# Modeling Acceleration at Impact

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## Main Question or Discussion Point

Hi all,

Background:
I'm working on a project where I am dropping an arduino with an accelerometer from ~100 ft in the air to measure it's acceleration during free fall and at impact. I need to compare my collected data with predicted models.

I have the model for free fall (just 9.8m/s^2), but I'm struggling to find a model equation for acceleration at impact. Perhaps I am overthinking this...

Attempt:
The best equation I have found is "The Rate of Deceleration Formula" which is:

So this will give me a constant.

I need to plot this model with my actual data that I collect. However, the units of deceleration are in m/s^2, and if I multiply this value by time, I will get a velocity.

Question:
Is the model for acceleration at impact a constant (whatever value the rate of deceleration turns out to be) and I am just intuitively wrong here? If it is not, do you know of a good model to use?

If it is a constant, that would mean that I'd intuitively expect the acceleration to nearly reach the model's rate of deceleration value before dramatically decreasing to 0 (as it settles on the ground).

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mfb
Mentor
Is this really what the accelerometer will show you?

Acceleration at impact will have some non-trivial shape that depends on how exactly the setup lands, which parts breaks how (if something breaks), which parts flex how much and so on. You can calculate the velocity change during the impact, you can make a rough estimate how large the acceleration will be, but predicting the acceleration shape during the impact accurately will be quite challenging.

predicting the acceleration shape during the impact accurately will be quite challenging.
Agreed, which surprised me when my professor called for it. However, given the scope of the class and timeframe given I am not expected to model the impact with such a high degree of accuracy. I'm focused on finding a general model, something that I can compare data to and explain how it is different from my actual data.

A.T.
I'm focused on finding a general model,
You already have a simple general model. The problem is determining the deceleration distance that you need in that model.

sophiecentaur
Gold Member
Is this really what the accelerometer will show you?
Perhaps it's assumed that 'before and during' measurements will be made.

Nidum
Gold Member
You could do a rough model if you assume that the Arduino survives the impact and remains largely intact apart from some crushing damage at the point of impact and if you restrict your model to one very simple case .

Measure or calculate the crushing characteristics of the board and determine the mass distribution .

Then analyse the case where the board comes down with long axis near vertical , hits the ground and rolls over .

You would need to decide on the nature of the ground . A hard unyielding surface would make calculations easiest .

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You could do a rough model if you assume that the Arduino survives the impact and remains largely intact apart from some crushing damage at the point of impact and if you restrict your model to one very simple case .
Yes, I have designed a housing that is set to crush a certain distance. It is not a perfect design but I will be basing my distance value off that.

I'm just mainly concerned that the deceleration model I found is actually correct for this application. Right now, this would be a linear model that intersects the y-axis at the maximum acceleration value and decreases very quickly (nearly straight down) to zero m/s^2.

You know that the contact force begins at zero, and ends either at the weight of the box or at zero, depending on whether you allow it to eventually land or not. You might model a zero-to-zero impact force with a simple triangle or as a single arch of a sine wave.

mfb
Mentor
I'm just mainly concerned that the deceleration model I found is actually correct for this application. Right now, this would be a linear model that intersects the y-axis at the maximum acceleration value and decreases very quickly (nearly straight down) to zero m/s^2.
That does not correspond to what you have shown in post 1.

If nothing breaks during the impact, in general I would expect the absolute value of the acceleration to increase over time, as things tend to get harder when compressed (compare it to a spring).