Of course many have pushed this capability farther than I have, but Rhett Alain at his Dot Physics blog reviewed some of these apps and did a brief review of the Pasco Sparkvue app. Pasco is a company that makes various sensors that are typically used in Physics classes. The Sparkvue app is made to allow the use of their sensors with the iPhone, but includes access to the iPhone accelerometers. I purchased this app, and will likely also purchase some of the sensors as well.
I was in New York City (Queens, actually) for a conference held by the American Society for Nondestructive Testing, ASNT. By a freak accident (the flight crew is quite adamant that such things must not happen), on takeoff from Laguardia Airport, I happened to have left the iPhone on (in airplane mode) and Sparkvue running with the y axis very close to parallel to the longitudinal axis of the airplane, recording data. Shockingly, the same thing happened upon landing at John Wayne Airport in Orange County. I have GOT to be more careful about this.
But, having gathered the data anyway, I thought I'd spend a few minutes playing with it. The Sparkvue software enables adjustment of units ("g's" or meters/second^2) and sampling rate. I used meters/second and 20 Hz. I've inserted graphs of the speeds determined by numerically integrating the acceleration data below, I cut off the takeoff data at about 30.3 seconds because that's when the aircraft "rotated" (lifted the nose wheel off the runway, that is, began to leave the runway) and I didn't account for the fact that the downward acceleration of gravity now had a component along the y-axis of the iPhone, giving a falsely high reading of acceleration (the Equivalence Principle).
I intend to go back and attempt to correct this by estimating the so-called "deck angle" (the angle between the aircraft's longitudinal axis and horizontal) and backing it out of the numbers. This will enable me to estimate the aircraft's acceleration once airborne.
For landing, I did approximately the same thing, but I wanted to know the touchdown speed of the aircraft. Data was recorded until the aircraft was at its taxi speed and turning off the runway. I estimated this to be 10 knots and used the "goal seek" facility of Excel to determine what starting speed would give 10 knots when acceleration was deemed to have reached zero.
I have no idea how accurate the accelerometers are in an iPhone, but the numbers calculated are within the realm of plausibility. I estimated Vr (rotation speed in pilot speak) to be about 152 knots, and touchdown speed to be about 90 knots. A knot is a nautical mile (6080 feet) per hour or about 1.15 statute miles per hour. The graphs are below: