"Tesla Turbine" Pumps

When used as a pump, the Tesla turbine is one of the simplest devices that exists. Its main component is simply a spinning disc – the disc is immersed in a fluid (like air, or water), the moving surface couples frictionally with the surface of the fluid, and makes the surface layer of fluid rotate with the disc. The fluid gets thrown outwards away from the rotation axis by centrifugal forces, and new fluid moves in to take its place. You then typically build a box around the container, with an inlet tube and outlet tube. The inlet feeds fresh fluid to the central axis of the disc, and the higher-pressure "centrifuged" fluid that collects around the disk edge is collected and allowed to escape via the outlet pipe.

You spin the disc (in either direction), and fluid jets through the device.

Now sure, we can do this sort of thing with a conventional bladed propeller, but those beasties have problems. The blades chop up the air or water, and create turbulence, which in turn encourages the assembly to vibrate, and small imperfections in the rotor construction can cause imbalances (and vibrations) that are different at different speeds. So bladed designs tend to be messy and noisy and juddery, and the blades' leading edges are prone to collecting buildups of dust or muck, or being damaged by collisions with any junk that happens to be caught in the fluid stream, which in turn messes up the aerodynamics of the blade and unbalances the assembly.

If you've ever built a PC to be especially quiet, you'll know that as the months pass, it gets noisier and noisier until you have to take the thing apart to clean the accumulated muck off the leading edges of the fanblades. In the case of ship's propellers these vibrations cause more extreme physical damage: sonoluminescence momentarily creates microscopic pockets of superheated steam that can etch pits into the bronze. All this work wastes energy and causes unwanted noise and vibration, and makes for additional engineering complications.

With the Tesla turbine fan, this violent interaction with the stream doesn't happen. For conventional propellers, surface friction wastes energy, with a Tesla disc, surface friction is the useful coupling mechanism that makes the thing work.

Nowadays, if you have a tropical fish tank or an outdoor pond with an ornamental fountain, the little cylindrical pump that circulates the water or drives the fountain is probably a small centrifugal Tesla turbine. Because it's bladeless, it means that any tiny creatures that get into the pump don't risk being chopped or hit by a big nasty blade, they might have a couple of bumps on the way through, but that's it. And weeds can't snag on the propeller blades and jam the pump, because there aren't any propeller blades to snag. So it's a comparatively creature-friendly and low-maintenance type of pump, if you want something to pump water for years without requiring any attention, or mashing up the microfauna.

Recently, they've also starting to consider using Tesla pumps for pumping blood. Blood includes all sorts of delicate gunge that doesn't like being disturbed too much, or it's liable to trigger a clotting reaction or an immune response. You don't want to smash up too many of the blood cells or start banging platelets together -- traditional blood pumps use clear tubing that's "massaged" by rotors to push the blood through, which makes for a nice simple high-visibility sealed unit, but you're still "squashing" some of the blood every time the pinched region travels along the tube.

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Perhaps the most surprising thing about Tesla pumps, apart from their simplicity, is how long it took us so many years to realise that these things were useful. A diagram of a conventional bladed fan gives you some indication of what a device does, but a simple smooth spinning disc in a box doesn't look as if it would do anything useful. Nikola Tesla got his turbine patent as late as 1913 claiming it as a novel device, Tesla pumps apparently started being generally manufactured in the 1970's, and a quick Google for references to radial bloodpump designs seems to only throw up results newer than 1990, most in the last five or ten years.

Sometimes we miss out on useful technologies because they require too much R&D or technical skill to get them to point where they actually work, but sometimes we also miss out on trivially-easy technologies that "work first time" because they're just too damned simple.

Rice and the Chessboard

In the story, an Emperor asks his mathematician to solve a difficult problem.

In payment, the mathematician asks for a chessboard with one grain of rice on the first square, two on the next, four on the one after that, eight on the next, and so on. The emperor agrees. Then the smart-alec mathematician points out that by the time we get to the sixty-fourth square, the number of grains of rice is astronomical. It's about 10^19, or 10,000,000,000,000,000,000. In binary, that's 1111,1111,1111,1111,1111,1111,1111,1111,1111,1111,1111,1111,1111,1111,1111,1111 , which is probably the largest number that you can express as a standard integer on a modern 64-bit processor running a specialist 64-bit version of Windows. One more grain of rice and you probably get an overflow error.

If each grain of rice weighs about 25 mg, then, when we double the last-square figure to get the total number of grains on the chessboard, I think we end up with something like 460 billion metric tonnes (minus one grain).

According to the story, the Emperor's response was to point out that this created a new problem that required the mathematician's involvement. As Emperor, he couldn't go back on his word, even if the mathematician allowed him to. An Imperial Decree couldn't be rescinded. On the other hand, that much rice didn't physically exist. The solution was to point out that if the mathematician didn't exist, the debt would cease to exist, too. So the Emperor signed the mathematicians' death warrant on the grounds that pulling this sort of trick on the Emperor counted as treason, and had him executed.

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Here's how to work out the result in your head, without using a calculator (or even pen and paper) :

Square 1 has one grain of rice. The next ten have 2, 4, 8, 16, 32, 64, 128, 256, 512 and 1024.

Every time that you advance another ten squares, you multiply the number on the square by 1024 (2^10), which is only slightly more than a thousand (1000, 10^3). As a first approximation, every ten-square move pretty much shifts the "decimal" version of the number three places to the left.

This means that when we move sixty squares, we're adding those three zeroes six times, giving us eighteen zeroes. That leaves just three more squares, so we go 2, 4, 8 … and write down a "guesstimate" figure of 8 ×10^18 for the number of grains on the last square.

This is an underestimate, but by how much? We treated 1024 as if it was 1000, so we have a missing factor of 1.024 that needs to be multiplied in six times to get to the proper answer. What's 1.024 raised to the sixth power? Eww. :(

Well, when we square "one-point-something", we get one, plus two times the "something", plus "the something-squared" ( (1+x)^2 = 1 + 2x + x^2 ).
If the something is very small, then something-squared is going to be extremely small, and hopefully so small that we can forget about it, and get away with just doubling the original small something.

So "1.024 times 1.024" gives 1.048, plus a little bit. Call it 1.049 .
Now we need "1.049 times 1.049 times 1.049", to get us up to that power of six.
A similar principle applies: cube something very close to one, and the tiny difference kinda triples (plus a little bit).
So we take 1.049, look at the part after the decimal point, 0.049, nudge it up to a nicer 0.05 , then triple that to give ~0.15 as the ratio that has to be multiplied into our original result to find the amount of undershoot correction.

"Eight" times the 0.1 is 0.8
"Eight" times the 0.05 should be half that, so 0.4 .
Adding them together, 0.8 + 0.4 is 1.2 (× 10^18).
That's our error .
Add that to the original guess of 8 (× 10^18), and we get our improved estimate, of ~9.2 ×10^18 .

… and if we check that against our calculator, which says that 2^63 = ~9.22 × 10^18, we were correct to two significant figures. Not bad for calculating something to the sixty-third power. Yayy Us!

Ten Things you can't do on an Apple iPad

Ten Things you can't do on an Apple iPad:

1. Watch broadcast TV
   The iPad has nowhere to plug in a DVB TV tuner dongle, and even if if it had, the iPad doesn't decode the MPEG2 video format used for standard-format DVB digital tv broadcasts. It's MPEG4-only. So you can't use it as a personal video recorder, and if you have an existing PVR, you won't be able to copy or stream the recorded MPEG2 files to the iPad. Unless your other machine's fast enough to convert to MPEG4 in real time, you'll have to transcode your files to MPEG4 first. Oh, and not all MPEG4 transcoder software produces files that play properly on the iPhone OS, so even if you do transcode, you still might not be able to watch the files.
   
   
2. Listen to the radio
   The iPhone chipset supposedly includes an onboard hardware FM radio, which the OS doesn't make available. In theory you can plug an FM receiver module into the iPhone/iPad docking connector, but in practice, it's cheaper to buy a separate radio (or a cheap MP3 player with a radio onboard). Apple don't make a separate snap-in radio, and third-party manufacturers ave been a bit reluctant to market one in case it becomes redundant overnight, if and when Apple decide to finally enable the internal device. Apple don't want you listening to FM until they can find a way to make money from it, and with FM, it's the radio station that gets the advertising revenue, not Apple.
   If you have a good internet connection, you can listen to a stack of radio stations online … as long as they don't use Flash as a delivery medium.
   Major radio stations are often also available via DVB ... but that's not an option with the iPad because of point (1).
   Many iPhone owners get their "fix" of radio by buying a speaker dock that includes an FM radio receiver, but fitting an iPad to one of these is a bit more difficult.
   
   
3. Watch DVDs
   Okay, so you don't expect the iPad to have a DVD drive, but netbooks at least have the option of plugging in a cheap USB-powered optical drive to play your DVD movies. Not the iPad. And even if it had a general-purpose USB port, standard DVD video is encoded in MPEG-2, so even if you find a way to get the DVD .vob files de-encrypted and onto the iPad, it won't play them. If a relative passes you a homebrew DVD with your family's home movies, you're back into Transcoding Hell. Transcoding on a mac probably produces "Apple-friendly" MP4 files, first time, every time ... on other platforms, don't count on it.
   
   
4. View or edit OpenOffice files
   Some organisations are trying to migrate away from using MSOffice files to more open formats, to avoid vendor lock-in. The main alternative suite is OpenOffice, which runs under Windows and Linux, can read and write all the main MS formats as well as its own "open" format, and also happens to be free. Apple don't seem to have a reader for "Ooo" files. They don't seem to much approve of open formats, and would rather you used Microsoft's apps and formats than open-source – they see open-source as a bigger threat than Microsoft.
   
   
5. Share photos.
   Jobs says that sharing photos is "a breeze" on the iPad. By "sharing", he presumably means, "tilting the screen so that other people can see it". If you want to actually give someone a copy of a holiday picture, you'll probably have to do it on a different computer, rather than the iPad. There's currently no "file export" media option. Budget picture frames usually have have picture sorting, import/export, and USB/SD card support functions, but the iPad doesn't, it's strictly a secondary device. Any serious file organisation is supposed to be done on a parent computer, so don't expect to be able to sort your piccy collection on the iPad while sitting comportably on your sofa.
   There is a USB/Cardreader accessory listed for the iPad ... the Camera Connection Kit ... but Apple currently only describe it as allowing you to import files to the iPad. To get the photos out of the iPad, you're supposed to synch to the iPad's "parent" PC or Mac, and then save them from that parent device. In which case, it'd be faster to upload the files directly to the parent machine without going via the iPad. Not exactly "breezy".
   
   
6. Use standard peripherals.
   As well as not having internal USB, the OS 3.x iPhone apparently doesn't support much in the way of bluetooth peripherals other than stereo headphones, and apparently doesn't even support Apple's own bluetooth keyboard. Apple's "official" external keyboard for the iPad is a dedicated iPad keyboard-and-stand, which only works in portrait mode. Heath and safety regulations say that you aren't supposed to use keyboards in an office environment unless they're adjustable, and this looks like it probably isn't. But Apple seem to have realised that this restriction sucked too much, and the iPad's OS 4.0 now seems to be more relaxed, and supports Apple's general-purpose bluetooth keyboard (which costs the same as the dedicated iPad keyboard).
   Unless the iPad's "OS 4.0" is a radical departure from 3.x, you probably also won't be able to zap contacts or notes or files into the iPad from general bluetooth peripherals, like you can with decade-old bluetooth-equipped Palm devices. I used to carry about a pocket-sized Targus folding keyboard and an OCR pen-scanner device with my old Palm organiser. Nothing like that seems to be available for the iPad.
   
   
7. Record stereo audio.
   Apple want you buying music, not recording it, so while the Apple dock connector has pins for stereo in, the official iPad Apple specifications don't commit to the pins doing anything. Maybe they're connected, maybe they're not. If they are, great. But its a brave third-party manufacturer who releases a product or connector for a function that an Apple device isn't guaranteed to have – even if your gadget works now, one OS revision later it might not (see also (2) external FM radio). As a playback-only media centre, the iPad again has the problem that onboard organisation is limited – you're supposed to do all your media organising on a separate parent computer, and iTunes usually won't recognise album art originating on a PC. Often it won't recognise PC-ripped tracks and let you download replacement artwork, either. Of course, if you're sick of watching CoverFlow "flipping" blank squares, you can always buy your albums over again as Apple downloads, or rip the CD's again using a mac ...
   
   
8. Use unapproved software.
   Apple reserve the right to decide what software you run on your machine, and there are certain sorts of applications they really don't want you to have. You normally aren't even allowed to load your own media files onto an iPhoneOS device unless the iTunes "sentry" approves – the iPx range won't emulate a basic thumb drive.
   You can often upload these "unapproved" apps and use your iPx gadget as a file caddy, by hacking past the Apple firmware's protection to expose the internal filesystem over USB – "jailbreaking" – but jailbreaking doesn't always work on all models, and it's too early to know what eventual proportion of iPads are likely to be jailbreakable.
   
   
9. Camera functions
   iPhone OS 4 is supposed to finally add proper support for camera functions, but the iPad doesn't actually have a camera. In theory it'd be easy to add support for a camera that snaps onto the dock connector, but AFAIK, no third-party manufacturer has yet produced one.
   It's probably easy in theory to support a swivellable webcam that can point forwards as a camera or backwards for video calls, but that'd need the device to be held upside down with the dock connector at the top. There's no technical problem with this … except that Apple's own OS 3.x applications refuse to work in upside-down mode. On OS4, the onboard applications are supposed to work in any orientation, but it's still a bit discouraging for manufacturers to know that if they launch a camera, it won't work well on v3.x devices. There's also the possibility that if Apple do decide to embrace the idea of an add-on camera, they won't make the function ready until they have a camera of their own to sell. You could buy rotatable snap-in cameras for some Palm organisers nearly ten years ago, so the iPad's still lagging behind in this respect.
   And there's some useful camera-aware apps: the Evernote notetaking apps let you snap images (memos, restaurant menus, street signs), save them with geotagging data, and apply OCR to add the text in the image to a searchable comments field. If you have a iPhone with Evernote, and someone shows you their contact details on their smartphone screen or a business card, you can snap a photo and get a text file. But without a camera, none of this cool stuff will currently work on the iPad. Evernote also has a nice voicenotes feature, but again, on the iPad ... no onboard mic.
   So, no Skype video calling.
   
   
10. SIM-swapping.
    The iPad isn't locked-in to a particular phone provider (hooray!), but the bad news is that if you've just bought a high-capacity service plan for your iPhone, and you want to transfer it to your iPad (which you expect to be using for all your serious mobile web-browsing from now on), you can't. The SIMs are physically different sizes. The iPhone uses a standard-sized SIM, the larger iPad uses a smaller mini-SIM. In theory, a mini-SIM with a holder can fit into a full-size SIM slot, but that chances are that if you're an existing iPhone owner, you won't have one of those. Apple enthusiasts have gotten used to Apple engineering-in incompatibilities with other manufacturers' products, but some have gotten a bit annoyed at what looks like a deliberate incompatibility with other Apple products.
    

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The iPad isn't really what Steve Jobs said it was. It's not a device that's designed to sit in some middle ground between netbooks and laptops, because those two types of device can do pretty much everything on the list.

The iPad's purpose is straightforward: it's designed to kill sales of the amazon Kindle, break amazon's stranglehold on ebook sales, and let Apple add ebook and magazine retailing to their existing music-and-movies portfolio. It's a conduit.
It has to be five hundred dollars in order to crush the Kindle DX, at $500 its facilities have to be limited in order to avoid undercutting Apple's own laptop range (which starts at a thousand dollars) and it has to be based on the iPod Touch (with an updated "iPhone OS" and a bigger screen) to give it an established sales channel, because that's the "other" OS that Apple have, because that preserves separation between the iPad and the more expensive OSX-based products, and because that makes it more difficult for people to dig out and redistribute downloaded paid-for content.

Those three things pretty much define it.