Air-powered CPS without a regulator

[Ben]

Edit 01-08: None of my ideas here would work because it's pressure that matters, no force. The pressure drops.

A recent thought of mine was of the possibility of air-powered CPS without a regulator. This seems impossible at first, but I have figured out a way it can theoretically be done. It is unlikely that we'll see this in homemade water guns due to how it must be done, but I'll email Big Bee about it. If he sees something in this, it might start a new type of water guns.

All that matters is the shape of the pressure chamber. As we know, pressure decreases as the water is removed because the air can expand. However, the pressure alone does not determine the total force on the water. The surface area of what the pressure is pushing on also matters. Therefore, you can keep a constant force on the water if you compensate for the pressure drop by increasing the total surface area of the water. That means that a pyramid-shaped or curved pyramid-like shaped pressure chamber will reduce the effects of air pressure drop off because as the pressure drops, the surface area increases.

Could someone be kind enough to make a drawing or animation of what I am considering?

I am thinking that with a correctly shaped chamber, most if not all of the effects of pressure drop can be counteracted with the changing surface area. A slightly changed design to allow flow to be eased out would be necessary for more optimal distance, but the force still would be fairly constant until the final part of the shot.

[Silence]

Sounds good, but clearly, this is probably something that can only be perfectly engineered using the resources of a corporation such as Buzz Bee Toys or a capable engineer (I know SSC does have some active engineer members...). I'm thinking of a sort of check valve system that has the air pressure push back on the spring when it is high, restricting the airflow, but the spring opens up a bit and allows more air through when the pressure decreases. I'm having a bit of trouble with the finer details, but I should be able to work it out; in the meantime, however, anybody may feel free to contribute and pick up where I've left off for now.

Note that my method will simply increase the air flow, rather than increasing the surface area of the water/plunger; it might work to have CPS capabilities, but the more physics-educated people (I haven't taken the class yet) would probably know. Also, note that if you design something based off of Ben's method, you can't just have a cone-shaped plunger (at least, I don't think you can); it's the vector of the face in the stream's direction that you need, and elongating a cone won't change that vector. I'll also go a bit more into something along the lines of what Ben suggested, maybe incorporating an iris-style plunger that opens up as the pressure decreases.

I'm wondering whether this will actually be cheaper/more practical/less complicated than the use of a regulator; all of my ideas seem a bit fancy and too far out of reach for a mass-produced soaker. It might just be a better idea to produce regulators simply designed for such a purpose; for example, it would be hard to produce lots of LRT-based soakers, but the actual CPS bladders were practical. Just a tip, though...I can't imagine CAP in the hands of everybody in a battlefield, unless it isn't as powerful as dekard's or SuperCAP.

[Ben]

I just did the math on this, and it's not feasible at all. To get the surface area necessary, the volume has to increase far too much, decreasing pressure even more. I suppose that tinkering with the pressure chamber might create nearly a desired effect, but mathematically it won't do much.

[Silence]

Yes, it's probably impractical, but I feel like researching it a bit more. Do you have any idea how air pressure regulators actually work (I checked HowStuffWorks, Wikipedia, etc.)? Maybe we can use a partially similar method to have a regulator system, but without the actual and complete mechanisms.

[Ben]

From what I know, a normal air pressure regulator has something similar to a ball valve that opens or closes depending on the input pressure and the settings. But, that is only how I believe they operate. HowStuffWorks, Wikipedia, and Google are no help here. I think it might be a good idea to try out one of our ideas and see how well they regulate.

[joannaardway]

Howstuffworks is fine:

http://entertainment.howstuffworks.com/scuba1.htm

It's a way down the page - but it can be found.

And ID of the chamber doesn't affect the output. Spherical AP PCs are similar in performance to cylindrical AP PCs. It's dependant on the ID of constriction points: The chamber to main tubing - tubing to nozzle.

[Ben]

I've actually been looking into the effect of PC shape on the force of the chamber. Cylindrical chambers' force reduces similarly to a spherical chambers'. In fact, the force of most shapes decrease inversely proportional to the remaining water.

However, I was able to make a shape that had nearly constant force. The problem was, the force was nearly always low. So yes, you can create constant force by changing the shape of an air chamber, but you won't get a good amount of force. Exponential functions have this quality.

For similar volumes, it appears that cylindrical chambers have a slight edge over other shapes in overall force, not how well it is kept constant.

If anyone is wondering what sort of calculations I did, to explain in simpler terms:

1) I made a function to revolve around the x-axis. This function represented the PC shape I desired.
2) Using volumes of revolution (intermediate Calculus), I found the volume of the revolved function. That multiplied by 14.7, atmospheric pressure, found the total amount of air in the chamber.
3) Using the volume of revolution function again but as a function varying by the top height of the water, I solved Pb*Vb=Pa*Va for Pa. b means before and a means after.
4) Using the equation Fp=P*A, I substituted in the pressure equation and area equation (the function for the top height of the water squared times pi). Fp stands for force of pressure. The resulting function I denoted as F(h).

This process gave me the function of the force on the water of the chamber based upon the . I am unsure whether or not the units I use are correct, but I figure that it does not matter when I am directly comparing one graph to another in the same incorrect units. I also am not sure if my process was completely correct, but Drenchenator did get the same result as I did when asked to do the same task, so I believe my process is correct.

I did make a generalized function for the force of the chamber based upon a function defining it's walls, but I'm afraid that it's too advanced for most of my readers. Even still, I'll likely feature this whole process in an article on SSC eventually. This actually has proven to be fairly interesting, despite it's tediousness.

Also, the ID of the pressure chamber does affect the output. The force of pressure is pressure multiplied by the surface area the pressure is pushing on. The surface area is a function of the radius which is half the diameter. Chamber ID affects force, which affects output.

[Silence]

@ Ben: You said that you found a shape that has somewhat constant, albeit low, force--are you sure it isn't just an exponential function, but divided by a large scalar? If so, the change in force will be relatively small, but that isn't always a good thing. You could divide the force at all points by the initial force and do the same for the other PC shapes, and those results might be more important.

[Ben]

I should have said that the shape that produces relatively constant force decreases rapidly from h=0 to become relatively constant from h=3 to h=10. However, I figure that someone could make a pressure chamber that starts off extremely powerful and reduces to a normal level of power, at least at the moment. Here is a scan of my calculations which should scale in most browsers. The final F(h) is at the bottom. Those will Calculus knowledge should be able to follow my work.

I am thinking that the flat top I made is at fault for not making the force even more constant. I'll do the calculations later to see. If it turns out that I do make a chamber that has relatively constant moderate force, that would be useful in more than just water guns.

[joannaardway]

I'm 90+% sure that it is Pressure, not force making the difference.

Consistent force means very little. I can perform full calculations without ever needing to know chamber shape.

Pressure is equal at all points in the fluid, so "pressure * ID of main piping (or nozzle)" is irrespective of the chamber ID.

I could never return a sheet of notes like that. My calculations spread across excel spreadsheets with no diagrams.

I have the PCgH calculations back now. I'll go and discuss them in that topic.

[Silence]

@ Ben: Ah, I finally see what you're saying! The shape difference just wouldn't form in my mind earlier, but this appears excellent! I believe you are correct in thinking that the top should continue to taper off to a point, and this certainly looks good now. While my physics skills are weak, you might need the PC walls to curve in a convex way. With a convex curve, the area will increase in a linear fashion. However, I'm not sure of the exact details, so I might be wrong.

Once again, I'm assuming this is only for commercial soakers such as those of Buzz Bee Toys. There's no way a DIYer could practically build a PC in that shape that can withstand high (and inconstant) pressure.

Now I can see why cylindrical and circular PCs would both have inconsistent force. Ideally, a rectangular one would have perfect dropoff (with the force directly related to the pressure), and in fact, the top parts of circular and cylindrical PCs might even have some non-regulated CAP qualities like the one you drew. I still believe that convex curves would work better than concave ones, but I am unsure of whether it will end up being like a semicircle when both sides meet at the top. A semicircular shape would be very easy to do with large PVC.

[Ben]

@joanna: ID and therefore force does matter. Pressurize an identical volume longer 1" tube to the same pressure as a far shorter 3 or 4" tube and shoot water out of one of them. You should easily see the difference in the force on the water - the larger ID tube will shoot further and more powerfully. That is why SuperCAP's output was ridiculously high for only 60 PSI gauge pressure.

@SilentGuy: Initially I tried the concave shape believing the same thing (I tried a function of x^2). However, I found that shaped PC performs similarly to a normal cylindrical one. The convex shape was my solution because the end curves out, giving the air less room for a longer period (if you understand what I am saying). Right now, the convex shape appears to be the only one that does anything different.

I tested the pointed convex shape and found an unusual force curve. Because the area approaches zero at the top of the chamber, so does the force. At about h=0.5, the force approaches a maximum. After that, it decreases somewhat rapidly to remain more constant but still decreasing afterwards.

I also tested a cone and found that it has a force function that is very similar to that of a cylinder.

I'll be testing a few other shapes and possibly make a small table displaying a force curve for selected shapes.

[Silence]

Maybe we have conflicting terminology...the picture displayed in the scanned calculations sheet that you linked shows what I'd call a concave shape. I was referring to a convex shape as one that's basically a circle (the cross-section is a circle, at least) with a plane cut through it to prevent the extreme dropoff at the end.

[Ben]

The correct shape for constant force has been found. I took the previous shape that produced constant force and made it larger so that the force was greater all of the time. I'll be spending some of my time this summer verifying whether or not my math was correct because this would be a valuable change in some water guns.

The problem with this design is the size. This'll be at least a few feet wide. I am thinking that the PC could be stored in a cylinder, with the space above the PC used as the water reservoir. The cylinder would be a backpack. Sounds interesting, but there's no way a DIY type person could make that. It'd still be easier to use rubber tubing.

[joannaardway]

I still don't get the ID stuff, but I can see a way to make the shape you have proposed...

I'm short on time, so I'll explain some other time.