Fruit, veg and undetermined

A reader writes:

How the hell did "prune juice" ever come to exist, since a prune is a dried plum and you can't get juice out of dried fruit? Do they mash them up and add water or something?

Isaac

There's a loophole.

Plums grown primarily to be dried are called "prunes", even before they're dried. They can also be eaten fresh, or juiced. Presto, a warrior's drink.

And now, some Bonus Botanical Trivia:

Many people believe nectarines to be a peach/plum hybrid. They're not. They're a smooth-skinned strain of peach, sharing an ancestor with the plum somewhere back in the history of stonefruit, but otherwise unrelated.

Somewhat fewer people believe nashi pears to be an apple/pear hybrid. They're not. They're a natural species, or, at any rate, as "natural" as the apples and pears that humans have been selectively breeding for thousands of years.

(I am greatly amused by Creationist publications that show a magnificent spread of delicious fruit and veg that God in His wisdom has provided for us; the Jehovah's Witnesses have a really nice version of this in one of their numerous happy-pictured books and pamphlets. I always have a hard time finding anything in those pictures that hasn't been gigantically changed from a near-inedible ancestor by human intervention. Possibly the coconut. Good luck opening that with your bare hands, Adam.)

Lemons, on the other hand, are a hybrid, though a pretty ancient one. Genetic analysis (PDF) has shown them to be a hybrid of the bitter orange and the citron.

If you always thought that grapefruit were hybrids too, you'll now be amazed to learn that you were right. The grapefruit only dates back to the 18th century.

Many people are also familiar with the factoid that, technically, the banana is a herb. Banana taxonomy has always been a nuisance, but this bit of pub-trivia information is not actually worth much.

In everyday grocery-shopping terms the banana is obviously a fruit, but in botanical terms it can defensibly be described as a berry, while the botanical "herb" is any non-woody flowering plant, most of which are inedible. (And, by the botanical definition, each individual kernel on an ear of corn is a separate "fruit". Don't get me started on cashews.)

All of these games with definitions and clashes between scientific and everyday terminology are pretty pointless. They make about as much sense as saying that because people who make coins for a living may refer to all of their input metals as "bullion", it is therefore sensible to invest in copper by the ounce.

Another one: In everyday usage, hardwood means wood that is hard. In scientific terms, though, it just means wood from non-flowering flowering [it was inevitable I'd get one of these wrong, wasn't it?] plants, so balsa wood is technically a hardwood.

Finally, and perhaps most interestingly, it turns out that the tomato is technically an amphibian.


Psycho Science is a regular feature here. Ask me your science questions, and I'll answer them. Probably.

And then commenters will, I hope, correct at least the most obvious flaws in my answer.

Fizzing the floors

A reader writes:

My mom's always been a strong proponent of vinegar as a miracle cleaner for almost anything, floors, windows, clothes, you name it. She recently discovered bicarbonate of soda, too, and has been using that for all sorts of stuff too, like in the dishwasher instead of the special powder.

When I visited the other day, she was washing the floors with a bucket that had hot water, bicarbonate of soda AND vinegar in it. Apparently the fizz when you add the vinegar gives you more "scrubbing bubbles". Except I vaguely remember from elementary school that an acid and a base cancel each other out, the example given having been exactly this, vinegar and washing soda.

So was my mom just washing the floor with salty water?

Joseph

Almost.

Vinegar and bicarbonate of soda are indeed the standard boringly-safe-science demonstration of an acid and a base neutralising, and the reaction does produce a salt, but not table salt.

Bicarb is NaHCO3, acetic acid is CH3CO2H. Acetic is the acid in vinegar - cheap "white vinegar", which is rather more economical for cleaning things than 50-year-old balsamic, contains nothing but nice clean industrial acetic acid and water.

The reaction is:

NaHCO3 + CH3CO2H -> CH3COONa + H2O + CO2

Those products are sodium acetate, water and carbon dioxide. The CO2 is invisible but heavier than air, and can be poured out of the reaction container to extinguish a candle, said candle being the most dangerous thing that exists in boringly-safe-science demonstrations.

Sodium acetate is sometimes used as a flavouring, because it tastes like salt and vinegar all by itself. ("Salt and vinegar" snacks in the USA are apparently likely to be flavoured with sodium acetate; here in Australia I think that's illegal for some reason. I don't think it's toxicity; sodium acetate is pretty innocuous.)

If you mix sodium bicarbonate and hydrochloric acid, HCl, then the reaction is the same except instead of sodium acetate, you get sodium chloride, which is everyday table salt.

(For this reason, bicarb is a very effective antacid. A teaspoon full of bicarb can turn nasty acid-reflux indigestion into a series of hugely satisfying CO2 belches in seconds. You'll have a pretty darn high-sodium diet, though, if like me you end up eating several spoonfulls of the not-that-bad-tasting-when-you-get-used-to-it substance per day. In that case, hie thee to a doctor and get yourself a prescription for one or another acid-production-reducing drug.)

You'd want to be careful making salt from bicarb and hydrochloric acid, though, because if you don't get your stoichiometry right and not add balanced amounts of the reagents, then there'll be left-over bicarb or hydrochloric acid at the end. This is also what will happen if someone decides to make a cleaning product out of bicarb and vinegar; they probably won't titrate the mixture, and so will have a surplus of one substance or the other. Surplus bicarb, as a base, will clean greasy things by, essentially, turning the grease into soap. Surplus vinegar, as an acid, will clean things by dissolving various kinds of dirt, like mineral deposits ("scale"), or rust.

For these reasons, and also the fact that plain water plus elbow grease can clean a lot of things pretty effectively (the basis for the popularity of "laundry balls", which don't actually do anything), people may come to the conclusion that a vinegar-and-bicarb concoction is a super cleaner, when in fact they'd be better off using a smaller amount of only one of the ingredients.

(At least, in this case, mixing the compounds will do no harm. Mixing bleach and ammonia, on the other hand, may greatly reduce the amount of time you spend doing household chores, on account of how you may now be dead.)

Oh, and sodium bicarbonate is not "washing soda"; that's sodium carbonate, Na2CO3, which is commonly used to "soften" hard water, which contains dissolved minerals that prevent soap from working properly. Sodium bicarbonate is "baking soda", named for its use as a leavening agent; if you mix bicarb into batter that's slightly acidic, the fizzy-neutralisation reaction occurs and creates lots of little CO2 bubbles in the batter. "Baking powder" contains dry bicarb and acid powder (usually tartaric acid). Add water, and the components react and fizz.

(See also, the delightfully popular recipe for "Swedish Lemon Angels".)

Getting back to sodium acetate, a supersaturated solution of it is used in "phase change" heat packs...

...which "freeze", liberating heat, when disturbed with the little clicker device inside, or when otherwise slapped around. You put the pouch in boiling water to re-liquefy its contents; the things can be used over and over indefinitely, as long as they don't spring a leak.

You can do something similar to this with numerous other fluids, but sodium acetate's properties suit it very well to the purpose. Even if you don't actually need a hand-warmer, I strongly recommend you buy one as a toy, since you can get them on eBay for about $5 delivered.


Psycho Science is a regular feature here. Ask me your science questions, and I'll answer them. Probably.

And then commenters will, I hope, correct at least the most obvious flaws in my answer.

Like being a rather small superhero

My friend Mark has an R/C quadcopter, with a First-Person View rig on it.

He came down from Queensland to visit us, and some other people, the other week.

And recorded some video, including some flying off Echo Point near where I live. Though with entirely too little buzzing of trees and tourists, or seeing how low he could go before the edge of the cliff tested the effectiveness of the copter's lost-signal configuration.

I am not in the Echo Point footage, because I was not there, because I am an idiot.

Sniffing glue

A reader writes:

How toxic is superglue?

All I really know about it is that it's technically called "cyanoacrylate", but the "cyano" part makes me nervous. The last episode of Mythbusters I saw had them sticking stuff to other stuff with superglue (which they called "super adhesive" for some reason) and they were wearing gas masks while doing it.

Am I endangering my health if I superglue a teacup together without lots of ventilation? My son's just now started building model airplanes and tends to stare so close at the model I'm expecting him to stick a propellor to his nose soon; is HE going to be poisoned too?!

Eva

At some point in the next few thousand words I may answer your question, Eva. You know how it is with me.

The magic acronym (or possibly initialism) to remember whenever you want to know how strongly a given substance desires to kill you is "MSDS", for Material Safety Data Sheet. You can find an MSDS for just about anything, provided you know the name of the substance in question. You usually don't need to know the exact chemical name, either; brand names, especially of pharmaceuticals, often work.

One popular substance can have a large number of MSDSes for it, sometimes with different data, because, for instance, a product sold under the same name by different companies may be made with different constituents. MSDSes may also differ even when they're talking about the exact same substance, because different manufacturers and importers and so on may have different testing regimes, or may just plain get stuff wrong. Generally speaking, though, you can trust MSDSes, even if you can't find one for the exact brand of, in this case, cyanoacrylate (which is known to the relevant chemists, and many hobbyists, as "CA") you're worried about.

When I say "just about anything" above, I mean it. Here's an MSDS (in PDF format, like most online MSDSes these days), for skim milk. Including rather excessive first aid procedures to employ in case the substance is ingested.

Here's one, and another, for olive oil. More over-enthusiastic warnings; apparently you're not meant to allow olive oil to make direct contact with the skin. MSDSes for innocuous substances are often like this, possibly for reasons having to do with the covering of arses, or perhaps because there was no "zero hazard" box for the MSDS-maker to tick.

"Portland cement should not be eaten." Don't eat talcum powder, either. Molasses isn't very worrying, as long as there's not too much of it.

OK, enough silliness. Search for MSDSes for cyanoacrylate, plus a common brand name or two like "Krazy Glue", and you'll get hits like this, this, this and this. Here's a whole page of MSDSes for Loctite products, including various other glues and threadlocks. There's a "safety" section in the Wikipedia article for CA, too, plus some MSDS links at the end.

What all of these agree on is that CA products of various kinds, from the water-thin stuff used to wick into gaps in plastic models through to various non-runny gel-type versions, are not nearly as poisonous as you'd think from their alarming "chemical" odour. The fumes are an eye and mucous-membrane irritant, and if you're sticking a whole room worth of furniture to the ceiling as they did on MythBusters then you'd be nuts not to wear some kind of breathing protection, but this stuff really isn't that bad. I don't think it even releases much in the way of horrifyingly deadly gases if you burn it, though again, this is not recommended.

(With regard to the title of this post, glues that people sniff to get high in a rather dangerous manner are generally based on some kind of solvent with psychoactive effects, though usually not effects that people living a life somewhere above rock bottom would consider worth the damage. Glues with no such solvent, like CA, PVA, hide glue or epoxy, often aren't particularly bad to inhale, which is just as well since they won't even get you high.)

Part of the reason why superglue isn't very poisonous is that its "set" state, a hard polymerised lump, isn't toxic. It's still listed as an "eye irritant" when hardened, but only in the way that sand is. And CA really wants to polymerise. All actual CA glue contains "inhibitor" chemicals in addition to the CA itself, to stop the stuff from instantly turning into a lump of plastic in the bottle. Several common compounds in the world, chief among them water, will "kick" CA into polymerising. And since your eyes and mucous membranes and so on are all rather damp, any CA vapour that hits them polymerises instantly.

Now, this is still not a good situation, since having a very thin layer of plastic accumulate inside your nose and on your eyeballs is not most people's idea of a good time, but the body can deal with tiny amounts of the stuff with no trouble. (This also means that all you probably need as the abovementioned "breathing protection" is a damp cloth tied around your face.)

You can take advantage of the effect water has on CA to accelerate its bonding, by for instance breathing heavily on the two pieces of something you're gluing before bringing them together, or even by spitting on the glue, in extremis. That won't give you a very good bond, but if you're in a hurry, it'll do. You can also sprinkle bicarbonate of soda on the glue, or dribble CA onto bicarb, to get an instantly set, hard but brittle filler material. (It's basically Bondo for plastic spaceships.)

There are also liquids, known as "CA accelerators" or "kickers", that give you an almost instant full-strength bond when they touch CA. You generally put glue on one piece, a spritz of accelerator on the other, then bring them together and zap, instant gluing of two parts that you didn't quite bring together straight, god damn it.

(The accelerators, needless to say, have their own MSDSes.)

I'm not sure how much variation there is between the different accelerators; these days I just buy whatever's cheapest on eBay. Note that CA accelerator tends to be rather volatile and thus prone to liberate itself from the spray-bottle faster than many people can use the stuff. I recommend you keep the sprayer in a Ziploc bag.

The fact that there are substances that kick CA better than water does is the base for products like the one described in this MSDS, which is for a CA formulation used for fingerprint "fuming". You can do this neat little science trick with any CA, not just special expensive law-enforcement CA:

One thing hobbyists discover pretty quickly about CA, especially if they're using accelerator as well, is that the polymerisation process is exothermic. The glue gets warm as it polymerises, the increased temperature speeds up the polymerisation, and with enough glue and enough accelerator (or just CA by itself, if it's on something with a lot of surface area - cotton is particularly bad) the result is boiling polymerising CA. I don't trust any hobbyist who hasn't emptied five whole dollars worth of discount-store superglue into a very disposable container in the back garden, then added some generous squirts of accelerator, and stood well back.

This is another CA hazard. If you spill a lot of it on your cotton-denim jeans (or somehow just manage to deliberately use an unusually large amount), the profoundly crappy time you'd reasonably expect to have in your immediate future may be made significantly crappier by some nasty burns.

Anybody who's ever used superglue will have stuck the wrong things together, though with any luck just one finger to another, not a square foot of garment to singed flesh. If possible, a good way to remove CA is mechanically, with sandpaper or a file or, for many glue-on-skin situations, a disposable razor. (Or you can just wait; as the outer layer of your skin naturally flakes off, the glue will go with it.)

CA can also be dissolved with acetone, but the MSDSes for acetone are rather more alarming than those for CA. There are less toxic glue debonders out there too; again, please accept my very personal recommendation of whatever's cheapest on eBay and isn't just acetone.

(CA is also not just kicked into polymerisation by water, but also slightly soluble in it. So a long hot bath or shower may help you out, provided you have enough un-stuck limbs to be able to operate the taps.)

While I'm giving unrequested buying advice, as far as CA itself goes, I just buy it from discount shops. Given CA's irritating propensity to go hard in the bottle, I like the few-dollar cardboard oblongs with multiple little separately-bubble-packed tubes, the more and the smaller the better. Unless you've got an ongoing meaningful relationship with a local hobby shop - which I recommend; it's worth paying a bit extra for stuff if wise counsel on various subjects, or just hours of entertaining chat, is available in return - I see no reason to buy fancy brand-name CA for almost any job.

Getting back to that alarming cyano group which is indeed hanging off the few different, but effectively almost identical, kinds of CA molecule, it is in this case not much to worry about, but certainly is if it's hanging off something less complex, like a potassium or hydrogen atom. I find the lethality of various cyanide compounds almost amusing, since it's yet another sign of the absence of "intelligent design" of even this one planet, let alone the whole universe.

I mean, what's the element that's the basis of all life on this planet? Carbon. What makes up 78% of the planet's atmosphere? Nitrogen. (Don't miss this sample!) What do you get when the two of them get together? Cyanide, a deadly poison. It's sort of the opposite of the sodium-plus-chlorine thing.

And while I'm rabbiting on, I was also amused by MythBusters' and/or Discovery Channel's determination to call the glue they were using "super adhesive", a term that doesn't really exist in nature, to the point where a couple of slip-ups when someone said "superglue" anyway made it to air. This is in line with MythBusters' general self-censorship policy, in which no brands not integral to the myth are blurred or taped over or covered with new labels reminiscent of Repo Man.

Sometimes this policy seems to make little sense, though. In a recent special episode, MythBusters shot a .50 AE round from a Desert Eagle into watermelons, and they called the gun a Desert Eagle, even though there are various other firearms that chamber that round. But in the episode a while back where they demonstrated what a bad idea it is to wrap your hand around the cylinder of a .50 Smith & Wesson revolver when firing it, not one mention was there of the brand of that gun, though anybody familiar with the preposterous hand-cannon arms race of recent years could have mistaken a S&W Model 500 for anything else.

(If you haven't been watching the nutty progression of ever-more-wrist-smashingly-powerful handgun cartridges and the you've-gotta-be-kidding-me guns that shoot them, compared to which the action-movie-staple .50 AE Desert Eagle's .44-Magnum-ish bullet energy looks positively feeble, then you could be forgiven for thinking a short-barreled Model 500 was some kind of flare gun. I wonder if even this has been surpassed by now?)

The "super adhesive" thing is particularly nutty, though, since they could have just called it cyanoacrylate.


Psycho Science is a regular feature here. Ask me your science questions, and I'll answer them. Probably.

And then commenters will, I hope, correct at least the most obvious flaws in my answer.

Pop goes the e-mail

UPDATE: This post is now thankfully out of date; my mail's working again now.

Owing to circumstances beyond the management's control, the e-mail address dan@dansdata.com currently bounces.

While I wait for the server admin at m'verygoodfriends SecureWebs to undo whatever he did that deleted the account, you can contact me on my ISP address, rutterd@iinet.net.au, or of course just chatter cheerfully in the comments to this post.

I think PayPal donations to dan@dansdata.com will still work, but you may be thanked for your donation with an error-550 bounce message, which is kind of rude. Sorry about that.

UPDATE: My mail's working again now

Lordy lordy, what a shame

I have always had a great enthusiasm for musical jokes.

(Which reminds me, I must brush up my Great Gig in the Sky/Imagine/Bohemian Rhapsody medley again. I leave identification of the points where I graft them together as an exercise for the reader, until I get around to making an MP3.)

If a musical joke involves a pipe organ, so much the better.

Herewith, therefore, I present you with the soundtrack of a swingin' cocktail party for all fifty million inhabitants of a Culture GSV!

Anyone with some experience of organ music will now, of course, know what the inevitable soundtrack will be, when unfortunate events later force the GSV to offload its population and convert most of its mass into engines and weapons...

They called it "big iron" for a reason

A reader writes:

After reading "Welcome to my museum", I'm now fascinated by the power supply equipment used on early Cray supercomputers. Can you explain more about the Motor-Generator Unit, and where you found the information? There doesn't seem to be much literature about it on the interwebs.

Colin

Cray Motor-Generator Unit

I found out about the extraordinary supporting equipment the Cray-1 needed in the "Cray-1 Computer Systems M Series Site Planning Reference Manual HR-0065", dated April 1983, which you can get in PDF format here.

I think I originally found that manual in the Bitsavers PDF Document Archive, here. They've got a bunch of other old Cray documentation in this directory, including document HR-0031, the manual for the optional Cray-1/X-MP Solid-State Storage Device (SSD).

You could very easily mistake that device for a modern SSD, except for minor details like how it had a maximum capacity of 256 megabytes, and was larger and heavier than some cows. I'm not sure quite how much larger and heavier, though, because that's covered by document HR-0025, which unfortunately doesn't seem to be online anywhere.

(The top-spec 256Mb version of the SSD did have a 1250-megabyte-per-second transfer rate, though, more than double the speed of the fastest PC SSDs as I write this. The Cray SSD's main purpose was apparently to serve as a fast buffer between the supercomputer's main memory and its relatively slow storage. Traditional supercomputers, as I've written before, were always more about I/O bandwidth than sheer computational power.)

The Site Planning Reference Manual is sort of a tour rider for a computer. Van Halen's famous rider had that thing about brown M&Ms in it as a test to see whether people at the venue had read the rider, and were thus aware that they needed to provide not only selected colours of confectionery, but also a strong enough stage and a big enough power supply. I presume the Site Planning Manual has in it somewhere a requirement that there be an orange bunny rabbit painted on one corner of the raised flooring.

(At this point I have to mention Iggy Pop's rider as well, not because it's at all relevant to the current discussion, but because it's very funny.)

I think the deal with the Motor-Generator Unit was that the Cray 1 needed not just enormous amounts of power (over a hundred kilowatts!), but also very stable power. So it ran from a huge electric generator connected directly to a huge electric motor, the motor running from dirty grid power and the generator, in turn, feeding the computer's own multi-voltage PSU. The Cray 1 itself weighed a mere 2.4 tonnes, but all this support stuff added several more tonnes.

(My copy of the HR-0065 manual is over on dansdata.com, hosted by m'verygoodfriends at SecureWebs, who in their continuing laudable attempts to wall off IP ranges corresponding to the cesspits of the Internet occasionally accidentally block traffic from some innocent sources, like an Australian ISP or two. If you can't get the file there, you can of course go to Bitsavers instead, or try this version, via Coral. You can use Coral to browse the whole of Dan's Data if SecureWebs isn't playing ball, though it may be a few hours out of date.)

The pulley paradox

A reader writes:

I was watching "Industrial Revelations" on Discovery, and I noticed a lot of Industrial Revolution factories running from one power source, a steam engine or waterwheel, with power distributed via a load of parallel overhead shafts, which brief Googling tells me are called line shafts. A belt runs from each shaft to each working machine, often with a free-turning wheel next to the one that drives the machine so the belt can be moved over onto the free wheel to "turn the machine off".

What I can't figure out is, what kept the belts on the wheels? They don't have ridges on the edges to contain the belt, they're not V- or U-profile with a matching belt shape, they're just flat metal as far as I can see, yet the belts don't fall off.

What the heck is going on, there?

Bec

Industrial Revelations is pretty good, though not, of course, a patch on The Secret Life of Machines. Most or all of it seems to be on YouTube. There are other series that have covered the same ground, too; Coltrane's Planes and Automobiles deserves a mention, and in the second-series episode of Industrial Revelations where Mark Williams, the presenter, demonstrates the fulling of cloth by trampling on it in a bucket but does not have the bucket authentically filled with fermented urine, it should be mentioned that in one episode of The Worst Jobs in History, the endlessly-associated-with-ordure Tony Robinson did the same job properly.

Where was I? Oh yes - belts.

Traditional flat leather drive belts were a pretty good piece of technology. They weren't even as much of a death-trap as you might think just looking at them, since they often had enough slack that getting some piece of yourself or your clothing caught between belt and pulley wouldn't necessarily whip you into the air or smash your face into the machine. Getting your hand caught in the moving parts of the steam engine or waterwheel gearing on the other end of the lineshafting system was bad, bad news, but if only a belt had grabbed you, you had at least a fighting chance of yanking yourself free. There usually wasn't even enough pressure between belt and wheel to instantly crush your hand.

I mean, look at the slack in this little number:

Long drive belt
(source)

Miles of belt, lots of slack.

But this arrangement looks even more insultingly physically impossible than lineshaft setups. That dang belt should fall off the engine right away, shouldn't it?

Occasionally, there's a flat belt that runs on a spool-like pulley with raised flanges on the edges, like the small receiving pulley in the above picture, or this one:

Belt running on spool-like wheel
(source)

That looks as if it ought to stay put without any magic. But in the background, there are two more of those seemingly impossible flat-pulley belts!

Some drive belts are constrained on one side, too, as in this setup for varying the speed of a machine:

Stepped drive-belt pulley
(source)

On all but the biggest of the Towers-of-Hanoi stepped sections of that pulley, the belt can only fall off on one side. But where's the power for the stepped pulley coming from? Another dang flat pulley, that's where!

Free-spinning idler wheels weren't the only way of stopping a machine, either; the middle belt in this piece of lineshafting...

Lineshafting
(source)

...has been taken off the wheel to stop it driving. That's "taken off", though, very probably not "fallen off". Left to its own devices, it'd stay where it was meant to.

As do all of these:

Belt-driven machine shop
(source)

OK, that's enough teasing. Why is it so?

The secret is that the "flat" pulleys on which the belts are running are not, actually, flat. If you look closely, at for instance the stepped pulley picture above...

Close-up of stepped drive pulley
(source)

...you can just about see that the pulley surface profile is slightly convex, or "crowned". The profile of the pulley is sort of like that of a wooden barrel, except less pronounced.

Wherever a flat belt is on a crowned pulley, it will tend to move towards the centre. This effect is reliable enough that some of the pulleys in a flat-belt power-transfer arrangement actually can be completely flat, as long as every belt runs over one or more crowned pulleys somewhere else.

For practical purposes, you can stop here. Slight convex profile to pulley equals flat belt staying in the middle of the pulley. Provided all other pulleys are well enough aligned, at least; if the pulleys aren't lined up very well then even if all of them are crowned, the belt may still "walk" off one of them. But basically, crowned pulleys equals centred belts.

If you want to know why crowned pulleys work as they do, things get a little more confusing. Confusing enough, actually, that the question can be presented as a puzzle, or even as a "paradox".

(Crowned pulleys are much more confusing than tax brackets, but I think less confusing than wind-powered vehicles that travel faster than the wind.)

The edge of a flat belt that is closest to the middle of a crowned pulley will be stretched a little more than the other edge of the belt, because the crowned pulley has a greater diameter in the middle. This gives the belt-edge toward the middle of the pulley higher tension and thus more traction than the other edge. So wherever the more tense, higher-traction portion of the belt wants to go, the whole belt will tend to go.

Any given point on the portion of the belt in contact with a pulley will, by definition, contact a point on the pulley. But when the pulley is crowned and the belt is not in the middle of it, the slight bend in the belt means a point on the tenser side of the belt, closer to the middle of the pulley, will be unable to stay in contact with the same point on the pulley as it rotates. The slight bend in the belt created by the crown profile points the belt away from the middle of the crown profile. All parts of the belt in contact with a pulley "want" to stay in contact with that same part of the pulley - that's sort of the whole point of friction belts on pulleys. But because the tenser edge of the belt, closer to the middle of the pulley, has more grip than the other edge, the whole belt tends to climb to the middle of the pulley.

Crowned pulley diagram

This illustration from The Elements of Mechanism, which I found on this page explaining the aforementioned "paradox", may help you visualise this. It certainly helped me. The point on the pulley (in this case two truncated cones, not a smoothly curved crown) which is under point "a" on the belt will end up at point "b" as the pulley rotates. The belt tries to stay frictionally stuck to the same part of the pulley, so it climbs to the middle.

(A "perfect" crowned pulley with a smooth curve is a bit of a nuisance to make, so some crowned pulleys have a flat centre and curved, or even conical, ends, and some are as shown in the above picture, just two truncated cones stuck together base-to-base. These designs don't work as well - a belt will wander on the flat part in the middle of the first type, and the ridge in the middle of the second type reduces grip and wears the belt - but they work well enough for many purposes.)

The crowned-pulley effect isn't very strong unless the crown shape is very pronounced, which would make the belts wear out quickly; this is why it can't compensate for more than slight misalignment of the pulleys. Pulleys with raised edges of one kind or another - including V-profile belts and pulleys and their relatives - can tolerate much more misalignment.

(An exaggerated crown shape does make the crown effect much easier to see, though. Famous Web-woodworker Matthias Wandel has a page about the crown effect too, that includes an exaggerated pulley.)

Although the era of lineshafting has long passed in the Western world, flat belts and crowned pulleys survive as conveyor belts, and in the strangest other places - the paper-handling machinery in photocopiers, for instance!

You can also set up a model steam engine to run a whole model machine shop via tiny line shafts. Most such setups, however...

...use O-ring belts and grooved pulleys:

This one...

...looks as if it may have proper flat belts and crowned pulleys, but the low resolution makes it hard to be sure.

This one, however...

...seems to have flat belts for everything but the initial engine connection

(You should be careful, here; model steam engines can be as dangerous to your wallet as model Stirlings.)

And now, a bonus video; why have mere pistons when you can have a turbine?


Psycho Science is a regular feature here. Ask me your science questions, and I'll answer them. Probably.

And then commenters will, I hope, correct at least the most obvious flaws in my answer.