iOS understanding accelerometer data of iphone in free fall

Question

Why is it that when i drop my phone from about 4 feet onto a pillow, and plot the magnitude of the user acceleration i get peak values of 1.5g then 1g then 2.5g then 1g then 2.5g then 0g in a 1 second time frame in free fall with 10 samples. Ideally it should be accelerating at a constant rate downwards due to gravity minus the air resistance, so why does the acceleration go up and down while in free fall? What is causing this noise?

Answer 1

Einstein discovered something obvious (but hidden in plain sight). That is: what we experience as gravity is actually acceleration. When on the ground, and not moving, we are actually accelerating upward at 1G (one earth gravity). So the earth is actually expanding outward from the center.

Now a funny thing happens with matter (or a large mass like the Earth): space and time around the mass actually collapses at the exact same rate as the expansion. That's why clocks run faster when you move away from the center of the earth or off the Earth's surface. This has been verified in countless experiments and must be taken into consideration in order for GPS satellites to function correctly (for example).

Now a true accelerometer will always measure 1G on the ground. When you released it, the accelerometer goes into "free fall" which means it is now moving at a constant velocity (not accelerating)and thus reads: 0G. Instead of the accelerometer accelerating, the ground accelerates up to meet the falling object because the ground has accelerated upward during the one second of weightless free-fall experienced by the accelerometer. The instantaneous acceleration when striking the pillow is therefore much higher than 1G. Using the pillow as a spring to gently introduce the new instantaneous velocity of the earth to the momentarily weightless accelerometer was a good idea.

Instantaneous acceleration to any instrument is very destructive... and iPhones very expensive.

Answer 2

The accelerometer is measuring force with respect to the iPhone case. When sitting still on the table, gravity is forcing the accelerometer chip into the bottom of the iPhone case with a force of 1G. When in free fall, both the accelerometer chip and the iPhone case will undergo the same downward force due to gravity of 1G. But then since, in free fall, both the chip and the case will be accelerating downward at the identical rate, there is no force of the chip against the iPhone case, they'll both be falling together, so you get a reading very close to zero G.

So 1 G while you hold it still up in the air. 0 Gs in free fall. Many G's during the deepest contact part of the bounce. 0 Gs during the up in the air part of the bounce rebound. Many G's during the next contact with the pillow, etc. Back to 1 G when sitting still on the pillow.

This is a slight simplification, as the measurement is actually of one part of the chip against another, but the argument still works, but more on a nano-scale.

Answer 3

The most important concept to understand before reading my post is that acceleration relative to the ground (not accelerometer reading) due to gravity will always be 1.0g. However, this acceleration can be diminished/enhanced by external factors such as air resistance, stopping force, applied force, etc.

It is important to recognize the difference between actual acceleration and the accelerometer reading before noticing the variation between my answer and the others. I have answered your question in terms of acceleration because your graph does not seem to reflect raw accelerometer readings, but rather acceleration relative to the ground. To clarify:

• Accelerometer value = abs(acceleration WRT ground - 1g)

Therefore:

• When acceleration is 0g (object is at rest), the accelerometer reads 1g.
• When acceleration is 1g (object is in free fall), the accelerometer reads 0g.

Here is a probable situation for each acceleration WRT ground that you posted:

1.5g: When dropping the iPhone, you probably accidentally applied a small force of ~0.5g, causing an acceleration of 1.5g (1.0g due to gravity + 0.5g applied).

1.0g: Once it is in actual free fall, it reads ~1.0g (acceleration due to gravity). This is the acceleration it should hypothetically be reading the entire time it is in free fall, neglecting air resistance.

2.5g: When it hits the pillow, it has an upwards acceleration of ~2.5g because it is stopping after having gained speed from gravity.

0.0g: After it has stopped, it has 0.0g of acceleration because it isn't accelerating. Acceleration due to gravity has been neutralized by the normal forced exerted by pillow.

Answer 4

Normally, when the phone is sitting on the table, the acceleration is 1G. In a free-fall the acceleration is 0G. I've never played with the iPhone accelerometer to know whether the support logic "fakes" 0G when stationary and "fakes" 1G when falling, but if it does it would inevitably be imperfect.

What you should see (from an un-fudged accelerometer) in a free-fall is starting at 1G, decreasing rapidly to 0G while falling, increasing rapidly to several Gs when it hits the "ground", then returning to 1G after rebounding stops, perhaps after several cycles up and down.

Answer 5

Is the phone spinning? Air resistance will vary depending on the "profile" presented in the direction of acceleration (down), which means acceleration will vary. The 0g sample is either a spot where the location of the sensor in the phone happened to be rotating/spinning downwards at the same rate as gravity, and/or the phone hit terminal velocity (not likely on a 4' fall).