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High school project - water bottle rocket

  1. Aug 15, 2007 #1
    Greetings ladies and gentlemen,

    I'm a highschooler, currently involved with a project regarding water-bottle rockets. My goal is to measure the force output of various water-air ratios of a water-rocket through force-sensors, and from that determine the maximum height reached by the rocket and I come here because I am in a bit of a predicament and would like to brainstorm with you to overcome my own insufficiencies.

    Initially I thought of using F = ma (or, in this case, a = F/m), but the problems started after that and I got strange numbers.

    In any case, what I ask of you is to aid me in finding a working equation for determining the (theoretical) maximum height reached by the water-bottle rocket, I'll include air resistance later on, but first I'd rather have this part sorted out (with gravity included).

    The Force sensors recorded the force output of the water-rockets during a timespan of roughly 0.25 seconds, and I have a graph of fluctuating force (fluctuations are probably due to the equipment used), a peak at the beginning and gradual decline, which is to be expected. I kept the pressure constant at 2.5 bar.

    I can't provide you with any specific numbers (at least not at this time), and my goal is to find something that can provide me with a distance(time) graph of the water-rocket, I'm at a loss as to how to approach this.

    Thank you for your time.

    [also, additional question, is the 'specific impulse' the impulse of the force graph divided by weight (mass*gravity)?]
  2. jcsd
  3. Aug 16, 2007 #2


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    Gold Member

    have you learned how to take derivatives yet?

    If you're using F = ma, and the rocket is spitting out water, then you have to consider that m is changing too. I'll throws some equations out there

    F = dp/dt <--- this is impulse

    p = mv <---- impulse is the time-derivative of this, momentum

    dp/dt = v*dm/dt + m*dv/dt <--- here's what happens when you take the derivative of momentum

    so F = v*dm/dt + ma

    where v is velocity, m is mass, a is acceleration, and t is time.
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