because the charge times are too slow, the range is too modest, and the electric power need is too large. To charge a 100 kWhr battery in an hour requires an electric feed of over 100 kW, about as much as a typical mall. With a, more-typical 24kW (240 V at 100 Amps) service the fastest you can recharge would be 4 1/2 hours.

So why not stick to gasoline, as with the Cadillac? My first, simple answer is electric control simplicity. A secondary answer is the ability to use renewable power from wind, solar, and nuclear; there seems to be a push for renewable and electric or hydrogen vehicles make use of this power. Of these two, only hydrogen provides the long-range, fast fueling necessary to make self-driving trucks and busses worthwhile.

Robert Buxbaum March 12, 2018. My company, REB Research provides hydrogen purifiers and hydrogen generators.

Yogurt making for kids

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Yogurt making is easy, and is a fun science project for kids and adults alike. It’s cheap, quick, easy, reasonably safe, and fairly useful. Like any real science, it requires mathematical thinking if you want to go anywhere really, but unlike most science, you can get somewhere even without math, and you can eat the experiments. Yogurt making has been done for centuries, and involves nothing more than adding some yogurt culture to a glass of milk and waiting. To do this the traditional way, you wait with the glass sitting outside of any refrigeration (they didn’t have refrigeration in the olden days). After a few days, you’ll have tasty yogurt. You can get taster yogurt if you add flavors. In one of my most successful attempts at flavoring, I added 1/2 ounce of “skinny syrup” (toffee flavor) to a glass of milk. The results were most satisfactory, IMHO.

My latest batch of home-made flavored yogurt, made in a warm spot behind this urn.

My latest batch of home-made flavored yogurt, made in a warm spot behind this coffee urn.

Now to turn yogurt-making into a science project. We’ll begin with a hypothesis. I generally tell people to not start with a hypothesis, (it biases your thinking), but here I will make an exception as I have a peculiarly non-biased hypothesis to suggest. Besides, most school kids are told they need one. My hypothesis is that there must be better ways to make yogurt and worse ways. A hypothesis should be avoided if it contains any unfounded assumptions, or if it points to a particular answer — especially an answer that no one would care about.

As with all science you’ll want to take numerical data of cause and effect. I’d suggest that temperature data is worth taking. The yogurt-making bacteria is called lactose thermophillis, and this suggests that warm temperatures will be good (lact = milk in Latin, thermophilic = loving heat). Also making things interesting is the suspicion that if you make things too warm, you’ll cook your organisms and you won’t get any yogurt. I’ve had this happen, both with over-heat and under-heat. My first attempt was to grow yogurt in the refrigerator, but I got no results. I then tried the kitchen counter and got yogurt, and then I heated things a bit more by growing next to a coffee urn, and got better yogurt; yet more heat and nothing.

For a science project, you might want to make a few batches of yogurt, at least 5, and these should be made at 2-3 different temperatures. If temperature is a cause for the yogurt to come out better or worse, you’ll need to be able to measure how much “better”? You may choose to study taste, and that’s important, but it’s hard to quantify, so that should not be the whole experiment. I would begin by testing thickness, or the time to a get some fixed degree of thickness; I’d measure thickness by seeing if a small weight sinks. A penny is a cheap, small weight, and I know it sinks in milk, but not in yogurt. You’ll want to wash your penny first, or no one will eat the yogurt. I used hot water from the urn to clean and sterilize my pennies.

Another thing that is worth testing is the effect of using different milks: whole milk, 2%, 1% or skim; goat milk, or almond milk. You can also try adding stuff to it, or starting with different starter cultures, or different amounts. Keep numerical records of these choices, then keep track of how they effect how long it takes for the gel to form, and how the stuff looks or tastes to you. Before you know it, you’ll have some very good product at half the price of the stuff in the store. If you really want to move forward fast, you might apply semi-random statistics to your experimental choices. Good luck.

Robert Buxbaum, March 2, 2018. My latest observation: what happens if you leave the yogurt to mold too long? It doesn’t get moldy, perhaps the lactic acid formed kills germs (?), but the yogurt separated into curds and whey. I poured off the whey, the unappealing, bitter yellow liquid. The thick white remainder is called “Greek” yogurt. I’m not convinced this tastes better, or is healthier, BTW.