Calculating the Acceleration of an Airplane using a Smartphone


As a web developer who loves physics, I’m always looking for ways to use what I know about web browser technology to do neat physics experiments. A few months ago I was sitting in an airport ready to return home. I had been thinking about the device orientation detection capability of smartphones for a while, and was wondering what I could do with it. With airplanes on the mind, I decided to use the small amount of time I had to write a quick webapp to record the orientation of my phone during takeoff. Since I could write this purely in javascript, I could safely put my phone into “Airplane Mode” and continue to monitor its orientation. Javascript’s “localStorage” could also save the data I accumulated. With the orientation data, I could then get a rough estimate of the acceleration profile of the airplane during takeoff (or any other time, really).

The webapp I wrote in about 30 minutes is not worth putting up here. It basically involved a start and stop button for the data. But it did the trick. Don’t worry, soon I’ll write one that will be easy for everyone to load onto their phones and tinker around with acceleration measurements.

All I needed to do was place my phone on the armrest of the seat and click start. Here’s a graph of the data:

Not too shabby! It’s pretty noisy, but you can see the takeoff pretty clearly.

So, what are we measuring?

We’re measuring the perceived tilt angle of the phone. Normally, if you tilted your phone forwards and backwards, the phone would measure the direction of gravitational force relative to the screen. So if you placed your phone on a level table, it would measure gravity directly into the screen. This would give you a tilt angle of zero (in front-back, and left-right axes). When you tilt your phone, the phone will detect gravity at some angle, and be able to give you the measure of that angle. You can play around with that here, if your phone or laptop supports it.

Airplane Takeoff

But what happens during takeoff? Well, gravity is no longer the only force the phone detects. Now it’s detecting the combination of gravity and the thrust of the airplane. As the airplane is rolling along the runway, this thrust will be horizontal (perpendicular to gravity). If you add up these effects, the result is that the phone interprets this as a tilt. The amount of tilt measured can be easily calculated:

If we want to, we can divide the top and bottom of that equation by the mass of the airplane. Then we can put everything in terms of accelerations:

We have the angle, and the gravitational acceleration value (9.8 m/s/s), so we can get the acceleration of the airplane. The data I’ve got here is pretty noisy, so let’s just do a rough estimation. At around 140s, the angle fluctuates between 16 and 24 degrees. So let’s ballpark it at 20 degrees.

… which gives us around 3.5 m/s/s.

How does this compare to the “actual” acceleration? Well, it’s hard to say what the real acceleration of the airplane was. This will depend on many factors; air resistance, number of passengers, … But still, we can estimate this from the airplane specs. For an A320, the thrust can vary between 111 - 120 kN, its operating empty weight is 42600 kg, and its maximum takeoff weight is around 77110 kg. So the maximum acceleration is maximum thrust divided by the weight while the airplane is empty:

which is about 2.8 m/s/s. The minimum acceleration is minimum thrust divided by maximum takeoff weight, which gives you 1.4 m/s/s.

So, we’re a bit off, but remember, this is quite a rough estimate from the data. Aside from the noisiness of the data, one major caveat is that we didn’t take into account the angle of the phone when the airplane wasn’t moving (it wasn’t quite at zero). But it still gives you an idea of the fun physics you can do with your phone.

Stay tuned for more smartphone physics fun.

Your JavaScript is Slow - Common and not-so Common Optimizations


Optimization considerations for any language can lead down a long and complex road. For JavaScript, things get even more complex because the same code can be run on a huge number of permutations of browser, version, OS, and machine (think mobile devices too).

Still, I was surprised how little information I found on the subject. A quick google search turns up a few great resources. To mention a few: An overview of Nicholas Zakas’s tips, Google’s “Make the Web Faster” article, and An older article by Jeff Greenberg.

These all are great resources, but they lack a few of the more surprising offenders in terms of bottlenecks. So I decided to post some information that I’ve discovered during my long hours on JSPerf. If you haven’t heard of JSPerf before, check it out.

What is it, you ask?

jsPerf aims to provide an easy way to create and share test cases, comparing the performance of different JavaScript snippets by running benchmarks. But even if you don’t add tests yourself, you can still use it as a JavaScript performance knowledge base.

In other words, you don’t need to wait around for someone to benchmark a test for you. You can do it yourself! (aside: At a later date, I’ll try to write some guidelines for intelligently creating test cases.) For now, I’m going to go over some of the common and not-so common bottlenecks to look for while trying to optimize your code.

Most Importantly…

Firstly, Don’t optimize on the fly. The big reason for this is that your implementation may change as you develop your code… so you might end up burning hours on unnecessary optimizations for algorithms that you end up scrapping by the end. You should also go hunting for your largest bottlenecks first. You don’t want to spend hours optimizing in the wrong place. Use a profiler (like chrome dev tools) to find these bottlenecks.

Secondly, Don’t sacrifice readability for speed! That’s what minifiers are there for. You might come across optimization tips like “don’t use long variable names”, or “avoid creating unnecessary variables”… but I say forget that! You should be minifying your code. Always. Period. That’s the most important optimization tip you can take away from this.

Consider the following…

// sure... this...
var NumberOfFingers = 4 + 1;

// is not as fast as this...
var n = 5;

… the first option is more readable. Similarly,

// this is faster...
function toRad( deg ){
	return deg*Math.Pi/180;
//... than...
function toRad( degrees ){
	var radiansPerDegrees = Math.Pi/180;
    return degrees * radiansPerDegrees;

the second option here will make people much less frustrated when they try to understand your program. And when you put that second option through a minifier like Closure Compiler, look what it becomes:

function toRad(a){return a*(Math.Pi/180)};

So there.

Finally, Don’t trust everything you hear! Javascript engines are changing all the time, and some optimization tips that applied to certain browsers in 2009 may not apply now. And those that apply now, may not apply in a year. It’s best to test these things yourself.

Unsurprising (common) Optimizations


Ok. So. Let’s start with some easy ones. What’s wrong with the following for loop?

for (var i = 0; i < catPictures.length; i++)
	catPictures[ i ].comment = 'lolz';

You guessed it. We aren’t caching the length of the catPictures array. It’s being recalculated every single cycle of the loop. If you don’t believe me, try it on jsperf.

As for which type of looping method is the fastest… results may vary. Here’s a suite of looping tests on jsperf for your pleasure. Generally it seems that the standard cached length for loop is empirically faster than other loops (including while loops and especially built-in .each methods).

Object lookups

Here’s another one that might be a walk in the park.

for (var i = 0, l = ids.length; i < l; i++)
    myFramework.utils.addText( ids[ i ], 'text' );

The problem with this is we can speed this up by caching the addText method. Every time we use a . to dig deeper into our objects we loose time. Here’s some better code:

var addText = myFramework.utils.addText;
for (var i = 0, l = ids.length; i < l; i++)
    addText( ids[ i ], 'text' );

Note: this is especially useful when you’re using document.getElementById and similar methods.

Local Scope > Global Scope

Finally, here’s one that I found surprising at first, but it makes total sense. Consider the following code.

var Fn1 = 0;
var Fn2 = 1;

function nextFibonacci() {
    var ret = Fn1 + Fn2;
    Fn1 = Fn2;
    Fn2 = ret;
    return ret;

We can actually improve on this by cacheing the values of the variables that are outside the scope of that function. This speeds things up because the interpreter has to look for variable names up the scope chain until it finds what it’s looking for. If the variables are declared within the same scope… it’s faster. Here’s the optimized version:

var Fn1 = 0;
var Fn2 = 1;

function nextFibonacci() {
    var f1 = Fn1,
        f2 = Fn2,
        f3 = f1 + f2;

    Fn1 = f2;
    Fn2 = f3;
    return f3;

If you don’t believe me, check out the JSPerf for this optimization.

Avoiding anything new

The new keyword certainly has its uses and circumstances. But if you’re creating a bunch of objects, especially in a loop, you should try to avoid creating them with new. Instead of var thing = new myObj(), try just using javascript object literals: var thing = { ... }. It will vastly speed up your code. Here’s the JSPerf for new vs object litterals.

Surprising (uncommon) Optimizations

Function declaration vs. Function expression

In my countless hours of tinkering around on JSPerf, I’ve discovered a lot of kooky thinks to watch out for in terms of performance. One of the most basic is how you declare your functions! To create a function you can either do it as a function declaration or a function expression. Here’s the difference:

// function declaration
function foo(){
	// stuff...

// function expression
var foo = function(){
	// stuff...

// self-executing function expressions
	// stuff...
// or...
	// stuff...

You can visit JavaScript Weblog for some of the finer points on the differences between function declarations and function expressions.

So turns out, that function declarations are much faster to create, as seen from this JSPerf. So if you’re creating a helper function, you might as well declare it and reap some of the speed benefits.

Use of the arguments object

You know that ever-so-useful arguments object you can use inside a function to access the arguments? Yeah. Don’t use it unless you have to. There’s a significant performance hit. Even if you just put the word “arguments” in your function… even in code that will never run… you will see a performance hit. Here are the specifics of arguments object performance effects.

Clever ways around slow native methods

Have you ever wondered if array = array.concat(otherarray) is really the fastest way to concatenate an array? Well, it may not be depending on your situation. Specifically, if you don’t mind modifying the original array, you can certainly get a vast improvement in speed by doing the following:

var arr1 = [1,2,3];
var arr2 = [4,5,6];
var push = Array.prototype.push;

push.apply(arr1, arr2); // arr1 == [1,2,3,4,5,6]

And here’s the JSPerf of this push-concat method. And even if you don’t want to modify the original array, you can perform an array copy of the original (with array.slice(0)) and use that one and it will still be faster!

Why does this work? It’s because the .push() method can push several elements passed as arguments (eg: .push(1,2,3,4)). So when you use it as the second parameter in an apply call, it’s like you’re doing: arr1.push(arr2[0], arr2[1], ...).

Another nice workaround that is even more dependant on the situation involves the situation of array element removal. If you want to remove an object from an array, an easy way to do it is:

myArray.splice( index, 1 );

But if you don’t care about the order then a faster method would be:

if ( index === (myArray.length - 1) )
	myArray[index] = myArray.pop();

It’s a very particular circumstance, but still, a great concept to keep in mind. Here’s the JSPerf.

Putting it all together

If you want to see how this all fits together, I’ve created a quick implementation of a PubSub library to show what kind of effect these optimizations can have. The actual usefulness of this pubsub implementation is questionable, I made it more for instructional purposes. Here’s a of the pubsub implementations. What I did was create two versions of it; an unoptimized version, and an optimized version (using the previously mentioned suggestions). I then created some test cases to test for instantiation time and execution time. Here is a JSPerf of the side-by-side performance results. You’ll probably find that the graph won’t help you, you should check the tabular version of the results and look at how the unoptimized/optimized versions of each operation compare.

Happy coding.