Recently my thoughts have been dedicated to making a system to accurately predict a water gun's stream distance and design efficiency (efficiency being a calculated value). While I had made some considerable progress, what I had been working on would take much more time to explain and to calculate than my new idea.

For a long time I had wanted to calculate the output at a specific instant. I could obtain a somewhat accurate number with the method described in my old "XP Physics" article which is no longer online. This method would completely replace that method for two reasons: it is far more accurate and it can describe output that is not constant or constantly changing. The inspiration for my XP Physics article was the Aqua-Nexus pages describing the "drop-off" of pressure with what I assumed to be approximate graphs.

Instantaneous velocity is an easy and common idea. It also isn't very useful except in comparisons. Instantaneous output on the other hand is very useful for several reasons. People have been taking the "average output" for years, which gives air pressure water guns a raw deal because they have about half of the output above that figure and half of the output below that figure. You can not tell how much the figure decreases simply by the average. Instantaneous output can also be used to determine when exactly the shot ends, as I had previously calculated in my old XP Physics article. Output would be best given with several methods: output when t=0, average output, and a graph of the output over the period of the shot.

We all know that water guns' water output, especially the output of non-regulated air pressure water guns, changes. For example, in a non-regulated air pressure water gun's output is constantly dropping. We now can see exactly how the output is changing by calculating the instantaneous output curve.

To calculate the output curve, you first must find a curve that displays how much water is shot over a period of time. The graph below is an example of a possible air pressure system's water. The x-axis represents time (t). The y-axis represents the amount of water shot thusfar in the shot. This test will be hard to make, though a small machine that records mass at certain fractions of a second as the mass is increasing would be the best way to generate this information. This is not the output curve.



The output curve is the derivative of this function. For those who are not familiar with basic Calculus, the derivative essentially is the graph of the slopes of the function. The derivative of the position function is the velocity function. The first graph can be said to be a "position" function for the output, though I am sure that is not the best way to describe the graph.

The first graph can and likely will be represented as a quadratic equation. That would not be the best way to represent the graph in my opinion. The graph will be best drawn with the data points visible as well as the equation made to fit. We do not know yet how the output curves will appear, and to prevent them from being shown as lines, which is not likely how they will appear, we should instead use regressions in the style of more detailed equations as seen fit in each situation.



This graph represents a potential output curve (or line), likely better known as a graph of the drop-off. Air pressure is known to reduce it's output, distance, and pressure as time goes on. You can see that easily in this graph.

This is my basic theory at the moment. I will be writing a much more in depth article eventually with everything including real data generated from a real water gun (likely my CPS 1000 and XP 150 because they are very good water). Output curves should be extremely useful for future water gun designers and those interested in water gun statistics.

interesting...Hasbro would get a heart attack if they found out we are using more advanced methods than them to design water guns...

They already know it. None of their guns made beat modded/homemade guns. If guns they made were so good then I don't know if people would mod.

@Dux, would you mod a gun that was based on the 2500 frame, that shot 80 feet on all nozzles, had a 2.5x, 5x, 10x, and 20x nozzles (based on output of course, not nozzle size) had a stream speed 8x that of a stock gun, and a 1L PC?

If it were physically possible without being gigantic and expensive, then yes. The power that kind of beast would need is a bit out of reach. 8x stream velocity and 80ft on all nozzles? According to my calculations, a mid-size CPS stock gun with 8x stream velocity would penetrate skin, like a bullet from a low-caliber gun. The Douchenator might not even have 8x, assuming that 1x is based off a mid-size CPS stock gun. If I were able to build a water gun with that kind of power, I would never use it in a war, the 8x could be extremely dangerous. The pc, however, is do-able, my first homemade has ~1.8 liter pcs.

EDIT: 8x would have enough FPS to penetrate skin 3.47 times over. AKA, not a good idea.

I finally figured out what you mean. That would be a cool idea. It is much more precise than the average such as 20x or 5x. What good is a 20x nozzle that stays at 4x for .01 of a second, then spurts out 30 mL over the course of the next .24 seconds?

That is completely correct. However, you are getting the units a little wrong. 4X is the same thing as writing 4 ounces per second (4oz/s), which is 120 ml per second. You can not say that 120 ml per second is shot in 0.01 of a second. You'd have to use a different unit, in this case mL. Something that can get a 20X output could have a total shot time of 1 second, but the first 0.25s could shoot most of the 600 mL needed to get that! That's not a full second shot time!

It would be a tedious task to make output curves for a lot of water guns, but then you can directly compare the water guns side by side in a graph. You may think twice about using that 20X because it might only have a shot time over 50% power for a very short period! You also might think twice about choosing a less constant air pressure water gun, favoring a more constant one such as the Super Soaker XP 150. Hopefully, these output curves will help people make better decisions in choosing water guns or help people design water guns with better output curves. The latter is my main goal.

A graph is what we have been waiting for a long time. People can say "this water gun has 100mL average output, but you must also remember it has drop off." Now you know how much it drops off, where the drop-off starts, and what the initial output or maximum output was. Pictures are worth a thousand words afterall. ;)

This sounds pretty good. But won't it be difficult to make the graphs? And tedious? But nkowing when you get severe dropoff would let me know when I should start pumping again and stop shooting. Comparison, of course, would also be useful.

Uh...I'm lost...I'm gonna have to read over all the previously said stuff more carefully, but I dont have much time so I'm just skimping...

Aye, I believe that's the main difficulty - working out a cheap and efficient way of measuring the output would probably be somewhat tricky.