2020 vertical jet tests
2020 vertical jet tests
Recently, for my PhD I did some tests on the height of jets of water, a glycerinwater mixture, and an isopropylalcoholwater mixture. Testing vertical jets is much simpler than measuring range. I have a height marker that I move down until it matches the height of the jet. See the attached photo. I can do these experiments much faster than a range experiment. The pressure can't go above about 20 psi because the tests need to be done indoors and the garage I'm using doesn't have a very high ceiling, but I'm sure I'll find a better facility in the future. If you're aware of any indoor places that can get a little wet (most water is caught by the pool) with a ceiling over 10 feet, let me know here.
The results were not entirely as expected. Some of the earlier tests showed the jets shooting higher than I thought was physically possible, so I made a few hypotheses about the cause, eventually narrowing it down to an effect that I was aware of but hadn't really fully internalized. Additional experiments confirmed my hypothesis. I was able to get one jet to shoot 50% higher than I thought was physically possible before, in fact. Not sure how to take advantage of this in water guns just yet, but it's something I'll be thinking about. I don't want to go into detail now. I'll post after I finish the paper on these experiments, to be published at the ILASSAmericas 2020 conference.
Anyway, all in all I am looking forward to 2020.
The results were not entirely as expected. Some of the earlier tests showed the jets shooting higher than I thought was physically possible, so I made a few hypotheses about the cause, eventually narrowing it down to an effect that I was aware of but hadn't really fully internalized. Additional experiments confirmed my hypothesis. I was able to get one jet to shoot 50% higher than I thought was physically possible before, in fact. Not sure how to take advantage of this in water guns just yet, but it's something I'll be thinking about. I don't want to go into detail now. I'll post after I finish the paper on these experiments, to be published at the ILASSAmericas 2020 conference.
Anyway, all in all I am looking forward to 2020.
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Re: 2020 vertical jet tests
That's really cool. I look forward to reading your results.
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Re: 2020 vertical jet tests
'atta boy, Ben! Actual experimentation along with a little photographic evidence is how you inspired me a few years back. I enjoy all the talk about theory and best practices; so, keep that coming, too. However, your physical creations are what made you famous. Making the time to build and experiment is easier said than done. Oftentimes, my biggest personal barrier is that I enjoy the "idea" of things even more than the physical incarnation of said things. I enjoyed designing my only homemade a lot more than I enjoyed making it.
Tim
Tim
Re: 2020 vertical jet tests
Thanks, M4 and Tim.
I'm hoping to build something new this summer. I have a new design approach now that hopefully will lead to substantial gains in performance. I had hoped to do some experiments to help test the design approach back in January but did not have the time. I'll hopefully finish them in May.
This year I'm also planning a big revamp of SSC. I know that I've said that for years, but my PhD has kept getting in the way. This revamp is going to completely redo the water gun theory sections. My hope is to have a technically accurate and accessible introduction to how to design and optimize water guns. Ideally a smart teenager can read the guides and build something impressive! There's a lot of misinformation on design out there, unfortunately, and even a fair bit on SSC. For example, I strongly doubt now that glycerin improved the range of Supercannon II. Most likely that was just random chance. The outdoor tests I've done during my PhD were very strongly affected by even slight breezes. Even the indoor tests I did with a jet larger than the one in the photo had issues. The range could dramatically change without changing any settings on the device! Given that, the experimental setup in the photo was designed to be highly repeatable. After eliminating wind this meant I had to use a high precision pressure regulator. If I redo the same test then most likely the height measurement will be within 1.5 inches. This finally allows me to figure out what works and what doesn't work.
I also have some ideas about how to take advantage of the new effect I mentioned in a practical case, but I want to keep this under wraps for now as it's patentable and I could see a variety of industries using it. Hopefully later this year I'll file the patent application and have a paper/post on how it works, assuming that my implementation actually works. I should be able to use the same experimental setup shown in the photo to test this.
I'm hoping to build something new this summer. I have a new design approach now that hopefully will lead to substantial gains in performance. I had hoped to do some experiments to help test the design approach back in January but did not have the time. I'll hopefully finish them in May.
This year I'm also planning a big revamp of SSC. I know that I've said that for years, but my PhD has kept getting in the way. This revamp is going to completely redo the water gun theory sections. My hope is to have a technically accurate and accessible introduction to how to design and optimize water guns. Ideally a smart teenager can read the guides and build something impressive! There's a lot of misinformation on design out there, unfortunately, and even a fair bit on SSC. For example, I strongly doubt now that glycerin improved the range of Supercannon II. Most likely that was just random chance. The outdoor tests I've done during my PhD were very strongly affected by even slight breezes. Even the indoor tests I did with a jet larger than the one in the photo had issues. The range could dramatically change without changing any settings on the device! Given that, the experimental setup in the photo was designed to be highly repeatable. After eliminating wind this meant I had to use a high precision pressure regulator. If I redo the same test then most likely the height measurement will be within 1.5 inches. This finally allows me to figure out what works and what doesn't work.
I also have some ideas about how to take advantage of the new effect I mentioned in a practical case, but I want to keep this under wraps for now as it's patentable and I could see a variety of industries using it. Hopefully later this year I'll file the patent application and have a paper/post on how it works, assuming that my implementation actually works. I should be able to use the same experimental setup shown in the photo to test this.
Re: 2020 vertical jet tests
I've decided to not publish the experiments I did in January at the upcoming spray conference and instead wait until I do more experiments in the future. I will need to find an indoor location that can get wet with a ceiling more than 9 feet tall, and then I can really start answering questions I've had for a long time.
Re: 2020 vertical jet tests
The posts above were made before the pandemic and seem rather distant now.
I'm planning some new outdoor experiments once it starts to warm up. The indoor vertical jet case is fairly limited by the ceiling height, and given that I don't have access to any building with a ceiling higher than 9 feet or so, I'll have to make do with outdoor tests, wind and all. This means that to get statistically significant results I'll have to make many more shots than I did in the indoor tests. How many more is what I plan to determine first.
Once the preliminary tests are done (assuming that the number of shots needed is reasonably low) then I'm going to start some new tests to figure out some things related to optimal nozzle diameter, an idea I've mentioned before but basically forgot about until relatively recently. My current theory gives a prediction of the optimal nozzle diameter to get a set range, so the tests will be designed to check the theory. If the theory is validated then we'll have a simple way to size nozzles in order to minimize flow rate for a given range. That'll increase how long your water will last.
I'm planning some new outdoor experiments once it starts to warm up. The indoor vertical jet case is fairly limited by the ceiling height, and given that I don't have access to any building with a ceiling higher than 9 feet or so, I'll have to make do with outdoor tests, wind and all. This means that to get statistically significant results I'll have to make many more shots than I did in the indoor tests. How many more is what I plan to determine first.
Once the preliminary tests are done (assuming that the number of shots needed is reasonably low) then I'm going to start some new tests to figure out some things related to optimal nozzle diameter, an idea I've mentioned before but basically forgot about until relatively recently. My current theory gives a prediction of the optimal nozzle diameter to get a set range, so the tests will be designed to check the theory. If the theory is validated then we'll have a simple way to size nozzles in order to minimize flow rate for a given range. That'll increase how long your water will last.
Re: 2020 vertical jet tests
Is this something you could put into spreadsheet formulas and share via Google Sheets? Or Share via Google Drive if maintained in Excel instead of Google Sheets?
Re: 2020 vertical jet tests
The theoretical optimal nozzle diameter equation is quite simple. You wouldn't really need a spreadsheet for it but could use one if you wanted to. Probably would be easiest to use a pencil or pen, paper, and a calculator.
Re: 2020 vertical jet tests
Ben, can you just post the formula then? Or perhaps this is already recorded somewhere in the forums. Can you point me to where this is recorded? Thank you.
Re: 2020 vertical jet tests
No, I haven't posted this before. I was keeping it under wraps for various reasons.
I'm posting this with the understanding that this is a work in progress, and new experiments might invalidate it or adjust the constant.
d_0 = (C_d* / R*_opt) * R
In the equation above, d_0 is the optimal nozzle diameter (the 0 refers to the nozzle exit; you could have other diameters marked differently), R is the desired range, C_d* (pronounced "CDstar") is the "reduced drag coefficient" in the language I used in my dissertation, and R*_opt (pronounced "Rstaropt") is a number determined through the theory.
Based on the theory, R*_opt = 5.9 in order to minimize the flow rate. There are different values for minimizing other objective functions like pump power if you're using a continuous pump. (All the hard part of the math is basically collapsed into this one number. It comes from the solution to a nonlinear algebraic equation derived in my theory.)
Based on some data I have, I estimate C_d* to be about 9.7e4 for water jets in air. (This number will vary appreciably if you change the fluid or have very bad breakup. I don't expect it to vary much for our case, however.)
So, basically, the experiment would determine whether the constant of proportionality C_d* / R*_opt predicted by the theory is right. I expect this sort of equation to be approximately correct even if the actual value of C_d* / R*_opt is off what the theory predicts.
To be clear: This will minimize the flow rate given a constant range. If instead you have a constant flow rate and want to maximize the range, the math doesn't work out so easily.
Also: The math indicates that the breakup length of the water jet and the firing angle (provided that it's not above 40 degrees or so) don't have practically significant effects on the value of R*_opt. While it might seem counterintuitive at first, keep in mind that I'm only claiming that the optimal nozzle diameter doesn't change much for the same range if you vary the firing angle. As you vary the firing angle, you'll have to also vary the pressure/flowrate in order to keep the range constant. If this doesn't make sense, let me know.
Edit: I've attached some handwritten notes for myself on the math part. Keep in mind that I don't derive everything here and that it's really only meant for my own use. I am going to write a longer paper after the experiments are done. I also attached a copy of a chapter of my dissertation with the basic trajectory theory, which doesn't have the optimal nozzle diameter part but is the starting point for the optimal nozzle diameter theory.
Edit 20210404: I updated the C_d* number. This update is significant as it means that the nozzle design could change the optimal nozzle diameter now.
Edit: 20210416: I updated the R*_opt number a bit as a bug in my code returned the wrong number before.
I'm posting this with the understanding that this is a work in progress, and new experiments might invalidate it or adjust the constant.
d_0 = (C_d* / R*_opt) * R
In the equation above, d_0 is the optimal nozzle diameter (the 0 refers to the nozzle exit; you could have other diameters marked differently), R is the desired range, C_d* (pronounced "CDstar") is the "reduced drag coefficient" in the language I used in my dissertation, and R*_opt (pronounced "Rstaropt") is a number determined through the theory.
Based on the theory, R*_opt = 5.9 in order to minimize the flow rate. There are different values for minimizing other objective functions like pump power if you're using a continuous pump. (All the hard part of the math is basically collapsed into this one number. It comes from the solution to a nonlinear algebraic equation derived in my theory.)
Based on some data I have, I estimate C_d* to be about 9.7e4 for water jets in air. (This number will vary appreciably if you change the fluid or have very bad breakup. I don't expect it to vary much for our case, however.)
So, basically, the experiment would determine whether the constant of proportionality C_d* / R*_opt predicted by the theory is right. I expect this sort of equation to be approximately correct even if the actual value of C_d* / R*_opt is off what the theory predicts.
To be clear: This will minimize the flow rate given a constant range. If instead you have a constant flow rate and want to maximize the range, the math doesn't work out so easily.
Also: The math indicates that the breakup length of the water jet and the firing angle (provided that it's not above 40 degrees or so) don't have practically significant effects on the value of R*_opt. While it might seem counterintuitive at first, keep in mind that I'm only claiming that the optimal nozzle diameter doesn't change much for the same range if you vary the firing angle. As you vary the firing angle, you'll have to also vary the pressure/flowrate in order to keep the range constant. If this doesn't make sense, let me know.
Edit: I've attached some handwritten notes for myself on the math part. Keep in mind that I don't derive everything here and that it's really only meant for my own use. I am going to write a longer paper after the experiments are done. I also attached a copy of a chapter of my dissertation with the basic trajectory theory, which doesn't have the optimal nozzle diameter part but is the starting point for the optimal nozzle diameter theory.
Edit 20210404: I updated the C_d* number. This update is significant as it means that the nozzle design could change the optimal nozzle diameter now.
Edit: 20210416: I updated the R*_opt number a bit as a bug in my code returned the wrong number before.
 Attachments

 trettel_water_2020.pdf
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 optimizationhandwrittennotes1.pdf
 (184.22 KiB) Downloaded 16 times
Re: 2020 vertical jet tests
I have changed the plan to instead do the tests indoors. I have found a source of precision microscale apertures that I could use to scale down the experiments so that they will fit within the space available, and also hopefully not require particularly high pressures. I ordered a 50 μm aperture that I'm going to try to fasten into a nozzle which can be attached to my experimental setup.
Stay tuned...
Edit: Alas, it appears that the micro apertures would not work due to bending. Off to the drawing board again... perhaps the tests will be outdoors after all...
Edit #2: Okay, looks like drilled nozzles might work. (These tests are complicated!)
Stay tuned...
Edit: Alas, it appears that the micro apertures would not work due to bending. Off to the drawing board again... perhaps the tests will be outdoors after all...
Edit #2: Okay, looks like drilled nozzles might work. (These tests are complicated!)
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