Wikipedia:Reference desk/Archives/Science/2018 December 18

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December 18

"Static discharge" circuit tech

I have a sense that electrical technology has progressed unimaginably in the past two centuries, yet with some notable exceptions the application of "static electricity" and "static discharge" has not (what I'm thinking of is more, perhaps much more, than about 4000 volts, with amperage so low as not to be more than a minor annoyance to humans). I know that static electricity circuits can be made easily for a lark [1], I know there's the ionocraft and even Van de Graaf generators used for X-rays and particle accelerators, but are there reliable, precise static electricity power supplies, perhaps pulsed, that you could safely touch (not high tension electric lines!), are there solenoids powered by static electricity, have people built relays and complex logic circuitry that uses it, and above all, can you generate an arbitrary waveform of ultra high voltage electricity (subject to the need to have some way to restrict total amperage) using small cheap components? Wnt (talk) 14:27, 18 December 2018 (UTC)

Are there reliable, precise static electricity power supplies, perhaps pulsed, that you could safely touch? Yes. They are called "hipot testers" and "ESD testers" and you can adjust the (high) voltage and (low) current up and down. Many of them put out a waveform with a rise and fall that mimics a static electricity shock.

Are there solenoids powered by static electricity? No. Too little energy.

Have people built relays and complex logic circuitry that uses it? Relays are just solenoids that activate switches, so no on that one. Modern logic circuits use transistors, which need to be protected from static electricity. Older vacuum tube and relay logic isn't so sensitive to damage, but there is too little erergy in static electricity to run either.

Can you generate an arbitrary waveform of ultra high voltage electricity (subject to the need to have some way to restrict total amperage) using small cheap components? If you want to include DC in your definition of "arbitrary" then no. If you are OK with AC only, just build a cheap low voltage arbitrary signal generator and step up the voltage with transformers (a cheap signal transformer will give you a signal suitable for driving a neon sign transformer). Or you can wind your own high voltage transformer if you really want cheap. --Guy Macon (talk) 17:34, 18 December 2018 (UTC)

Converting angular to linear velocity

I have a question about determining the linear (tangential) velocity of a point rotating with some angular velocity at a distance d from a center, and more specifically, the metrological aspects thereof.

As everyone knows, it's simple enough:

v = ω · d

as long as the angular velocity ω is expressed in radians-per-unit-time.

So my questions are:

1. What if ω is not in radians?
2. How do you resolve the unit discrepancy?

With respect to #2, as my high school physics teacher taught me lo these many years ago, it's not enough to get the right numeric answer, you've got to get the units right, too. And when you use the expression above, with angular velocity in a unit using radians, you end up with a result in units of (distance · radians) / time, while you presumably intended to get a conventional velocity expressed as distance/time. So how to get rid of the radians?

I have an answer, but I've never seen it expressed this way. I believe that a more explicit, unit-agnostic version of the expression would be

v = ω · 2π · d / ¤

where the 2π term is in there because we're obviously dealing with the circumference of a circle somehow, and where ¤ is the number of angle units in a circle: 2π if you're using radians, 360 if you're using degrees, or 1 if you're using full rotations (as in RPM).

So the question is not so much "does this work?". (It does, with the two 2π terms nicely canceling out if you are using radians.) Rather, does anyone else formulate it this way, and has anyone ever identified a "constant" (basically another name for 1) like my ¤? (I belatedly notice that the indispensable units program does have "circle" as a unit, which is heartening.)

This is basically a simpler version of the debates that play out when comparing MKS to the various flavors of CGS. (As it says at Advantages and disadvantages, "A key virtue... is that 4πε₀ is replaced by 1".) So what I think I'm asking here is, if the 2π and ¤ terms drop out (are replaced by 1) in the "simpler" radian-time-distance system, what's the more-complicated system that radian-time-distance is simpler than, and how is angular-to-linear velocity conversion expressed there? —Steve Summit (talk) 15:28, 18 December 2018 (UTC)

• I'm confused why you don't just convert angular velocity to radians-per-unit time if it were in some other unit. That seems like a trivial operation. --Jayron32 15:30, 18 December 2018 (UTC)

+1 on that. One thing to bear in mind is that radians and degrees are formally unit-less, they are ratios. What Steve's teacher said is true but unhelpful in this case. That is, if you do a dimensional analysis of an equation in radians, it'll give exactly the same answer as a dimensional analysis in degrees. You could even argue that the circle constant is already indicated by the choice of angular measurement. Greglocock (talk) 19:30, 18 December 2018 (UTC)

Note the bold Wikilink when I state your equation:

v = ω · d

where:

v = Tangential velocity

ω = angular velocity

d = distance from center of rotation

Dimensional analysis insists that an equation have the same dimensions on its left and right sides, which is the first part of "getting the units right". In this equation the units are those of v, the speed, which is LT^-1. That means "length/time" and you may meet that again in the form dx/dt called velocity, the derivative of position with respect to time if you take an interest in Calculus. You are free to select the actual units as long as they are consistent, as in these two examples:

v metres per second = ω radians per second · d meters (using metric units)

or

v feet per hour = ω radians per hour · d feet (using imperial units)

...or any other units of time and distance used consistently will work.

To your questions:

1. What if ω is not in radians? - Angular velocity ω has to be a unit of angle rotated per time. It provides only the T^-1 part of the dimension of the right side of the equation. These values are equal: 1 radian/second = 1/(2π) rotations/second = 57.296... degrees/second (approximate) so you are free to convert between them.

2. How do you resolve the unit discrepancy? - There is none when you realize that the equation is giving tangential velocity which must be thought of as conventional velocity at a point in time. Of course you don't get rid of the given fact that the motion over any finite time is not straight but in a curve, but that does not dictate a change of units. An object such as a bullet tumbling through the air has both straight-line and tangential velocities which one can add together if one wants to estimate the air resistance due to friction. DroneB (talk) 21:08, 18 December 2018 (UTC)

So the real issue here turned out to be that I had never thought of angles as dimensionless. I really thought they were more "real" units. (I just about argued with @Greglocock: for asserting that they were unitless ratios.)

@Jayron32: asked why I couldn't just trivially convert my angles to radians if necessary. That's fine if you're working with ordinary numbers. But I'm working with a system which deals with formally unitful quantities wherever possible. (It is somewhat akin to Boost.Units. The intent, among other things, is to avoid bugs like the one that doomed the Mars Climate Orbiter mission.) With this system, it's considered wrong to extract values as particular units and work with them as ordinary numbers -- that defeats the purpose of carrying the units around. With this system, I would have had to write (and the co-worker who originally wrote the code did write) the equivalent of

angular_rate.extract(radian/sec) * dist.extract(meter)

and this resulted in an ordinary number which had to be converted back to a unitful quantity by explicitly re-tagging it as meters. In our system, it's almost always wrong to extract raw values, perform math on them, and then convert back to quantities. I instructed the co-worker to replace

double v = angular_rate.extract(radian/sec) * dist.extract(meter)

vel = quantity(v, meter/sec)

with

vel = angular_rate * dist

But this then resulted in a dimensional mismatch, since it computed something with units of angle · distance / time. Our analysis of this failure (an analysis which, embarrassingly enough, tended to contradict my usual argument that unitful quantities are always easier and more convenient to use) resulted in the question I asked here. But it looks like the real bug is that our system treats angles as a distinct unit, incommensurate with scalars.

Thanks for everyone's answers. —Steve Summit (talk) 11:37, 19 December 2018 (UTC)

@Scs: I don't think it's wrong to give angles units. I am personally a big fan of making up units as necessary to annotate a calculation -- for example, when diluting a solution, you can put "mL conc." and "mL dil." and the calculation can be audited with units (converting molar into mol/ml whatever explicitly), whereas otherwise it is "just ratios" and people can make the most embarrassing errors if they're in a hurry. In your case, you can address this explicitly with the factor-label method, making the equivalences:

1 full rotation = 2 pi radians 1 full rotation = 2 pi d (which may be in inches or whatever; note "d" is a radius as you defined it)

So if we start at, say, 0.5 rad/sec rotation and a 4 inch radius,

v = (0.5 rad/sec) * (1 rotation/2 pi radians) * ((4 inch * 2 pi) / 1 rotation) = 2 inch/sec.

The impulse to skip the units is generally treacherous, because the intuitive process you want to do can generally always be written in units and otherwise you're just doing algebra in your head for the heck of it. Even some of the hard ones nobody does with units will give way to just a little thought, for example you can add (273 K - 0 C) to any computation because you can add zero to anything, and preserve units instead of making a special case. You could also specify some really weird things like + ln( mol/L) in certain calculations, though that takes more adjustment to fundamental definitions.

As an aside, I should say that by far the most interesting case to apply any of this to is Planck's constant. It is the fundamental unit of action, energy times time, but it has the units of angular momentum, but for light it is the linear momentum per wavelength, i.e. divided by frequency i.e. times time. Any path to an intuitive understanding of quantum mechanics has to depend on all that making sense in a metrological way, which seems to depend on an understanding of moment of inertia and mass... let's just say I haven't gotten very far as of yet with that. ;) But I feel sure it's important. Wnt (talk) 15:16, 19 December 2018 (UTC)

I know what you mean about "factor-label" (though I hadn't heard it called that). And indeed your (0.5 rad/sec) * (1 rotation/2 pi radians) * ((4 inch * 2 pi) / 1 rotation) ends up being pretty darn close to my ω · 2π · d / ¤ ! —Steve Summit (talk) 05:37, 20 December 2018 (UTC)

I should redirect Factor-label method to dimensional analysis which has a section on it. The key difference is that your formula tends to look kind of like a random series of operations, where ideally a factor-label computation should take only a few pieces of data (ideally, none, if you phrase it just so) and everything else involves multiplication by 1 or, rarely, addition of 0. In other words, one rotation is 2 pi radians, so you know you can multiply by that ratio, and the same is true for the circumference being one rotation, and you can even say that, for purposes of this computation, 0.5 radians is one second, in the sense that every time you have one occur you have the other occur, and so inevitably, the result is equal to 1 also, in some conceptual sense: 2 inches is what happens in one second. Wnt (talk) 15:25, 20 December 2018 (UTC)

Can Tapir's be ridden or domesticated?

Can a Tapir be domesticated and ridden?Naraht (talk) 22:34, 18 December 2018 (UTC)

By any chance, is this a veiled question about biblical literalism? If so, you might find this publication relevant: ..."the issue cannot be resolved by reference to normal scholarship," a statement that can be considered in isolation as about the most intelligent thing that can be said about the issue. (Please don't construe this as an endorsement of any of the madness or other conspiracy-theories associated with the horse/tapir topic).

In actual fact, tapirs are not commonly domesticated in any part of the world.

Nimur (talk) 01:31, 19 December 2018 (UTC)

Where are tapirs mentioned in the Book of Mormon? ←Baseball Bugs ^{What's up, Doc?} carrots→ 01:42, 19 December 2018 (UTC)

As far as I can tell, they are not, by that name. However it does mention "horses" and "asses", neither of which are native to the New World, though there were horse species that survived possibly as late as 7600 years ago (according to Horse#Taxonomy and evolution). Apparently some Mormon exegetes identify these with tapirs or deer. That's just from a brief search; I don't remember ever hearing of this before, and I'm not sure I got it all right. --Trovatore (talk) 04:11, 19 December 2018 (UTC)

Joseph Smith might not have known there were no horses in the western hemisphere until our ancestors brought them over. ←Baseball Bugs ^{What's up, Doc?} carrots→ 04:28, 19 December 2018 (UTC)

From the Mormon point of view, that hardly matters; the angel Moroni would presumably have known. --Trovatore (talk) 04:30, 19 December 2018 (UTC)

Were there ever tapirs in the western hemisphere? ←Baseball Bugs ^{What's up, Doc?} carrots→ 05:27, 19 December 2018 (UTC)

Most tapirs are in the western hemisphere. Iapetus (talk) 10:39, 19 December 2018 (UTC)

D'oh! ←Baseball Bugs ^{What's up, Doc?} carrots→ 13:06, 19 December 2018 (UTC)

If you go to the Creation museum you can see Jesus riding a dinosaur so I'm sure it's possible ;-) Dmcq (talk) 10:59, 19 December 2018 (UTC)

Probably more fun than riding a tapir. ←Baseball Bugs ^{What's up, Doc?} carrots→ 13:06, 19 December 2018 (UTC)

Since humans wiped out New World horses in the first place, there's no scientific way to rule out that some royal family might have kept some in captivity or on an isolated preserve/island etc.; I don't believe in the Book of Mormon to make that jump on its behalf but it can't be called unscientific if someone does, just a different choice of what historical sources to credit without other corroborating evidence. Wnt (talk) 15:23, 19 December 2018 (UTC)

Is there any indication of why they would have done that? ←Baseball Bugs ^{What's up, Doc?} carrots→ 19:10, 19 December 2018 (UTC)

Of course not. I don't think they did do it. The point is though, if somebody in Nebraska hits a 2500-year-old horse skeleton with his shovel tomorrow, scientists will be skeptical, but they're not going to run around in circles yelling it's impossible. Some explanation would be devised. Wnt (talk) 04:24, 20 December 2018 (UTC)

Your alter ego said they did. ←Baseball Bugs ^{What's up, Doc?} carrots→ 04:59, 20 December 2018 (UTC)

Our article says human caused extinction is only one of the generally accepted theories. More to the point though, I admit I'm mostly unfamiliar with Mormon theology but it seems clear from this discussion we aren't just talking about random horses that just happened to survive, but domesticated horses. The generally accepted extinction date range is long before domestication, although I presume we have no indication they were ever domesticated in North America anyway, rather those domesticated elsewhere were brought over later.

So not only would they have had to survive somewhere a lot longer than commonly believed, but they would have been either kept despite not being domesticated, or these ones which happened to survive in the wild far longer than we are aware of would have had enough survivors to be domesticated, or they were domesticated a lot earlier in North America than elsewhere but we never found signs of that. And either way, despite this successful domestication, they would have still been allowed to die off. (I guess you can come up alternatives like them being brought over after domestication but no signs of this have yet been found and again they were allowed to die off.)

Besides us not finding signs of these horses, we also haven't found their chariots. This source [2] which mentions the verses does mention some non-LDS sources who believe horses did survive, generally that they never died out at all but later interbred with those brought over by the Spanish, although their evidence seems weak and I would expect we should have definite detection of such an occurrence in the genetic profiles of horses in North America within a decade or two if it really happened. Frankly I think we should have already found it [3].

BTW that earlier source also mentions tapirs, it seems that they do sometimes allow children to ride on their backs. But I'd note that from what I can tell, there's no mention in the Book of Mormon of people riding horses anyway. Instead while the horses were domesticated, the only indication of what they were used for is pulling chariots (of unknown purposes) and as food. Well even the chariot bit doesn't seem to be directly mentioned but the chariots and horses do seem to be associated with each other. (Incidentally is the elephant thing supposed to be before or after they moved to North America?)

Nil Einne (talk) 19:53, 20 December 2018 (UTC)

Thank You. It was for information in regards to that, but I am not a believer in the Book of Mormon as Scripture. Naraht (talk) 08:02, 22 December 2018 (UTC)

Is bad web typography a Sin? Andy Dingley (talk) 11:35, 19 December 2018 (UTC)

It's a multitude of Sin's. ←Baseball Bugs ^{What's up, Doc?} carrots→ 05:00, 20 December 2018 (UTC)

Yes, it is, how do I atone?Naraht (talk) 08:02, 22 December 2018 (UTC)

Where's the bad web typography? Nyttend (talk) 23:16, 23 December 2018 (UTC)

If it's not the "plural" Tapir's, it's too subtle for my feeble brain. ←Baseball Bugs ^{What's up, Doc?} carrots→ 00:26, 24 December 2018 (UTC)