# Find Vertical Displacement

#### Pasquale

Hi everyone, I'm a programmer, I'm doing a program for the simulation of some experimental data, the data is recorded by a device and that the register is the acceleration components along the (x, y, z), time (starting from 0, and aumentanto of each recording delta t), orientation (azimuth, roll, pitch),

my goal is to be able to extrapolate a graph (elevation, time), the data is recorded by a device inside a passenger compartment, with the y-axis pointing upwards. I read a lot about projectile motion, I think it's what I have to simulate substantially.
So for the calculation of the elevation, I would have thought to apply this formula:

y = Viy * t + 0.5 * aiy * t2

I thought to derive the speed through the Euler method, since dispose of acceleration and time data.

From this speed I should now extrapolate the vertical and horizontal speed, and if I understand correctly, the formula should be:
Viy =Vi * sin (Φ), the problem for me is to calculate precisely the angle Φ.

There is a way to calculate this angle?

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#### scottdave

Science Advisor
Homework Helper
Gold Member
Your formula to calculate position [ y = Viy * t + 0.5 * aiy * t² ] is correct only while the acceleration is constant.
It sounds like your device will be collecting acceleration data (which potentially is changing). You could approximate that the acceleration is roughly constant during a small time period Δt, and get an approximation to the solution.

I am not sure what the angle Φ is representing here, to be able to comment on it. Does your device have a datasheet which explains the measured values? That could be helpful.

#### FactChecker

Science Advisor
Gold Member
2018 Award
If you are only interested in elevation, then pitch is $\phi$

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