High school project - water bottle rocket

[black fury]

Greetings ladies and gentlemen,

I'm a high schooler, 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)?]

 

[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.

 

[charng]

Hello there,

It's great to see that you are conducting a project on water bottle rockets. This is a very interesting and fun way to learn about physics and forces.

To determine the maximum height reached by the water bottle rocket, you can use the following equation:

h = (v^2 * sin^2θ)/2g

Where:
h = maximum height
v = initial velocity of the rocket
θ = launch angle
g = acceleration due to gravity (9.8 m/s^2)

To calculate the initial velocity, you can use the following equation:

v = √(2 * P * V)/m

Where:
P = pressure (in bar)
V = volume of water in the rocket
m = mass of the rocket (including water)

To get more accurate results, you can also take into account the air resistance by using the following equation:

F = 0.5 * ρ * v^2 * Cd * A

Where:
F = air resistance force
ρ = air density
v = velocity of the rocket
Cd = drag coefficient
A = cross-sectional area of the rocket

I would recommend conducting multiple trials with different water-air ratios and measuring the initial velocity and launch angle for each trial. This will help you get a better understanding of how these variables affect the maximum height reached by the rocket.

As for your additional question, specific impulse is defined as the thrust produced by a rocket engine per unit of propellant consumed. It is typically measured in seconds and is calculated by dividing the thrust by the propellant flow rate.

I hope this helps you with your project. Good luck!