What factors are influencing a woosh rocket?

Question

I asked this over at Physics, but no one seemed to know, so I'll try here:

If I fill a plastic bottle with a small amount of rubbing alcohol, shake it around and hold a match to the bottle neck, I'll get a flame wooshing out of the opening. This can easily be used to propel the bottle upwards, like a rocket. I tried it already, there are lots of youtube videos about this, and NASA has instructions for the experiment as well.

When trying to go for maximum speed or height of the rocket, there are a few factors influencing this experiment. Here are the ones that I can think of:

Some related to the bottle:

volume, shape, aerodynamics, weight, size of opening, possibly shape of the bottle (long and thin or short and fat) When the bottle neck is smaller it creates a stronger thrust.

Others related to the propellant:

How fast does it burn, how dense is it (especially compared to air), how heavily does it vaporize. If the vapor is denser then air it all floats out of the opening of my bottle before I can light it and I don't have as much fuel.

As you might be able to see, I don't know a lot about the propellants.

So here's my question:

What are the factors related to the propellant, that influence the launch height and speed of the woosh rocket.

What's the best propellant to choose for a woosh rocket, and why?

Answer 1

Your major concern is going to be how easy it is to ignite the fuel, because the fire, ideally, must be contained by the rocket to produce any useful thrust. If the fuel is just flowing out of the bottle and then ignites at a distance, the only thrust you are going to get is a slight push. Easy to ignite pretty much always mean more dangerous to handle, so a good propellant is mostly dependent on what risks you are willing to take, or what you are actually allowed to acquire in your area. That said, I can recommend gasoline, maybe with additives for it to burn more easily, as a powerful fuel. That is surprisingly close to the RP-1 used in real rockets. Ethanol is another example of good commonly available fuel. Using other oxidisers than air is making your design at least an order of magnitude more complex, and falls outside the scope of a woosh rocket.

Secondly, the shape of the nozzle is important, an ideal shape to aim for is a Lavall nozzle. This turns the random motion of the gas molecules into a relatively straight stream. As you correctly point out, a smaller stream is indeed giving you a more efficient use of the pressure, but this advantage is at some point less important than the reduced thrust. Merely just hoovering is not getting it anywhere.

To maximize your altitude per unit delta-v, the optimal speed is terminal velocity. Therefore, you want your rocket to accelerate quickly at first, in order to reach it and not loosing a lot of delta-v to gravity drag, but then slow down the acceleration to not exceed it and loose delta-v to air drag. In a model rocket, where you can not adjust the thrust much in flight, this is always a trade off. Giving the rocket a more aerodynamic shape rise the terminal velocity. Then the optimal thrust is going to be higher.

Chemical rockets are dangerous! I hope you know what you are actually doing.
If you want a more gentle start to hobby rocketry, advanced water rockets can provide a lot of fun challenges, without the risk of you loosing an eye.