Experiment help

[Skifyre]

Hey everyone,
Being an IB student requires one to write a 4000 word essay on a subject of your preference. Mine is physics. So, I wisely decided to conduct an experiment based on model rocketry; namely potassium nitrate and sugar rockets, but dry compacted like Grant Thompson does it in the video linked below.



The thing I tried finding out is how varying the throat diameter of the rockets (by changing the size of the drilled hike through the end plus) affects the maximum force exerted by them on a force plate.

So I conducted the experiment with said force plate, connecting it to a laptop with logger pro, and I got some results, in terms of force time graphs. They deviated a lot from one another, even within trials of the same diameter, but overall a trend was still visible; as I had predicted, the smaller the diameter of the throat, the more the pressure, the more the flow rate and therefore the greater the force exerted on the force plate. I justified my hypothesis with past experience, where when I created ones with smaller holes, they tended to accelerate a lot faster, judging by eye. Using Newton's second law this would mean greater force. My question is, am I correct in my assumption? What is the relationship between the throat diameter and the force exerted by model rockets? Help would be very much appreciated

 

[Bat-mite]

https://www.grc.nasa.gov/www/k-12/rocket/nozzle.html

https://www.instructables.com/id/Build-a-High-Power-Rocket-Nozzle/

 

[Nytrunner]

Very nice project, It sounds like it's been instructional and rewarding already!

A simplification of the factors affecting thrust of a rocket nozzle can be expressed with the following equation;

 

[prfesser]

My question is, am I correct in my assumption? What is the relationship between the throat diameter and the force exerted by model rockets? Help would be very much appreciated

It gets a bit complicated.

An increase in nozzle throat size increases the area of that throat. Pressure = force/area, so if chamber pressure remained the same, the force or thrust must also increase, all other things being equal. But all other things aren't equal...

...because an increase in throat size allows gases to escape faster, so that the chamber pressure *decreases*. Generally the chamber pressure decreases faster than the increase in nozzle throat, so the bottom line is: increasing the nozzle throat will decrease the thrust and vice versa. However...

...because decreasing the nozzle throat size increases the chamber pressure, there is a limit to the effect. The limit is known as RSD --- rapid spontaneous disassembly.

Best -- Terry