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Challenge

Weigh yourself using your smartphone and no additional hardware

Solving for mass based on jump acceleration & time airborne

Mac

Imagine the phone is held tightly in a two-handed grip pressed into sternum just above heart and the user jumps vertically as high as they can, starting from a normal standing position.

What would a plot (force over time) of the phone’s accelerometers look like throughout a jump?

1. Lowering into a partial crouch, chest leaning forward a bit. Feet still on the ground

2. Rapid extension of leg muscles from crouch to stretching upright posture. Upward motion. Feet still on ground.

3. Moment of transition from “standing” to “airborne”. Toes leave contact with ground

3.5. maximum vertical height

4. landing: feet hit ground, downward deceleration absorbed into crouching position similar to #1

5. body returns to starting position (relaxed standing)

The slope of the curve of the plotted accelerometer data gives us instantaneous acceleration.

see figure of accel vs time for human jump here: imgur.com/a/gnRUe [1]

I would expect the slopes to be opposite but similar (close to same absolute value) for phase 2 & phase 4 (jumping & landing), with the jumping phase taking longer than the landing phase. Landing phase has steeper slope.

Hypothesis: the duration of the jumping phase (#2) depends on the mass, height, and muscle strength of the jumper:

– The duration is faster (shorter) for a 50kg person than a 100kg person of the same height & strength.
– The duration is faster for a short person vs a taller one of the same mass and strength
– the duration is faster for a stronger person vs a weaker one of the same height and mass.

The user gives us their height. We want to estimate their mass. But we need to correct for variations in “strength”. Maybe we can do so by looking at how the acceleration plot changes over a series of 10 repeated jumps.

Mass & height will remain constant over 10 jumps in a row. A consistent increase in time spent jumping (phase 2) and decrease spent airborne (phase 3) over 10 jumps could be an indirect measure of individual strength.

If we had the accelerometer data of 100 people of a wide range of known masses & heights jumping 10 times in a row, we could find a linear or polynomial “best-fit” regression equation relating mass ‘Ma’, height ‘H’, and “coefficient of muscle force ‘S’, maybe something like the following (where ‘a’ and ‘b’ are coefficients to solve)?

eq.1)    S ≈ average change in duration of phase_2 vs phase_3 over 10 jumps (idea is to “normalize” by comparing jump acceleration vs time airborne)

eq.2)    avg_duration_phase_2 ≈ (a*Ma + b*H)*S

eq.3)    Ma ≈ ((avg_duration_phase_2 / S) – b*H)/a

the idea being that a larger person will take longer to accelerate for the same air “hang time”.

Next steps would be to 1) find / collect data and check if a simple linear equation like above fits, 2) derive more realistic / accurate system of equations from mechanics & solve w/ linear algebra.

Further reading:

Volume from camera

Marko

You could take a photo or video of yourself. The software would extrapolate volume and object weight by cross referencing image data bases.

Weight Model DB

kenneth

Simply uses a Visual Analytical Comparison Database. This database would be propagated using a finely-tuned comparative 3D model/mass/weight system which would then output a database of comparative visual/weight images. The algorithm would compare a subject’s submitted image (and height) with a databased image to precisely “guess the weight”. Kind of an image-to-3D weight analyzer.

Angle of Mattress Incline

Krafesen

Okay, so what if you were to stand in the centre of your mattress each day and place your smartphone so it was resting against your foot. The incline your smartphone is on can be measured with the compass / gyro and will determine your mass. The problem is that sheets and blankets will drastically influence it, so ideally there would be no coverings on the mattress.

Jump to Weigh

MyheroPrank

I’m not completely sure if this is possible, but I believe there would be a way to measure weight by jumping alone. If the device data inputs could measure the peak height of the jump and then the peak velocity reached on the descent, then a calculation should be able to determine the mass of the object. The tricky part is getting a consistent trajectory, not necessarily the height as that will be measured, but any movement on the x / z axis will likely influence the figures.

Office Chair Decelleration

jg87

So after exploring the jumping approach, it appears that there won’t be enough variation in velocity / acceleration to accurately differentiate weights. So how could we observe a similar effect but with increased differentiation? Enter, the humble office chair. The time required to go from the highest setting to the lowest setting of a gas lift office chair will vary depending on the weight applied. Obviously calibration will be required for each chair, however once beyond that, a few early attempts show very consitent outcomes.

I see the user opening the smartphone application and selecting ‘weigh yourself’. The user will then have 5 seconds to place the device in a fixed position relative to the chair – on the chair itself, or firmly in a pocket. Once the time is up, the device will beep, signalling that the user can now release the chair. Using the required data sensors (I’m not entirely sure which ones), the phone will commence timing once the chair starts to move and complete timing once the chair has stopped. Using the data from the initial calibration each time should be able to be converted into a weight measurement.

The biggest hurdles to overcome will be accurately commencing and completing the timer.

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