# Bottle Rocket Thrust for Elementary Numeracy?

1. Jan 2, 2012

### narrator

Hi,

I'm wanting to do a fun numeracy exercise for my students. I'm planning to have them construct bottle rockets, take measurements and then calculate/graph how high their rockets get using simple triangulation. From that, I was hoping to get them to calculate what the thrust was of their individual rockets. It could turn into a competition for 3 categories: best made, highest launch, and greatest thrust.

What I need, is a formula to work out what the thrust is, from the height achieved, nozzle diameter and perhaps an average weight (from start to finish of the flight). Can anyone suggest a useable formula? And if anyone wants to suggest of a better way of approaching this, I'd love to hear.

As a bit of background, I teach/train numeracy to upper level HS students in a program for "disconnected school refusers" (15 to 18yo's). The program has 3 levels - foundation, intermediate and senior, but the senior level would be like year 10 mathematics, with the most difficult level being algebra (There is no trig' prescribed). (For those at foundation level, many don't have any higher than year 6.. but that's a whole other discussion.) As we have all levels generally in the one class, I hope to tailor the handouts to each of the levels.

edit: As prompted by one of the answers so far, the bottle rocket type I was planning to use is like the one in this link.

Last edited: Jan 2, 2012
2. Jan 2, 2012

### Thundagere

I suppose you could use kinematics to calculate the initial velocity, and use conservation of momentum to find the force, then go from there.
Of course, the issue is finding the time that the force is applied over.

3. Jan 2, 2012

### Tea Jay

Could someone with only algebra and no trig do kinematics for this though?

Geometry to do the triangulation to get the height is straightforward enough, but, without approaching limits, etc, and no trig, getting an accurate thrust over time, etc, might be overreaching their tools.

It might be better to have them calculate thrust for the rocket by weighing it full of propellant and empty, timing the launch/flight time to apex...and triangulating the height of the apex.

That would give factors that would be translatable with their current tool set I think.

It would give an average at least...but if a team was to mark the times at the different heights...they could plot the flight trajectory...giving a time to distance plot which would give more data points, its speed for each segment, etc.

I'm not sure if bottle rocket means the kind full of pressurized water, or the Roman Candle types....full/empty weighing is of course easier for a water filled rocket.

Last edited: Jan 2, 2012
4. Jan 2, 2012

### narrator

Thanks for your reply, Tea Jay. The kind I was thinking of "helping" them to make is like the one in this link. There's a few other designs on the web.

5. Jan 2, 2012

### Tea Jay

OK, that's what I was thinking along the lines of as well.

Maybe add "Lightest" and/or "highest altitude per gram of weight" and/or "straightest flight" as a category?

"Best Made" sounds highly subjective/open ended. That makes it harder to work towards.

When working with kids, if trying to encourage them, I like to have more categories so more people can win something...ideally everyone gets a pat on the back at least, etc. ;)

The industry that this would correlate with stresses the power to weight ratios, precision, etc...so, a student can PLAN things with a vision of these concepts as driving forces, rather than how "cool it looks" and other things that a HS kid might be otherwise more focused on. The thickness of the paint, how much glue, using bracing bands to allow more psi in the bottle vs the weight added to overcome, the shape and diameter of the nozzles, etc...are challenges.

Last edited: Jan 2, 2012
6. Jan 2, 2012

### narrator

Good ideas. You're right of course. Cheers! :)

7. Jan 2, 2012