Posts Tagged ‘ipad’

Structural analysis and the iPad

April 22nd, 2010 at 3:02 pm

If you’re curious about the iPad, you probably read this iFixit article, documenting the disassembly of an iPad. I thought it was well done and quite fun to read, but I was brought up short by this bit of design interpretation in Step 29:

  • The glass seems quite thick (~1.18 mm), which is not a huge surprise considering the size of the iPad. Compare that to about 1.02 mm for the iPhone.
    • The iPad would require thicker glass due to the increased “lever arm” caused by pressing down at the center of the screen. This is analogous to the difficulty of bending a one inch section of a ruler compared to bending the entire twelve inch ruler.

What iFixit seems to be saying is that Apple increased the glass thickness from 1.02″ to 1.18″ to make up for iPad’s increased width and height. Specifically, they’re saying the thickness was determined by the flexibility of the glass under the load of a finger pressing on the center of the screen. This is certainly incorrect.

I’m not saying there isn’t a lot of truth in what iFixit wrote: a long ruler is more flexible than a short one, and making the glass thicker will decrease its flexibility. But their sense of scale—which is essential to good structural design—is way off.

The internet is loaded with articles about how programmers think, and it’s not hard to find articles about how electrical engineers think. This isn’t surprising; the computer and electronics crowd are disproportionately represented online because online is their thing. Less common are articles about how mechanical and structural engineers think, so I’m going to use this small mistake by iFixit to write one.

The short explanation

The short explanation for why iFixit was wrong is, unfortunately, not especially short, but here goes:

The flexibility of a flat plate is governed by three things:

  1. The modulus of elasticity. Also known as Young’s modulus in honor of the English scientist Thomas Young and typically given the symbol E, the modulus of elasticity is a property of the material of which the plate is made. The flexibility of a plate is inversely proportional to E—doubling E cuts the flexibility in half.
  2. The width. The flexibility of a plate is proportional to the square of its width—doubling the width quadruples the flexibility.
  3. The thickness. The flexibility of a plate is inversely proportional to the cube of its thickness—doubling the thickness decreases the flexibility to one-eighth of its previous value.

To compare the relative flexibilities of the iPhone and iPad glass, we compare these three properties.

We’ll start by assuming that the glass used in the two devices is of the same type and has the same modulus of elasticity. This may not be exactly true, but is probably pretty close,1 so the modulus will not factor into the iPad/iPhone difference.

The width of an iPad is about 3 times that of an iPhone, which gives it a 9-fold increase in flexibility. If Apple wanted to match the flexibility of the iPhone, it would have to increase the thickness of the iPad’s glass by a factor of

\sqrt[3]{9} = 2.1

This is much more than the change from 1.02 to 1.18 mm that iFixit measured. So Apple was not trying to match the flexibility of the iPhones’ glass. In fact, the iPad’s glass is nearly six times more flexible than the iPhone’s:

\frac{3^2}{(\frac{1.18}{1.02})^3} = 5.8

What is the governing criterion for the thickness of the glass? I don’t know, but it’s easy to think of a couple of possibilities:

If I had to bet, I’d put my money on impact resistance as the controlling factor for glass thickness.

The longer explanation

The following is mostly for my own amusement, so if you’re thinking about bailing out, don’t worry. You won’t offend me.

Remember when I said the flexibility of a plate was governed by three things? I lied, but just a bit. Here, from Timoshenko’s2 Theory of Plates and Shells, is the equation for the maximum deflection of a simply-supported rectangular plate with a concentrated load at its center:

It looks nasty, but it’s not really that complicated. Let’s start with a description of all the variables:

The flexibility is, by definition, the deflection generated by a given load, so if we want to compare the flexibility of the iPad glass to the iPhone glass, we need to compare their w_{max} values for the same P.

Timo simplifies the formula down to just

w_{max} = \alpha \frac{P a^2}{D}

where4

\alpha = \frac{1}{2 \pi^3} \sum_{m = 1, 3, 5, \ldots}^\infty \frac{1}{m^3}\left( \tanh \alpha_m - \frac{\alpha_m}{\cosh^2 \alpha_m}\right)

Substituting in the definition of \alpha_m, we get

\alpha = \frac{1}{2 \pi^3} \sum_{m = 1, 3, 5, \ldots}^\infty \frac{1}{m^3}\left( \tanh \frac{m \pi b}{2 a} - \frac{\frac{m \pi b}{2 a}}{\cosh^2 \frac{m \pi b}{2 a}}\right)

and we see that \alpha is a function of the aspect ratio, b/a, only.

Back to the simplified equation, substituting in the definition of D and rearranging a bit, we get

w_{max} = \frac{12 (1- \nu^2)}{E}\;\alpha\; \frac{P\:a^2}{t^3}

From this formula, you can see that the effects of the modulus of elasticity, the width, and the thickness are just as I described them in the short explanation. You can also see the two things I left out.

First is Poisson’s ratio, \nu. This is a material constant, and because we’re assuming the iPad and iPhone have the same type of glass, it should be the same for both devices and not factor into the flexibility difference at all.

(In fact, Poisson’s ratio doesn’t vary much, even across widely disparate materials; values between 0.2 and 0.4 are the most common. Plug those values into (1 - \nu^2) and you’ll see why changes in Poisson’s ratio are seldom worth worrying about, even if you’re comparing different materials.)

Second is the aspect ratio, b/a, which, as we’ve seen, determines the value of \alpha. The aspect ratios of the two devices are different, about 1.3 for the iPad and about 1.9 for the iPhone. That difference does have an effect, but it’s pretty small.

Timo helpfully gives us a table from which we can look up values of \alpha for various aspect ratios. This sort of table was really helpful to working engineers back in 1940, when the book was first published, and was still helpful in 1959 when the second edition, the edition I have, was published. Nowadays we have a computer to calculate the infinite series. I wrote this little Octave script to calculate \alpha for any aspect ratio.

1:  #!/usr/bin/env octave -q
2:  
3:  # Solution for maximum deflection of centrally-loaded simply-supported plate.
4:  # See Timo Plates and Shells, article 34, pp. 141-143.
5:  
6:  r = eval(argv(){1})           # aspect ratio from command line
7:  m = linspace(1, 39, 20);      # odd indices only
8:  beta = pi*r*m/2;              # what Timo calls alpha_m
9:  alpha = sum((tanh(beta) - beta./cosh(beta).^2)./m.^3)/(2*pi^3)

For the iPhone, \alpha = 0.0164; for the iPad, \alpha = 0.0143. That was a lot of messing around for piddly 10-15% effect.

Now you can see why I lied to you in the simple explanation. The scale of the difference in flexibility is governed almost entirely by the modulus, the width, and the thickness. And because we’re comparing glass to glass, it all comes down to the width and the thickness.

  1. The strength of glass can be varied over a wide range by thermal and chemical processing, but the modulus tends to be more consistent from one glass to the next. ↩

  2. Stephen Timoshenko was one of the giants of 20th century mechanics. Not only was his own research influential, but his many books constitute an encyclopedia of analytical techniques in engineering mechanics. The computer science analog to Timo’s work would be Knuth’s Art of Computer Programming series. ↩

  3. Yet another material constant, this one named after the French scientist Siméon Poisson. ↩

  4. In the excerpted scan, Timo doesn’t include the restriction that the m takes only odd values, but it’s implicit in his earlier derivation of the formula. ↩

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Post #1233 | 1 Comment

Scripting and the iPad

April 6th, 2010 at 9:20 pm

I’m happy to see that Alex Payne has retracted some of the ill-considered things he said about the iPad back in January. While it would be nice to think that his change of heart came from listening to his elders, the real reasons he no longer thinks of the iPad as the harbinger of a computer dystopia are

  1. he’s a smart guy and willing to question his own views; and
  2. he now has an iPad and likes it.

In fact, this latest post of his has one really good criticism of the iPad:

Apple should lift restrictions on running interpreted code on its mobile devices. Let people run Basic, Python, and Ruby interpreters on iPad and iPhone; we could make amazing tutorial applications for these and other programming languages. Let them run emulators for obsolete devices so intellectual property for them that has passed into the public domain can live on. Given that users can do much of this by virtue of Safari containing a JavaScript interpreter, the restriction seems arbitrary and backwards.

Of course, I say this is a good criticism because it’s my criticism. The apparent inability to script the iPad is the main reason I won’t be getting one—at least for a while.

What do I mean by apparent inability? Well, certainly you can’t use Perl, Python, or Ruby (or Basic or AppleScript or any other language best not to think of on a full stomach), but the iPad is sort of scriptable. As I said in January, the presence of Numbers gives the iPad an interpreter—assuming that IF, AND, and OR are among its 250 predefined mathematical functions.

More important is the JavaScript interpreter. We’ve certainly learned over the past few years how “real” web apps can be. Of course, you need space on a server to deliver web apps, and your iPad needs an internet connection to access them.

Or does it? One of the iPad’s most interesting features is the ability it gives apps to share certain types of files with other apps. Here’s Andy Ihnatko’s description of how it works:

The iPad OS still denies onboard apps the ability to access each others files and data. But there’s a mechanism that lets these apps tell the OS “Here are a list of filetypes that I know how to handle” and also to allow the user to easily steer a file to an app that can edit or view it.

If your boss emails you a Word document and you tap the document icon, Mail will present an “Open In …” button. Tap it to bring up a list of Word-compatible apps on yor iPad. Select the app you want, and the app will launch and import the document.

Any app can implement this and add its known filetypes to the service. A comic book reader can handle .CBR and CBZ files; a photo editor might offer to handle .PSDs … etc.

The feature delivers a lot of solutions in the ongoing problem of moving docs on and off the device. If you use a cloud storage service like Box.net, for example, the Box.net iPad app can present you with a list of all of the desktop documents you’ve saved in the cloud, and allow you to import and edit them into any appropriate iPad app.

One would think, then, that Safari would tell the OS that it knows how to handle HTML files,1 and you could, therefore, run certain web apps—those that are self-contained and don’t require communication with a server—locally. No one has confirmed this, despite my plea on Twitter.

As I learned quite a while ago, you can run self-contained web apps on the iPhone, but not in Safari. You have to use one of the many transfer-and-view applications, like Olive Toast’s Files. Unfortunately, in my limited experience, these apps don’t provide a user experience as good as Safari’s.

So, iPad users: can you answer my Twitter question. Can you transfer HTML files to your iPad and open them in Safari? Because if you can, that opens up a much broader realm for scripting.

Update 4/7/10
In the comments, reader jih mentions data: URLs as a possible workaround if there’s no way to open local HTML files in Safari. These data: URLs work on the iPhone, so I see no reason they wouldn’t work on the iPad. Here’s a simple explanation and example.

  1. And possibly CSS and JavaScript files, too, although it can only handle them in the context of an HTML files. In practice, it’s the ability to handle HTML that counts, because the CSS and JavaScript can always be embedded. ↩

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Post #1214 | 3 Comments

Misty water colored memories

January 30th, 2010 at 4:12 pm

Among the many disadvantages of middle age are: the loss of suppleness in both your mind and body; the simultaneous loss of hair where you want it and growth where you don’t; and the recognition that people in Cialis commercials are meant to represent you (albeit much better looking). One of the few advantages is the pleasure you get from complaining about how the world is going to hell in a handbasket and how much better things were in your day.1 I’m sorry to say that an unfortunate side effect of this week’s iPad announcement is that pre-middle-agers are now horning in on nostalgia, a pastime that should be restricted to their elders.

For example, both Mark Pilgrim (37) and Alex Payne (26!) have written little essays on how the iPad is going to destroy the idyllic world in which they grew up and blossomed, replacing it with a harsh dystopia in which turtlenecked priests in Cupertino decide who may learn to program and who may not. The essays have struck a chord with other wet-behind-the-ears programmers who are worried that the rise of appliance computers will push out the kind of open, tinkerable computers they grew up with.

Maybe they’re worried because they’re so young they’ve never seen change before. I have no doubt that iPad-like devices will change the way computing is done, and I have no doubt that this will make the practice of programming very different 10-15 years from now. But it doesn’t worry me, because I’m old enough to have seen changes at least as drastic.

When I took my first programming class— Well, let’s stop right there. When I started programming, almost everyone learned to program by taking a college-level class. This was the late 70s, and although the personal computer revolution was under way, PCs were by no means common.

The first order of business in my introductory programming course was learning how to use a keypunch machine. That’s how we made the stacks of cards fed into the computer. We almost never saw the computer itself. Computer operators—talk about a priesthood!—would come out of the machine room, pick up the stacks of cards, and do God knows what to them. Some time later (often hours later), the cards would be returned to us along with a printout of the results, which were usually a set of compiler errors.

A year or two later, when I first sat down to work at an interactive terminal, it was an absolute revelation. I could correct my typing errors by backspacing!

The march of computing history has been toward greater accessibility. More computers, more people using computers, and more people able to program their computers. I don’t see this changing.

The nature of programming will definitely change, just as it has in the past. My first computer programs were compiled, and hardcore programmers wrote in assembly language. Nowadays it’s more common for people write in interpreted (or perhaps semi-compiled) languages. No one seriously considers this to be a sign of the death or programming.

I was particularly struck by one part of Mark Pilgrim’s essay. He talks about starting in BASIC on an Apple ][e and then moving on to a Mac, where he played with MacsBug and ResEdit. The thing is, in 1984 much of what is now being said about the iPad was being said about the Mac. You couldn’t write programs on the first Macs, development was done on a Lisa. It wasn’t until HyperCard that the Mac had a simple, free, Apple-supported development environment that kids could play around with.

I’m not predicting a native development environment for the iPad, but I wouldn’t be surprised to see Apple loosen its restrictions as time goes on. And in the meantime, the iPad will come with a JavaScript interpreter, which clever people will be able to use for some elementary scripting. And Apple will be violating the letter of its own “no interpreters” policy when it ships Numbers. I’m not saying spreadsheets are the best way to learn programming, but then again, neither was BASIC.

So buck up, Gen Xers and Gen Yers and whatever other Gens there are! Things won’t be as bad as you fear.

And get off my lawn.

  1. This does not, of course, prevent you from also lecturing the young on how tough the world used to be and how easy they have it. Memory loss allows a certain inconsistency. ↩

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Post #1164 | 2 Comments

The iPad checklist

January 28th, 2010 at 12:03 pm

Early on in yesterday’s presentation, Steve Jobs listed seven tasks the new iPad had to be better at, when compared to either a smartphone or a notebook computer, to justify its existence.

Every task on the list had its own little section of the presentation, and at the end Jobs basically said “We think we’ve done it.” Generally, I’d agree, but not with every item on the list.

Browsing

I give this one to the iPad. For what most people do all the time, and what everyone does most of the time (thank you, Mr. Lincoln), the iPad will be better than a notebook computer because of its direct manipulation of the items on the screen and its greater portability. There will, no doubt, be sites that won’t fit nicely into its 1024×768 screen, but those are few and far between. (I can say this with some authority. My notebook computer is an old iBook G4 with that same screen size; horizontal scrolling is very rarely needed, and when it is it’s mainly because I have my Dock on the side, eating up 50 pixels or so.)

That the iPad will be better for browsing than a smartphone should be obvious. The larger screen more than makes up for the reduced portability.

Email

For many people, the iPad will beat the smartphone and the notebook, but I’m not one of those people. Nor, I suspect, are most of the people who’ll be writing reviews of the iPad, so don’t be surprised to see the iPad’s email client get low marks. If your emails tend to have a lot of writing in them or tend to have multiple attachments, the notebook will always be a better email machine. The prospect of using a real external keyboard with the iPad doesn’t change this; adding a keyboard nullifies the iPad’s portability advantage.

There are, however, people for whom email is mostly a matter of reading and categorizing, with writing that is seldom more than a paragraph or so. For these people the iPad’s combination of portability and size will make it superior, although they may be scared off by reviews of the virtual keyboard written by people who type for a living.

Smartphones are probably still the best email machine for the constant traveler, but I wouldn’t be surprised to find the iPad beating out the smartphone for many of these folks. I often see these people eating lunch at WiFi hotspots, and if the iPad can take over for their Filofax/DayRunner it will also turn into their email machine.

Photos

To me, this isn’t even close. Smartphone screens are way too small and keyboards make notebooks too clunky. Unless its software is extremely badly written, the iPad will be almost perfect for viewing photos.

A sidenote: I like the idea, mentioned in the presentation, of having the iPad act as a digital picture frame when its not otherwise in use. But because the dock connector is on one of the narrow sides, the picture frame will always be in portrait mode, which

Maybe a third party will come up with a better way to use the iPad as a digital picture frame.

Video

Let’s start by stating the obvious: watching video on the iPad will not be better than watching it on a big screen TV or in a movie theater (if you can find a theater with a reasonably quiet audience). But the iPad isn’t supposed to be better than a TV or a theater, it’s supposed to be better than a smartphone or a notebook computer. And I think it is, because it has a better balance of size and portability.

The 4:3 aspect ratio has some people puzzled, and some are scoffing at the letterboxing of wide screen movies. But let’s say Apple was limited to 1024 pixels in the long direction, perhaps by the economic constraint of delivering a $500 product, perhaps by the geometric constraint of making a handheld device that’s less than 10″ in the long direction. Either way, your movie isn’t going to be more than 1024 pixels wide. Should Apple make a skinny device with fewer pixels in the short direction—1024×576 would give a 16:9 aspect ratio—or should it fatten up the device to be more usable for other applications and letterbox the movies? I think the right answer is obvious, and that’s what Apple did.

Update 1/29/10
Take a look at the specs for the 16:9 JooJoo (née CrunchPad).1 Yes, it’s 1366×768 pixels, but it’s also nearly 13″ long, more than three inches longer than the iPad and nearly a pound heavier (2.4 lb vs 1.5 lb for the WiFi-only models). That’s a big reduction in portability, a reduction that Apple clearly didn’t want to make.

Music

As with photos, I think this one isn’t even close, except this time I’d say the clear winner is the smartphone, and there’s no way a larger device could be better. A music player needs only enough screen space to help you navigate your collection; everything beyond that is a waste. The 250 million iPods Apple has sold so far is proof of that. Are you going to walk around town or work out at the gym listening to music on your iPad? Of course not.

Games

I’m not the right person to judge this one, because I’ve never really gotten into playing electronic games. I was in college before video games took off, and I think the mania has to take hold of you when you’re in your early teens at the latest.

I’m not even sure a winner can be declared in this category, because games can be designed—and are designed—specifically for the platform on which they run. For games that fit perfectly on the iPhone screen, the extra real estate of the iPad will mean nothing. The iPad, in turn, will certainly be able to play games that wouldn’t fit on an iPhone. I tend to think the direct manipulation available on touchscreen devices makes them superior to notebooks, but there may be games where the clicking of a few tactile buttons is essential to the experience.

eBooks

The iPad wins this category in a rout. It is the same size and shape as a book (in fact, its height, width, and weight are a very close match to a particular book on my shelf: the first edition of Matt Neuburg’s AppleScript: The Definitive Guide from O’Reilly), which will make it very comfortable to read. I use Stanza on my iPhone, and I like having a few books in my pocket at all times, but there’s no way it can compare to the iPad.

Final score

For me, the iPad would be the winner in 5 of the 7 categories. For a lot of other people, it would win in 6 of the 7. Given that there was really no chance of it being a better music player (what was Apple thinking when they added that category?) this is a damned good score.

Does this mean I’ll be running out to get an iPad in a few months? No. The 7 items on Apple’s list aren’t everything I’m looking for. But they did make a pretty good case.

  1. No, I don’t expect the risible JooJoo to actually be released. My point is that even its vaporous specs don’t look so good when compared to the iPad. ↩

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Post #1162 | 2 Comments