# Accelerometer vs linear acceleration during an impact

I am trying to understand the relation between the accelerometer and linear acceleration during impacts.

At work we have an accelerometer and gps onboard sensors installed in a few cars. The accelerometer records at 400 Hz and gps speed at 10 Hz, for a duration of 4 s. The accelerometer data are recorded in units of g. Recently we crashed some cars together (one parked, the other moving) and recorded the simultaneous outputs from the accelerometer and gps. For one of the crash tests the veocity at the point of impact is 1.58m/s and an estimated mass of 1500 kg.

Using the impact force equation, $$F_{avg} = 0.5 * mv^2 /s$$ (from https://www.engineeringtoolbox.com/impact-force-d_1780.html) and F = ma, I've estimated the acceleration at impact is $$\approx$$-2.5 $$ms^2$$ (assuming s= 0.5 m, which is the crumple zone). This is roughly the peak observed acceleration when the gps speed is converted to acceleration. See the image below (the y-axis is just magnitude). .

However, the magnitude recorded by the accelerometer i.e. $$\sqrt{(x^2 + y^2 + z^2)}$$ (which is measured in units of g and corrected for gravity) at that moment is 2.05 g (see image below).

During the impact there is only one force (ignoring gravity) acting on the moving vehicle, i.e. the impact force. So how do I explain the discrepency between the accelerometer and linear accelartion?

As far as I understand the accelerometer reading is basically force/mass. Once gravity is removed, shouldn't the value of the accelerometer readings be equivalent to the linear acceleration due to the impact?

I hope this isn't to convoluted.