Question

Is it possible to determine the speed at which someone is shaking their iPhone? This would be the time they start moving to the ending point where they are now going back to the origin. Basically it is one swipe that I’d like to measure the speed of. This discussion comments on initial speed: http://discussions.apple.com/message.jspa?messageID=8297689#8297689. It seems that the important component of distance is lacking in the iPhone to get a good measure of speed.

Answer 1

Sure, it sounds like all you’d need to do would be to numerically integrate the acceleration twice to get the distance traveled. For instance, look at Calculate the position of an accelerating body after a certain time

Note that you’ll have to subtract gravity from the measured acceleration to get the kinetic acceleration, which is what you should integrate. As for how to do that, re: GoatRider’s comment: I might try storing the last measured acceleration whose magnitude was equal to gravity (I think that’s 1 in iPhone units?). Then for each acceleration measurement you make whose magnitude is greater than 1, subtract the last known acceleration of gravity – this will need to be a vector subtraction – and use that as the kinetic acceleration. Of course, this assumes that the user keeps the phone in the same orientation throughout the swipe, which I think would be approximately true.

Unfortunately, there’s no technique you can use to distinguish between gravitational acceleration and kinetic acceleration in general – that is, a determined user could always find a way to fool whatever algorithm you might come up with. (Trivia: that’s called the equivalence principle, and it’s the foundation of Einstein’s theory of general relativity)