Model rocket question (MY LAST RESORT) (and this is NOT a homework question)

[xxADTRxx]

Alright everybody, I REALLY need help on this and I only have a limited time. So I took a video of a model rocket and using the video analysis software, Tracker, I have a graph of position vs. time. Now I don't know calculus yet (only in pre-calc as of now), so the derivation of the graph won't work for me. How can I calculate the acceleration of this rocket, and then, based on that acceleration, use SUVAT equations to find the maximum height. I used an Estes C6-5 engine and the rocket has a mass of 0.0598kg (59.8g). I've also attached a picture of the graph.

 

[A.T.]

Alright everybody, I REALLY need help on this and I only have a limited time. So I took a video of a model rocket and using the video analysis software, Tracker, I have a graph of position vs. time. Now I don't know calculus yet (only in pre-calc as of now), so the derivation of the graph won't work for me. How can I calculate the acceleration of this rocket, and then, based on that acceleration, use SUVAT equations to find the maximum height. I used an Estes C6-5 engine and the rocket has a mass of 0.0598kg (59.8g). I've also attached a picture of the graph.

If x the position then 2a is the acceleration based on your fit.

 

[NascentOxygen]

That was an interesting way to analyse the flight. Though it's not exactly the graph I'd have expected to see. Why upside down?

It's a poor scale for humans, we can't see how well the points fit the curve, though the computer isn't handicapped by this.

Regardless, as A.T. says, acceleration according to the general equation s=½At² + ut
means your parameter a corresponds to ½A, so Acceleration = 2a

Interpreting your equation of best fit, at t=0 the rocket starts from a height of 1.8 and a speed upwards of 5/sec, and accelerates downwards at 117/sec². The flight is over in 1/3 sec?

You mention the weight of the rocket, but won't it be continuously losing weight during flight?

 

[potatoecannon]

Was there much horizontal movement in the launch? That will skew your (vertical-only based) calculations.

The SUVAT equation model is for constant acceleration, which you will not have in this case.
It would be an approximation, though it might still be sufficient for you.

You need a piece-wise partial differential equation to account for the changing mass during launch, and then constant mass during unpowered flight/freefall. (not first-year calculus either unfortunately).

There is also air drag to take into account, which usually requires a numerical method to solve.

Your best bet would likely be to set up an Excel spreadsheet to calculate the flight numerically (ie set up a spreadsheet with small timesteps [fraction of a second], and apply the equations of motion for each timestep). Have a column for your mass, height, velocity, acceleration, force..., and fill down the equations.
This is also handy for having all the values to graph out after however you need.

If you haven't, have a read on NASA's site - they have lots of good rocketry information:
http://exploration.grc.nasa.gov/education/rocket/rktpow.html

Good luck

 

[NascentOxygen]

If OP's plot is a close fit for a parabola, then that meets the criterion for constant accⁿ, surely? Though we are unable to judge how well the fit is due to graphing shortcomings.

 

[potatoecannon]

My thoughts are that:
1) Yes the graph is inverted (up is in direction of decreasing x).
2) The graph is from a video of only the launch, due to the 1/3 seconds & large # (units?) of acceleration.
3) The graph is a good fit for the points plotted (lower-left corner gives the calculated standard deviation).
4) There is not enough data. We do not know if the rocket left the camera view after this, or if there was more points afterward that were trimmed out. Therefore, we do not know for certain when the thrust kicks out & gravity takes over.

HOWEVER, if we assume:
a) The rocket motor dies at that point & gravity takes over,
b) The rocket flew perfectly vertically,
c) Air resistance will be negligable.

Then you can take the velocity at that the last point & gravity constant, feed it into the generic v=a*t (to calculate how long from motor cutout until apex of flight), then feed that time, the gravity constant, and the altitude & velocity @ motor cutout into y=1/2*a*t² + v_o*t + y_o to calculate the estimated final altitude.

 

[NascentOxygen]

3) The graph is a good fit for the points plotted (lower-left corner gives the calculated standard deviation).

Stats are all well and good, but an initial speed of 5m/sec into the ground is not exactly a good fit to reality.