# High school project - water bottle rocket

1. Aug 15, 2007

### black fury

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.

[also, additional question, is the 'specific impulse' the impulse of the force graph divided by weight (mass*gravity)?]

2. Aug 16, 2007

### Pythagorean

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.