Maximizing a Water-Propelled Bottle Rocket Launch

[Heat5444]

I'm going to make a water propelled pop bottle rocket for a competition. The bottle holds 1.5 liters and we are going to fill some amount of it with water and pressurize it to 75 psi. When triggered, water will come out of the hole in the cap and propel the rocket. The rocket is perfectly aligned and will only go directly upwards.
What is the most effective water-air ratio and cap diameter for going as high as possible?
Rocket weight without water: 151 gr

 

[berkeman]

I'm going to make a water propelled pop bottle rocket for a competition. The bottle holds 1.5 liters and we are going to fill some amount of it with water and pressurize it to 75 psi. When triggered, water will come out of the hole in the cap and propel the rocket. The rocket is perfectly aligned and will only go directly upwards.
What is the most effective water-air ratio and cap diameter for going as high as possible?
Rocket weight without water: 151 gr

Welcome to the PF.

What reading have you done so far for this project? What do you think the tradeoffs are for the amount of water and air in the rocket?

Also, how did you pick 75PSI? Are you pretty sure the bottle will hold that pressure? What type of fitting will you use to fill the rocket with the compressed air? What kind of exit nozzle design are you considering?

 

[Heat5444]

I have gathered some materials like pop bottles and made a crude rocket that can go in a straight line.It weighs about 151 grams It's not that stable or aerodynamic but making it more stable and aerodynamic will not effect the mass of the rocket too much.

If it has too much water, it will be too massive to accelerate in the first place and it will lower the center of mass which will make it less stable; if it's too low, it will run out of water too fast. I don't think this is too important as log as it does not interfere with the center of mass.

75 psi is coming from contest rules so 1,5-liter pop bottles are probably fine handling it.

When we stick the rocket to the trigger mechanism, it's going to fill it with an electric pump from the exit nozzle.

I think exit nozzle is going to be the most important part because it determines the upwards force but we haven't decided on a particular design right now.

 

[Andy SV]

I have found that water rockets work very well when you start with an empty bottle and fill with pressurized water. The energy and reaction mass run out at the same time. The water will not expand so a nozzle should not either
What do the rules say about hot water ?

 

[berkeman]

I have found that water rockets work very well when you start with an empty bottle and fill with pressurized water. The energy and reaction mass run out at the same time. The water will not expand so a nozzle should not either
What do the rules say about hot water ?

What's pressurized water?

 

[Andy SV]

really? ... Go turn on the sink and look at it

 

[berkeman]

really? ... Go turn on the sink and look at it

Whelp, I'm going to take the calm high road here, and ask a couple of technical questions...

What is the volume of 1 liter of water at 1atm?

What is the volume of 1 liter of water at 1000atm?

How much does the volume of pressurized water at 1000atm expand as it transitions to 1atm?

 

[Andy SV]

Ok look ... just because water can not be compressed does not mean it can not be under pressure.
Something that in under pressure is pressurized pressure-ized
Experiencing pressure
http://www.dictionary.com/browse/-ize

 

[berkeman]

I have gathered some materials like pop bottles and made a crude rocket that can go in a straight line.It weighs about 151 grams It's not that stable or aerodynamic but making it more stable and aerodynamic will not effect the mass of the rocket too much.

If it has too much water, it will be too massive to accelerate in the first place and it will lower the center of mass which will make it less stable; if it's too low, it will run out of water too fast. I don't think this is too important as log as it does not interfere with the center of mass.

75 psi is coming from contest rules so 1,5-liter pop bottles are probably fine handling it.

When we stick the rocket to the trigger mechanism, it's going to fill it with an electric pump from the exit nozzle.

I think exit nozzle is going to be the most important part because it determines the upwards force but we haven't decided on a particular design right now.

So a simple Google Images search yields lots of great information about previous work on this type of project. Have you tried that?

https://images.search.yahoo.com/sea...ket+directions&fr2=piv-web&fr=yset_chr_syc_hp

 

[Averagesupernova]

Ok so concerning this pressurized water bit. Take several approaches to filling a water rocket with a volume of water and compressed air. The question is what percentage of the bottle volume should be water. If we dump in 2 percent volume of water and the rest air compressed to 75 PSI it should not be difficult to see that the water will be expelled long before the pressure drops very far. In other words, there is still enough energy in the bottle as there is plenty of compressed air left with no water left. Take the opposite approach and fill the bottle to 99 percent water and the remaining 1 percent with compressed air and we will run out of compressed air (energy) before we run out of water. The idea is to run out of both at about the same time. This is accomplished by simply hooking the empty bottle at atmospheric pressure to a water spigot with 75 PSI of pressure and let it fill. It is a starting point. Experiment from there with the ratio of total volume/water volume at a constant PSI of 75.

 

[berkeman]

After a PM conversation, it turns out that I misunderstood what @Andy SV was trying to say in his post. He meant the same thing that @Averagesupernova said in his later post. Sorry that I misunderstood your meaning, Andy.

I have found that water rockets work very well when you start with an empty bottle and fill with pressurized water. The energy and reaction mass run out at the same time. The water will not expand so a nozzle should not either
What do the rules say about hot water ?

The idea is to run out of both at about the same time. This is accomplished by simply hooking the empty bottle at atmospheric pressure to a water spigot with 75 PSI of pressure and let it fill. It is a starting point.

 

[Averagesupernova]

@berkeman I wanted to bust your chops on this lol. But I thought I would attempt to post something a bit more neutral and stay somewhat constructive.

 

[berkeman]

@berkeman I wanted to bust your chops on this lol. But I thought I would attempt to post something a bit more neutral and stay somewhat constructive.

Thanks. Yeah, I thought he was displacing all the air -- my misunderstanding.

 

[Heat5444]

Ok so concerning this pressurized water bit. Take several approaches to filling a water rocket with a volume of water and compressed air. The question is what percentage of the bottle volume should be water. If we dump in 2 percent volume of water and the rest air compressed to 75 PSI it should not be difficult to see that the water will be expelled long before the pressure drops very far. In other words, there is still enough energy in the bottle as there is plenty of compressed air left with no water left. Take the opposite approach and fill the bottle to 99 percent water and the remaining 1 percent with compressed air and we will run out of compressed air (energy) before we run out of water. The idea is to run out of both at about the same time. This is accomplished by simply hooking the empty bottle at atmospheric pressure to a water spigot with 75 PSI of pressure and let it fill. It is a starting point. Experiment from there with the ratio of total volume/water volume at a constant PSI of 75.

I think I can do few dozens of experiments and find the perfect ratio but I came to PF for math. I know there is a way to calculate the perfect ratio because we know all the variables involved like pressure, size and water loss rate etc. I just don't know how.
So, can someone show me how to calculate this without experiments?

 

[Heat5444]

I think I can do few dozens of experiments and find the perfect ratio but I came to PF for math. I know there is a way to calculate the perfect ratio because we know all the variables involved like pressure, size and water loss rate etc. I just don't know how.
So, can someone show me how to calculate this without experiments?

After posting this, I realized water loss rate is connected to thrust and thrust is connected to mass(which goes back to water-air ratio again), and speed of the water coming from the nozzle which is connected to the diameter of the nozzle(I think?).
Can there be a formula that we plug in the weight, volume, pressure and it gives us the diameter of the nozzle and water-air ratio for the most time that thrust is greater than gravity?

 

[Heat5444]

I have found that water rockets work very well when you start with an empty bottle and fill with pressurized water. The energy and reaction mass run out at the same time. The water will not expand so a nozzle should not either
What do the rules say about hot water?

Rules do not state anything about hot water.

 

[Averagesupernova]

I searched for a formula the first day you posted this and came up with nothing. The consensus is that there are too many variables to come up with a simple formula. Think of it this way: If it were reduced to a simple formula it would not be much of a contest because everyone would Taylor their rockets about the same.

 

[RonL]

If you want to get to the heart of the OP, there are books written by Robert Truax who designed Evel Knievel's rocket powered motorcycle used in his attempt to jump the Snake River. Also he made attempts at speed records at Bonneville.
https://en.wikipedia.org/wiki/Skycycle_X-2

http://newatlas.com/214-mph-in-25-sec-water-powered-record-stands-the-test-of-time/11622/

I could not copy and paste "Robert Truax" from the wiki page ?? anyway as I understand the key is in how much heat energy is held in water with relation to air volume as pressure declines, Robert published books that explained all this, I'm not sure how easy they are to find.

 

[Heat5444]

I searched for a formula the first day you posted this and came up with nothing. The consensus is that there are too many variables to come up with a simple formula. Think of it this way: If it were reduced to a simple formula it would not be much of a contest because everyone would Taylor their rockets about the same.

You are right, there is no formula for this. But can't we construct one? I mean there's not that many variables. I tried to make one but I don't know enough about the relationship between the speed of ejected water and nozzle size.
If we make the formula it would be great. Because the contest is not about the highest or best, it's about using science to make the rocket. So that kind of formula would guarantee country finals for me.

 

[Inventive]

Since this experiment involves fluid dynamics, I would like to suggest reading about fluid dynamics and Bernoulli equations to possibly generate the equations you are seeking.

 

[gr71cj5]

Help from NASA, they even have a simulator program for you: https://www.grc.nasa.gov/WWW/k-12/VirtualAero/BottleRocket/about.htm